This invention relates to measuring apparatuses and methods of using them such as for example apparatuses for measuring physical parameters, such as pressure, flow rates of liquids, chemical organic vapor concentrations and temperature.
Commonly, measuring instruments are affected by noise, nonlinearity and interference. Noise is related to random error—differences between the measured physical parameter value and the actual physical parameter value that cannot be corrected by additional information. Nonlinearity is a systematic error that arises from assuming a linear response of the instrument. Many transducers have an approximate mathematical linear relationship between its electrical signal voltage output and the measured physical parameter value. This linear relationship can greatly simplify the data processing of the instrument. There are trade offs between ease of data processing and precision in the design of such instruments. If accuracy and precision are more important than ease of data processing for a given application, then these nonlinear errors must be considered and treated. Additional information concerning these nonlinearities can be used to correct the measured physical parameter value. Interference is another systematic error that arises from the influences of other physical parameters on the measured signal. Information on these other physical parameters can be used to correct the original measured physical parameter value. This patent is mainly concerned with treatment of these last two error contributions: nonlinearity and interference.
For example, in one type of measuring apparatus, the depth of water is measured by sensing the pressure at the bottom of the water with a pressure sensor. The pressure sensors in these instruments are transducers that convert pressure to voltage. This pressure sensor has a voltage signal output which can be converted to a pressure signal value which can be further translated into a depth measurement by converting the pressure into units of depth. In some instruments, the depth measurement is used to determine the velocity of flow as in U.S. Pat. No. 5,275,042 or average velocity as in U.S. Pat. No. 5,371,686. Due to natural electrical “white noise” which is not predictable from additional information, the measured pressure parameter value has a noise contribution to the measurement error. These sensors are further assumed to have a linear mathematical relationship between the actual pressure and signal voltage output. Since this relationship is only approximate, the measured pressure parameter value has a nonlinear contribution to the measurement error. These sensors are also affected by temperature, another physical parameter. The measured pressure parameter value has an interference contribution to the measurement error.
In another type of sensor, chemical organic vapor concentrations are sensed by a tin oxide bead that varies its resistance to current as a function of organic vapor level changes due to competition between the organic vapor and oxygen in the air. The organic vapors reduce the tin oxide to metallic tin; whereas, the oxygen oxidizes the tin back to tin oxide. Tin and tin oxide have different electrical resistances. In this type of transducer, the measurement is affected by temperature and humidity. Temperature and water vapor in the air influence the resistance of the tin oxide bead. This effect is used in several other types of instruments such as for example in an analyzer of water for organic impurities as described in U.S. Pat. No. 6,123,904. The above two examples are provided for illustration since there are many different sensors in many different types of apparatuses that are affected by noise, nonlinearity and interference. The accuracy and precision of these sensors is reduced because the output signal voltage is also affected by other physical conditions such as temperature or humidity.
It is known to improve the precision of measurements by using higher-order, multivariant polynomial calibration curves to correct the measurements for nonlinearity and interference. It is also known to obtain the optimum coefficients of terms in the polynomial calibration curve by any of several methods including the least squares regression method. Commonly, the calibration curve is applied to measurements through a microcontroller.
In the prior art use of polynomial calibration curves, the general form of the polynomial such as the number of terms and the degree of the terms must be selected before the coefficients can be determined. Although the general form of the polynomial greatly influences the precision obtained from the use of the calibration polynomial, no completely satisfactory automatic approach for some calibration needs is known.