DE102015200295A1 - Method and apparatus for determining training data points for creating a model for a physical system - Google Patents

Abstract

The invention relates to methods for determining a rating measure (G) for a training data set determined by a test method from training data points, wherein the training data record is created by sequentially applying input values of input quantities (E, E1, E2) of a number (s) of measurement points to a physical system (2) is determined, wherein the evaluation measure (G) depends on or corresponds to a number of training data points selected from the training data set, wherein the training data points are selected such that in no area of one of the input values of the input quantities (E, E1, E2) defined input space is exceeded a predetermined maximum point density.

Description

Technical area

The invention relates to the field of methods for measuring physical systems and creating models with which the behavior of the physical system can be mapped mathematically.

State of the art

Various modeling techniques can be used to create mathematical-physical models for mapping the behavior of physical systems. In particular, the use of non-parametric, data-based function models, such as Gaussian process regression, uses training data for modeling. Such training data are usually recorded on a test bench and depict the behavior of the physical model. For this purpose, output values for at least one output variable at a number of predetermined measuring points are determined, wherein the measuring points each correspond to a combination of input values of one or more input variables. Since physical systems are usually also influenced by the dynamic behavior of the input variables, the training data can also take into account the gradients of one or more of the input quantities, i. the input quantities and their gradients form the input data space for the training data points.

In order for a function model modeled from the training data points to best represent the real behavior of the physical system, the training data points should as uniformly as possible fill in the entire input variable range permissible for the physical system.

For measuring the physical system on the test bench, measurement points must therefore be selected which fill the input data data space as completely and uniformly as possible. Staggered so-called "shifted chirp" signals or Sobol ramp signals can be used, for example, for excitation of the physical system.

Although the known methods generate measurement points distributed almost evenly over the input data space, training data points with unequal distributions may result depending on the method. In order to select a suitable method by which input quantity data is determined, it is therefore necessary to provide a criterion which makes it possible to compare the measuring methods for measuring the physical system with one another.

Since deviations occur in the test bench between the input values of the input variables provided by specifying the measuring points and the actual values resulting from the physical system, the room-filling property of the measuring points can not necessarily be maintained during the execution of the test method. The reasons for this may be, for example, that the excitation rate, i. The gradients of the input variables, can not be implemented by the respective positioner of the physical system, since they have only a limited response. Furthermore, communication delays between the tester and the physical system may result in misrepresentations of the physical system's behavior in the measured training data points.

Disclosure of the invention

According to the invention, a method for evaluating test methods for generating training data according to claim 1 and a corresponding device according to the independent claim are provided.

Further embodiments are specified in the dependent claims. According to a first aspect, a method for determining a score for a training data set from training data points determined by a test method is provided, wherein the training data set is determined by successively applying input values of input values of measuring points to a physical system, wherein the score of a number of the training data set selected training data points depends on or corresponds to. The training data points are selected as those training data points, such that a given maximum point density is not exceeded in any area of an input size space defined by the input values of the input variables.

Test methods are based on a set of predefined measurement points that are successively applied to a physical system, wherein corresponding output values of an output variable are detected in the physical system. The combination of a measuring point, ie in each case one input value of the input variables and / or their gradient with the associated output value of the output variable supplied by the physical system forms a recorded training data point. The training data points determined in this way then serve as a mathematical To create a model that describes the behavior of the physical system in terms of output.

One idea of the above method is to evaluate the training data points acquired with the aid of a test method such that a comparison with other test methods or test methods based on sets of other measurement points is possible. In particular, the evaluation method is based on a determination of the maximum amount of acquired training data points that are distributed in the input size space so that no maximum point density of training data points is exceeded in any range of the input size space. The maximum predetermined point density may be predetermined or result from the size of the input data space and a predetermined number of maximum detectable data points.

Depending on the test method used, the point density of the training data points in areas in the input data space may exceed the maximum point density provided. The training data points in this area are less suitable for creating the physical model. It is therefore envisaged, when determining an evaluation measure for the test method, not to consider the training data points which increase the point density of the training data points beyond the maximum point density. The remaining training data points determine by their number the evaluation measure for the test method used or the quality of the test method used.

By being able to determine an evaluation measure for a test method or a set of measurement points used in the test method, test methods or the used set of measurement points can be compared with each other, such that a selection of the training data record of the test method with the highest evaluation measure for use is possible for modeling.

Furthermore, the maximum point density can be determined from a predetermined maximum number of measuring points depending on a size measure for the input size space.

It can be provided that the evaluation measure is specified as the ratio of the number of selected training data points and the maximum number of measurement points.

According to one embodiment, the training data points may be selected as those training data points that maintain a predetermined minimum distance to all other training data points, wherein the selection of the training data points is performed to maximize the number of selected training data points.

In particular, the selected training data points can be determined by iteratively removing respectively the training data points from the determined training data record for which the number of training data points spaced a smaller distance than the predetermined minimum distance is the maximum.

According to a further aspect, a method for comparing a plurality of test methods with respectively different sets of measurement points of training data sets, wherein the test methods are evaluated according to the above method with a weighting measure and those or those test method with the or the largest weighting for a creation of a model mapping the physical system. In this way, the training data sets underlying the testing method can be compared in terms of their fitness for the physical model, and the most suitable for modeling.

Furthermore, the selected training data sets of the test methods with the largest weighting measures can be combined to obtain a common training data record for creating the physical system mapping model.

According to a further aspect, a test stand having a test device for measuring a physical system by means of a test method is provided, wherein the test device is designed to determine a measure of the usability of an amount of measurement points underlying the test method according to the above method.

Brief description of the drawings

Embodiments are explained below with reference to the accompanying drawings. Show it:

1 a schematic representation of a test bench for measuring a physical system by means of a test method;

2 exemplary curves for curves of measured data points for input variables and resulting output values of an output variable;

3 a flowchart illustrating a method for determining an evaluation measure for a test method.

4a to 4d an illustration of the method for reducing the density of points determined by means of a test method training data points below a predetermined maximum point density; and

5a and 5b a representation of determined training data points before and after a reduction of the number of training data points for reducing the point density below the maximum point density in each area of the input data space.

Description of embodiments

1 shows a test bench 1 in which a physical system 2 with the help of a test device 3 can be measured. Examples of test stands are engine test stands for measuring internal combustion engines or subsystems thereof.

For measuring the physical system 2 become input values of input quantities E as measuring points of a training data set from a training data memory 31 provided and in measuring cycles consecutively from the test device 3 to the physical system 2 created. In each measurement cycle, a respective resulting output value of an output variable y of the physical system is calculated 2 detected. This includes the physical system 2 at least one sensor 21 to get the output values of the output to the test device 3 to convey. The output values y are respectively related to the applied input values of the approached measuring point in a training data memory 31 the test facility 3 saved.

The measurement points provided for determining the training data points, which correspond to a combination of input values of the input variables, can be determined offline and the test device 3 to be provided. The provided measuring points are successively sent to the physical system 2 created and detected a resulting output value of the output to be measured.

The set of measuring points can be created by different methods of generation. In 2 By way of example, temporal profiles of input values and a corresponding course of output values of an output variable are shown for two input quantities E1, E2. The input values are in the case shown created by means of a chirp method with variable displacements (shifted chirp), so that as many different combinations of input values of the input variable and combinations of the respective gradients of the input variables in the course of the execution of the test procedure to the physical system 2 be created.

However, other methods of providing test data points for carrying out the test method are also conceivable, such as using Sobol ramps and the like.

The set of measurement points of the training data set is preferably chosen so that the input data space is filled as uniformly as possible. Furthermore, the input variables at the measuring points should be the physical system 2 with different combinations of possible excitation frequencies. A training data point results in each measurement cycle as a combination of the applied input values of the input quantities, the gradient values resulting from the application of the input values for the input quantities, and the output value of the output variable. In particular, the training data points in each measurement cycle may also be formed as a combination of the applied input values of the input variables of one or more past values of the input variables and the output value of the output variable in order to take into account gradients of the input variables.

The processing logic 32 is further configured to make an evaluation of the thus determined training data set from training data points with respect to a room-filling property. A corresponding method for determining such an evaluation measure is in connection with the flowchart of 3 described below.

In step S1, the measurement points are generated or provided and sent to the physical system 2 created.

The output value of the output quantity y corresponds to a reaction of the physical system to the application of the measuring point and, in the case of dynamic systems, to previously applied measuring points. Training data points are determined as described above from the values of the applied input variables and the resulting output quantities which are assigned to one another in each case temporally. Overall, a training data set with a number of training data points is determined and provided in step S2.

The provided training data points can now due to limitations of the input variables and / or their gradients or due to systemic influences and Disturbances in the entire input data space lead to regions of varying point densities. Since the number of training data points that can be processed to create a function model is limited, in particular for reasons of computation time, the distribution of the training data points into the input data space of one or more areas where the maximum point density is exceeded and areas in which only a very low point density is present. The maximum point density results from a ratio of the maximum number of s of recordable training data points and a volume measure for the input space to be covered by the measurement points.

Since the areas in which the maximum point density is exceeded do not contribute to the improvement of the functional model to be created, there are surplus training data points which do not contribute to the quality of the test procedure performed. It is envisaged to provide a score based on the number of usable training data points that corresponds to or depends on the number of useful training data points.

The usable training data points result as those training data points distributed in the input data space such that the maximum point density is not exceeded in any area of the input data space. a corresponding procedure is schematically in the 4a - 4d for a training data space with an input E and a resulting output y. To do this, according to the 4a in step S3, determining the distances from each of the training data points to each other of the training data points in the input data space. The training data points are indicated as "x". An area A in which the maximum point density is exceeded is bordered by a dashed line.

The maximum point density results in a minimum distance which two adjacent training data points should have in the training data space so that the maximum point density in an arbitrarily large area within the input data space is not exceeded. For example, the minimum distance of two training data points may be specified as 1 / s.

In step S4, as in FIG 4b shown schematically, for each of the training data points, the number of those adjacent training data points determined, to which the minimum distance is exceeded.

If it is determined in step S5 that training data points are present which have a distance to adjacent training data points which is less than the predetermined minimum distance, the number of adjacent training data points whose distance is smaller than the predetermined minimum distance are counted for each of the training data points in question. Those training data points having the highest number of training data points spaced too close are correspondingly removed from the training data set. This is in 4c in which the training data point A has been removed.

In particular, in step S5, one or more of those training data points may be removed from the training data set in which the number of further training data points that are too close is greater than a predefined threshold value.

In step S6, it is checked if training data items have been removed in step S5. If this is the case (alternative: yes), the method is continued with step S4, wherein the determination of those adjacent training data points, to which the minimum distance is fallen below, is now carried out for the remaining training data points. Otherwise (alternative: no), i. If there are no training data points in the remaining training data set which are too close to one another (smaller than the minimum distance), the method continues with step S7.

The reduced training data set resulting from the method of steps S4 to S6 is now used in step S7 as a set of training data points that is evaluated. The training data points of the reduced training data set now again correspond to the criteria of equal distribution within the input data space.

The evaluation measure G is now the number a of the remaining training data points of the reduced training data set, which can be determined as an absolute value or relative to the theoretically resulting maximum number s of training data points as G = a / s. The maximum number of training data points is given or results from the maximum point density and the size of the input data space.

For comparison of several test methods, each with different sets of measuring points, reduced or selected training data records can now be created and evaluated according to the above method. In doing so, for creating a mathematical model describing the physical model, only the selected training dataset of the largest score test method or the selected training datasets of the largest scoring test methods are used for constructing a physical system mapping model. In particular, the selected training data sets of the largest scoring test methods may be suitably combined to obtain a common training data set for constructing the physical system mapping model.

In 5a For example, an input variable data space having two input quantities E1, E2 and an output variable y is shown. One recognizes a number of possible training data points corresponding to an equal distribution in the input size space and by a measurement with training data points determined in a selected test method corresponding to the measurement points shown by dashed lines. Using the method described above, training data points determined using the measurement points are removed which violate the criterion of exceeding the maximum point density in a region of the input size space. The result is a number and distribution of remaining training data points, as in 5b are shown.

It can be seen that, although the physical system 2 has been measured with a large number of measuring points, the number of training data points is significantly reduced by applying the above method. The resulting number of training data points is dependent on the amount of measurement points on which the test method is based and represents an evaluation measure with which test methods can be compared based on measurement points determined using different methods.

Claims (10)

Method for determining a rating measure (G) for a training data record determined by a test method from training data points, wherein the training data record is generated by consecutively applying input values of input quantities (E, E1, E2) of a number (s) of measurement points to a physical system ( 2 ) is determined; wherein the score (G) depends on or corresponds to a number of training data points selected from the training record; wherein the training data points are selected so that in any area of an input size space defined by the input values of the input quantities (E, E1, E2) a predetermined maximum point density is exceeded. The method of claim 1, wherein the maximum point density of the predetermined number (s) of measuring points is determined depending on a size measure for the input size space. The method of claim 2, wherein the score (G) is expressed as a ratio of the number (a) of the selected training data points and the number (s) of measuring points. Method according to one of claims 1 to 3, wherein the training data points are selected as those training data points that comply with a predetermined minimum distance to all other training data points, wherein the selection of the training data points is performed so that the number (a) of the selected training data points becomes maximum. The method of claim 4, wherein the selected training data points are determined by iteratively removing each of the training data points from the determined training data set for which the number of training data points spaced less than the predetermined minimum distance is at a maximum. A method of comparing a plurality of test methods each having different sets of measurement points of training data sets, wherein the test methods are evaluated according to a method according to one of claims 1 to 5 with a rating measure and those or those test methods with the or the largest evaluation measures for a creation one the physical system ( 2 ) imaging model. The method of claim 6, wherein the selected training data sets of the test methods with the largest weighting measures are combined to obtain a common training data set for constructing the physical system mapping model. Test bench ( 1 ) with a test device ( 3 ) for measuring a physical system ( 2 ) using a test procedure whereby the test equipment ( 3 ) is designed to determine an evaluation measure (G) about a usefulness of an amount of measuring points on which the test method is based, in accordance with a method according to one of claims 1 to 5. Computer program, which is set up to carry out all the steps of a method according to one of Claims 1 to 7. A machine-readable storage medium on which a computer program according to claim 9 is stored.

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