Matrix inversion
Principal Components
Time blocks and tracking channels
Frequency resolution and zero-padding
Fourier transform
Partial Contributions
Time Domain conversion
By default, the analysis will include the full-time series, with FFT settings as specified on the Preferences page. If a matrix inverse is being performed, the full matrix will be included in the inverse by default.
However, it is possible to change these settings in the Settings card, as shown in the figure below. In particular, it may be necessary to truncate the matrix inverse to ensure noise is not propagated through the analysis. Currently, these settings are defined manually, although future SOURCE releases will provide smart suggestions for doing the matrix inversion.
Settings for the analysis
Here, the settings are defined for (truncation of) the matrix inverse. By default, the complete matrix including all singular values (and no truncation) will be used. It is also possible to truncate the inverse, by performing a Singular Value Decomposition (SVD) at each frequency line. In particular, it is possible to manually set:
The Nr. of singular values: the number of singular values included in the calculation, ordered in descending magnitude.
A Relative threshold: the relative threshold of included singular values, as a fraction of the highest singular value.
An Absolute threshold: the absolute threshold of included singular values.
For setting the thresholds, it is useful to review the CMIF and condition number of the FRF matrix.
During an in-situ analysis, you can perform a Principal Component Analysis. You can either apply Response PCA to the indicator channels (before matrix inversion) or Force PCA to the resulting Blocked Forces (after matrix inversion).
To apply PCA, complete the next steps:
Open the analysis Settings.
In Principle Components select the Decomposition.
According to the selected Principle Component setting, a Singular Value Decomposition is calculated from the spectra. Principal components are then built from the left singular vectors and their associated singular values. This results in spectra that have Principal Components as columns, instead of the time blocks of the original data.
Here, the settings are defined for cutting the time blocks from the complete time series, which is then used in the FFT calculation.
By default, the entire time series will be cut into blocks using a block length such that the resulting frequency spacing of the FFT will match that of the loaded FRF data (e.g. 1 sec blocks for 1 Hz frequency spacing), along with 50% overlap. One can also manually set the start time, end time, block length and overlap of the time blocks.
It is also possible to set a tracking channel as block method. A tracking channel could be, for example, a bench speed, a channel measuring rotation, a strain gauge, etc. One channel should be set as tracking in the Mapping Channel card. When selecting a tracking channel as block method, it is necessary to define:
Block length: the length of the block (see the figure below).
Tracking channel: if multiple channels are set as tracking, the correct one must be selected.
Tracking values: start and end value of the tracking channel. E.g. in a run-up, it might be interesting to select the range 80-120 kph. In this case, you should enter "80:120", or "80:0.5:120" to specify steps different than 1. This field uses a syntax that is similar to MATLAB. If the analysis rather requires a few discrete values, they can be specified as comma-separated input. e.g. "100, 250, 500, 600".
Tolerance: the tolerance for the signal fluctuation (see the figure below). For example, a tolerance of 5 kph on a tracking value of 100 kph will mean that the analysis would accept the data in the range 100 ± 5 kph, so 95-105 kph.
Tracking alignment: you should decide if the alignment is done on the left, center or right (see the figure below).
Tracking channels parameters
Since in SOURCE all the calculations are done in the frequency domain, it is necessary that the frequency resolutions of the operational and FRF data coincide. In the Analyze module, you can manually specify the frequency resolution of the results. If you do not specify it, the results will have the same frequency resolution as your FRF data. It is necessary that the frequency resolution of the operational data match this frequency resolution.
The frequency resolution of the operational data depends on the length of the time blocks, according to the following equation: $$ \Delta f=\frac{1}{\mathrm{block \; length}} $$. SOURCE automatically creates time block so that the frequency resolution of your operational data will match the one of your FRF data or the one you specified.
However, in SOURCE it is also possible to specify the length of the time blocks. If this specified block length matches the targeted frequency resolution, no further actions are done (see Case 0 in the figure). If the specified block length would not result in the targeted frequency resolution (according to the previous equation), then SOURCE will manipulate the data of the time blocks. This is explained by the following examples (and in the figure):
Case I: zero-padding.
If the frequency resolution of the operational data would be 1 Hz but the specified/FRF frequency resolution is 0.5 Hz, zero-padding is applied. This means that zeros are added at the end of the time block until it has a block length of 2 seconds (which corresponds to a frequency resolution of 0.5 Hz).
Case II: data cropping.
If the frequency resolution of the operational data would be 1 Hz but the specified/FRF frequency resolution is 2 Hz, the data is cropped. This means that the data points at the end of the block are deleted to result in a block length of 0.5 seconds (which corresponds to a frequency resolution of 2 Hz).
Note that if you specify a frequency resolution that is different from the one of your FRF, SOURCE uses the nearest neighbor method to match the frequency lines of the operational and FRF data in the calculations.
Workflow for the application of zero-padding and for the data cropping
Here, the settings are defined for converting the time blocks to frequency blocks. By default, a Hann window is used, and the FFT will be calculated up to the Nyquist frequency of the time signal or the frequency limit of the loaded FRF, whichever is lower. It is also possible to change the window type and set a different (lower) frequency limit for the FFT calculation. The defaults can be changed on the Preferences page.
DC compensation is implemented to separate the DC component from the signal before windowing.
DC component is separated from the signal
Windowing and FFT
DC component is added to the spectrum
Here, we are given the option to also calculate the partial contributions from each of the individual forces. By default, the partial contributions are not computed.
If the Include partials box is checked, partial contribution will be computed. If nothing is entered in the Partial groups entry, the contribution from each of the individual forces will be computed. However within this entry one can also combine e.g. the X/Y/Z contributions at each of several interfaces. In this box, enter the indices of the forces which should be combined, separated by commas. For example, entering "1-3, 4-6" or "1 2 3, 4 5 6" will compute the partial contributions for the first three forces combined, and for the following three forces combined.
Blocked Forces and component TPA syntheses can be transformed back to the time domain. This conversion can be activated in the settings of the Analyze card, selecting Time Domain conversion. To perform this step, it is necessary to have the Auralization license in SOURCE. To know more about the auralization in SOURCE, see 8.1 Auralizing a dataset.
The time domain conversion takes place after the blocked forces and TPA computation. The steps that SOURCE does to perform the conversion are the following:
Apply an inverse FFT to obtain time blocks from the spectral results;
Apply a Hann window over the time blocks to ensure a smooth transition between the blocks;
Merge the blocks to generate a continuous time signal;
Compensate for any windowing that was applied in the spectral analysis.
The recommended settings for the purpose of auralization are the following:
Rectangular window
50% overlap
In this Settings field, you can also apply a low-pass filter, a high-pass filter, or both. To apply the filtering, you must type the cutoff frequency in the field. The cutoff frequency must be specified in Hz.
Both filters are applied to the spectral data before being converted to the time domain. The filters approximate a Butterworth response with a filter order of 8 and zero phase delay.
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10.1 Creating an analysis10.3 Results