PROCEDURE FOR CALIBRATION OF A MEASURING DEVICE

Description

[0001] The present invention relates to a method for calibrating a measuring device for several products.

[0002] All types of measuring devices must be calibrated before commissioning. During this calibration, the calibration parameters are determined for a calibration approach, for example, a linear approach, by seeking the best possible match between given measured values ​​and the corresponding reference values. Calibration procedures and the associated determination of a set of calibration parameters are generally well known. Calibration procedures can usually also be performed automatically.

[0003] In microwave humidity measurement technology, for example, possible differences between calibration relationships of different products have so far been taken into account by calibrating the measuring system for each product independently of the other products. This requires the same calibration effort for all products. In addition, each individual calibration is subject to the same susceptibility to potential deficiencies in the data set, such as statistical outliers in the measurement, insufficient variance in the reference values, or an insufficient number of measurement points. A frequently chosen calibration approach is multi-linear regression, which assumes a linear relationship between the measured variables xj of the measuring system and the reference variable y: y = c 1 x 1 , i + c 2 x 2 , i + ⋯ + c n , i + ϵ i (i: Index der Einzelmessung ∈ ℕ ).

[0004] In this approach, it has become common to refer to the factors as weights and the additive constant as the offset value. The epsilon value describes the measurement errors that occur during the measurement. In microwave humidity measurement technology, the measured variables include, for example, the broadening of the resonance curve, the shift in the resonance frequency, a humidity angle, a temperature value, and the like. The reference variables for such a measurement system are, for example, the humidity and density of the measured object.

[0005] The above equation for linear regression has proven itself in matrix notation, resulting in the following expression: y ⇀ = X ⋅ c ⇀ + ϵ → with the matrix X X = x 1 , 1 x 2 , 1 ⋯ x j , 1 ⋮ ⋱ ⋮ x 1 , N x 2 , N ⋯ x j , N and the vector c ⇀ c → = c 1 c 2 ⋯ c j T

[0006] The calibration parameters differ in the weights ci, which are each multiplied by the measured value and converted into an offset value cn , which is independent of the measured values 11 leads to a shift. The calibration parameters are determined as follows: c → = X T X − 1 X T y →

[0007] This approach to determining the calibration parameters is based on the linear calibration model described above and determines the calibration parameters for it. The vector ε is then determined after the calibration weights have been determined in a known manner, for example using a residual matrix.

[0008] For verification purposes, it has generally been customary to determine the significance of the calibration parameters. The measure used for this verification is the so-called p-value. In test theory, this is a measure of evidence for the credibility of a null hypothesis. The null hypothesis for each calibration parameter consists in the assumption that its value is zero. For a p-value greater than, for example, 5%, the influence of the measured variable on the target variable is considered insignificant, and the corresponding calibration parameter is rejected from the above approach. This process is referred to as " Feature Selection " iteratively. The goal of the iterative calibration is achieved when all non-significant observations xj were removed from the calibration model. Conventionally, higher-order measures, such as quadratic dependencies, are tested first and zero-order terms are removed last.

[0009] DE 10 2007 057 092 A1 discloses a method for measuring moisture and / or density in a material to be measured, using a microwave transmitter, a microwave receiver, and an evaluation unit. In this measuring method, the phase and amplitude of the microwave radiation transmitted through the material to be measured are determined for a number of frequencies. Using the complex-valued transfer function of the measuring arrangement, the complex-valued transmission function of the material to be measured is calculated from the determined values ​​and transformed into the time domain as a complex-valued time-domain function. From the time-domain function, the time of the maximum value of the main pulse is determined as parameter A, and the width of the main pulse is determined as parameter B. The moisture and density of the material to be measured are determined as a function of parameters A and B. DE 102 53 822 A1 discloses a method and device for automatic sensor calibration.Laboratory measurements are carried out and the resulting laboratory measurement data are used to correct the online measurement values ​​generated by the sensors.

[0010] From the document US 2003 / 121755 A1 a method for calibrating authenticity testing devices for banknotes and coins is known, in which calibration data and criteria for classification are derived from measured values.

[0011] The invention is based on the object of providing a method for calibrating a measuring device which is suitable for simplifying the calibration process for several products in such a way that relationships in the data for different products are recognized.

[0012] According to the invention, the object is achieved by the method having the features of claim 1. Advantageous embodiments form the subject matter of the subclaims.

[0013] The method according to the invention is provided and intended for the calibration of a measuring device for a plurality of products. According to the invention, the method has the features of claim 1. The method according to the invention provides that a set of reference variables Y is provided. The provided set of reference variables contains at least one reference variable to be determined by the measured variables. As with any calibration process, a set of measured variables is measured. The individual measured variables can be differentiated according to type. Furthermore, a distinction can be made as to the product for which the measured variables were recorded and during which of the measurements the measured variable was measured. This creates a set of measured values ​​(X p< ={xp< i,j}), where j represents one or more measured variables, p the measured products, and i multiple measurements.To the set of measured values, a set of reference quantities (Y p< ={yp< i i-th reference quantity}) with at least one reference quantity (Y) to be determined by the measured quantities (x P< i,j ) is added.

[0014] The method according to the invention further provides that the measured variables for all products are summarized to form an extended set of measured values. In a next step, a first set of calibration parameters is provided which has one or more weights for one or more products. The one or more products are summarized within a product family if they have at least the same weight for their products. An equal weight means that the weight values ​​do not differ significantly from one another. The method according to the invention further provides that at least one further set of calibration parameters is determined for a submatrix of the extended matrix of measured values. For this purpose, one or more sets with further weights can be determined within the first product family and several products with the same weights can be summarized to form a further product family.Sub-product families are therefore formed for the first product family. Outside the first product family, further sets with further weights are determined and one or more products with the same weights are combined to form another product family. By-product families are thus formed, which can then of course also form sub-product families. In the product families, the one or more weights are linked to the measured value independently of the product. The at least one offset value is added to the link between weights and measured values. For this set of calibration parameters, the measuring device is calibrated for the extended set of measured values. The special idea of ​​the invention is that the measured values ​​for two or more products are combined and treated equally.

[0015] An important aspect here is that before calibration it is not known which products in a data set belong to a product family. This relationship is also determined from the measured values. This approach is surprising at first, because the actual expectation is that the more precisely the product is defined and identified, the more accurately the measuring device can be calibrated for this product. However, with regard to possible measurement inaccuracies or statistical fluctuations in the measured values, this approach is disadvantageous. The particular advantage of the inventive approach is that one or more weights can be found for the products that are independent of the type of product within the product family. These product-independent weights can be determined much more accurately during the calibration process than weights that only have a smaller database due to their product dependency.In the method according to the invention, the products of a product family are designed in such a way that at least one of the weights for two or more products of the product family can be determined independently of them. This also includes the case where, if two measured values ​​are required for the measurement process to determine the output variable, a first weight is selected to be product-independent and a second weight to be product-dependent. In this case, the product-independent weight can be determined statistically significantly more accurately than the product-dependent weight.

[0016] In a further development of the procedure, the weights are linked to the measured values ​​by multiplication. This results in a linear approach for determining the variables. Alternatively, it is also possible to link the weights to the measured values ​​using polynomials or to include the measured values ​​in the form of products and / or quotients. Depending on the chosen approach, different calculation methods can be used to determine the first and subsequent sets of calibration parameters.

[0017] In a preferred embodiment, the significance of the specific calibration parameters is determined with their weights and / or offset values. This is done by determining that no significance can be established for the inequality of the weights and offset values ​​for different products. If the inequality is not significant, the values ​​for the weights and offsets can be equated. To test the significance of the weights and offset values, a null hypothesis is formulated that the difference between the values ​​for two products is zero. The probability of this null hypothesis being true is determined. When testing the offset values, the difference between two offset values ​​or two weights for two products is calculated. The null hypothesis to be tested is then that the difference has the value zero.If this null hypothesis cannot be rejected, i.e. the difference parameter has the value zero, both products of the product family can be equated with regard to the calibration parameter examined (weights, offset values).

[0018] In the method according to the invention, the calibration parameters are determined using multi-linear regression. This is well-known and can be performed reliably. To differentiate between products in the data, non-numeric, categorical variables are inserted. These indicate, for example, that the measured values ​​belong to different products. In the extended data matrix, the non-numeric, categorical variables serve as dummy variables to differentiate between the measured values. For this purpose, columns can be added to the extended matrix of measured values ​​that contain a "1" for individual products and mark other products with a "0."

[0019] In a preferred embodiment, the microwave measuring device is designed as a microwave resonator that determines a shift in its resonance frequency and / or a broadening of its resonance curve. Based on these two values, values ​​for the moisture content of the product, for example, can be determined. Other measured variables, such as temperature and / or humidity angle, are preferred, as they also contribute to the output variables, such as the moisture content of the product.

[0020] The method according to the invention is explained in more detail below using an exemplary embodiment. The exemplary embodiment relates to moisture measurement as carried out using microwave measurement technology. Different products within a product family often differ only slightly from one another, be it due to an additional or omitted ingredient, a different leaf position on the stem of plants or a slightly changed product structure. Such slight differences and variations can lead to slight deviations in the water molecule bonding in the product and thus to a slight change in the calibration coefficients. More significant variations, for example due to additional ingredients that differ greatly in their dielectric properties, can, however, lead to greater deviations in the calibration parameters.Physical similarity can be tested using a fitted null hypothesis. Typically, a significance level, such as 5%, is set for the test and compared with the p-value. The smaller the p-value, the more reason there is to reject the null hypothesis. If the p-value is smaller than the specified significance level, the null hypothesis is rejected. If, however, the p-value is greater than the significance level, the null hypothesis cannot be rejected.

[0021] In the known approaches to calibrating a measuring device, the null hypothesis is always used: the calibration parameter ci of a product in the product family is not different from zero. This test is therefore used to determine whether the hypothesis that the measured variable associated with the calibration parameter contributes nothing to the result is a likely assumption. This hypothesis in determining the calibration parameters means that each product in a product family must always be considered in isolation. The calibration parameters are determined for each product in the product family and then tested for their significance.

[0022] The method according to the invention works with aggregated measured variables, in which two or more products of the product family are combined into an expanded set. In this case, the significance test examines whether the difference in the calibration parameters of two products of the product family is significantly different from zero. This means that, if the null hypothesis cannot be rejected, these two products can be calibrated using the same calibration parameter. In this sense, the calibration parameters of the two tested products of the product family are product-independent and equal.

[0023] This new null hypothesis is weaker than the conventional null hypothesis because the calibration utilizes additional information about the similarity between members of the product family. This lowers the quality requirements for the data set and reduces the calibration effort accordingly. This reduction has particular advantages in the practical use of the measuring device because, in the event of a minor change to the products within a product family, no new calibration process is required. Instead, the previously determined calibration parameters can be adjusted along with the new measured values, and existing calibration parameters can potentially continue to be used despite the change to the product within the product family.

[0024] To implement this idea, it is necessary to summarize the measured values ​​obtained for different products into an expanded set of measured values. One possible approach here is so-called dummy coding, also known as a proxy variable. In statistical data analysis, a variable with the values ​​0 and 1 (yes / no variable) is introduced, which serves as an indicator for the presence of a multi-level variable.

[0025] To mathematically account for this categorical assignment, a separate dummy variable is introduced for each member of the product family and 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 takes the following form: y i = c 1 ⋅ x i + c 2 + Δ c 2 ⋅ 0 f ü r Kategorie A 1 f ü r Kategorie B + ε i .

[0026] In this equation, c 1 denotes the calibration weight with which the measured quantity xi contributes to the output quantity yi. The offset value c 2 is formulated as a common coefficient for categories A and B. In addition, there is now a categorical distinction between categories A and B, whereby no further offset value is added for category A, and the additional offset value Δc 2 is added for category B.

[0027] The quantity ε i is also an additive expression that occurs together with yi as the output quantity and does not depend on the measured value xi. The above summarized means for category A: y i = c 1 ⋅ x i + c 2 + ε i and for category B y i = c 1 ⋅ x i + c 2 + Δ c 2 + ε i .

[0028] With these dummy variables, an extended data matrix is ​​simply created by adding an additional column in the following form: X = x 1 A 1 0 ⋮ ⋮ ⋮ x N A A 1 0 x 1 B 1 1 ⋮ ⋮ ⋮ x N B B 1 1

[0029] In the data matrix, the right column causes the parameter Δc to be multiplied by zero for the measured values ​​of category A and the measured value Δc to be multiplied by 1 for the measured values ​​of category B. The epsilon quantity ε i is added independently of the measured values ​​to compensate for any measurement errors that occur. For this new data matrix, the p-values ​​for the calibration parameters can be calculated. Since the new calibration parameter Δc 2 represents the difference between the offset values ​​of two categories, its p-value indicates whether this difference is significant or whether the two offset values ​​can be combined. This scheme can be applied to all other calibration parameters.

[0030] For the further calibration parameters, a distinction can be made between an internal and an external development: In internal development, the calibration parameters that have not yet been determined are further determined within a product family. In this case, it can happen that insignificantly different parameters occur here, so that further product families arise within the product family. For example, products 1, 3 and 5 may have the same values ​​with regard to the first weight, i.e. only insignificantly different values. However, with regard to the second weight, products 1 and 5 may have the same values, while the weight for product 3 has a significantly different value. In addition to internal development, there is also an external development, in which calibration parameters are sought for products that have not yet been grouped into a product family, for example products 2 and 4.If, for example, an identical calibration parameter is found for products 2 and 4, this can serve as the starting point for an internal development. The result of the internal and external development is that as many products as possible are grouped into product families, thereby reducing the number of calibration parameters to be determined and improving the statistical basis for parameter determination.

[0031] The method described above with the modified null hypothesis leads to similarities in the data being recognized and used for calibration. The invention also proposes a method in which the calibration parameters of different products are combined. In principle, it is possible that for products in category A and category B, some calibration parameters are the same and other calibration parameters are significantly different. To simplify the method, it can therefore be provided that the difference parameters with the highest p-value are combined into one group, with all calibration parameters of these two products then being equated. This method can then be repeated with the product family reduced by one product, until, for example, the calibration parameters are constant across all product families. The invention will be described below with reference to Figure 1explained in more detail. For Figure 1 Two data sets were simulated according to the following models: y A = 0 , 5 ⋅ x A + 2 + ε A , y B = 0 , 5 ⋅ x B + 1 + ε B .

[0032] The reference uncertainty ε is assumed to be equally distributed for both categories with ε = + / - 0.26. This means that the data of the two categories differ only in their offset value by 1, but not in their slope. The data sets are in Figure 1 The upper data points, shown in lighter color, have a good R 2< value of 0.894, which indicates a good model fit. The lower values, shown in dark color, have an R 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 lying in a narrow range between 2.5 and 3.5, is of poor data quality and therefore does not allow the slope parameter to be reproduced with sufficient accuracy. Data set A, with its 25 data points, has a wide value range with good quality, although the slope parameter only reaches 92% of the actual slope due to the relatively high reference uncertainty (cf. 0.4638 with 0.5).

[0033] However, the gradient parameter c 1 determined by the method according to the invention is: c 1 = 0 , 46 .

[0034] Due to the large difference in the weighting factor, it is almost identical to the gradient value from category A. Accordingly, the difference of the offset parameters Δc 2 is exactly 1, although both offset values ​​c 2 are too large due to the gradient parameter being slightly too small.

[0035] The data values ​​from the example are summarized in Figure 1 in the following table: Category (k) N σ k 2 Weight factor c 1 k c 1 c 2 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

[0036] It is clearly visible that with the conventional method, the slope parameter c 1 is 0.46 and 0.18, depending on the product, and thus does not accurately represent the model's slope of 0.5. The two right-hand coefficients in the table are calculated using the method according to the invention and are significantly more accurate in both the offset value and the magnitude of the values.

[0037] In practice, this means that product B, with its low-quality data set, benefits from the good quality of the data set of product A and is therefore calibrated with the same quality as product A.

Claims

1. Method for calibrating a measuring device for several products, comprising the following steps: - Measuring a set of measured values (Xp={xpi,j}) with several measured variables (j > 1), for several products (p) and with several measurements (i), - Providing of a set of reference variables (Yp ={ypi i-th reference variable}) with at least one reference variable (Y) to be determined by the measured variables (xPi,j), characterised by - Summarising the measured values (Xp) for all products into an extended data matrix of the measured values(X' ), to which non-numerical, categorical variables are attached as dummy variables to differentiate between the measured values, - Determining a first set of calibration parameters (C' ) from the measured values (X') of the data matrix, which has one or more weights( c j p ) for one or more products (p), wherein the one or more products (p) are summarised within a product family which has an equal weight (cj) for at least its products, which is independent of the product, - Determining at least one further set of calibration parameters (C" ) for a sub-matrix of the expanded data matrix of the measured values (X') for calibrating the measuring device, the non-numerical, categorical variables being assigned further weights of the further set of calibration parameters(C" ), wherein ∘ one or more sets with further weights are determined within the first product family and several products (p) with the same weights( c j p ) are combined to form a further product family, and ∘ outside the first product family, further sets with further weights are determined and several products (p') with the same weights( c j p ′ ) are combined to form a further product family, ∘ until all weights have been determined for the calibration of the measuring device2. Method according to claim 1, characterised in that the weights of the first set and the further weights inside and outside the first product family are determined in a predetermined sequence, the weights on which the reference variable is most weakly dependent being determined first.

3. Method according to claim 1 or 2, characterised in that, in addition to the weights, one or more offset values (Δc) are also determined, which are added to the measured values multiplied by the weights.

4. Method according to one of claims 1 to 3, characterised in that the weights can also be linked to polynomials of the measured values, whereby weights can also be provided for products and / or quotients of measured values.

5. Method according to one of claims 1 to 4, characterised in that no significance of the inequality is statistically determined for the weights and / or offset values for different products and the different products are then combined in a product family to form this weight if the inequality is not significant.

6. Method according to one of claims 1 to 5, characterised in that the calibration parameters are determined by a multi-linear regression.

7. Method according to one of claims 1 to 6, characterised in that the sub-matrix of the measured values for determining the calibration parameters corresponding to the first product family or the further product families is determined on a subset of the measured values (Xp).

8. Method according to claim 6 or 7, characterised in that for testing the significance of the offset values, a null hypothesis is formulated to the effect that the difference in the offset values (Δc) of two products is zero.

9. Method according to one of claims 1 to 8, characterised in that a microwave measuring device is calibrated.

10. Method according to claim 9, characterised in that the microwave measuring device is designed as a microwave resonator which determines a shift in the resonant frequency and / or a broadening of a resonance curve.

11. Method according to claim 9 or 10, characterised in that further measured variables of the microwave measuring device are the temperature (T) and / or the humidity angle (φ).