JPS63210713A - Formation of correction curve - Google Patents

Abstract

PURPOSE:To obtain a continuous curve from data of many points, to make the influence of noises hard to exert, and to attain high-speed access by dividing many measurement data into several groups and performing regressive approximation, group by group. CONSTITUTION:The measurement data of all measurement points are divided into plural groups which consist of plural continuous measurement points and share measurement points at border parts. Then, the input/output relation of a measurement section to which each group belong is regressively approximated. Then, an optional output value which is set according to a constant standard is substituted in an approximate curve (approximation expression) to calculate a corresponding input value. When plural input values are calculated in this calculating process because of the presence of an overlapping approximation section, those input values are approximated regressively to find one input value. Then, polygonal line approximation connecting virtual measurement points is performed by using corresponding data of output values and input values found as mentioned above to generate a correction coefficient table. Consequently, the influence of noises is hard to exert and access is attained at a high speed.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a correction curve forming method for determining a correction curve (correction formula) from obtained measurement data during sensor calibration or the like.

More specifically, in a measuring device that corrects and outputs sensor output using a computer, etc., the correction curve (correction formula) used for this calculation process is determined and stored in advance in the computer as a correction coefficient table. This invention relates to a correction curve forming method.

[Conventional technology]

Conventionally, typical methods for obtaining correction curves from measurement data include the broken line approximation method, in which measurement points are connected linearly and the correction formula for each section is stored in the form of a table (correction coefficient table), and the minimum square Regression approximation methods are known, such as multiplication, in which a regression curve is determined from a plurality of pieces of measurement data.

[Problem that the invention seeks to solve]

However, the former polygonal line approximation method is susceptible to noise and requires a large amount of measurement data (measurement time) and memory capacity in order to perform highly accurate correction. In addition, in the latter regression approximation method, high-order, multi-point regression is easily affected by noise, and depending on the computer's ability, the term Σχ" may quickly overflow, making it difficult to approximate a continuous function for multiple points. Furthermore, if a high-order correction curve (correction formula) is adopted, a lot of calculation time will be required when performing correction calculations by a computer (when used).

The present invention eliminates the deficiencies and limitations of the conventional method as described above, and can obtain a continuous curve from data at multiple points.
The purpose of this invention is to provide a correction curve forming method that is less susceptible to noise and can be accessed quickly during use.

[Means for solving problems]

The correction curve forming method of the present invention includes a process of dividing measurement data of all measurement points into a plurality of groups each consisting of a plurality of consecutive measurement points and sharing measurement points at the boundary; The process of regressively approximating the input-output relationship for each measurement section to which a group belongs, and calculating the corresponding input value by substituting arbitrary output values set according to a certain standard into these approximate curves (approximation formulas). When multiple input values are calculated due to the existence of overlapping approximation intervals in this calculation process, the process of regressively approximating these input values to obtain one input value, The method includes a step of creating a correction coefficient table by performing a polygonal line approximation connecting these virtual measurement points from the corresponding data of output values and input values.

[For production]

In this way, by dividing a large amount of measured data into several groups, performing regression approximation for each group, and combining the obtained curves in the first order, the regression approximation for each interval is It is a low-order one, making it possible to obtain a continuous curve from multi-point data and making it less susceptible to noise.Also, by substituting an arbitrary output value into the obtained correction curve, Since the corresponding input values are obtained and a correction coefficient table is created using broken line approximation, the approximation formula can be a linear equation that is easy to calculate, and the intervals of the correction coefficient table can be arbitrarily set independently of the intervals of measured data. can be set to allow high-speed access.

〔Example〕

An embodiment of the correction curve forming method of the present invention will be described below with reference to the drawings.

FIG. 1 is a characteristic diagram showing the input/output relationship of sensors to be calibrated. For example, when the sensor is a temperature detector, the input value (X-axis) is the temperature and the output value (Y-axis) is the detected output. In the figure, W! is the measurement range and fJ is the expected output range.

Further, the X marks indicate measurement points, and the manufacturing regular intervals (X-axis) are approximately equal intervals. Measurement data (L, Y,) corresponding to such a large number of measurement points are captured.

Therefore, as shown in Fig. 2, this large amount of measurement data is
It is divided into a plurality of groups G, each consisting of a plurality of consecutive measurement points. Additionally, these groups share measurement points at their boundaries. m is the measurement interval corresponding to each group. The number of measurement points included in each group is selected in consideration of the efficiency of regression approximation, which will be described later.

After the measurement points are divided into groups, the input-output relationship is approximated by regression for each Numaden section to which each group belongs. The form of the approximation equation at this time is arbitrary, but since the number of measurement points in the group is not so large, it is not a very high-order equation. In addition, this approximate expression is organized into the functional form x=g (ν) in consideration of later use. X is an input value and y is an output value.

FIG. 3 shows the relationship between the approximate curves obtained as described above. As shown in the figure, each approximate curve has a mutually overlapping portion. Here, the range W of the output value V
Divide y into L equal parts and assume arbitrary (equally spaced) output values yk. This output value uk is substituted into the primary approximation equation g(ν) to obtain the input value Jek Xk=gCνk) corresponding to the output value ν. At this time, at a position where two approximate curves exist, such as ν, two input values are obtained from each approximate curve, but in this case, as shown in FIG. Two input values xk1. χ2. It is adopted as the average value tc x b. Moreover, this operation is not limited to the average, and may also be calculated by @return including the previous and subsequent points. Note that the average can be considered as a regression based on two measurement points.

After the data corresponding to the output value 11hζ input value xk is obtained in this way, a correction coefficient table is created by performing a broken line approximation connecting these virtual measurement points. At this time, @ (one approximate interval) in the table is Wy/L. Further, the equation representing the polygonal line is χ = aΩ ν + bΩ (yh≦II<U h++), and the coefficients aQ and bQ are stored in the table.

In addition, in the coefficients au, bQ, the coefficient values ak, bk in the k-th interval are ah = CXk++-Xb) / (#hya, -ν
, ) b h = X h - u k' a k.

The correction coefficient table is organized as follows.

Here, the number of coefficients depends on the order of the approximate expression.

Now, how to use the correction coefficient table created as described above is as follows. First, when the measurement output Ym is given in the actual measurement state, the width of the table (Wy
/L), which coefficient in the table to use is calculated. in this case.

Since the width of the table is constant, from the formula Q s = Ym/ (IFy/L), Q
11′! The Ith coefficient is selected. Note that in the above equation, Qll is an integer, and the remainder is rounded down or rounded up. Therefore, this measurement output Ym is corrected and outputted by xtn=a (ltn+Ytn+bAm. As is clear from the above equation, the measurement output Ym
Since the selection of a correction coefficient from and the calculation using this correction coefficient are very simple linear equations, high-speed access is possible.

In this way, 1! I Even if there are a large number of fixed points, dividing this measurement data into several groups, performing regression approximation for each group, and sequentially combining the obtained curves at their overlapping parts, it is possible to A continuous curve that approximates these data can be obtained from the data. Furthermore, since regression approximation is performed in each section, it is less susceptible to noise. Furthermore, an arbitrary output value is substituted into the obtained correction curve to obtain the corresponding input value, and a new correction coefficient table is created using broken line approximation.
The approximation formula can be a linear formula that is easy to calculate, and the interval of the correction coefficient table can be arbitrarily set independently of the interval of the measured data, allowing high-speed access as described above. .

In addition, in the above explanation, the case where the measurement intervals for regression approximation are set at equal intervals is illustrated, but the method of selecting the approximate intervals is not limited to this. For example, the selection of the approximate intervals is not limited to this. It may be of. In addition, the approximation formula in regression approximation is not limited to the n-th degree polynomial, but also logarithmic functions,
It may also be a sine wave function, a spline function, etc. Further, in the correction coefficient table, a linear equation is adopted for speeding up the calculation, but if there is sufficient calculation time, the memory capacity can be reduced by using a higher order equation.

Further, even if the following equation is used, the memory capacity can be similarly reduced by making the width of the table a function of the output value.

〔Effect of the invention〕

As explained above, in the correction curve forming method of the present invention,
The process of dividing the measurement data of all measurement points into multiple groups each consisting of a plurality of consecutive measurement points and sharing the measurement points at the boundary, and the process of dividing the measurement data of each measurement point into each group to which each group belongs. The process of regressively approximating the output relationship, and the process of substituting arbitrary output values set according to a certain standard to these approximate curves (approximation formulas) and calculating the corresponding input values, and this calculation process overlaps. When multiple input values are calculated due to the existence of an approximation interval that Since the process includes a process of creating a correction coefficient table by performing a broken line approximation connecting these virtual measurement points from the data, the regression approximation for each interval is of low order, and a continuous curve can be created from multi-point data. In addition to being able to obtain
It is possible to realize a correction curve forming method that can be accessed at high speed during use even though it is not affected by noise.

[Brief explanation of the drawing]

FIGS. 1 to 4 are explanatory diagrams showing one embodiment of the processing steps in the correction curve forming method of the present invention. X...Input value, ν...Output value, WX・
...Measurement range, wy... Range of output value y, ×...Measurement point. Trace I Figure 2 Figure 3 Route Figure 4

Claims (1)

[Claims] The process of dividing the measurement data of all measurement points into multiple groups, each consisting of a plurality of consecutive measurement points and sharing the measurement points at the boundary, and the input/output of each measurement section to which each group belongs. The process of regressively approximating the relationship, and the process of substituting arbitrary output values set according to certain standards to these approximate curves (approximation formulas) and calculating the corresponding input values, overlap in this calculation process. When multiple input values are calculated due to the existence of an approximation interval, the process of calculating one input value by performing regression approximation between these input values, and the corresponding data between the output value and input value calculated in this way. A correction curve forming method comprising the steps of: performing a broken line approximation connecting these virtual measurement points to create a correction coefficient table.