Advances in nonparametric item response theory for scale construction in quality-of-life research

We introduce the special section on nonparametric item response theory (IRT) in Quality of Life Research. Starting from the well-known Rasch model, we provide a brief overview of nonparametric IRT models and discuss the assumptions, the properties, and the investigation of goodness of fit. We provide references to more detailed texts to help readers getting acquainted with nonparametric IRT models. In addition, we show how the rather diverse papers in the special section fit into the nonparametric IRT framework. Finally, we illustrate the application of nonparametric IRT models using data from a questionnaire measuring activity limitations in walking. The real-data example shows the quality of the scale and its constituent items with respect to dimensionality, local independence, monotonicity, and invariant item ordering.

Introduction
This special section of Quality of Life Research is devoted to nonparametric item response theory (IRT) models [1]. In this introduction, we review nonparametric IRT models, provide references to more detailed texts, and show how the diverse set of papers in the special section fits into the nonparametric IRT framework. Nonparametric IRT models are generalizations of a large class of parametric IRT models including the Rasch model, the 2-parameter and 3-parameter logistic IRT models for binary item scores, and the partial credit model and the graded response model for polytomous item scores. Van der Linden [2] introduces these parametric IRT models extensively. Sijtsma and Van der Ark [3,Chap. 4] discussed how nonparametric and parametric IRT models are related in one large family of which the most general members are nonparametric IRT models. Parametric IRT models are special cases of nonparametric IRT models.
Their generality renders nonparametric IRT models more flexible than most parametric IRT models.
IRT models are used for establishing whether a set of items intended to measure a particular attribute together constitute a scale for measurement. Examples of attributes are pain experienced by patients suffering from burn wounds [4], health-related quality-of-life aspects, such as physical functioning, general health perceptions, vitality, and social functioning [5], and adherence to medication and lifestyle for patients with hypertension [6]. Roorda et al. [7] used IRT models for scaling a set of items measuring activity limitations in rising and sitting down in patients with lowerextremity disorders living at home, and Sijtsma et al. [8] used nonparametric IRT models to analyze the World Health Organization Quality-of-Life scale (WHOQOL-Bref). In the special section, Feng et al. [9] applied nonparametric IRT models to the EQ-5D, a widely used generic measure of health, and based on the scaling results reinterpreted the EQ-5D scales. The number of articles using IRT models and other scaling techniques for constructing scales and assessing measurement quality Quality of Life Research published over the years is very large. It shows the paramount importance of well-founded measurement.

Features or nonparametric and parametric IRT modeling
The main difference between nonparametric and parametric IRT models is that the nonparametric models rest on assumptions about people responding to items in a test or a questionnaire that are more liberal than the assumptions parametric models make. For example, nonparametric IRT models assume that the relation between the probability of a patient giving a positive response to an item indicating ease of climbing the stairs and the underlying attribute of physical functioning is monotone-the better physical functioning, the more ease climbing the stairs-and parametric IRT models assume the relation not only is monotone but also logistic. This extra condition renders the relation more restrictive and the fit of the IRT model to the data more problematic. For example, the nonparametric model of monotone homogeneity [10; 1, Chap. 3] assumes monotone item response functions (IRFs), which can have any shape and intersect mutually ( Fig. 1, all curves), and the logistic IRFs of the Rasch model all have the typical S shape while running parallel (Fig. 1, dashed curves). The models are equal in that sets of items comprising a test or questionnaire measure one attribute such as physical functioning and represented mathematically by one latent variable (typically denoted by ; Fig. 1). In addition, the models assume that there are no other attributes or covariates active affecting the covariances between item scores, so that inter-item covariances vanish when conditioning on the latent variable. These assumptions are unidimensionality and local independence, respectively. Parametric IRT models generalize to multiple latent variables thus allowing various attributes simultaneously to affect response probabilities (Fig. 2). Nonparametric IRT focuses on search algorithms to identify separate item clusters measuring different attributes or aspects of the same attribute. Fig. 1 Four items having monotone IRFs consistent with the monotone homogeneity model, of which two (dashed logistic curves) also follow the Rasch model Fig. 2 The IRF of a dichotomous item in a two-dimensional latentvariable model. The first latent variable (θ1) is on the x-axis, the second latent variable (θ2; label not shown) is on the y-axis, and the probability of obtaining item score 1 given the values of θ1 and θ2 is on the z-axis Other features render nonparametric IRT models interesting. First, for binary-item tests and questionnaires consistent with the model of monotone homogeneity, ordering persons by their number of positive scores (the total number of 1 scores or the sum score) is stochastically equal (i.e., with possible random violations) to ordering them by means of their latent-variable scores. This property says that one does not need the latent-variable scores for ordering persons and that simple sum scores will suffice albeit with random error (Fig. 3). This is a strong result, because it holds for scales when the model of monotone homogeneity fits the data well, and one need not estimate latent-variable scores at all. Because the Rasch model and the 2-parameter and 3-parameter logistic models are special cases of the model of monotone homogeneity, these parametric IRT models imply the ordering property using the sum score as well. Unlike nonparametric IRT models, parametric IRT models estimate the latent variable and assign estimates to persons. If the purpose is to order persons on a scale, it does not matter whether one uses the estimated or the sum score. Both scores are liable to unreliability due to random error, and may not perfectly reflect the error-free ordering of persons. Unlike nonparametric IRT models, parametric IRT models allow the assessment of scale-dependent measurement precision using the estimated . For polytomous-item tests and questionnaires, the ordering of persons by their sum scores approximates their ordering by latent-variable scores quite well, but may contain small but unimportant distortions.
Second, one might argue correctly that assuming logistic IRFs provides efficient item information by means of ing expected (i.e., mean) sum score, E X + | . Expected sum scores E X + | have the same ordering as -values. Last line: Sum-score values X + obtained by randomly drawing from the histograms. Unreliability causes different orderings of X + and in this particular draw estimated difficulty, discrimination and perhaps pseudoguessing parameters, but the fact that nonparametric IRT models do not commit to specific parametric IRFs, instead estimating the whole function for each item from the data allows a complete picture of item response behavior for each item. This allows the researcher to see that the item only works well for people high on the scale of, for example, physical functioning, but not for the majority (Fig. 4, solid curve), or that the IRF only has a weak and irregular relation with physical functioning and is a candidate for replacement ( Fig. 4, dashed curve). Researchers and scale developers want to know these things and make decisions about maintaining, deleting or replacing items from preliminary tests or questionnaires. Only having estimates of where an item is located or whether it distinguishes people well at a particular scale location is useful but knowing the complete picture has greater diagnostic value for item assessment. Estimating IRFs of course is liable to sampling error and involves several rather arbitrary decisions [11]. Third, the fact that nonparametric IRT refrains from assumptions about response behavior that may be mathematically convenient but unnecessarily restrictive from a psychological or health-related point of view-which content-driven theory predicts that IRFs are S-shaped or run parallel-renders it more laborious when assessing whether the model is consistent with the data. Various methods exist for assessing IRF monotonicity and local independence and exploring the dimensionality of an item set, and several run into problems related to combinatorial explosions and the curse of dimensionality. They often provide a wealth of detail about goodness of fit, but have trouble summarizing these details into discrete often binary conclusions such as keeping an item or deleting it from the test or questionnaire. Parametric IRT models have the advantage of concentrating on a few parameters per item rather than estimating whole curves but at the basis of several of their goodness-of-fit statistics lie the observable data features that nonparametric IRT models explore in detail but find hard to summarize. Whereas nonparametric IRT sometimes struggles with all the details it wishes to involve, the level of granularity of parametric IRT may be too low, occasionally missing interesting data features. Of course, these characterizations are somewhat exaggerated to make our points but help to understand the topic of this article.

Goodness of fit of models to data and robustness when models fail to fit
Sijtsma and Van der Ark [1] discussed a methodology in ten steps for investigating the goodness of fit of the nonparametric IRT models of monotone homogeneity and double monotonicity to the data collected with a (preliminary) test or questionnaire. The authors focus on the simple case of one test or questionnaire administered once to a sample from the population of interest. The first three steps concern aspects of data examination, in particular, recoding of item scores, handling of inadmissible and missing values and finally the identification and handling of outliers. These steps are useful in any scale analysis, not particular a nonparametric IRT analysis and we will skip them here. The next four steps numbered 4-7, concern scale identification and are highly Fig. 4 Two IRFs showing one item that works well only for people with high latent-variable levels (solid curve), and one IRF that has a weak and irregular relation with the latent variable and is a candidate for replacement (dashed curve) relevant in the nonparametric IRT context. The authors claim that these four steps together identify one or more scales that satisfy the model of monotone homogeneity and, if desirable, investigate whether the identified scales also are consistent with the more restrictive model of double monotonicity that requires the monotone IRFs not to intersect. Both models enable a person ordering using the simple sum score and the latter model also enables an item ordering by item means that is the same, with the exception of possible ties, across the scale of the latent variable. The last three steps again are relevant to any scale analysis model, not only nonparametric IRT, and are reliability estimation for the sum score, determining norms tables for the interpretation of sum scores of individuals, and the comparison of scaling results across meaningful subgroups of the population in interest. Due to their generality, we will also skip these last three steps.
We illustrate the steps briefly using data from the physical health questionnaire Climbing Stairs (PHQ-CS) [12]. The 15-item questionnaire was administered to 759 subjects with lower-extremity disorders living at home. Each item consists of a statement that describes a problem a patient might encounter when climbing stairs, and the respondent either endorsed the statement (score 1) or not (score 0). The first 12 items pertain to 6 aspects of stair climbing (takes longer, different way, with difficulty, hold on to banister, use walking aid, helped by someone) that are applied to going up and going down, respectively. The last 3 items pertain to the frequency of climbing stairs. The complete PHQ-CS is available from [12].

Step 4-scalability
A nonparametric IRT scale analysis usually starts with the determination of the dimensionality of the item set. That is, do we need one or more latent variables to explain the data structure and in case of multidimensionality, do the items divide neatly across two or more subclusters of items that are interpretable and form a basis for separate scales? Mokken [10] (also, see [13], Chap. 4) proposed an automated item selection algorithm based on scalability coefficient H producing one or more preliminary scales in which both the individual items and the total item (sub)set satisfy minimum requirements for H (called lower bounds). The requirements ascertain reliable person ordering on a scale spanned by the item (sub)set. Straat et al. [14] proposed an alternative item selection algorithm based on a genetic search. Brusco et al. [15], proposed an alternative clustering procedure. Zhang and Stout [16] discussed the DETECT procedure based on conditional covariances between item scores and Bolt [17] discussed related proposals. Van Abswoude et al. [18] used simulated data to compare various dimensionality assessment procedures. After determining a preliminary division of items in one or more item sets, for each set the assumptions of the nonparametric IRT models are investigated. In their contribution to the special section, Koopman et al. [19] discuss item selection based on scalability coefficients for clustered data common in much health research.
For the PHQ-CS, Mokken's [10] automated item selection procedure produced the same results for lower bounds in the range from 0.0 to 0.4 (Table 1,  Step

5-local independence
To investigate the assumptions of nonparametric IRT models, one needs properties the models imply that do not contain the latent variable and can be computed directly from the data. An example is conditional association, and a special case of this property is the correlation between two item scores conditional on a function of the scores on one or more of the other items. Such a function is the sum score on these items, also called the rest score, which replaces the latent variable. These covariances must be nonnegative when the model of monotone homogeneity holds; negative values are inconsistent with the model. Straat et al. [20] used such conditional covariances to identify item pairs that are locally dependent, suggesting that their covariance does not only depend on the attribute one wishes to measure, but also on other, undesirable influences. Such items may be candidates for removal or replacement, or the researcher may maintain them when she assesses the inconsistency not serious enough. Also, see [21] for an approach based on nonparametric regression and the parametric bootstrap. For the PHQ-CS, using the method of conditional covariances [20] we detected several locally dependent item pairs (Table 1, last column). As this method was not investigated thoroughly, results should be interpreted with care [1].

Step 6-monotonicity
To investigate whether response probabilities of a positive answer or picking a particular response category or a higher one are monotone related to the latent variable, again we need to assess a function the model of monotone homogeneity implies that does not contain the latent variable and can be computed directly from the data. Such a function conditions the response probabilities for an item on the sum score based on the other items, which is the rest score we discussed previously and replaces the latent variable. This is the observable property called manifest monotonicity [22]. Various nonparametric regression methods were proposed for assessing the monotonicity assumption, based on binning [23], kernel smoothing [11,24], and spline fitting [25,26]. Local decreases in estimated IRFs suggest that the item is ineffective for measurement at those scale ranges, but model-consistent local increases that have an almost flat slope may also be informative. Figure 5 shows the estimated IRFs of the PHQ-CS. The IRFs were estimated using kernel smoothing setting bandwidth h = .08 [11]. Using the banister is the most popular coping strategy, whereas using assistance is the least popular. The IRFs of items pertaining to the same aspect of ascending and descending are remarkably similar. Items 2, 5, 11, and 14 show minor violations of monotonicity.
In their contribution to the special section, Falk and Fischer [27] study a flexible approach based on monotonic polynomials that provides a compromise by modeling items with both complex and simpler response curves. Their study investigates the suitability of items with IRFs described by monotonic polynomials for inclusion in patient-reported outcomes item banks.

Step 7-invariant item ordering
The test is more informative when the ordering of the items by means of response probability or item mean score is the same, except for possible ties, for each measurement value. This means that if we know that for a particular scale value the probability of giving a positive response is greater for item j than item k , we know that this ordering is the same-but never opposite-for all other scale values. This is different in parametric IRT models, where one often takes the ordering of items' location parameters as their ordering according to difficulty or popularity, but when IRFs intersect, this is an incorrect conclusion (Fig. 6). Various methods exist for investigating whether sets of binary or polytomous items have an invariant ordering; see [28] for an automated methodology. Groundbreaking theoretical work was due to Rosenbaum [29], whereas Tijmstra et al. [30] provided new results.
Data analysis experience shows that an invariant item ordering is restrictive, rarely achieved for the whole set of items. For the PHQ-CS, an IIO is not achieved either, Table 1 Scaling results for PHQ-CS.
Step 4 (Scalability) and Step 5 (Local Dependence): Automated item selection for lower bounds .0, .4, and .5; estimated item scalability coefficients ( Ĥ j ) plus standard error ( SE ) for the scale consisting of all 15 items; overview of positive locally dependent (PLD) item pairs Columns 'Item' and 'Statement' adapted from "Measuring activity limitations in climbing stairs: development of a hierarchical scale for patients with lower-extremity disorders living at home", by Roorda et al. [12], Appendix. Copyright 2004 by Elsevier. Reprinted with permission a 1: item is selected into the first scale, 2: item is selected into the second scale; etc. Blank: item is unscalable b If not a blank, the item may be in one or more positive locally dependent item pairs; the number indicates the other item in the positive locally dependent item pair(s) as the estimated IRFs in Fig. 5 cross. However, except for the item pair that relates to the aspect of 'climbing in a different way' (items 2 and 8), the pairs of items pertaining to the remaining five aspects seem to approximate an invariant ordering. 'Holding on to the banister' (items 4 and 10) is invariantly more popular than the remaining four aspects, 'taking longer' (items 1 and 7) is invariantly more popular than the remaining three aspects, 'climbing with difficulty' (items 3 and 9) is invariantly more popular than the remaining two aspects, and 'using a walking aid' (items 5 and 11) is invariantly more popular than 'being helped by someone' (items 6 and 12). The aspect 'climbing in a different way' is less popular than 'using walking aids' and more popular than 'climbing with difficulty' for the majority of patients, but not for the low-scoring patients.
When applied to real-data analysis, the previous four steps often provide detailed information on dimensionality, local  [12]. See Table 1 for the full item content Fig. 6 Two intersecting IRFs independence, monotonicity, and invariant item ordering, and the researcher finds herself confronted with the question how to weigh and combine the information to draw a conclusion about the scale(s). In this special section, Crisan et al. [31] critically discussed a summary measure called crit that was proposed as a heuristic tool to help researchers finding their way in the output of a Mokken Scale Analysis [23]. The four analysis steps pertain to the situation in which a test or questionnaire is administered once to a sample from the population of interest, but in repeated measurement, the issue of response shift-that is, a change in patients' perspective on the meaning of an item-may reveal itself through a change in item ordering at the individual level. In this special section, Dubuy et al. [32] mentioned chronic diseases where patients regularly adapt to their life circumstances, resulting in a different interpretation of items when tested repeatedly. In their contribution to the special section, these authors discuss a method to study this phenomenon of response shift for patient-reported outcomes.

Discussion
Nonparametric IRT scaling puts fewer constraints on the data than several parametric IRT models do. This way, nonparametric IRT retains a larger number of items from preliminary test and questionnaire versions, which not only is efficient but also provides a good fit to the state of theory development for attributes in social, psychological, and health sciences. That is, theories for attributes may predict an attribute as cumulative (e.g., intelligence) or categorical (e.g., typologies), but theories do not (yet) predict that response probabilities for different items run parallel or can be described sufficiently well with one, two, or three parameters. In all fairness, data analysis experience has taught us that the data structure at best only approximates unidimensionality, local independence, monotonicity, and invariant item ordering, and there always is at least some discrepancy between model predictions and data structure. The crucial issue with all modeling attempts is not whether the model fits the data, but whether the discrepancy of model and data is small enough for the model properties to hold for the application at hand. Much research addresses whether statistical tests provide a Type I error that is almost equal to the significance level the researcher choses, and how particular data features not anticipated by the model affect a statistical test's power. The question of the magnitude of discrepancy between IRT model and data is difficult to answer, because there are so many ways in which data can digress for the model's prediction. Moreover, the practical use of a test or a questionnaire determines the cost or utility of false positives and false negatives in relation to correct decisions based on the sum score. The five articles in this special section provide valuable psychometric contributions to the further development of measurement in the health sciences.
Funding The authors did not receive funding for this article.

Data availability
The data are not publicly available.
Code availability Computer code is available from the R package mokken [33,34].

Conflict of interest
The authors have no conflicts of interest to disclose.
Ethical approval This retrospective study involves the reanalysis of questionnaire data. The Institutional Review Board of Child Development and Education at the University of Amsterdam (number 2021-CDE-13947) granted ethical approval.
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Online cleaning method of power grid energy anomaly data based on improved random forest

Aiming at the problem of high root mean square error of traditional power grid energy anomaly data online cleaning, a power grid energy anomaly data online cleaning method based on improved random forest is designed. Firstly, an outlier data recognition model of isolated forest is designed to identify outliers in the data. Secondly, an improved random forest regression model is established to improve the adaptability of random forest to mixed abnormal data, and the data trend is fitted and predicted. Finally, the improved random forest data cleaning method is used to compensate the missing data after removing the mixed abnormal data, so as to clean the abnormal energy data of the power grid. The experimental results show that when the amount of power grid energy anomaly data increases, the cleaning root mean square error of the experimental group is significantly lower than that of the control group. The method in this paper solves the problem of high root-mean-square error in the online cleaning of abnormal data of traditional grid energy.

Introduction
The power grid contains huge real-time data, which is closely related to the safe operation of the power system and plays a decisive role in the safety and reliability of the power grid. The power grid needs to generate and consume a lot of electric energy in the process of working. Under the condition of normal work, it will still produce bad data, affect the decision-making of the system and threaten the safety of the whole power grid. Data cleaning is not only applied in power grid, but also in the fields of data mining and total data quality management. The definitions of data cleaning are different in different fields, and there is no unified definition of data cleaning. Therefore, using professional technology to detect and correct bad data will help to ensure the normal operation of power grid and the normal supply of power energy. So far, scholars at home and abroad have done a lot of theoretical and practical research on the detection and correction of power grid energy big data, and summarized two widely used cleaning methods. One is the identification and cleaning method of abnormal data of power grid operation based on Spark framework. Abnormal data are extracted from big data through data mining algorithms such as clustering or neural network, and cleaned under Spark framework. The other is the missing value cleaning method of power grid data based on improved low rank matrix completion. This method mainly sets the threshold according to a certain confidence level, carries out hypothesis test combined with the relevant knowledge of probability theory, and then completes the missing value of data by improving the low rank matrix to realize anomaly cleaning. In the actual operation of the power grid, it is very difficult to ensure the accuracy and completeness of user electricity data collection. Affected by sensor failures, transmission line failures, natural weather and other complex factors, users' electricity consumption data will have varying degrees of data omissions and errors. This article refers to these user electricity consumption data as abnormal data. In the above two methods, the data recognition is abnormal due to too many repeated searches, or the normal data is judged as bad data, resulting in a high root mean square error in practical applications.
The data set does not need standardization, and the training speed is fast. It can be applied to largescale data sets. Default values can be processed (as a separate class) without additional processing. Due to the out of bag data (OOB), the unbiased estimation of the real error can be obtained in the process of model generation without losing the amount of training data. In the training process, the interaction between features can be detected, and the importance of features can be obtained, which has a certain reference significance. Because each tree can be generated independently and simultaneously, it is easy to make a parallelization method. Because of its simple implementation, high precision and strong anti overfitting ability, it is suitable to be used as a benchmark model in the face of nonlinear data. Based on this, this paper designs an online cleaning method of power grid energy anomaly data based on improved random forest to solve the problems existing in the previous cleaning methods.

Improved random forest
In order to adapt to the compensation of mixed missing data, the random forest algorithm is improved to obtain an improved random forest algorithm with strong adaptability [1][2] . The X excluding abnormal data is linearly interpolated, and then the filling matrix containing target compensation variables is obtained through matrix transformation. Then, the random forest regression model is used to predict the filling matrix, and the integration idea is used to output tb times [3][4] . The specific methods for improving random forest are as follows: In step 1, the missing value in X is interpolated by linear interpolation method to obtain matrix R, which is expressed as: In formula (1): the sample size of R and X is the same, which is m × n dimensional matrix, n is the number of variables, and m is the number of data samples contained in a single variable.
In step 2, take column i in X as the target filling column, and the remaining n-1 column in R except column i as the relevant variable column to form the filling matrix Rfill, I = 1, 2, 3,..., n, expressed as: In step 3, a training matrix Dzv is randomly selected from D to complete the establishment of random forest regression model.
In step 4, take the relevant variable column in Rfill as the input and the target filling column as the output to predict the missing value of column i to obtain the t-th prediction value y(t), t = 1, 2, 3,..., tb.
Step 5 if t < tb, then t = t + 1, return to step 4; otherwise, take the average value of tb predictions as the final compensation value yz, and replace the missing value in xi with yz to complete the update of matrix X.
Step 6 if i < n, i = i + 1, repeat the above steps; otherwise, stop prediction and complete data compensation for X [5][6] . The above is to improve the overall step flow of random forest algorithm.

Classification of grid energy anomaly data
According to the analysis of the original data of power grid energy, the abnormal data of power grid energy are mainly divided into the following three categories: outlier data, duplicate data and missing data. Outliers are data that deviate significantly from the rest of the values [7] . Duplicate data is the data with the same value at multiple times. According to the dynamic characteristics of power grid operation process, this kind of data is determined as abnormal data. Missing data refers to data not collected at a certain time or data vacancy [8] . However, there are many energy data variables and parameters in the power grid, and the abnormal data do not appear in a single type, but often appear in a variety of abnormal characteristics at the same time. At present, the research on online data cleaning of power grid energy anomalies is limited to cleaning methods for single type of abnormal data, and there is no mixed abnormal data cleaning method for different types. When the traditional probability distribution, clustering algorithm and intelligent algorithm are used to clean different types of mixed abnormal data, the effect is still difficult to meet the requirements of data quality during power grid operation. Therefore, this paper proposes a data cleaning method based on improved random forest to clean different types of mixed abnormal data.

Identification of grid energy anomaly data based on improved random forest
In order to quickly and accurately identify abnormal data, an abnormal data identification model based on isolated forest is constructed. IF is a decision tree ensemble learning method. IF algorithm first divides the known and continuous time data set randomly, and then realizes fast and accurate identification by using the difference between abnormal data and normal data. The IF model consists of a isolation tree, and the algorithm steps are as follows: Step 1 randomly select a sub sample matrix Xz from the training data matrix X as the set of root nodes of the b-th tree, where b = 1, 2, 3,..., a and a are the number of root nodes, and the training data matrix X and sub sample matrix Xz are expressed by the formula: In formula (4,5), the matrix is m × n dimensional matrix, n is the number of variables, and m is the number of data samples contained in a single variable; u is the number of samples, u = mn; Xz is mz × nz dimensional matrix, nz is the number of variables, mz is the number of data samples contained in a single variable, 0 < mz ≤ m, 0 < nz ≤ n.
Step 2 perform binary segmentation on Xz: randomly select a column vector xj, j∈{1, 2, 3,..., mz} from Xz, and randomly select a cutting point T from the set of column vectors xj, as shown in formula (6). (6), r is a random number between 0 and 1. If X z (i, j) ＜ T, all variables in row I of matrix X z are divided into left subtree nodes. If X z (i, j) ≥ T, all variables in row i of matrix X z are divided into right subtree nodes, i = 1, 2, 3,..., m z . When all the data in X z is divided, the left subtree node set forms matrix X left and the right subtree node set forms matrix X right .
Step 3 record the path length hn of the node where Xleft and Xright are located. hn is the number of edges from the root node to the current node. If hn is greater than or equal to the tree height hmax or the number of sets in nodes is less than or equal to mz, stop training and complete the construction of a single isolation tree; otherwise, perform binary division for Xleft and Xright, and repeat step 3. The tree height hmax is: hmax Ibu  Step 4 if b < a, b = b + 1, repeat step 2 and step 3, otherwise stop training and complete the establishment of if model. IF divides and isolates the data in X. the normal data needs to be divided and isolated for many times and is in a high-density area; abnormal data needs to be isolated by a few divisions and located in low-density areas.

Eliminate abnormal data of power grid energy
After the data is calculated by the IF model, different high and low density areas are formed. The density area where the data is located is reflected by calculating the abnormal value score of the data, and the data with high score is eliminated. The path length of xij output from IF model is hij, and xij is the element in matrix X. calculate the outlier score of xij through hij, and the formula is: In formulas (8 and 9), c(u) is the average path length of all data in X; ξ Is Euler constant; E(hij) is the average path length of data xij in a isolation tree. When the value of S(hij, u) approaches 0.5, it indicates that the data has no obvious abnormal state; When the value of S(hij, u) approaches 1, it indicates that the data is an abnormal value. After obtaining the outlier score of each data, combined with the equivalence and missing characteristics of the data, the following three kinds of data are eliminated from X: For the first data, xij with outlier score S(hij, u) greater than 0.75 in X is eliminated and replaced by 0. For the second data, replace the missing data in X with 0. For the third data, c1 or more consecutive xij with the same value in X are eliminated and replaced with 0.

Complete the online cleaning of abnormal energy data of power grid
From the above analysis, it can be seen that the identification and cleaning of non clean data is difficult to ensure the complete elimination of non clean data, especially the multi-dimensional nature of power grid energy abnormal data, which brings difficulties to cleaning. With the gradual improvement of the fineness of the cleaning, the operation performance of the knowledge base system will gradually decrease, and the information contained in the abnormal energy data of the power grid will be gradually lost, which can not quickly and effectively solve the problems caused by the non clean data. Data cleaning across data sources is mainly to ensure the correlation between metadata by matching the semantic constraints between multiple data sources. Assuming that the metadata feature set is sdfrewa, the following two constraints need to be met to complete metadata cleaning. First, if the two vertices of the edge representing the metadata relationship must be metadata objects, they are expressed by a formula, as shown in formula (10).
, , e f t E f t V    (10) In formula (10), e refers to the directed edge of the metadata feature;   , f t refers to the coordinate point corresponding to the metadata feature; E refers to the directed edge combination of metadata features; V refers to the vertex set of metadata features. Second, if the relationship between two metadata objects can only be one-way, it can be expressed by formula, as shown in formula (11).
On the basis of satisfying formula (11), the syntax and semantics of energy metadata characteristics in the power grid operation process can be analyzed, and then the energy effective information can be extracted and tracked, so as to complete the online cleaning of power grid energy abnormal data. Therefore, through data cleaning, the quality of power grid energy data can be improved.

Experimental preparation
The grid energy data information of a cross-border power enterprise in recent 5 years is selected and introduced into the simulation experiment software to build a virtual power database. Two computers with Windows 10 and 16GB memory capacity are selected to simulate the sending and receiving of power grid energy data. Another computer with Windows 10 and 32GB memory capacity is selected to simulate the transmission environment of power grid energy data, and the experiment is carried out with the abnormal power grid energy data as the sample data. This paper uses the online cleaning method of power grid energy abnormal data based on improved random forest design to clean the ICPEPT 2021 Journal of Physics: Conference Series 2108 (2021) 012067 IOP Publishing doi:10.1088/1742-6596/2108/1/012067 5 power grid energy abnormal data online, and then uses the traditional method to clean the power grid energy abnormal data online. 1000 grid energy anomaly data are randomly selected, of which 500 grid energy anomaly data are cleaned online by using the design method in this paper and set as the experimental group, and the other 500 grid energy anomaly data are cleaned online by using the traditional method and set as the control group. The root mean square error of the experimental group and the control group in the online cleaning of power grid energy anomaly data was compared. The lower the root mean square error, the higher the accuracy of the online cleaning method of power grid energy abnormal data, so as to obtain a higher accuracy online cleaning method of power grid energy abnormal data.

Experimental results and analysis
According to the above experiment preparation, complete the comparative experiment, record the data information generated during the experiment, and display the experimental results in the form of tables. The specific experimental results are shown in Table 1.  Table 1, when the amount of grid energy abnormal data increases, the cleaning root mean square error of the experimental group is significantly lower than that of the control group, which can realize high-precision online cleaning of grid energy abnormal data. The main reason is that the experimental group can realize intermittent deletion mixed continuous deletion data cleaning based on the improved random forest. Therefore, the comparative experiments show that the online cleaning method proposed in this paper can effectively reduce the root mean square error of online cleaning of power grid energy anomaly data and improve the online cleaning accuracy. The mean square error of the cleaning data using this method is less than 0.21, while the mean square error of the cleaning data of the control group is higher than 0.75. It further ensures the quality of power grid energy data, meets the needs of power grid construction at the present stage, and has higher application value.

Conclusion
Aiming at the problem of energy abnormal data in the process of power grid operation, an online cleaning method of power grid energy abnormal data based on improved random forest is proposed in this paper. Firstly, the random forest algorithm is used to identify the outlier data. Then, outlier data, duplicate data and missing data are eliminated to obtain the mixed type missing data set. Finally, the improved random forest algorithm is used to compensate the missing data sets of mixed types. The effectiveness of IRF data cleaning algorithm is verified by taking the actual sewage data, and the following conclusions are obtained: the random forest algorithm can eliminate the outlier data in the power grid energy data. In the mixed type missing data set, the improved random forest algorithm has better cleaning effect than other algorithms, and is suitable for cleaning mixed type abnormal data. For data cleaning algorithms, some research institutions have proposed data preprocessing, sorting neighbor method, multiple traversal data cleaning method, cleaning with domain knowledge, integrated data cleaning with database management system and so on. Based on the differences between Chinese data and Western data, Chinese data cleaning not only transplants the cleaning methods of Western data, but also has its own unique cleaning methods. According to the deficiency of current data cleaning research, the main research directions of data cleaning in the future are: the research and development of Chinese data cleaning tools; do in-depth research on the application of data mining methods in the field of data cleaning; the efficiency of duplicate record identification needs to be further improved; cleaning of unstructured data; interoperability between data cleaning tools; universality of data cleaning scheme. The improvement and optimization of Chinese data cleaning technology will be further studied in the follow-up.


Improving Search by Utilizing State Information in OPTIC Planners Compilation to LP

Automated planners are computer tools that allow autonomous agents to make strategies and decisions by determining a set of actions for the agent that to take, which will carry a system from a given initial state to the desired goal state. Many planners are domain-independent, allowing their deployment in a variety of domains. Such is the broad family of OPTIC planners. These planners perform Forward Search and call a Linear Programming (LP) solver multiple times at every state to check for consistency and to set bounds on the numeric variables. These checks can be computationally costly, especially in real-life applications. This paper suggests a method for identifying information about the specific state being evaluated, allowing the formulation of the equations to facilitate better solver selection and faster LP solving. The usefulness of the method is demonstrated in six domains and is shown to enhance performance significantly.

Introduction
Automated Planning (often called AI Planning) is concerned with formulating a sequence of actions that transforms a system from a given initial state into a desired goal state. One strength of AI Planning is domain-independence: a single general planner can plan in a wide range of different application domains. Examples of domains in which Planning was used include space (Chien et al. 2000), battery usage (Fox, Long, and Magazzeni 2011), and software penetration testing (Obes, Sarraute, and Richarte 2013). To facilitate application in realistic problems, planners need to reason with expressive models of the world. Such models can be temporal: finding a plan with timestamped actions, taking into account action durations and concurrency, and numeric: considering variables that change discretely, or continuously, over time (Fox and Long 2003).
To solve expressive problems that contain temporal constraints, the planner requires a scheduler -A technique for assigning values to the action's timestamps that would result in a valid plan. For example, the temporal planners SAPA (Do and Kambhampati 2001) and Temporal Fast Downward (Bell et al. 2010) utilize the decision epoch mechanism, Crikey 3 (Bemporad, Ferrari-trecate, and Morari 2000) uses Simple Temporal Network (STN). To solve hybrid problems that contain temporal as well as discrete and continuous change, the planner would require more complex approaches. For instance, SMTPlan formulating the problem into SAT (Cashmore et al. 2016), ENHSP using interval relaxation (Scala et al. 2016), DiNo discretizing time (Piotrowski et al. 2016), and qtScoty using convex optimization (Fernández-González, Karpas, and Williams 2017).
This work focuses on a family of planners that uses Linear Programming (LP) solvers to schedule the plan. This family includes COLIN , POPF (Coles et al. 2010), and OPTIC (Benton, Coles, and Coles 2012). Planners from this family were used in a variety of real-world applications including robotics, (Cashmore et al. 2015), Autonomous Underwater Vehicle (AUV) control (Cashmore et al. 2014), Micro Aerial Vehicles (MAV) control (Bernardini, Fox, and Long 2014) and space applications Denenberg and Coles 2018). These planners perform forward state-space search starting from the initial state. At each search state, an LP solver is used once to determine whether a consistent schedule for the plan exists. If no consistent schedule exists, the search branch can be pruned. If the state is consistent, the LP is then used several more times to bound the numeric variables and thus tightening the space of applicable actions in this state, narrowing the search space ahead. Recent work (Denenberg, Coles, and Long 2019) has shown that solving LPs at every state multiple times may cause the search process to become slow and ineffective.
The contribution of this work is twofold: 1. We propose a better translation from the search state to LP. Our new compilation allows the better selection of optimization tools required for the consistency check of the problem, possibly eliminating the necessity of an LP solver.
2. We propose methods for using information from a given state to compute the current variable bounds in the search, thus calling the solver fewer times and improve the performance of any planner from the OPTIC family.
The rest of the article is ordered as follows: Section 2 describes the problem and the current way OPTIC planners Leg1 Leg2 Obs1 Obs2 Obs3 Obs4 Obs1 start dist.
Obs4 start dist. Figure 1: The flying observer solve it. Section 3 presents the suggested methodology. Section 4 presents the performance of the suggested improvements in a variety of different domains.

Problem Definition
A temporal planning problem with discrete and linear continuous numeric effects is a tuple: where P is a set of propositions and V a set of numeric variables. A state S is defined as a set of value assignments to the variables in P and V. I is such a set representing the initial state of the system. G is the goal: a conjunction of propositions in P , and linear numeric conditions over the variables in V , of the form ..w i and c ∈ R are constants). An action changes the values and carries the system from one state to another. An action is defined as a tuple as well: where d is the duration of the action constrained by a conjunction of numeric conditions. pre ⊢ and pre ⊣ are conjunctions of preconditions (facts and numeric conditions) that must be true at the start and end of the action, pre ↔ are invariant conditions (preconditions that must hold throughout the action's duration), eff ⊢ and eff ⊣ are instantaneous effects that occur at the start and end of the action. Such effects may add or delete propositions p ∈ P (eff + , eff − ) or update a numeric variable v i ∈ V according to a linear instantaneous change: where u, v i ∈ V are numeric variables, and c, w i ∈ R are weights. eff ↔ is a conjunction of continuous effects that act upon numeric variables throughout the action's duration. In this work, we assume all change is linear and is of the form: where c ∈ R is a constant. The planner is required to find a set of actions in A and their schedule, that would carry the system from the initial state to the goal state. (Denenberg, Coles, and Long 2019) first introduced this example; it is an anonymized model of a real-life problem. In this domain, named flying observer, the planner is required time distance Precondition Can start observing Figure 2: Distance Requirement to plan an Unmanned Aerial Vehicle (UAV) observation mission. The UAV is required to fly legs over a defined stretch of land containing objects to be observed. Each leg is of different length. Each observation has a different duration and requires a different type of equipment. A target-start distance defines the area within the leg in which the observation must take place. The observation can only occur when the UAV has flown more than the target-start distance of that leg (flown l ≥ target-start o ). A continuous numeric effect of the fly l action updates the distance flown so far in a leg:

Running Example
where Vel l is the flight velocity. Fig. 1 illustrates an instance of this domain: in this instance, two legs are defined (marked in solid blue lines). In each leg, two observations are required (marked in red, pattern-filled lines). All observations have a target-start distance defined, but for clarity, only the starting distance of the first and last observations are shown.
In order to perform an observation, a defined piece of equipment needs to be calibrated and configured for a specific observation. Once the observation is done, the equipment needs to be released to become available for future observations. The domain comprises the following actions: take-off l (dur=5; pre ⊢ ={on-ground,first-leg l }; eff ⊢ ={¬on-ground, flown l =0}; eff ⊣ ={flying l }), set-course l1,l2 (dur=1; pre ⊢ ={done l1 , next l1,l2 }; eff ⊢ ={¬done l1 }; eff ⊣ ={flying l2 , flown l2 =0}), fly l (dur= distance l / speed l ; pre ⊢ ={flying l }; pre ↔ ={flown l ≤distance l }; eff ⊣ ={done l , ¬flying l } eff ↔ ={ dflown l / dt +=1}), configure o,e (dur=1; pre ⊢ ={available e , optionfor o,e }; eff ⊢ ={¬available e } eff ⊣ ={configuredfor o , pending o,e }), The target distance precondition and temporal constraints force the observe actions to fit within the fly action. The meaning of the precondition is illustrated in Fig. 2: The blue line is a depiction of the distance change as the UAV flies over the leg. The dashed red line is the precondition signifying the distance required for the start of the observation. When the distance reaches the value required in the precondition, the observation can start. Notice that this problem is, in fact, temporal, the numeric constraint can be easily converted to a temporal one depending on the manifestation in the temporal state can be seen in Fig. 3.

OPTIC and Forward Search
The OPTIC family of planners is based on the methodology of converting a state to an LP described in COLIN paper ). Here we survey that methodology.
To find a path from the initial state to the goal, OPTIC performs Forward Search. Starting from the initial state, OP-TIC branches over applicable actions, exploring partiallyordered but un-time-stamped sequences of instantaneous actions. Durative actions are converted to a pair of instantaneous snap-action. Snap-actions mark the start (A ⊢ ) and end (A ⊣ ) of a durative action A. A ⊢ has preconditions pre ⊢ A and effects eff ⊢ A; A ⊣ is analogous. We define the set A inst to contain all instantaneous actions in A, including snapactions.
A state S in the search can be thought of as a set containing: propositions (S.p ⊆ P ) that are true in S, and upper (S.max (v)) and lower (S.min(v)) bounds on the value each variable in V can hold in S. In the initial state, all variables have max (v) = min(v) = v I the value of v specified in the initial state; max (v) and min(v) will only differ from each other in following states if a durative action with a continuous effect has acted on the variable.
An action is deemed applicable if all its propositional invariants are satisfied by S.p and if all numerical invariants can be satisfied by any value between S.max (v) and S.min(v). The planner compiles a list of all open applicable (named openlist). Search proceeds by popping the first state from the openlist: in our work, we use WA* (W=5), so sort the openlist by h(S) + 5.g(s), using the temporal-numeric RPG heuristic of COLIN .
All successors S ′ of S are generated by adding or deleting all propositions in eff + a and eff − a respectively, and applying all discrete numeric effects to both max (v) and min(v) for all v ∈ V affected by eff num a . This guarantees the S ′ to be propositionally consistent.
OPTIC then transforms all the temporal constraints to the following form: where Lb, U b ∈ R are the upper and lower bounds of a time interval. OPTIC also adds the necessary ordering constraints to the plan. The action that has just been applied is ordered after the following: last actions to add each of its preconditions, actions whose preconditions it deletes, and actions with numeric effects on variables it updates or refers to in preconditions/effects. All ordering constraints are of the form t j − t i ≥ ǫ, where t j ,t i are the times at which the new and existing action must occur, respectively, and ǫ is a small positive constant. The temporal and ordering constraints, formulated as Eq. (5), constitute a STN and the planner uses a Simple Temporal Problem (STP) solver to check for temporal consistency. If the STP can solve all equations (i.e., assign values to all time-steps such that the equations are valid), then the STP was able to find a schedule, and the state is temporally consistent. If S ′ is propositionally and temporally consistent, the planner will compile the problem into an LP and then check for numerical consistency. Each step of the plan i is given an LP variable t i . Each variable v ∈ V is given three LP variables for each step i: v i , v ′ i , and δv i . v i denotes the value of v just before applying the action in step i, and v ′ i is the value right after the action's application. The planner applies Eq. (3) to the affected variable thus: where v, u ∈ V are the numerical variables, u n i is the value of the nth numerical variable at step i. w n s are weights.
δv i is the value of the sum of all changes currently acting on v. Recall; in this work, each continuous effect is defined by a constant. When a new action is applied at step prev, the contribution of its effect is added to δv prev ; when an effect ends at step i, the value is removed from δv i .
The value of v i denoting the value just before the application of the action at step i can be computed thus: where i is the current step index and prev is the index of the last step in which the value of v was computed. Note; if the calculation of the value of v is required for an invariant in step j, the next time v will be computed the time interval will be t i − t j , regardless whether δv is changed or if the action is acting on v.
If the STN or LP finds that the state S ′ is inconsistent (i.e., there is no solution, no schedule that would enable achieving the state), it is pruned, and the search will not advance down that branch. If the state is consistent, then the LP solver is called two more times for each variable v to optimize it and compute the new max (v) and min(v) using the standard temporal/numeric relaxed planning graph heuristic of Colin . It is then inserted into the openlist, providing h(S ′ ) = ∞, i.e., the heuristic does not indicate S ′ is a dead-end.
Note that when no numerical change is present, it is sufficient to use STN to prove consistency. When continuous changes or numeric constraints are present, the LP solver is required for the proof of consistency.
In addition to the consistency check, the LP is also used to compute the bounds max (v) and min(v) of S ′ . If all continuous actions on v have ended, then the last defined value v i can be maximized and minimized to compute the bounds.
If v had a continuous effect start but has not yet ended, another time variable is added to the LP denoted t now , representing the latest timestamp. For each variable with an active effect, a variable v now is added. t now is ordered after all Step Action variables constraints comment 0 TakeOff Step2 after Step1  (8). The LP solver then minimizes and maximizes v now to find the possible bounds. (Denenberg, Coles, and Long 2019) showed that though it was previously thought that calling the LP solver is beneficial both for state consistency and for the variable bound update, in large real-life domains, the calls to the LP solver may slow the search down. The premise was that the LP problems solved are small, and therefore the call to the offthe-shelf solver would not be computationally expensive. However, it was shown that in some real-life applications, this was not true: when the state contained many actions and multiple variables, the LP grew large and the solving of which became slow. Table 1 demonstrates the process of converting a state into an LP. The table shows the LP equations for the partial-plan: take-off, fly ⊢ l0 , observe ⊢ o1,l0 , observe ⊣ o1,l0 (for conciseness we assume that take-off is instantaneous and no configure actions are required).
The first action receives a single time variable t 0 . The second action F ly ⊢ l0 , receives a time variable t 1 , which is ordered after t 0 , and the value of f lown is computed. The value before the fly action is the initial assignment, which is 0. Since there is no instantaneous effect on the action's start, the value just after the application of the action is the same. The invariants on the value are enforced just after the beginning of the fly action. The same process is repeated for the next action Observe ⊢ o0 : assigning a time variable for the action, calculating flown before and after the application of the action, and enforcing invariants. Note the ordering constraints formulated as temporal constraints in all actions. Also, the f lown variable is computed at each step, and its value depends on the previous step.
The next section will describe a method for changing Eq. (8) in a way that would allow calling the LP solver fewer times, and compile certain problems containing numerical constraints and change as STP.

Informed Selection of Solver for Consistency and Update
The OPTIC methodology described in the previous chapter was developed to accommodate the general case in which hybrid planning is to be done, covering all possible state types. The planner uses the general representation both in consistency check and in the variable update. It was shown in (Denenberg, Coles, and Long 2019) that the general approach could, at times, lead to slow solving. In this section, we propose two new methods for identifying two specific cases that frequently arise in the state in real-life problems. In such cases, the use of an LP solver can be made redundant, facilitating faster solving. In other cases, information from the current state may be injected into the problem definition to allow for faster solving.
The first method examines the latest added action that carried the system from state S to state S ′ . The second involves a conversion of specific numeric constraints and effects into STN form. Finally, we describe how both these processes can facilitate a more effective update of variable bounds.

Observing the Latest Action
As stated previously, OPTIC solvers attempt to prove inconsistency with an STP first. Then if continuous numeric effects and numeric constraints are present in the current state, the planner compiles the problem as an LP. OPTIC planners treat each state in the most general way: in the general case, every action may render the new state inconsistent. However, using knowledge about previous states, some instances in which the LP solver can be avoided may be found.
Consider the state TakeOff ⊢ , TakeOff ⊣ , Fly l1 ⊢ , configure o1,e2 ⊢ : The partial plan contains continuous numeric effects on the variable f lown l0 . Therefore, to prove this partial plan consistent, OPTIC requires an LP solver. However, since the planner is performing forward search, to reach this state, the planner must have been in a previous state, which it found consistent: TakeOff ⊢ , TakeOff ⊣ , Fly l1 ⊢ . The configure action that is added does not require the value of f lown l0 , and its effect is propositional.
Assume the state S is propositionally, temporally, and numerically consistent. The new state S ′ , which is reached from S by addition of action A ∈ A inst cannot be rendered numerically inconsistent if A does not contain any numerical effects or constraints. Furthermore, since OPTIC only examines states S ′ that are generated to be propositionally consistent, the state only has to be tested only for temporal consistency.
Thus, if an added action A contains only propositional or temporal constraints and effects, the state S ′ can be deemed consistent by using the STP, and an LP is not required.
Note that if this test has determined that S ′ is consistent, there is no need for a numerical variable bound update, as those do not change.

Reformulation of LP
During the search, OPTIC compiles the state into an LP, as depicted in the previous section. This transformation is done in a step-wise manner, meaning each step is transformed into  No consideration is taken as to what effect a step has on a variable; as long as the value of the variable is required, its value will be computed, and the next step will use said computed value. The notation t prev denotes the previous step at which the value of variable v was calculated, and the next step i > prev that computes the value of v will use the value stored in v prev .
Here we suggest making a distinction between two types of steps that affect the value of v: A step containing a start or end of a continuous numeric effect and a step that does not. The later is a step containing numerical constraints on v but does not change the value of δv. To distinguish between the two, we propose two notations ef f for steps that start or end an effect and const for steps containing only constraints.
Using the new notation t p ef f would be the last time in which v had an effect start or end, v p ef f would be the value of v calculated at that time point. Then Eq. (8) is written thus: The conversion of the equations is demonstrated in the previous example: this is presented in Table 2. Notice the difference between Table 1: The effect acting on the variable f lown l0 started in step 1, and therefore the computation of f lown l0 2 f lown l0 3 is always done with respect to step 1.
If no continuous numeric actions have been acting on v before the last action at t p ef f , then the value of v p ef f is a constant. This is seen in our example. The value of f lown l 0 ′ 1 is the same as the initial assignment. This conversion extremely useful when all constraints are of the form: where v ∈ V and C ∈ R. This constraint is written as a less than-equal-to constraint. Without loss of generality, this includes all constraints that have a single variable on one side and a constant on the other. If v p ef f is constant, then using Eq. (9) when enforcing Eq. (10) at step i, we can write Notice that at step i, all the variables on the right-hand side of Eq. (11) are known and are constant. Therefore, Eq. (11) can be formulated for each step i as a constraint of the form of Eq. (10) as long as v p ef f is constant. Notice that the numerical constraint in Eq. (10) is converted to a temporal constraint. If all constraints in the state can be converted thus, then the problem is, in fact, an STN, and the LP solver is not required. The example given above can be converted in such a way. The constraint f lown l0 2 > T arget dist o1 can be converted to t 2 − t 1 > (T arget dist o1−f lown l01) / 1 . All numeric constraints in this partial plan can be converted in the same way. This means that even though continuous numerical effects and numerical constraints are present, this problem is temporal, and can be solved with an STP.
If all numerical constraints were converted to temporal, the planner could determine consistency using the STN. However, updating the bounds is still required. Observing Eq. (8), we note that since v p ef f is constant, the maximum and minimum of v i are dependent on the interval The minimal size of the interval is zero. The maximum may be drawn from the state: if another constraint exists such that limits t i or if t p ef f is a start action beginning an effect, and is the only continuous numeric effect present, the maximal interval is the duration of the action. If no such value can be derived from the problem, then the interval is set to infinity. If δv i > 0 then the minimum value for v i is when T i = 0 and is min (v i ) = v p ef f ; and the maximum is max (v i ) = v p ef f + δv ef f T i . The case in which δv i < 0 is analogous. This update method does not require an external solver and, therefore, very fast. (Denenberg, Coles, and Long 2019) have shown that the variable update is often the task that is most computationally expensive as it requires several calls to the LP solver, depending on the number of numerical variables in the partial plan. The previous section has detailed several cases in which the variable update can be avoided or done without the use of an LP. Here we attempt to facilitate faster LP solving in the update phase in case it is still required. The LP solver may use one of several optimization methods; however, the selection of the method, as well as the method speed, depend on whether the feasible space is bounded and in which direction. We would like to supply the solver with information about variable boundlessness. We cannot use the bounds from the previous state S as those might have changed by action A.

Efficient Variable Update
Therefore, we again examine the snap action A added in the last step that carried the system from previous state S to the current state S ′ . Recalling state S contains bounds on v (S.max (v) andS.min(v)). We wish to determine whether the action A is capable of expanding the limits of v, causing the interval [min(v), max (v)] to grow if A causes the bounds to contract, or if the interval retains its size but shifts.
If an instantaneous numeric effect exists, then the bounds on the latest defined v i (the step at which all continuous ef-

Evaluation
In this section, we examine the performance of the proposed changes in six different domains, which stem from four physical world examples. The domains brought here were chosen to demonstrate both the strengths and the weaknesses of the contribution: The first four illustrate the family of cases in which the contribution is meaningful, shedding light not only to the benefits of our suggestion but also to ways in which to better model a problem for any OP-TIC family planner. The other two domains are brought to demonstrate cases in which the contribution is not useful, in an attempt to assess the price of using it. As this work's contribution is in improving the OPTIC family of planners, we compare our suggestions with the performance of the latest implementation of OPTIC, and apply our improvements to the same code base, and name it OPTIC with Injected Information (OPTIC-II).
The results and results of other additional tests on various IPC domains are publicly available at extra data 1 .
All tests were performed on an Intel i7-8550U CPU@1.80GHz×8 with 8GB RAM. The PDDL files of the domains, the respective problems, and result data will be published on a public website. Runtime results are presented in Table 4. "X" in the table means the runtime was over 1000s. Since the domains and processes are deterministic no statistical analysis is required, as results may only vary due to CPU noise.

Domains
Flying Observer We demonstrate OPTIC-II on a set of previously published domains. The first is the flying ob-server that (Denenberg, Coles, and Long 2019) has presented as a domain stemming from the industry. Two distinct models of this physical domain were tested: The first is identical to the running problem. The second variant of this domain has a requirement that the observer is flying before configuring or releasing pieces of equipment.
The problems in the first variant all require a single observation to be made in each leg. The instances are described in Table 3.
In all instances of the second variant, six observations are defined for each leg, where the first and last leg both share an observation that cannot be performed in the first leg. The fact the observation cannot be used in the first leg may lead the planner down a branch, which would not be useful. The first instance contains two legs, the second three, and so on. (Denenberg, Coles, and Long 2019) showed that these problems are challenging for the planner.
Factory Floor Quality Assurance (QA) This domain describes QA sampling planning on a factory floor. A machine produces parts at a specific rate; at some point, several parts are taken for sampling. The number of produced parts is limited for storage reasons. This domain is similar to the previous domain (the flown distance is analogous to produced parts); only here, we limit the total number of parts that can be produced, adding a global numerical invariant condition. In this domain, too, we have two variants -one allowing the calibration of measuring machinery before the beginning of the manufacturing process, and one that does not. As in the previous domain, the second variant is used for instances that require multiple samples of the same part.
Single Rover IPC Domain and Linear Generator The Single Rover domain is a standard domain taken from the standard IPC 3, and ) used it to demonstrate the hybrid planning mechanism.
The Linear Generator is yet another standard domain that was widely used in previous papers. It describes a generator consuming fuel to generate energy. The generator may be refueled from auxiliary tanks. All actions affect the main-tank fuel quantity, and the fact that all actions contain numerical change and constraints it was expected OPTIC-II to show little to no improvement in solving problems from this domain.

Results
Implementing the changes suggested in this work requires additional tests before building an LP. These tests and checks come with a computational price. However, as can be seen in Table 4, that price is not high. In the Linear generator domain and the single rover, none of the changes are useful. In most states, the information from the applied action cannot reduce the computations, and the problem is not convertible to temporal. This is because in many states, for instance, there are often two continuous linear actions operating on the same variable. The changes not being useful mean that all checks will be false when running OPTIC-II, and the LP solver will be used just as in OPTIC. The results show that OPTIC-II indeed performs a bit slower when used in these domains.  In the four domains from the Flying Observer and QA, OPTIC-II performs far better than OPTIC. We present the results of all three suggested changes, the contribution of each change separately, and possible combinations to better understand the results.
Efficient Variable Update In Section 3.3, we suggest using information about the current action to update the variables' bounds efficiently. This improves the LP solving in the variable update stage of the search. Therefore, we expect this change to be more prominent when the planner handles large plans that result in larger LP problems, and when a large amount of variables needs to be updated.
In Table 4, the line named "Sec. 3.3" presents OPTIC performance when only this change is present in the four domains taken from (Denenberg, Coles, and Long 2019). It can be seen that this change contributes to the performance is more prominent in higher instances where the plan is, indeed, quite long and contains many variables.
Though this change's contribution is not visible in simple academic domains, it helps scale large problems such that arise in a real-life domain and, therefore, useful.
Observing the Latest Action In Section 3.1, we suggested using information about the current action to decide whether an STP can be used to prove temporal consistency even though a numeric change is present in the state. This change may lower the number of LPs that will be solved during the search and, therefore, speed up the search. The runtime results of OPTIC running only this improvement is dubbed "Sec. 3.1" in the table.
In the first four domains, we see a significant reduction of LPs solved in the search 2 , which results in a faster search. In the last two domains, the reduction is minimal, and so the 2 The number of states proved consistent with an LP out of the visited states is given in the extra data, and will be published online tests slightly slow the search process.
Reformulating the LP The last contribution we examine is the one described in Section 3.2. For implementation reasons, this change was only applicable to the previous change. This change was useful in both the flying observer domains. When applied to these domains, all problems were converted to temporal, and no LPs were solved. The result was a significant improvement in planning speed.
In the QA domains, only some of the states were converted from numerical to temporal, and therefore the change was less prominent. The planner was able to identify that the requirement for the total amount of produced parts was the variable that prevented the conversion. If the domain expert believes the total amount limit cannot be reached, he can remove that constraint from the domain and allow for much faster Planning. Thus, using this method, we can improve performance, and perform knowledge engineering, presenting the model expert with possible ways to improve the planning process.


SDL Trados and Tmxmall: A Comparative Study of Computer-Aided Translation Tools

Technological development has brought about a series of changes, including influences on the traditional translation industry which is unable to meet the future needs due to its low efficiency and limited forms. Computer-aided translation software, shortened as CAT software, is therefore developed. Featuring powerful memory and fast computing speed of computers, CAT software allows translators to give full scope to creativity, which enhances traditional translation efficiency. In recent years, both CAT software and cloud translation software have been rapidly developed. The latter is built based on cloud computing technology, and is emerging one after another. This article, taking such CAT software as SDL Trados and such cloud translation platform as Tmxmall as examples, studies similarities and differences between the two different kinds of tools in terms of operation interface, translation project management and corpus management. By analyzing features of the two tools, this article seeks to provide references for translators and software engineers.

TRADOS (Translation & Documentation Software)
was originally established by two German engineers, Jochen Hummel and Iko Knyphausen, and was later acquired by SDL [1] . SDL Trados, the new name of Trados, is the first company to deliver the concept of translation memory and apply it to CAT software. At present, SDL Trados holds over 70% market shares in the global language translation software market [2] . The software, SDL Trados Studio, is available in different user interface languages including Chinese, English, Korean, Japanese, and German. Besides, it offers settings of language pair, and can achieve translations between more than 60 languages.
SDL Trados Studio (hereinafter referred to as Trados) supports dominant operating systems, such as Windows 7, Windows 8, and Windows 10. The termbase within Trados supports for a wide array of format, not only sound and pictures, but also video and audio.

Tmxmall
Shanghai Yizhi Information Technology Co., Ltd. (Tmxmall ) was established in September 2014 in China.
The company, which is mainly engaged in researches and applications of data products and technologies of cloud corpus, is at the leading level at home and abroad in the technologies of corpus alignment, massive corpus data management and real-time retrieval. Tmxmall offers corpus alignment tool, corpus retrieval and exchange platform, characteristic corpus management system, cor-Copyright © 2020 Ran Cheng doi: 10.18282/jnt.v2i4.1379 This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
-pus mall trading platform, online translation management platform, etc., being a comprehensive platform integrating corpus production, management, and sharing transactions.
While Trados represents classic translation software, Tmxmall stands for a newly emerging cloud translation platform. Trados offers offline translation operations, but the price of the software is expensive. Contrary to Trados, network environment is indispensable for Tmxmall users, and there's no need for them to purchase software, yet there are paid items during translation, which is the biggest difference between the two tools. In addition, the author compares the similarities and differences of the tools in terms of operation interface, translation project management and corpus management to provide reference for translators and software engineers.

Similarities and differences between SDL Trados and Tmxmall
The tools adopted in this study are SDL Trados Studio 2019, and current online version in Tmxmall official website (https://www.tmxmall.com/). Tmxmall works in a browser on the basis of the Internet connection. Firstly, users need to register an account, and log into the main interface of its website, including introduction to the company and its products and services. When selecting the products and services options, users can find the main functions, including intelligent translation, corpus alignment, big data retrieval, corpus management, corpus sharing, open platform and services. Besides, corresponding working interface will be jumped to after users clicking on these options.

Management of translation projects
Compared with the traditional translation, management of translation projects is a major improvement for CAT software. Team cooperation can be realized through project management with the project being distributed to different translators in time sequence after being divided into different sections and stages. In this method, an efficient team cooperation on translation is therefore realized.
To create a translation project in Trados, users need to first create a new project by selecting Project at the navigation pane, and fill in the project information. Secondly, users need to add a single file or files form a folder for translation, and then add or create translation memories and terminology databases. After that, users Compared with Trados in terms of the management of translation projects, Tmxmall translation platform is more convenient in both project creation and task receiving. Project information can be clearly seen in the management interface, such as the creator, creation date and submitting deadline. Although there is no fee required when users translate files manually within the platform. However, it charges money on each project when users export translated files, and payment can be made through Alipay, WeChat, bank transfer, and etc.

Corpus management
Corpus management, which is the main function for CAT software's comparison, is about the management of translation memories and terminology databases. Users have a preference for CAT software that features larger inventory capacity and more ordered way of management. Translation memories refer to a language database that stores and retrieves source language segments and their corresponding translated version of the segments.
The terminology database can store and retrieve the source term and its corresponding translated version of the term.
The format of translation memories is .sdltm for Trados 2019. There are mainly two methods that can obtain this format. One is by aligning bilingual documents, and the other is by upgrading .tmx format memory generated from other translation software. The procedure of first method is presented as follows. First, click on the align document from the menu and select a single file pair to create the new translation memory and complete its general information. Second, add documents in the order of the previously checked source language and target language, and select the exported alignment file format. The .tmx format is commonly chosen. Thirdly, users need to check whether the aligned text is neat or not. If there is an error, users can disconnect it by clicking on the wrong line connecting the source text and the target text, and reconnect it with the mouse. When the alignment is complete, users need to click the finish button. It should be noted that the source text and the target text can be connected at will in the alignment process, but the text cannot be segmented. In such situation, an over long alignment of sentence segment will reduce the matching degree and lead to the situation that the matching sentence segment cannot be retrieved during the use of translation memories. Besides, users may use the upgrade memory function to upgrade it to .sdltm format after exporting the text in .tmx format, and add the file to the ongoing translation project or directly import it into the created translation memory.
As for Tmxmall, import formats of translation memory support .tmx, .sdltm, .xls, and .xlsx. The procedure to create translation memories on Tmxmall translation platform is presented as follows. First, click on the language asset form Yicat. Second, select translation memory management to create the new TM, or merge different TMs and use them in translation. Translators can also search TM under the Yicat, and search the one you need by entering the name directly. Offline translation software is hard to obtain this kind of function. In addition, functions of corpus quick search, .tmx file search under the big data retrieval are available for translators to select corpus and TM online. Corpus can be managed under the corpus management option, where TMs owned by user's own and shared corpus can be viewed by classification. There are two sections for corpus sharing, corpus mall and TM ROBORT, where users can buy corpus from all over the world and can select different types of corpus, source language and target language. TM ROBORT also support analyzing, retrieving, merging, importing and spliting the corpus. With this function, the value of TM can be deeply dug, and a more convenient and flexible user experience is provided.
From the perspective of TM, Trados is more stable but supports fewer formats. While Tmxmall is more convenient and features larger storage capacity, due to its advantages of Internet cloud platform, becoming more popular among users.

Termbases
MultiTerm is a program used for creating termbases For termbases, creating termbases are rather complicated in Trados. It focuses on self-producing and self-using and users don't need to pay for a second time.
While, Tmaxmall, featuring sharing information, supports more formats and is easier for users to create termbases. However, it is charging on almost all operations, filling with commercial atmosphere.

Conclusion
Through analyses above, it is easy to find the classic translation software such as Trados and cloud translation platform such as Tmxmall have their own advantages and disadvantages. The biggest advantage of classic translation software is that there is no need for Internet connection and payment for the second time, and has many functions. Its disadvantage is that the operation steps are complicated. Cloud translation platform, however, has simpler operation steps, which can effectively improve the work efficiency of translators. Besides, the platform doesn't had requirements on hard disk capacities due to a large amount of language materials are saved in the cloud. The disadvantage is that it totally works based on network connection and has fewer functions compared with Trados. The author aims to provide references for those who are engaged in translation-related work by comparing the advantages and disadvantages of the two tools, which is helpful to save their time in selecting software. Meanwhile, this article also provides references for software developers to further improve software performance.


Development of Aircraft Movement Simulation in Airport Airside Area

Soekarno-Hatta Intl Airport had become busier every and each year passed. Based on Airnav’s data in 2016, there was about 1.200 aircraft movement, included take-off and landing, happened in Soekarno-Hatta Intl Airport in one day. These numerous movements made SoekarnoHatta Intl Airport became the 12th busiest airport in the world based on Airport Council International (ACI). The long queue of the aircraft at the taxiway is deniable and became one of the problems that needs to be resolved. This research would make aircrafts movement simulation in Soekarno-Hatta Intl Airport’s taxiway(s) using Rockwell Arena Simulation software. The simulation results would be total taxiing time of an aircraft, which intersection(s) that traffic happened, and the total of aircraft(s) that doing taxi in and taxi out. This simulation would help to determine and evaluate the factors that initiated the queue in the taxiway and modify taxiing route to reduce the traffic. The results of this research can be applied by the airport as a reference for scheduling aircraft’s departing or arriving, develop airport airside facility, and to improve taxiing route so the duration of aircraft’s taxiing time can be reduced.

Introduction
Soekarno-Hatta International Airport took a big part in Indonesia's economic growth. Soekarno-Hatta International Airport is the gate to people around the world who went to Indonesia with very purposes, like businesses, diplomatic agreement and also became tourist destinations. These reasons had risen the number of the flight, increase the traffic and aircraft movement in Soekarno-Hatta Intl Airport and made it became the 12th busiest airport in the world based on Airport Council International (ACI) [1]. The traffic at Soekarno-Hatta Intl Airport had delivered it to the last position on the On-time ranking departure performance based on Flightstats website, for August 2018 flights. With total 21.559 flights, the flight that has on-time departure are 51,46% and the flight that got delayed (+15 min.) are 48,54% [2][3].
The aircraft traffic that happened in Soekarno-Hatta Intl Airport airside become one of the reasons the flight became delayed. The traffic could be seen at the holding bay of taxiway when the aircraft will take-off. This traffic gave a bad impact to the airlines because it would cost them more. Based on Indonesia National Carriers Air Association (INACA), a flight that had delayed for 20 minutes would add cost about $1.000 for the extra fuel for longer taxiing time [4,5].

Taxiing
Taxiing is a process to move the aircraft in the ground from one place to another one with its own power. Like when the aircraft move from the terminals to the edge of the runway before take-off. Aircraft's taxi speed limited to 20 knots; it also depends on the circumstances. In a straight long taxiway and without obstacle around, the speed could be reached 30 knots. However, remind if the taxi speed over 20 knots, it would need a strong control of the nose wheel to avoid over-controlling-nose-wheel-risk. In the turning side, the speed must be reduced to the speed limits of aircraft when turning, 10 knots [6].

Taxiway
The taxiway is a path for aircraft at an airport that connects runway to the terminal area and service hangars. In some busy airport, that have high aircraft movement, the configuration would be used is the one-way parallel taxiway. This configuration has a purpose to reduce aircraft queue time in taxiway so the aircraft mobility will be faster when it doing landing or take-off. Busy airports also add taxiway in some strategic place along the runway, so the aircraft that just landed could be cleared away quicker from the runway. This type of taxiway called exit taxiway [7].

Methods
This research would make aircrafts movement simulation in Soekarno-Hatta Intl Airport's taxiway(s) using Rockwell Arena Simulation software. This software already used by many global companies to simulate their problems to resolve the issues and do their business. In this simulation, there will be some assumptions that would be used: 1. The aircraft speed will be assumed as 20 knots, the average speed of aircraft taxiing speed. 2. The reduction of speed and linear acceleration will be assumed none in the taxing process. 3. The runway that would be used in this simulation is the runway on the west side (07L and 07R) for take-off and landing process, which will be in random sequences. 4. The flight that would be simulated are the flight that scheduled between 15.00 WIB to 22.00 WIB based on Soekarno-Hatta Intl Airport west-side-runway historical data. 5. The duration of an aircraft's taxi time from one point to another point using Linear Movement methods. 6. The runway will be used 50 percent to take-off and 50 percent to landing. 7. The distance between the points will be found by using a scale comparison method using Corel Draw software.

Simulation's Flow
The simulation will be using the flow that shows in Figure 1. It would start by inputting the flight data and the distance between taxiway intersection data. The next step is to make algorithms and models of each taxiway segments. After that integrate all the small segments to one big algorithm before running the simulation. If the simulation error, we need to identify the error(s) in the algorithm or the model, and after that fixed the error(s). If the simulation running smoothly, the next step is checking the results. If the data make sense and valid, we can make the conclusion and end the simulation. But if the data do not make sense and/or not valid, so we need to re-check the algorithm and model.

Taxiing Route
Taxiing route is the path that the aircraft used from runway to terminal or the contrary. Every aircraft that will depart from or arrive at every terminal have its own taxiing route. The aircraft that will depart will have a different route with the aircraft that will arrive, although it is from or heading to the same terminal. The taxiing route from 07R and 07L runway based on "Airport Information for WIII" that published by Jeppesen could be seen at Table 1 and Table 2 Flights that would be simulated are the flights that scheduled between 15.00 WIB to 22.00 WIB. This range is chosen because based on the historical data, the west side of the runway is used mainly at these hours. Official website of Soekarno-Hatta Intl Airport shows at that time range the aircraft movement is busier and dominated by the aircraft that approach the airport. It shows the arrival's movement will be busier than the departure's movement.

Entity Input
The entity input needed at the create module at the software, and it will be based on the total number of flights. The entity input would be a frequency of the aircraft start to depart or arrive in minutes. The triangular distribution would be used, to show the average, minimum, and maximum value. The minimum and maximum value will be picked randomly. Table 4 contains information about the flight's frequency from and to Soekarno-Hatta Intl Airport between time range between 15.00 to 22.00 western Indonesia time (WIB).

Results and Discussions
The results of this simulation have three outputs: waiting time, transfer time, and total time. Waiting time is the time that used by the aircraft to wait on the queue. Transfer time is the time that the aircraft used for taxiing. Total time is the sum of waiting time and transfer time while taxiing. From Table 5, the sum of waiting time, transfer time, and total time for the aircraft that would depart from and arrive at each terminal is shown. The time that has blue color are the entities type that had higher time than the rest of the result.
The highest average waiting time happened in entity A3U, when the aircraft landing and heading to Terminal 3 Ultimate. The highest maximum waiting time happened in A2E entity when the aircraft landing and heading to Terminal 2E. The highest average transfer time showed at D1A entity when the aircraft will take off and its origin terminal is Terminal 1A. The highest maximum transfer time showed from A1B entity when the aircraft landing and heading to Terminal 1 B.
The highest average total time happened in entity D1B, when the aircraft will take off and its origin terminal is Terminal 1B. The highest maximum total time happened in A2E entity when the aircraft landing and heading to Terminal 2E. Table 6. Waiting time at hold area.   Table 6, we could mark the holding areas that have waiting time more than 5 minutes. These areas will be shown as red spots in Figure 2. The areas that have waiting time more than 5 minutes are: 1. Hold 46, the intersection between taxiway WC1 and taxiway NP2, 2. Hold arr 07R, the intersection between taxiway SP2 and taxiway SC3, 3. Hold NC41, the intersection between taxiway NC4 and taxiway NP1, 4. Hold NC42, the intersection between taxiway NC4 and taxiway NP2, and 5. Hold NC51, the intersection between taxiway NC5 and taxiway NP1.

Analyzation and Case Study
The simulation's result in the previous section shows the entity that has high waiting time, and the path could be seen in Table 1 and Table 2. From the existing taxiing route, there are 5 intersections that have waiting time over than 5 minutes. This result the total time of the aircraft need for taxiing could be exceeding 20 minutes. High waiting time impacted by the parallel taxiway that not used efficiently in each runway side. From Figure 3, the green path shows taxiing route path for the aircraft that will take-off at runway 07L from Terminal 2 and Terminal 3 Ultimate. The red path shows taxiing route path for the aircraft that will be landing from runway 07R to Terminal 2 and Terminal 3 Ultimate. From this illustration, it shows that parallel taxiway NP2 used by the aircraft from two different directions, so if there are aircraft that will be take-off at runway 07L from Terminal 2 or Terminal 3 Ultimate, the aircraft that already landed at runway 07R and heading to Terminal 2 and Terminal 3 has to wait in taxiway WC2.
This may add more waiting time in taxiway WC2, it would take longer even more if the aircraft that will be take-off came from Terminal 3 Ultimate. On the south side also has the same problems with the north side. It showed in Figure 4, the red path shows taxiing route path for the aircraft that landed in runway 07L and heading to Terminal 1. The blue path shows the taxiing route path for the aircraft that landed at runway 07R and heading to Terminal 1, 2 and Ultimate 3. From the illustration, it shows that parallel taxiway SP2 used by the aircraft from two different directions, so if there are aircraft landed at runway 07L and heading to Terminal 1, the aircraft have to wait at the intersection between taxiway SC3 and taxiway SP3.

Improvement Route
Because of the problems at runway 07 L and 07R are impacted by the parallel taxiway that used by two different paths, we propose to each side parallel taxiway used by one path only, so the aircraft not needed to waiting for other aircraft to passed from another direction. For the north side, taxiway NP2 should be used just for taxiing route from the west to the east side.
For the taxiway NP1, it should be used just for taxiing route from the east to the west side. For the south side, taxiway SP2 should be used just for the taxiing route from the east to the west side and taxiway SP2 should be used just by the taxiing route from the west to the east side, as presented on Figure 5 and Figure 6.  With the improved taxiing route in Figure 5 and Figure 6, the duration of waiting time would be shorter. This caused by the queue to take turns between two aircraft from different directions is just from taxiway SP1 to taxiway SP2 in the south side. The same happened at the north side, the taxiing waiting distance will be shorter so other aircraft will not have a long queue, just from taxiway WC1 to taxiway WC2, as presented on Figure 7 and Figure 8. These results is in the same agreement to others [8,9].

Conclusions
This study has improved a taxiing route, shorter duration of waiting time, and improved the aircraft queue from different directions is just from taxiway in the south sides. The same happened at the north side, the taxiing waiting distance will be shorter so other aircraft will not have a long queue. This model may be applied to other airports for scheduling aircraft's departing and arriving, develop airport airside facility, and reducing the taxiing duration of the aircraft significantly.