METHOD FOR CALIBRATING A MEASURING APPARATUS

Abstract

A method for calibrating a measuring apparatus includes measuring a set of measured values for products including one or more measured variables. A first set of calibration parameters is determined having one or more weights for one or more of the products. The one or more products is grouped within a first product family. Some of the products in the first product family comprise an equal weight. At least a second set of calibration parameters is determined where one or more sets of additional weights are determined within the first product family. Products with equal weights are grouped into a sub product family within the first product family. Weights for the products outside of the first product family are determined and products with equal weights are grouped into another product family until all weights are determined.

Claims

1-13. (canceled)

14. A method for calibrating a measuring apparatus for a plurality of products, comprising: measuring a set of measured values (X.sup.P={X.sup.p.sub.i,j}) for the plurality of products, wherein the set of measured values comprises one or more measured variables (j); providing a set of reference variables (Y.sup.p={y.sup.P.sub.i i-th reference variable}), determining at least one of the set of reference variables (Y) based on the one or more measured variables (x.sup.p.sub.i,j); grouping the set of measured values (X.sup.p) for the plurality of products into an expanded matrix of the measured values (X); determining a first set of calibration parameters (C) comprising one or more weights (c.sub.j.sup.p) for one or more of the plurality of products (p), wherein the one or more of the plurality of products (p) is grouped within a first product family, wherein the one or more of the plurality of products in the first product family comprise an equal weight (c.sub.j) that is independent of a product; determining at least a second set of calibration parameters (C) for a submatrix of the expanded matrix of the measured values (X) to calibrate the measuring apparatus; determining one or more sets of additional weights within the first product family, wherein products (p) with equal weights (c.sub.j.sup.p) are grouped into a sub product family within the first product family; and determining weights for the plurality of products outside of the first product family, wherein products (p) with equal weights (c.sub.j.sup.p) are grouped into another product family until all weights are determined for the calibration of the measuring apparatus.

15. The method according to claim 14, further comprising determining the weights of the first set of calibration parameters and the additional weights inside and outside the first product family, wherein the weights on which the set of reference variable least depend are determined first.

16. The method according to claim 14, further comprising: determining one or more offset values (c); and combining the one or more offset values to the measured values multiplied by the weights.

17. The method according to claim 14, further comprising linking the weights to polynomials of the measured values, and wherein weights are provided for at least one of (i) products and (ii) quotients of measured values.

18. The method according to claim 16, further comprising grouping different products in a same product family when any weight difference or offset difference between them is determined to be statistically insignificant.

19. The method according to claim 14, further comprising determining the calibration parameters by multilinear regression.

20. The method according to claim 14, further comprising determining the submatrix of the measured values for determining the calibration parameters corresponding to the first product family or additional product families for a subset of the measured values (X.sup.p).

21. The method according to claim 16, further comprising testing a significance of the one or more offset values by formulating a null hypothesis such that a difference between the offset values (c) of two products is equal to zero.

22. The method according to claim 14, further comprising inserting the measured values and the products of the product family by non-numerical, categorical variables.

23. The method according to claim 22, further comprising inserting dummy variables to differentiate the products when grouping the expanded matrix.

24. The method according to claim 14, further comprising calibrating a microwave measuring apparatus.

25. The method according to claim 24, wherein the microwave measuring apparatus is configured as a microwave resonator that determines a shift in one of: (i) a resonance frequency; and (ii) a widening of a resonance curve.

26. The method according to claim 24, wherein the one or more measured variables of the microwave measuring apparatus are at least one of (i) temperature (T) and (ii) moisture angle ().

Description

BRIEF DESCRIPTION OF THE DRAWING

[0014] FIG. 1 graphically illustrates two data sets simulated according to two models.

DETAILED DESCRIPTION OF THE INVENTION

[0015] The method according to the invention furthermore provides that the measured variables for all products are grouped into an expanded set of measured values. In a subsequent step, a first set of calibration parameters is provided that possesses one or more weights for one or more products. The one or more products are grouped within a product family when they at least have an equal weight for their products. An equal weight means that the weight values do not significantly differ from each other. The method according to the invention furthermore provides that at least one additional set of calibration parameters is determined for a submatrix of the expanded matrix of the measured values. For this purpose, one or more sets with additional weights can be determined within the first product family, and several products with equal weights can be grouped in another product family. Subproduct families of the first product family are therefore formed. Additional sets with additional weights are determined outside of the first product family, and one or more products with equal weights are grouped in another product family. Ancillary product families are therefore formed, which of course can then again form subproduct families. In the product families, the one weight or several weights are linked to the measured value independent of the product. The at least one offset value is added to the linkage of weights and measured values. For this set of calibration parameters, the measuring device is calibrated for the expanded set of measured values. The particular idea of the invention is to combine the measured values for two or more products and treat them in the same way.

[0016] One important consideration is that it is unknown before calibration which products of a data set belong to a product family. This context is also determined from the measured values. This approach is surprising at first since the actual expectation is that the more precisely the product is delimited and determined, the more precisely the measuring apparatus can be calibrated for this product. This approach is, however, disadvantageous with regard to measuring inaccuracies or statistical fluctuations that may arise in the measured values. The particular advantage of the approach according to the invention is that one or more weights for the products can be found that are independent of the type of product within the product family. These product-independent weights can be determined much more accurately within the framework of the calibration process than weights that only have a smaller database due to their product dependence. In the method according to the invention, the products of a product family are such that at least one of the weights for two or more products of the product family can be determined independently therefrom. This also includes the instance in which a first weight is selected independent of the products and a second weight is selected depending on the products if two measured values are needed for the measuring process to determine the output variable. In this case, the product-independent weight can be statistically determined much more accurately than the product-dependent weight.

[0017] In one embodiment of the method, the weights are linked to the measured values by multiplication. This yields an overall linear approach for determining the variables. Alternative to this, it is also possible to link the weights to the measured values by polynomials or include the measured values in the form of products and/or quotients. Depending on the selected approach, different computational methods can be used to determine the first and remaining sets of calibration parameters.

[0018] In one preferred embodiment, the significance of the determined calibration parameters is determined using its weights and/or its offset values. This is accomplished in that no significance can be found for the inequality of the weights and offset values of different products. If the inequality is insignificant, then the values for the weights and offsets can be equated. To check the significance of the weights and offset values, a null hypothesis is formulated such that the difference of the values for two products is equal to zero. The probability of the occurrence of this null hypothesis is determined. When testing the offset values, the difference between the two offset values or two weights is formed for two products. As a null hypothesis to be tested, it is then investigated whether the difference has the value zero. If this null hypothesis cannot be rejected, i.e. if the difference parameter has the value zero, both products of the product family can be equated with respect to the investigated calibration parameter (weights, offset values).

[0019] In an embodiment of the method according to the invention, the calibration parameters are determined by a multi-linear regression. This is well known and can be reliably performed. To perform the differentiation of the products in the data, non-numerical categorical variables are inserted. These are used, for example, to indicate that the measured values belong to different products. In the expanded data matrix, the non-numerical, categorical variables serve as dummy variables to differentiate between the measured values. For this, columns can be appended in the expanded matrix of the measured values that contain a 1 for the individual products and identify other products by a 0.

[0020] In one preferred development, the microwave measuring apparatus is designed as a microwave resonator that determines a shift in its resonance frequency and/or a spreading of its resonance curve. Proceeding from these two values, values of the moisture of the product can, for example, be determined. Other measured variables, the temperature and/or moisture angle, are preferred which also contribute to the output variables, such as the moisture of the product.

[0021] An embodiment of the method according to the invention will be further explained below with reference to an exemplary embodiment. The exemplary embodiment refers to moisture measurement as is performed with the aid of the microwave measuring technique. Different products within a product family frequently only differ from each other slightly, be it by an additional or omitted additive, a different leaf position on the stem of plants, or a slightly changed product structure. Such minor differences and variations can lead to slight deviations in the binding of the water molecule in the product and therefore to a small change in the calibration coefficients. Stronger variations, for example from additional additives that strongly differ from each other in terms of their dielectric properties can, however, lead to stronger deviations in the calibration parameters. The chemical and physical similarity can be checked with the aid of an adapted null hypothesis. Normally, a significant level such as 5% is set for the test and compared with the p-value. The smaller the p-value, the greater the justification to reject the null hypothesis. If the p-value is less than the given significance level, the null hypothesis is rejected. If the p-value is in contrast larger than the significance level, the null hypothesis cannot be rejected.

[0022] In the known approaches for calibrating a measuring apparatus, the null hypothesis is always used; the calibration parameter ci of a product of the product family does not differ from zero. It is accordingly checked whether the hypothesis is a likely assumption that the measured variable assigned to the calibration parameter does not contribute to the result. This hypothesis when determining the calibration parameter leads to the fact that the product of a product family must always be considered isolated for itself. For each product of the product family, the calibration parameters are determined and then tested for their significance.

[0023] The method according to the invention works with the grouped measured variables where two or more products of the product family are grouped into an expanded set. In this case, the significance test seeks to find if the difference in calibration parameters of two products of the product family significantly differs from zero. For these two products, this means that if the null hypothesis cannot be rejected, the same calibration parameter can be used for calibration. The calibration parameters of the two tested products of the product family are in this sense product-independent and equivalent.

[0024] This new null hypothesis is weaker than the conventional null hypothesis because the additional information on the similarity of the members of the product family is used in the calibration. This blunts the requirement on the quality of the data set, and the calibration effort is correspondingly reduced. In the practical use of the measuring apparatus, this reduction has particular advantages since, when the products within a product family change slightly, another calibration process is not needed; instead, the calibration parameters that have already been found can be adapted together with the new measured values, and existing calibration parameters can possibly still be used despite the change to the product within the product family.

[0025] To implement the idea, it is necessary to group the measured values obtained for the different products into an expanded set of measured values. One potential approach for this is so-called dummy coding that is also termed a proxy variable. In statistical data analysis, a variable is introduced with the expression 0 and 1 (yes/no variable), which serves as an indicator for the presence of a multilevel variable.

[0026] In order to mathematically account for this categorical assignment, a separate dummy variable is introduced for each member of the product family as well as for each measured variable. For the simplest case of a linear regression with identical weights and only two categories A and B, the calibration equation assumes the following form:

[00005]$y_i=c_1.Math.x_i+c_2+c_2.Math.\left\{\begin{array}{c}0\mathrm{for}\mathrm{category}A\\ 1\mathrm{for}\mathrm{category}B\end{array}\right\}+{}_i.$

[0027] In this equation, c.sub.1 designates the calibration weight with which the measured variable x.sub.i contributes to the output variable yi. The offset value C.sub.2 is formulated as a common coefficient for the category A and B. There is also the categorical distinction between the categories A and B, according to which an additional offset value is not contributed for category A, and the additional offset value c2 is added for category B.

[0028] The variable .sub.i is also an additive expression that jointly occurs with y.sub.i as the output variable and does not depend on the measured value x.sub.i. To summarize the above, for category A, this means:

[00006]$y_i=c_i.Math.x_i+c_2+{}_i$

and for category B

[00007]$y_i=c_i.Math.x_i+c_2+c_2+{}_i.$

[0029] With these dummy variables, an expanded data matrix results simply from an additional column in the following form:

[00008]$X=\left(\begin{array}{ccc}{x}_1^{\left(A\right)}& 1& 0\\ .Math.& .Math.& .Math.\\ x_{N_A}^{\left(A\right)}& 1& 0\\ x_1^{\left(B\right)}& 1& 1\\ .Math.& .Math.& .Math.\\ x_{N_B}^{\left(B\right)}& 1& 1\end{array}\right)$

[0030] In the data matrix, the right column causes the parameter c to be multiplied by zero for the measured values of category A, and the measured value c to be multiplied by 1 for the measured values of category B. The epsilon variable .sub.i is added independent of the measured values in order to compensate for the measurement errors that arise. For this new data matrix, the p-values can be calculated for the calibration parameters. Since the new calibration parameter c2 represents the difference between the offset values of two categories, its p-value provides information on whether this difference is significant or can be combined for the two offset values. This approach can be transferred to all of the calibration parameters.

[0031] For the other calibration parameters, a distinction can be made between an inner and an outer development: With the inner development, the calibration parameters within a product family that have not been determined are determined. The case can arise that parameters again occur which are not significantly different so that additional product families arise within the product family. For example, with regard to the first weight, products 1, 3 and 5 can have equal values, i.e. only insignificantly different values, but with regard to the second weight, products 1 and 5 can have equal values, whereas the weight for product 3 has a significantly different value. In addition to the inner development, there is also an outer development in which calibration parameters are sought for products not yet grouped into a product family, such as products 2 and 4. If an identical calibration parameter is then found, for example, for products 2 and 4, this can form the starting point for an inner development. The result of the inner and outer development is that as many products as possible are grouped into product families, which reduces the number of calibration parameters to be determined and improves the statistical basis for determining the parameters.

[0032] The above-described method with the modified null hypothesis results in the fact that similarities in the data are recognized and used for calibration. The invention also proposes a method in which the calibration parameters of different products are combined. It is possible in principle for some calibration parameters to be identical for products of category A and category B, and other calibration parameters to be significantly different. To simplify the method, it can therefore be provided that the difference parameters that have the highest p-value are combined into a group, wherein all calibration parameters of these two products are then equated. This method can then be repeated with the product family reduced by a product as long as, for example, the calibration parameters remain constant over the product family. In the following, the invention will be explained in more detail with reference to FIG. 1. In FIG. 1, two data sets were simulated according to the following models:

[00009]$y^{\left(A\right)}=0,5.Math.x^{\left(A\right)}+2+{}^{\left(A\right)},$$y^{\left(B\right)}=0,5.Math.x^{\left(B\right)}+1+{}^{\left(B\right)}.$

[0033] Let the reference uncertainty be equally distributed for both categories with =+/0.26. This means that the data of the two categories only differ in terms of their offset value by the value 1, but not in terms of their slope. The data sets are shown in FIG. 1. The upper data points which are shown lighter have a good R.sup.2 value of 0.894 which indicates a good model fit. The lower values which are shown dark have an R.sup.2 value of 0.0239, which indicates a poor fit, a so-called poor model fit. This means that data set B with only five data points, which lie in a narrow range between 2.5 and 3.5, is of low data quality and therefore does not permit the reproduction of the slope parameter with sufficient precision. The data set A with its 25 data points possesses a larger value range with good quality, even though the slope parameter only reaches 92% of the actual slope (see 0.4638 with 0.5) due to the relatively high reference uncertainty.

[0034] The slope parameter c.sub.1 determined with the method according to the invention is however:

C.sub.1=0.46.

[0035] Given the large difference in the weight factor, it is almost identical to the slope value from category A. Accordingly, the difference in the offset parameter c.sub.2 is exactly met with 1, even though both offset values c.sub.2 are too large due to the slightly too small slope parameter.

[0036] The data values from the example in FIG. 1 are summarized in the following Table 1:

TABLE-US-00001 TABLE 1 Category (c) N .sub.k.sup.2 Weight factor c.sub.1.sup.(k) c.sub.1 c.sub.2.sup.(k) A 25 2.05 49.3 0.46 0.46 2.1 B 5 0.04 0.17 0.18 0.46 1.1

[0037] It can clearly be seen that, in the conventional method, the slope parameter c.sub.1 is once 0.46 and once 0.18 depending on the product, and therefore does not match the slope of the model well with 0.5. The two right coefficients in the table are calculated using the method according to the invention and are much better in line with the modeling both in terms of the distance of the offset value and in terms of the level of the values.

[0038] In practice, this means that product B with its lower quality data set profits from the good quality of the data set of product A and is therefore calibrated with same quality as product A.