Systematic selection of representative patterns for serial products

Abstract

To provide a computer-implemented method of determining representative parameterized simulation models of a parameterizable simulation model for a product, in particular a steer-by-wire steering system and / or a steering system for highly automated driving.SOLUTION: A method disclosed herein comprises: calculating a dissimilarity metric based on each pair of a plurality of pairs of parameterized simulation models, each pair resulting in a distance, thereby resulting in a plurality of distances, where the dissimilarity metric is optionally based on a gap metric, a ν-gap metric, and / or an L2 metric; and selecting a predetermined number of the parameterized simulation models based on the plurality of distances to obtain a plurality of representative parameterized simulation models.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] Prior art Serially produced products, such as steering systems, especially mass-produced products, are subject to variations in product parameters, such as friction, elasticity and / or inertia, due to manufacturing tolerances and precision.

[0002] Furthermore, serially produced products are subject to additional parameter variations due to, for example, wear and / or aging due to environmental influences. All value ranges and value combinations that occur in practice of the parameter variations of serially produced products form the so-called "operational design domain" (ODD), or roughly in German "Betriebsbereich fuer die Auslegung", of a serially produced product. [Background technology]

[0003] Typically, a simulation model (or model for short) of a product includes only its essential or relevant characteristics, and therefore, deviations between the real behavior and the modeled behavior occur due to simplifications. Parameter variations within the ODD cause additional deviations for each individual serially manufactured product between its real behavior and the corresponding simulation model, which often focuses on the representativeness of the product with nominal parameters. This simulation model, including model deviations or model uncertainties due to simplifications and variations within the entire ODD, often forms the basis for developing closed-loop control of the product and / or for simulation-based product release. Currently, because a complete characterization of the model uncertainty of a serially manufactured product is generally too laborious, simulation models are compared to a small number of real product patterns (or patterns for short).

[0004] Typically, the product patterns are as follows: Patterns with minimum, maximum and / or nominal product parameters that are most important according to the expert opinion, for example; ·Patterns with product parameters defined by experts is selected.

[0005] Therefore, it is not guaranteed that the selected product patterns are sufficiently representative of the entire ODD and thus allow for characterization of model uncertainty due to simplifications and variations within the ODD. [Prior art documents] [Non-patent literature]

[0006] [Non-Patent Document 1] Book “Essentials of Robust Control”, by Kemin Zhou and John C. Doyle, 1st edition, Pearson, 1997, ISBN: 9780135258332, Chapter 17 [Non-patent document 2] Publication “Frequency domain uncertainty and the graph topology”, Glenn Vinnicombe, IEEE Transactions on Automatic Control, vol. 38, no. 9, pp. 1371-1383, Sept. 1993, DOI: 10.1109 / 9.237648 Summary of the Invention [Problem to be solved by the invention]

[0007] The problem to be solved underlying this disclosure can be seen to be providing a method that allows for the selection of manufacturing patterns that are sufficiently representative for, for example, serially produced products. A further problem to be solved can be seen to be allowing for the characterization of model uncertainty due to, for example, simplifications and variations in the ODD.

[0008] Compared to conventional steering, steer-by-wire (SbW) steering systems and / or steering systems for highly automated driving (HAD) have more stringent prescriptive requirements for product release. To ensure that the more stringent release requirements for (mass) serially produced SbW and HAD steering systems do not inordinately increase the costs of real-world testing and trials compared to conventional steering, the industry is focusing on simulation-based release processes. For such simulation-based releases, a validated and / or verified simulation model of the steering system with known model uncertainties is important.

[0009] In principle, several different approaches are known for validating and / or verifying different aspects of a simulation model or the entire model. However, no approach currently exists that allows for a systematic or complete characterization of model uncertainty due to simplifications and variations within the ODD of a (mass) serially manufactured product. In particular, no method exists for systematically or optimally selecting, for example, a few product patterns that are representative of the entire ODD with quantifiable residual uncertainty, and thereby allow for a systematic characterization of model uncertainty within the ODD.

[0010] Furthermore, steering systems are subject to non-negligible parameter variations and are often operated in closed-loop control circuits. Therefore, for steering systems, robust controllers are often designed using established techniques in control engineering. However, this design methodology presupposes a model with known uncertainties for the product. For controller design, there is currently no technique for constructing one or more models with known uncertainties that also have a known range of representativeness within the ODD and are both representative for the entire ODD.

[0011] Therefore, a further problem to be solved underlying this disclosure can be seen as constructing one or more models with known uncertainties for controller design that also have a known range of representativeness within the ODD, and that are both representative for the entire ODD.

[0012] In systems theory, different indices are known to quantify the dissimilarity of two systems - in the following, systems and products can be treated as equivalent - and to compare them. In the following, the gap index, the v-gap index and the L2 index will be described.

[0013] The gap index quantifies the dissimilarity of the open-loop input / output characteristics of two systems P1 and P2 with respect to their stability and performance characteristics under closed-loop control using a scalar in the real interval [0,1]. An index result close to 0 means that the two systems are very similar, and that the respective P1-stabilizing controllers will also stabilize system P2 with similar closed-loop control performance. An index result of 0 means that the considered systems P1 and P2 exhibit exactly the same behavior. On the other hand, an index result close to or equal to 1 means that systems P1 and P2 are very dissimilar. Furthermore, the gap index can be used to describe the robust stability of closed-loop control circuits with model uncertainty. An explicit controller design is required for the evaluation of the gap index. Details about the definition and properties of the gap index are given in Chapter 17 of the book "Essentials of Robust Control", by Kemin Zhou and John C. Doyle, 1st edition, Pearson, 1997, ISBN: 9780135258332.

[0014] The system-theoretic description and implications of the ν-gap index are very similar to those of the gap index, but the two theories are fundamentally differently defined. To evaluate the ν-gap index, controller design is not required, but a rotational speed study of the systems P1 and P2 to be compared is required. Details about the definition and properties of the ν-gap index can be found in Chapter 17 of the book "Essentials of Robust Control" by Kemin Zhou and John C. Doyle, 1st edition, Pearson, 1997, ISBN: 9780135258332, or in the publication "Frequency Domain Uncertainty and the Graph Topology" by Glenn Vinnicombe, IEEE Transactions on Automatic Control, vol. 38, no. 9, pp. 1371-1383, September 1993, DOI: 10.1109 / 9.237648.

[0015] The definition of the L2 index corresponds to the ν-gap index without the use of rotational frequency testing. For this reason, although the descriptions and implications of both indices are similar, the L2 index has less theoretical persuasive power. For details on the definition and properties of the L2 index, see Chapter 17 of the book "Essentials of Robust Control" by Kemin Zhou and John C. Doyle, 1st edition, Pearson, 1997, ISBN: 9780135258332.

[0016] All three dissimilarity measures introduced have the following well-known properties: These indices quantify the dissimilarity of two systems with respect to stability and performance characteristics under closed-loop controlled operation, based on their closed-loop uncontrolled input / output behavior. The index results can be used to determine whether two systems P1 and P2 are sufficiently similar so that P1 can be considered representative for P2. The indicator results may be interpreted as the (system-theoretic) distance between the systems being compared. For all systems to be compared, L2 result ≦ ν-gap result ≦ gap result holds. [Means for solving the problem]

[0017] Disclosure of the Invention A first general aspect of the present disclosure relates to a computer-implemented method for determining a representative parametrized simulation model of a parametrizable simulation model for a product, particularly for a steer-by-wire steering system and / or a steering system for highly automated driving.

[0018] The method includes calculating a dissimilarity metric for each of a plurality of pairs of parameterized simulation models, resulting in one distance for each pair, thereby resulting in a plurality of distances. The dissimilarity metric may be based on, for example, a gap metric, a v-gap metric, and / or an L2 metric.

[0019] The method further includes selecting a predetermined number of parameterized simulation models based on the plurality of distances, resulting in a plurality of representative parameterized simulation models.

[0020] A second general aspect of the present disclosure relates to a computer system configured to perform a computer-implemented method according to the first general aspect (or an embodiment thereof) for determining a representative parametrized simulation model of a parametrizable simulation model for a product.

[0021] A third general aspect of the present disclosure relates to a computer program configured to perform the computer-implemented method according to the first general aspect (or an embodiment thereof) for determining a representative parameterized simulation model of parameterizable simulation models for a product.

[0022] A fourth general aspect of the present disclosure relates to a computer-readable medium or signal storing and / or including a computer program according to the third general aspect (or an embodiment thereof).

[0023] According to a method according to a first general aspect (or an embodiment thereof) proposed herein, a small number of product patterns can be systematically selected based on model-based criteria such that they are representative of the entire ODD of a serially produced product with quantifiable residual uncertainty.

[0024] In particular, the method (or embodiments thereof) according to the first general aspect proposed herein offers the following advantages over the prior art: A systematic approach to selecting product patterns that are representative of the overall ODD; Quantifiable residual uncertainty of the product pattern across ODDs, · Systematic characterization of model uncertainty due to simplifications and variations within the ODD is possible; · The calculable representativeness range of each product pattern within the entire ODD, · Systematically derivable requirements for manufacturing accuracy of product patterns; · Systematically derivable requirements for the design of robust closed-loop control of the product; and / or Search for product parameters or combinations of product parameters that significantly change the product's behavior can be achieved.

[0025] The method according to the first general aspect (or an embodiment thereof) proposed herein may be used during the design and / or system development (i.e. after the design stage) when developing a real product - for example in a steer-by-wire (SbW) steering system.

[0026] For example, during the design phase, the method may be used to systematically select (e.g., a small number of) product patterns that are representative for all realistic value ranges and value combinations of parameter variations in serially produced products (i.e., for the entire ODD). Furthermore, intermediate results of the method can be used to discover individual product parameters or combinations of product parameters that have a particularly strong influence on product behavior.

[0027] In subsequent system development, the uncertainty between the real-world product behavior and the modeled behavior of the product within the overall ODD can be systematically characterized based on representative product patterns, due to parameter variations and simplifications during modeling. The simulation model, including the characterized model uncertainty, can then be used for the development of the product's closed-loop control and / or for simulation-based product release.

[0028] Additionally, for example, in system development, any number of controller design models (i.e., one or more representative models for controller design) including associated model uncertainties, each with a known range of representativeness within the ODD and together representative for the entire ODD, can be systematically constructed using the methods proposed herein. These controller design models may be used, for example, to systematically develop gain-scheduled closed-loop control for a product that takes into account the known model uncertainties and ranges of representativeness.

[0029] The method according to the first general aspect (or an embodiment thereof) proposed herein may be used in the context of a process for simulation-based release, in particular of SbW steering systems and HAD steering systems. In this case, it is necessary to select a product pattern that is representative for the entire ODD, for example for validation and / or verification of a simulation model for the steering system. Furthermore, the method proposed herein may in principle also be used for model validation and / or verification and / or in the course of simulation-based release for other (mass) serially produced products.

[0030] The method according to the first general aspect (or embodiments thereof) proposed herein may be implemented fully or partly numerically, which is advantageous as it does not rely on a parametrizable simulation model being provided in analytical form. [Brief explanation of the drawings]

[0031] [Figure 1] FIG. 1 illustrates a schematic diagram of an exemplary embodiment of a computer-implemented method for determining a representative parameterized simulation model of a parameterizable simulation model for a product, in particular for a steer-by-wire steering system and / or a steering system for highly automated driving. [Figure 2] FIG. 1 illustrates an exemplary embodiment of a computer-implemented method based on an adjacency matrix. [Figure 3a] FIG. 1 illustrates an example ODD with multiple parameterized simulation models, three of which are selected as representative parameterized simulation models. [Figure 3b] FIG. 3b illustrates the exemplary ODD of FIG. 3a with three selected representative parameterized simulation models. DETAILED DESCRIPTION OF THE INVENTION

[0032] Detailed Description The method 100 proposed in this disclosure may be directed to enabling the selection of a product pattern that is sufficiently representative for a series of manufactured products. Alternatively or additionally, the method 100 may be directed to enabling characterization of model uncertainty due to simplifications and variations in the ODD. Alternatively or additionally, the method 100 may be directed to building one or more models with known uncertainties for controller design that also have known ranges of representativeness within the ODD and that are both representative for the entire ODD.

[0033] In the following, we describe a model-based systematic selection of representative product patterns.

[0034] Method 100 may be directed to first determining a representative parameterized simulation model of the parameterizable simulation model. Alternatively or additionally, method 100 may be directed to determining a representative parameter sample in the ODD. Alternatively or additionally, method 100 may be directed to selecting a representative product pattern.

[0035] Selecting the representative product pattern may be based on a determined representative parameterized simulation model of the parameterizable simulation model and / or on representative parameter samples in the ODD.

[0036] The method 100 may be fully or partially numerical and therefore may be used even when a parametrizable simulation model does not exist in analytical form.

[0037] First, a computer-implemented method 100 for determining a representative parameterized simulation model of a parameterizable simulation model for a product is disclosed. The product may be, in particular, a serially produced product, i.e., manufactured in a continuous production manner. Although method 100 may also be used for non-serialized or low-volume products, method 100 is particularly useful when it is desired to produce multiple homogeneous products that may vary (e.g., due to manufacturing and / or materials). The multiple homogeneous products may include, for example, more than 1e5 products per year, more than 5e5 products per year, or more than 1e6 products per year.

[0038] The product may be, for example, a steer-by-wire steering system. Alternatively or additionally, the product may be a steering system for automated driving, in particular for highly automated driving.

[0039] A parametrizable simulation model may be, but is not necessarily, analytical.

[0040] For example, as shown generally in FIG. 1, method 100 includes calculating 130 dissimilarity metrics for each of a plurality of pairs of (typically different) parameterized simulation models, resulting in one distance for each pair, thereby resulting in a plurality of distances.

[0041] The dissimilarity index may be based on a gap index, a v-gap index, and / or an L2 index. In particular, the dissimilarity index may be a gap index, a v-gap index, or an L2 index. Alternatively, the dissimilarity index may be based on a combination of the gap index, the v-gap index, and / or the L2 index. The dissimilarity index may output a quantitative measure for the dissimilarity of a pair of parameterized simulation models, i.e., a quantitative measure for how similar or dissimilar the two parameterized simulation models of a pair are. To that extent, the dissimilarity index may also be referred to as a similarity index or a comparison index. The quantitative measure output by the dissimilarity index may be referred to as a distance. If the two parameterized simulation models of a pair are similar, the distance may be small. In particular, if the two parameterized simulation models of a pair are identical (i.e., maximally similar), the distance may be zero. On the other hand, if the two parameterized simulation models in a pair are dissimilar, the distance can be increased.

[0042] For example, as shown generally in Figure 1, the method 100 further includes selecting 140 a predetermined number of parameterized simulation models based on the plurality of distances, resulting in a plurality of representative parameterized simulation models. Exemplary results of such a selection process are shown in Figures 3a-3b.

[0043] The representative parameterized simulation models may be defined such that the distance from each parameterized simulation model (within the ODD) to each representative parameterized simulation model (also in the ODD) that is closest to the parameterized simulation model (in terms of the dissimilarity metric) is minimal. For example, these distances may be minimal in a predetermined finite-dimensional norm. For example, before using the finite-dimensional norm, the distances may be modified, particularly weighted, based on knowledge already existing at the time of performing method 100, e.g., about the product and / or its ODD.

[0044] In this case, a minimum distance can be identified, in particular a minimum distance in a finite-dimensional norm. The minimization can be performed in a mathematically exact or approximate sense. For example, it may be sufficient to find a local minimum instead of a global minimum. Thus, selecting 140 a predetermined number of representative parameterized simulation models can be performed either exactly or approximately based on multiple distances.

[0045] The predetermined finite-dimensional norm may be, for example, a p-norm for any p in the interval [1, +Inf], where +Inf represents positive infinity. In particular, the p-norm may be, for example, a sum norm (i.e., p=1). That is, in that case, the sum of all distances may be the smallest. In another example, the p-norm may be a Euclidean norm (i.e., p=2). That is, in that case, the Euclidean distance may be the smallest. In yet another example, the p-norm may be a maximum norm (p=Inf). That is, in the case of the maximum norm, multiple representative parameterized simulation models may be defined such that the maximum value of all distances from each parameterized simulation model to each representative parameterized simulation model closest to the simulation model is the smallest.

[0046] For example, as optionally shown schematically in FIG. 1 , method 100 may further include determining 110 a plurality of parameter samples within an operational design domain (ODD) for the product. Each parameter sample within the ODD may include one or more parameters of a parametrizable simulation model. The ODD may be defined by a numerical and / or analytical description. Determining 110 a plurality of parameter samples within the ODD may be performed, for example, to ensure sufficient uniform coverage of the ODD. Such sufficient uniform coverage may be performed, for example, based on pseudorandom numbers. Pseudorandom numbers (e.g., via Mersenne Twister) are typically uniformly distributed. Alternatively or additionally, such sufficient uniform coverage may be based on Latin Hypercube sampling. Alternatively or additionally, such sufficient uniform coverage may be based on Sobol sequences. In particular, such sufficient uniform coverage may be based on a combination of pseudorandom numbers, Latin Hypercube sampling, and / or Sobol sequences. By already assuming a sufficiently uniform coverage, a better and more efficient representative parametrized simulation model can be selected 140 of the parametrizable simulation models.

[0047] Step 110 is referred to as "Sampling ODD" in the exemplary embodiment of FIG.

[0048] Alternatively, determining 110 multiple parameter samples may relate to only a portion of the ODD (eg, for a particular problem or for subsequent investigation of the ODD).

[0049] 1 , the method 100 may further include forming 120 a parameterized simulation model based on the parameterizable simulation model and a plurality of parameter samples in the ODD. In this case, for example, the parameterizable simulation model may be evaluated with respect to each one of the parameter samples. Alternatively or additionally, in this case, a surrogate model for the parameterizable simulation model may be created for each one of the parameter samples.

[0050] A parametrizable simulation model may be, but is not necessarily, analytical. If the parametrizable simulation model is not analytical (e.g., a black-box simulation model), it may not be possible to easily evaluate the parametrizable simulation model with respect to each one of the parameter samples. In such a case, for example, a surrogate model for the parametrizable simulation model can be created for each one of the parameter samples using numerical simulation. Therefore, such a surrogate model can also be considered a parametrized simulation model of the parametrizable simulation model. Therefore, to that extent, creating a surrogate model for each one of the parameter samples may be considered to be parametrizing the parametrizable simulation model. To that extent, the (parametrizable) simulation model itself may be considered parametrizable if it does not exist in analytical form.

[0051] Step 120, in the exemplary embodiment of FIG. 2, is referred to as “determining PUM for all ODD samples based on PAM,” where PAM represents a parameterizable simulation model and PUM represents multiple parameterized simulation models.

[0052] 1, the method 100 may further include determining 141 a measure for representativeness of the representative parameterized simulation model based on a predetermined number and / or a minimum distance, particularly a minimum distance in a finite-dimensional norm. The measure for representativeness may include, for example, a quantifiable residual uncertainty of the product pattern with respect to ODD.

[0053] 1, method 100 may further include adjusting 150, particularly increasing, the predetermined number if the measure of representativeness does not meet a predetermined criterion. For example, the predetermined criterion may be met if the measure of representativeness is sufficiently large. After adjusting 150, particularly increasing, the predetermined number, method 100 may be repeated, and more particularly, for example, until the measure of representativeness meets the predetermined criterion (i.e., for example, until the measure of representativeness is sufficiently large).

[0054] For example, as optionally shown schematically in Figure 1, method 100 may further include forming 131 a (e.g., symmetric) adjacency matrix based on the distances. In particular, the elements of the adjacency matrix may include the distances. The adjacency matrix may enable more efficient implementation of method 100.

[0055] Forming 131 the adjacency matrix may further be based on the order of the parameterized simulation model, which may be unrelated, for example, the order in which the parameter samples in the ODD are determined.

[0056] Step 131 is also referred to in the exemplary embodiment of Figure 2 as "calculating index-based adjacency matrices for all PUM pairs," where PUMs again represent multiple parameterized simulation models, and thus each PUM pair is a pair of two PUMs. Here, index-based adjacency matrices represent adjacency matrices.

[0057] Selecting 140 the predetermined number of parameterized simulation models based on the plurality of distances (resulting in a plurality of representative parameterized simulation models) may include a full factorial search on the adjacency matrix. Alternatively or additionally, selecting 140 the predetermined number of parameterized simulation models based on the plurality of distances may include clustering the adjacency matrix (e.g., directly or sequentially). Alternatively or additionally, selecting 140 the predetermined number of parameterized simulation models based on the plurality of distances may include converting the adjacency matrix into equally spaced auxiliary points (in view of the dissimilarity metric) and clustering these auxiliary points. Selecting 140 the predetermined number of parameterized simulation models based on the plurality of distances may include a combination of a full factorial search on the adjacency matrix, clustering the adjacency matrix, and / or converting the adjacency matrix into equally spaced auxiliary points (in view of the dissimilarity metric) and clustering these auxiliary points. Clustering the adjacency matrix may be performed such that the adjacency matrix is ​​fully provided for clustering (also referred to herein as direct clustering). Alternatively or additionally, the clustering of the adjacency matrices may be performed such that the adjacency matrices are provided for clustering sequentially and in parts (i.e., piecemeal). The latter may be more computationally and / or memory efficient. The auxiliary points and / or clustering of auxiliary points (either alone or in combination) may have numerical advantages.

[0058] Step 140 based on the adjacency matrix is ​​referred to in the exemplary embodiment of FIG. 2 as “retrieving representative PUM and / or ODD samples based on the adjacency matrix,” where again, PUM represents a plurality of parameterized simulation models and adjacency matrix represents an adjacency matrix.

[0059] For example, as optionally shown schematically in FIG. 1 , the method 100 may further include determining 160 each parameter sample associated with the representative parameterized simulation model as a representative parameter sample of the parametrizable simulation model.

[0060] Also, as optionally shown schematically in, for example, FIG. 1 , method 100 may further include determining 161 a product pattern associated with a representative parameterized simulation model, resulting in a plurality of representative product patterns. Determining 161 a product pattern associated with a representative parameterized simulation model may be based, among other things, on representative parameter samples of the parameterizable simulation model. Determining 161 a plurality of representative product patterns may be performed, among other things, on a similarity relationship, for example, by comparison with a database of stored parameter samples of real product patterns. If the similarity is not satisfactory, one or more instructions may be output on how to produce a sufficiently satisfactory representative product pattern from the real product pattern (e.g., by brushing, shimming, etc.).

[0061] Steps 160 and 161 are referred to in the exemplary embodiment of Figure 2 as "defining a representative pattern based on representative PUMs and / or ODD points," where again, the representative PUMs represent a plurality of representative parameterized simulation models, and the ODD points represent ODD samples.

[0062] For example, as optionally shown schematically in FIG. 1 , the method 100 may further include configuring 170 a closed-loop control of the product based on at least one representative parameterized simulation model. Configuring 170 the closed-loop control of the product may, in particular, be based on a plurality of representative parameterized simulation models. This may allow for designing and / or configuring a robust closed-loop control of the product. In particular, this may allow for a particularly robust and reliable configuration of the closed-loop control of the product. This may, in particular, increase the safety of the product.

[0063] Also, as optionally shown schematically in, for example, FIG. 1 , the method 100 may further include checking 171 one or more requirements for the product based on at least one representative parameterized simulation model. Checking 171 one or more requirements for the product may be based in particular on a plurality of representative parameterized simulation models. This allows for a robust and reliable construction of the product. This also allows for, in particular, increased safety of the product.

[0064] For example, as optionally shown schematically in FIG. 1 , the method 100 may further include identifying 172 one or more of the representative parameterized simulation models and / or representative parameter samples that have a greater impact on the product and / or its behavior (e.g., steering behavior). This may be performed, for example, by sensitivity analysis. This may improve understanding of the product and its behavior. This may be particularly useful in the case of relatively high-dimensional ODDs, since in that case the ODDs can no longer be examined directly.

[0065] 2 shows an exemplary embodiment of the method 100, which may include, for example, the following steps: "Sampling ODD" "Determine PUM for all ODD samples based on PAM" "Compute the index-based adjacency matrix for all PUM pairs" "Searching for representative PUM and / or ODD samples based on the adjacency matrix" "Define a representative pattern based on representative PUM and / or ODD points" The steps can be performed in this order.

[0066] FIG. 3a shows an exemplary ODD with multiple parameterized simulation models. For each of these parameterized simulation models, the corresponding parameter samples are shown as solid dots in the ODD. The ODD is a two-dimensional Cartesian product space in this example, i.e., the ODD is formed by two parameters (one in the x-direction and the other in the y-direction), and these two parameters can each take on values ​​within an interval. In general, the ODD may not be a Cartesian product space and may be of (arbitrary) variety. The dimensionality of the ODD may be arbitrary.

[0067] In this example, three of the multiple parameterized simulation models or their parameter samples are selected as representative parameterized simulation models or their parameter samples in the ODD 140, 160. The latter are each indicated by a cross in the ODD. The three representative parameterized simulation models are selected in this example so that the distance (measured by a dissimilarity metric) from each parameterized simulation model to its closest representative parameterized simulation model is smallest 140, 160.

[0068] In this example, the distance (by a dissimilarity metric) from each parameter sample in the ODD (or more precisely, their parameterized simulation models) to the representative parameterized simulation model that is closest to the parameter sample can be shown in 3D, i.e., in the z direction perpendicular to the drawing plane. In 2D, instead, several isolines are shown based on this magnitude in the z direction. For example, three solid lines form an isoline, i.e., have the same z value. Furthermore, three further isolines are shown—extending around the cross. In addition to these isolines, the boundaries of the influence range of each representative parameterized simulation model (dashed lines intersecting at a single point) are also drawn.

[0069] FIG. 3b shows the exemplary ODD of FIG. 3a with three selected representative parameterized simulation models (more precisely, their parameter samples).

[0070] Also disclosed is a computer system configured to perform the computer-implemented method 100 for determining a representative parameterized simulation model of a parametrizable simulation model for a product. The computer system may include a processor and / or a main memory.

[0071] Further disclosed is a computer program configured to perform the computer-implemented method 100 for determining a representative parameterized simulation model of a parameterizable simulation model for a product. The computer program can exist, for example, in an interpretable or compiled form. The computer program may be (even partially) loaded into a computer's RAM for execution, for example, as a sequence of bits or bytes.

[0072] Further disclosed is a computer readable medium or signal storing and / or including the computer program. The medium may include, for example, one of RAM, ROM, EPROM, HDD, SSD, etc., on / in which the signal is stored.

Claims

1. 1. A computer-implemented method (100) for determining a representative parameterized simulation model of a parameterizable simulation model for a product, in particular for a steer-by-wire steering system and / or a steering system for highly automated driving, comprising: The method (100) comprises: - calculating (130) a dissimilarity measure for each pair of a plurality of pairs of parameterized simulation models, resulting in one distance per pair, thereby resulting in a plurality of distances, optionally the dissimilarity measure being based on a gap measure, a v-gap measure and / or an L2 measure; selecting (140) a predetermined number of parameterized simulation models based on the plurality of distances, resulting in a plurality of representative parameterized simulation models; A method comprising:

2. The plurality of representative parameterized simulation models are defined such that the distance from each parameterized simulation model to the respective representative parameterized simulation model that is closest to the respective parameterized simulation model is minimum, particularly in a predetermined finite-dimensional norm. The method (100) of claim 1.

3. The predetermined finite-dimensional norm is a p-norm for p in [1, +Inf], in particular a sum norm, a Euclidean norm, or a maximum norm.

3. The method (100) of claim 1 or 2.

4. The method (100) comprises: determining (141) a measure for the representativeness of the representative parameterized simulation model based on the predetermined number and / or a minimum distance, in particular a minimum distance in the finite-dimensional norm; Optionally, adjusting (150), in particular increasing, said predetermined number if said measure of representativeness does not meet a predetermined criterion; The method (100) of claim 2 or 3, comprising:

5. The method (100) comprises: determining (110) a plurality of parameter samples within an operational design domain (ODD) for the product, optionally each parameter sample within the ODD comprising one or more parameters of the parametrizable simulation model; forming (120) the parameterized simulation model based on the parameterizable simulation model and the plurality of parameter samples in the ODD, in particular the parameterizable simulation model is evaluated with respect to each one of the parameter samples and / or a surrogate model for the parameterizable simulation model is created for each one of the parameter samples; The method (100) of any one of claims 1 to 4, comprising:

6. determining (110) the plurality of parameter samples in the ODD is performed based on pseudorandom numbers, Latin Hypercube sampling, and / or Sobol sequences, in particular, so that the ODD is sufficiently uniformly covered; The method (100) of claim 5.

7. The method (100) comprises: determining each parameter sample associated with the representative parameterized simulation model as the representative parameter sample of the parameterizable simulation model (160); 7. The method (100) of claim 5 or 6, comprising:

8. The method (100) comprises: forming an adjacency matrix based on said plurality of distances (131); The method (100) of any one of claims 1 to 7, comprising:

9. Selecting (140) the predetermined number of parameterized simulation models based on the plurality of distances includes: a full factorial search on the adjacency matrix; Clustering the adjacency matrix, and / or Transforming the adjacency matrix into equally spaced auxiliary points and clustering the auxiliary points. The method (100) of claim 8, comprising:

10. The method (100) comprises: determining (161) a product pattern associated with the representative parameterized simulation model, in particular resulting in a plurality of representative product patterns based on the representative parameter samples of the parameterizable simulation model (161); The method (100) of any one of claims 1 to 9, comprising:

11. The method (100) comprises: configuring (170) a closed-loop control of said product based on at least one representative parameterized simulation model, optionally based on a plurality of representative parameterized simulation models; and / or Checking one or more requirements for said product based on at least one representative parameterized simulation model, and optionally based on a plurality of representative parameterized simulation models (171). The method (100) of any one of claims 1 to 10, comprising:

12. The method (100) comprises: Identifying one or more of the representative parameterized simulation models and / or the representative parameter samples that have a greater impact on the product (172). The method (100) of any one of claims 1 to 11, comprising:

13. 13. A computer system configured to perform the computer-implemented method (100) of any one of claims 1 to 12 for determining a representative parameterized simulation model of parameterizable simulation models for a product.

14. 13. A computer program configured to perform the computer-implemented method (100) of any one of claims 1 to 12 for determining a representative parameterized simulation model of parameterizable simulation models for a product.

15. A computer readable medium or signal storing and / or including a computer program according to claim 14.

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