Method and apparatus for measuring a unit to be tested

Abstract

Method for measuring a physical unit (2) with a number of measuring points (X) in order to obtain a value of an output quantity (y) in each case, comprising the following steps: - Determining (S4) a measurement point (y) to be measured next depending on a given data-based functional model, which is designed in particular as a Gaussian process model; - Performing (S4) the measurement of the physical unit (2) at the next measuring point to be measured (x) i+1 ), to obtain a resulting value of the output quantity (y i|1 ) to obtain; - Update (S5) the data-based functional model with the next measurement point to be measured (x i|1 ) and the value of the output variable (y i|1 ), where determining the next measuring point to be measured (x i+1) is carried out depending on a confidence level (h1) determined by the measuring point (x1), which indicates a risk to the physical unit (2) at a measurement point (x1). 1+1 ) specified operating state, wherein the confidence quantity (h) is specified using a data-based confidence model depending on the measurement point (x), wherein the data-based confidence model is in particular designed as a Gaussian process model.

Description

Technical field

[0001] The invention relates to test methods, and in particular methods for providing measurement points with which a physical unit to be tested can be tested. In particular, the present invention relates to methods for providing measurement points within system boundaries. State of the art

[0002] When measuring a physical unit with measurement points, it is necessary to position the measurement points in such a way that as many combinations as possible of input values ​​in different excitation modes, i.e., combinations of input gradients, are measured, thus achieving a spatially and dynamically comprehensive coverage of the input data space with measurement points. The output values ​​obtained for the measurement points during the measurement process can serve as training data for creating a data-driven, non-parametric functional model.

[0003] For the technical unit being modeled, e.g., a gasoline engine, it is particularly important that the physical limitations of the unit are not violated during measurement, for example, on an engine test bench, in order to prevent damage to the unit. During the measurement process, the measurement technology monitors the unit to detect combinations of input values ​​that could compromise the system before damage occurs.

[0004] In general, approaches that provide for the pre-generation of all measurement points for the survey are disadvantageous, as they cannot reliably avoid unexpectedly occurring system-critical operating conditions. The publication DE 10 2013 209 851 A1 discloses a method for the subsequent adaptation of an at least partially data-based functional model, which corresponds to a sum of a basic functional model, in particular a data-based one, and an additive error model, comprising the steps of providing the basic functional model, acquiring training data, determining the data-based additive error model based on difference training data, which represent differences between the measured values ​​of the training data and the function values ​​of the data-based basic functional model at the measurement points of the training data, and modifying the training data and / or the additive error model so that function values ​​of the data-based functional model remain within a specified adaptation range.

[0005] The publication DE 10 2013 206 304 A1 relates to a method for determining a non-parametric, data-based functional model from provided training data, wherein the training data contains a number of measurement points defined by one or more input variables, each with associated output values ​​of an output variable, comprising the following steps: - Providing different measurement uncertainty values ​​for some or all of the measurement points of the training data; and - Determining the non-parametric, data-based functional model according to an algorithm that depends on the measurement points of the input variables, the respective assigned output values ​​of the output variable, and the respective assigned measurement uncertainty values.

[0006] Document CN101 477 375 A1 discloses a method for verifying sensor data based on matrix singular value association rules. Disclosure of the invention

[0007] According to the invention, a method for measuring a physical unit with a set of measuring points according to claim 1 and the corresponding device according to the dependent claim are provided.

[0008] Further details are provided for in the dependent claims.

[0009] According to a first aspect, a procedure for measuring a physical unit with a number of measuring points, in order to obtain a value of an output quantity at each point, is provided, comprising the following steps: - Determining the next measurement point to be measured, depending on a given data-based functional model, which is designed in particular as a Gaussian process model; - Performing the measurement of the physical unit at the next measuring point to be measured in order to obtain a resulting value of the output quantity; - Updating the data-based functional model with the next measurement point to be measured and the value of the output quantity, wherein determining the next measurement point to be measured is carried out depending on a confidence quantity determined by the measurement point, which indicates a risk to the physical unit in an operating condition specified by the measurement point, wherein the confidence quantity is specified by means of a data-based confidence model depending on the measurement point, wherein the data-based confidence model is in particular designed as a Gaussian process model.

[0010] One idea behind the above procedure is to minimize the number of potentially system-critical measurement points when measuring a physical unit. To this end, a method is provided that, based on the measurement points already measured, uses a data-driven functional model to determine the next measurement point, which is then applied to the physical unit to determine the next value of the output quantity. The determination of the next measurement point to be applied to the physical unit can depend on a confidence level that indicates the certainty of applying the measurement point to the physical unit. This allows for the creation of an experimental design better suited to the output quantity being measured.

[0011] Furthermore, the next measurement point to be measured can be determined depending on an optimization procedure, with which the next measurement point to be measured is sought that has a maximum entropy with respect to the data-based functional model with respect to the output quantity.

[0012] It may be planned that the next measurement point to be measured will be determined depending on an optimization, according to xi+1−argmaxx4∈X Var(y4|x4,Di,0y) with μg8−νσg8≥0, where v = Φ-1(p) is a given confidence parameter, x x a query point, D1 the data points which include the measurement points and the associated values ​​of the output quantity, µ g8 the expected value, θ y a hyperparameter vector of the data-based functional model and σ g8 the standard deviation of the predictive distribution q(q ∗ |x ∗ ,c,h,Xθ h ) are equivalent to.

[0013] In particular, it may be provided that the data-based functional model is created using previously measured measurement points.

[0014] It may be provided that the data-based confidence model is updated after measurement with the determined measurement point to be measured next and the determined value of a system state variable.

[0015] In particular, the system state variable can be a state variable of the physical unit that results from the operating state and is not directly adjustable.

[0016] According to one embodiment, the method can be repeated, in particular until a termination condition is met, wherein the termination condition is met upon reaching a certain number of determined measurement points, upon reaching a certain model accuracy for the output variable, or upon reaching a minimum number of determined safe measurement points. Brief description of the drawings

[0017] The embodiments are explained in more detail below with reference to the accompanying drawings. These show: Fig. 1 a representation of a test system for measuring a physical unit; Fig. 2 a representation of a restriction area and a safety boundary for a two-dimensional entrance space; Fig. 3. A flowchart illustrating a procedure for measuring a physical unit using online generated measurement points. Description of embodiments

[0018] Fig. Figure 1 shows a schematic representation of a test or inspection system 1, which is configured to measure a physical unit 2. A physical unit 2 can be, for example, an internal combustion engine of a motor vehicle or subsystems thereof. A measurement unit 3 controls the physical unit 2 with a sequence of measurement points X, which lead to specific operating points of the physical unit 2. The measurement points X typically comprise a number d of several input variables, which are represented in an input variable vector x ∈ ℝ. d The input variables are grouped together and thus form a measurement point x. Furthermore, a permissible range of values ​​applies to each of the d input variables. Additionally, the control of the physical unit 2 results in one or more output variables y, which are measured at the measurement points X.

[0019] As a rule, to fully measure the physical unit 2, the measuring points X are varied over a large area within the permissible value ranges in order to achieve the most space-filling possible occupancy of the input data space by the measuring points.

[0020] The measurement points, together with the corresponding values ​​of the output quantity, form data points D1 - (y,X) with the outputs y ∈ ℝ 1 to the entry points X ∈ ℝ 1×d

[0021] The data points can serve as training data points for training a data-driven functional model, which is a non-parametric functional model. For example, a Gaussian process model of the following form can be used as the data-driven functional model. E(y4|χ4,Di,θy)=∑l=1lαiσf2exp(12∑j=1d(χl,j−χk,j)λj2) Where the query point the resulting value of the output quantity, which is best estimated by the data-driven function model using the expected value, α ∈ ℝ i a prediction vector that results from training the Gaussian process model, the magnitude of the covariance function and λ f correspond to a dimension-wise length scaling. The positive hyperparameters of2 and λ1,.....,λ d are in the hyperparameter vector θ y summarized.

[0022] The use of non-parametric, data-driven functional models is based on a Bayesian regression method. The fundamentals of Bayesian regression are described, for example, in CE Rasmussen et al., "Gaussian Processes for Machine Learning," MIT Press 2006. Bayesian regression is fundamentally a data-driven method. During the training process, abstract parameters are determined that parameterize the space of model functions and effectively weight the influence of individual data points from the training data on the subsequent model prediction.

[0023] The abstract hyperparameters θ yare determined by an optimization procedure. One possibility for such an optimization procedure is the optimization of a marginal probability density. The marginal probability density -p(y IX, 0") describes the plausibility of the measured values ​​of the output quantity y, represented as a vector y, given the model parameters θ. y , and the measurement points X.. In model training, p(y|X,θ) is used. y ) maximized by finding suitable hyperparameters that lead to a course of the model function determined by the hyperparameters and the training data and that represent the training data as accurately as possible.

[0024] The Gaussian marginal probability density p(y|X,θ) y ) of the Gaussian process model corresponds to a multivariate normal distribution N(y|0, K + σ 2 I), where σ 2 the variance of the centered Gaussian model noise and K ∈ ℝ i×iThe covariance matrix between the previously measured data points X is given by the vector θ. y are the hyperparameters of the chosen covariance function, including the model variance σ 2 In summary, the quadratic exponential covariance function is usually chosen, as in the formula above for the expected value of the model prediction, although other functions are also conceivable.

[0025] The next measuring point to be measured x i+1 ∈ ℝ d will then be determined as This measuring point x 1+1 corresponds to the point with maximum entropy with respect to the Gaussian process model regarding the output quantity.

[0026] The optimization problem above reduces to , since entropy is a monotone function with respect to the variance of is. This is Var(y4|χ4,Di,θy)k44−k4T(K+σ2I)k14+σ2 with the covariance function value k ∗∗ ∈ ℝ of the new point and the vector k ∗∈ ℝ 1 with covariance values ​​between the new and all previously measured i points.

[0027] If an experimental design is to be created for multiple output variables, a Gaussian process model can be created for each output variable, and then the sum of the entropies of the respective models can be used as an exploration criterion. Weighting can also be applied to this summation to emphasize individual output variables more strongly.

[0028] A definition of a safety constraint is provided, intended to virtually prevent the measurement of uncertain points. For example, a measurable range of measurement points can be defined by a physical restriction of the unit. The permissible values ​​of the input variables of the measurement points can be specified accordingly using expert knowledge. In particular, the restriction can be determined by a confidence level for the individual input variables, which may be further restricted by additional linear or nonlinear constraints. This a priori defined input space will henceforth be referred to as X⊂ℝd. An example of such an entrance hall is in Fig. 2 for a two-dimensional input vector graphically as X⊂ℝ2 depicted. The designated entrance area. X X now possesses a disjoint decomposition into a reliably measurable area. X† and an essentially unmeasurable area X. These two areas are separated by the decision boundary. X0, which contains the points that can still be measured with certainty.

[0029] To now obtain a fairly reliable measurement of X To perform X with the aforementioned exploration scheme, it is necessary that the physical unit to be measured provides feedback on how close the measurement of X is. i|1 the unit to its load limit X0 This has resulted in a function being applied near the decision boundary (dotted area in Figure 2). h:X→(−1,1) The confidence level is defined. It can also be specified that this function is noisy. Near the load limit, h ≈ 0. In the case of measuring an internal combustion engine on a test bench, the function h is the equivalent of the test bench monitoring. The aim is to combine the physical unit with this additional information, i.e., the function. h:X→(−1,1), to measure and to learn an equivalent to test bench monitoring through the confidence quantity h.

[0030] The confidence level h initially corresponds to a quantity that indicates the risk to the physical unit under an operating condition specified by the measurement point. Since specifying a dependency of the confidence level h on the operating condition defined by the measurement point is generally not possible using expert knowledge, the confidence level h is defined as dependent on one or more system state variables that are neither input nor output variables. For example, in the case of an internal combustion engine, a pressure in a gas flow system (intake manifold pressure) or the engine temperature can be assumed to be such a system state variable.

[0031] To learn h, a generalized Gaussian process classification model is introduced. This yields positive class labels in the highly measurable range, i.e., for the inner hatched area in Fig. 2 the labels c i= +1. Similarly, in the area that is certainly not measurable, in the outer hatched area, one obtains in Fig. 2 negative labels c i = -1. The adoption of these labels facilitates the definition of h and the unnecessary qualitative distinction between very safe and very uncertain entry points.

[0032] To obtain a consistent Gaussian classification model, it is important that for each measurement point either a label c (as a simplified confidence measure) or a value of the confidence measure h according to an expert specification is available. For this purpose, in addition to the initial variable, one or more system state variables required by the expert specification are measured or determined, and a corresponding value for the confidence measure h is calculated according to the relevant procedure.

[0033] Furthermore, let g be the desired, non-noisey discriminative function of a confidence model. For a data set D n, which now results from the measured system outputs y ∈ ℝ m , all input points X ∈ ℝ n×d , Labels c ∈ ℝ k and noisy describative function values ​​h ∈ ℝ l Given that l + k = n, the model probability p among the desired values ​​g ∈ ℝ is obtained. n to p(c,h|g,X)=∏i=1lN(hj|gj,τ2)∏i=1kΦ(cigi).

[0034] where τ 2 The variance of the normally distributed noise with respect to h and Φ(.) is the cumulative distribution function of the standard normal distribution. The vector y here contains only m ≤ n entries, since not all n points could necessarily be reliably measured and therefore might not have yielded an initial value. In the desired ideal case, m = n.

[0035] Since the model probability v(c,h|g, X) is no longer Gaussian and therefore an exact analytical calculation of the posterior distribution p(g|c,h,X) is not possible, an approximation method can be used to determine a Gaussian approximation q(g|c,h,X) ≈ p(g|c,h,X). For example, a Laplace approximation can be used to determine the approximation. This yields the approximated posterior distribution as follows: p(g|c,h,X)≈q(g|c,h,X)−N(g|μ,Σ), where µ = argmax g (p(g|c,h,X)) ∈ ℝ x and Σ = (W + K -1 ) -1 ∈ ℝ n × n with the diagonal matrix W=−∂2∂g∂gTlog(p(c,h|g,X))|g=μ The covariance function used here to generate K = ℝ n×n may differ from the modeling of the output variables, in particular through the induced hyperparameters, which include τ 2 in the vector θ hsummarized. This allows us to determine the distribution of the sought-after describative function g. ∗ for test points x ∗ ∈ ℝ d write as q(g∗|x∗,c,h,X,θh)=N(g∗|μg∗,σg∗2)=N(g∗|k∗T,K−1μ∗k∗ k∗TW12B−1W12k∗) with B=I+W12KW12∈ℝn×n, where µ g8 the expected value and σ g8 the standard deviation (square root of the variance) of the predictive distribution q(q ∗ |x ∗ ,c,h,X,θ h ) are.

[0036] To ensure near-certain exploration behavior of the algorithm, the probability of an error occurring in each iteration should be less than or equal to 1p for p ⊂ (0,1). Formally, this means that the probability Pr Pr(θ4>0|x4,c,h,X,0h)>p is.

[0037] This condition can be transformed into μg∗−νσg∗≥0, where the confidence parameter v = Φ¯ 1(p). Finally, this, combined with the exploration criterion above, yields the optimization problem to be solved in each iteration step: xl+1=arg maxx4←X Var(y∗|x∗,D1,θy) so that: μg∗−νσg∗≥0.

[0038] The optimization problem can be solved, for example, using a Newton-Raphson method, since the moments of the Gaussian process for the system outputs and those of the discriminative Gaussian process for the confidence model are sufficiently differentiable with a suitable choice of covariance functions. This is certainly true when using the quadratic exponential covariance function. To ensure that the optimization problem given above is not empty, i.e., that at least one point exists that satisfies the constraint, at least m0 certain starting points can be specified, with m0≥(2N(12(1+4νη−1)))1min(ν√3η,ν√3η3) dh measuring points at which the label The hyperparameter η > 0 is a prefactor of the covariance function for the discriminative Gaussian process. The prefactor η, like the other hyperparameters of the covariance function for the discriminative Gaussian process, is given a priori.

[0039] The m0 starting points can be chosen arbitrarily, in extreme cases even always at the same location, i.e. they can be identical.

[0040] The choice of v can be arbitrary. However, if one... ν=Φ−1(1−δn−mo) Assuming that the probability ∈ (0,1) of at least one error occurring in the measurement of unit 2 with n points according to the above iterative scheme can be chosen sufficiently small and can therefore be explored safely with a probability greater than or equal to 1 δ.

[0041] The maximum number n of points to be measured (size of the experimental design) can generally be used as a termination criterion. However, it is also conceivable to terminate after a certain model accuracy of the Gaussian process model for the system outputs has been achieved, or after reaching a minimum number m of safely navigable points.

[0042] Of course, sparse Gaussian process models can also be used as a basis for the standard models employed here. This then enables faster calculations for the online determination of the experimental design, in order to minimize, for example, the waiting times of the test bench for the next measurement point.

[0043] In Fig. Section 3 briefly outlines a possible method for measuring a physical unit using a flowchart.

[0044] In step S1, a data-driven functional model is initially provided, which is trained on, or based on, an initial number m0 of measurement points and corresponding values ​​of the output variable. The data-driven functional model is defined by the data points D. i and the parameter vector θ y defined.

[0045] In step S2, a data-driven confidence model is provided, which is trained on, or based on, the first number m0 of data points and corresponding values ​​of a predefined confidence level. The data-driven confidence model is defined by the data points D i and the parameter vector θ k defined. The basis of the data-based confidence model is the predefined restrictions of the input variables of the measurement points and the definition of the confidence variable h according to an expert specification.

[0046] In step S3, the optimization now takes place. xi+1=arg maxx∗∈X ​​Var(y∗|x∗,Di,θy) st:μg∗−νσg∗≥0 as described above, to measure the next measuring point x i|1 to obtain.

[0047] In step S4, the measurement point x, which is to be measured next, is now being measured. i|1 the value of the output variable y i+1 determined and furthermore the confidence level h is determined according to a specification, from which h i+2 or c i+2 results in the data points D i are now being supplemented with the newly measured data point.

[0048] In step S5, the data-based functional model is created based on the new set of data points D. i1 trained or updated. Training methods can be performed with and without adjustment of the parameter vector θ. y can be applied. To limit the necessary computing capacity, the parameter vector θ can be used. y They can only be adjusted after a certain number of calculation cycles.

[0049] In step S6, the data-based confidence model is based on the new set of data points D. i-1 The training process involves training methods with and without adjustment of the parameter vector θ. k can be applied. To limit the necessary computing capacity, the parameter vector θ can be used. k They can only be adjusted after a certain number of calculation cycles.

[0050] Step S7 checks whether a termination condition exists. A termination condition can be determined by the number of measurement points to be surveyed. If the termination condition is not met (alternative: Yes), the procedure continues with step S3. Otherwise (alternative: No), the procedure is terminated.

Claims

[1] Method for measuring a physical unit (2) with a number of measuring points (X) in order to obtain a value of an output quantity (y) at each point, comprising the following steps: - Determining (S4) a measurement point (y) to be measured next depending on a given data-based functional model, which is designed in particular as a Gaussian process model; - Performing (S4) the measurement of the physical unit (2) at the next measuring point to be measured (x) i+1 ), to obtain a resulting value of the output quantity (y i|1 ) to obtain; - Update (S5) the data-based functional model with the next measurement point to be measured (x i|1 ) and the value of the output variable (y i|1 ), where determining the next measuring point to be measured (x i+1) is carried out depending on a confidence level (h1) determined by the measuring point (x1), which indicates a risk to the physical unit (2) at a measurement point (x1). 1+1 ) specified operating state, wherein the confidence quantity (h) is specified using a data-based confidence model depending on the measurement point (x), wherein the data-based confidence model is in particular designed as a Gaussian process model. [2] Method according to claim 1, wherein the next measuring point to be measured (x i+1 ) is determined depending on an optimization procedure, with which the next measuring point to be measured (x) is selected. i|1 ) is sought which has a maximum entropy with respect to the data-based functional model with respect to the output quantity (y). i+1 ) exhibits. [3] Method according to claim 2, wherein the next measuring point to be measured (x i+1 ) is determined depending on an optimization, according to xi+1−arg maxx∗∈X ​​Var(y∗|x∗,Di,0y) with μg8−νσg8≥0, where v = Φ -1 (p) a given confidence parameter, x a query point, D i the data points, which include the measurement points and the associated values ​​of the output quantity, µ g8 the expected value, θ y a hyperparameter vector of the data-based functional model and σ g* the standard deviation of the predictive distribution q(g4|x4, c, h, X, 0 h ) are equivalent to. [4] Method according to any one of claims 1 to 3, wherein the data-based functional model has been determined using previously measured measurement points (X). [5] Method according to claim 1, wherein the data-based confidence model after measurement with the determined measurement point to be measured next (x 1+1 ) and is updated with the determined value of a system state variable. [6] Method according to claim 5, wherein the system state variable is a state variable of the physical unit (2) that results from the operating state and is not directly adjustable. [7] Method according to any one of claims 1 to 6, wherein the method is carried out repeatedly, in particular until a termination condition is met, wherein the termination condition is met upon reaching a number of determined measurement points, upon reaching a certain model accuracy for the output variable or upon reaching a minimum number of determined safe measurement points. [8] Device, in particular a computing unit configured to perform the method according to any one of claims 1 to 7. [9] Computer program configured to perform all steps of a method according to any one of claims 1 to 78. [10] Machine-readable storage medium on which a computer program according to claim 9 is stored.

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