DE102013214967A1 - Method and device for adapting a data-based function model - Google Patents

Abstract

The invention relates to a method for adapting a data-based function model, in particular a Gaussian process model, comprising the following steps: providing support point data by which the data-based function model is defined and the support point data points each having an operating point and a target value associated with the operating point Include target size; Providing a measuring point and a value of the target variable detected at the measuring point; - determining that support point data point which has a least importance according to an importance function; and - replacing the determined node point by the measuring point according to a replacement criterion.

Description

Technical area

The invention generally relates to engine control units in which function models are implemented or calculated as data-based function models. In particular, the present invention relates to methods for updating data-based functional models in the engine control unit online, i. H. resource-saving, adapt.

State of the art

For the implementation of functional models in control units, in particular engine control units for internal combustion engines, the use of data-based functional models is provided. Frequently, parameter-free data-based function models are used, since they can be used without specific specifications from training data, ie. H. a set of training data points that can be created.

An example of a data-based function model is the so-called Gaussian process model, which is based on a Gaussian process regression. Gaussian Process Regression is a versatile method for data-based modeling of complex physical systems. The regression analysis is based on usually large amounts of training data, so it makes sense to use approximate solutions, which can be evaluated more efficiently.

For the Gaussian process model there is the possibility of a sparse Gaussian process regression, in which only a representative amount of support point data is used to create the data-based function model. For this purpose, the support point data must be selected in a suitable manner from the training data.

The Csato, Lehel; Opper, Manfred, "Sparse On-Line Gaussian Processes"; Neural Computation 14: pp. 641-668, 2002 discloses a method for determining support point data for a sparse Gaussian process model.

Other methods for manipulating training data or for generating support point data are, for. B. off Smola, AJ, Schölkopf, W., "Sparse Greedy Gaussian Process Regression", Advances in Neural Information Processing Systems 13, pp. 619-625, 2001 , and Seeger, M., Williams, CK, Lawrence, ND, "Fast Forward Selection to Speed Up Sparse Gaussian Process Regression," Proceedings of the 9th International Workshop on Artificial Intelligence and Statistics, 2003 , known.

Disclosure of the invention

According to the invention, a method for adapting a data-based functional model according to claim 1 and a device, a system and a computer program according to the independent claims are provided.

Further advantageous embodiments are specified in the dependent claims.

• – Bereitstellen von Stützstellendaten, durch die das datenbasierte Funktionsmodell definiert ist und die Stützstellendatenpunkte mit jeweils einem Betriebspunkt und einem dem Betriebspunkt zugeordneten Zielwert einer Zielgröße umfassen;
• – Bereitstellen eines Messpunkts und eines an dem Messpunkt erfassten Werts der Zielgröße;
• – Bestimmen desjenigen Stützstellendatenpunkts, der gemäß einer Wichtigkeitsfunktion eine geringste Wichtigkeit aufweist; und
• – Ersetzen des bestimmten Stützstellendatenpunkts durch den Messpunkt gemäß einem Ersetzungskriterium.

According to a first aspect, a method is provided for adapting a data-based function model, in particular a Gaussian process model, comprising the following steps:

• Providing support point data, by which the data-based function model is defined, and the support point data points each having an operating point and a target value of a target variable associated with the operating point;
• Providing a measuring point and a value of the target variable detected at the measuring point;
• - determining that support point data point which has a least importance according to an importance function; and
• Replacing the determined support point data point by the measurement point according to a replacement criterion.

The above method provides a way to adapt an existing data-based functional model when new measurement data is available. In particular, the data-based function model can be embodied as a Gaussian process model and is defined by hyperparameters and a set of support point data. The calculation of function values of the data-based function model is usually carried out online in an engine control unit, while hyperparameters and support point data are calculated in advance and provided in a dedicated memory area in the engine control unit.

For many applications, the online adaptation of functional models is necessary to ensure a consistently high performance of the physical system to be operated. Common applications of model adaptations are the correction of component tolerances or the correction of parameter drifts over the life of components.

When using data-based function models, adaptation of the model in the engine control unit, which is intended to model system functions or to control the physical device, is generally not possible by recalculating the data-based function model due to limited computing capacities.

According to the above method, it is therefore provided to use further measurement data acquired by the control unit during operation of the physical system and to replace a support point data point of the support point data defining the data-based function model with a data point defined by the acquired measurement data, if a replacement criterion is met. The replacement criterion evaluates the importance of the support point data point of the data-based function model and selects the support point data point of least importance to replace it with the measurement data point. In this way, the data-based function model can be permanently adapted by including newly acquired measurement points in the data-based function model. By replacing the least significant support point data point, the set of support point data points can be extended by a new measurement point without increasing the total amount of support point data points. This sets the number of node data points so that the amount of memory space needed to store the node data remains constant and does not change during subsequent adaptations. This can also ensure that the time duration for the calculation of the data-based function model remains constant, so that an unchanged calculation horizon can be assumed in the control unit.

The above method for online adaptation of data-based function models is particularly advantageous if not all support point data points could be determined via a test bench, for. B. because the operating points on the test bench are not adjustable or because the input variable range is very large, so that the acquisition of training data is very time consuming.

Furthermore, the replacement criterion may be satisfied if a projection-induced error of the provided measurement point is greater than the distance of the target value of the least significant support point data point from the function values of the applicable data-based function model.

In particular, the projection-induced error of the measurement point provided may be γ _* = k _** - k T / * K ^-1 k _* where k _** corresponds to an autocovariance of the measurement point provided and k _* corresponds to a vector with covariance function values between the provided measurement point and the current support point data points. The covariance matrix K contains the covariance function values between all current support point data points.

It can be provided that the importance function for the importance of a support point indicates a difference, in particular a distance, of the target value of a support point data point from the function value of the data-based function model at the corresponding support point.

In particular, the importance function γ _j = k _jj - k T / jK -1 \ jk _j where k _jj corresponds to an autocovariance value of the j-th node of the node data, the vector k _{j to} the covariance function values between x _j and all other node data points of the node data and K _{\ j of} the covariance matrix without the j-th row and column corresponding to the considered node point.

According to one embodiment, the data-based function model may correspond to a Gaussian process model and hyper parameters of the Gaussian process model may be adapted after replacement of a support point data point by an optimization method, in particular by means of a gradient descent method.

• – Stützstellendaten bereitzustellen, durch die das datenbasierte Funktionsmodell definiert ist und die Stützstellendatenpunkte mit jeweils einem Betriebspunkt und einem dem Betriebspunkt zugeordneten Zielwert einer Zielgröße umfassen;
• – einen Messpunkt und einen an dem Messpunkt erfassten Wert der Zielgröße bereitzustellen;
• – denjenigen Stützstellendatenpunkt zu bestimmen, der gemäß einer Wichtigkeitsfunktion eine geringste Wichtigkeit aufweist; und
• – den bestimmten Stützstellendatenpunkt gemäß einem Ersetzungskriterium durch den Messpunkt zu ersetzen.

According to a further aspect, an apparatus, in particular a control unit, is provided for adapting a data-based function model, in particular a Gaussian process model, wherein the apparatus is designed to:

• Provide support point data by which the data-based function model is defined and which includes support point data points each having an operating point and a target value of a target value associated with the operating point;
• To provide a measuring point and a value of the target value detected at the measuring point;
• To determine the support point data point which has a least importance according to an importance function; and
• To replace the determined support point data point by the measurement point according to a replacement criterion.

In another aspect, a system is provided that includes the above device and a physical device operated by the device.

Brief description of the drawings

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

1 a schematic representation of an overall system with an engine control unit for controlling a physical device using a data-based functional model; and

2 3 is a flow chart illustrating a method for adapting hyperparameters and node data defining a data-based function model.

Description of embodiments

1 shows a system 1 with a control unit 2 and one by the control unit 2 to be controlled physical device 3 , In one example, the control unit 2 an engine control unit that uses an internal combustion engine as the physical device 3 operates. To operate the physical device 3 receives the control unit 2 via sensors 31 in the physical device 3 Instantaneous values of state variables Z, which represent a current state of the physical device 3 specify. Furthermore, the control unit provides 2 Control variables A available, through which the physical device 3 is operated based on the state variables Z. In the control unit 2 one or more functional models may be provided which are designed to determine one or more of the drive variables A or contribute to this.

The control unit 2 comprises an integrated control module in which integrated in a main computing unit 21 and a model calculation unit 22 are provided for the purely hardware-based calculation of a data-based function model. The main calculator 21 and the model calculation unit 22 are via an internal communication connection 24 , such as As a system bus, with each other in communication. In addition, a storage unit 23 provided in the software code for the main unit 21 and model data for the calculation of data-based function models are stored.

Basically, the model calculation unit 22 essentially hard-wired and therefore not as the main computing unit 21 , designed to execute a software code. Alternatively, a solution is possible in which the model calculation unit 22 to provide a constrained, highly specialized instruction set for computing the data-based function model. In the model calculation unit 22 no processor is provided. This enables a resource-optimized implementation of such a model calculation unit 22 or a surface-optimized design in integrated construction.

The use of non-parametric, data-based function models is based on a Bayes regression method. The basics of Bayesian regression are, for example, in CE Rasmussen et al., Gaussian Processes for Machine Learning, MIT Press 2006 , described. Bayesian regression is a data-based method based on a model. To create the model, measurement points of training data and associated target values of an output are required. The creation of the function model is based on the use of support point data, which correspond to the training data in whole or in part or can be generated from these. Furthermore, abstract hyperparameters are determined which parameterize the space of the model functions and effectively weight the influence of the individual measurement points of the training data on the later model prediction.

The abstract hyperparameters are determined by an optimization method. One possibility for such an optimization method is an optimization of a marginal likelihood p (Y | H, X). The marginal likelihood p (Y | H, X) describes the plausibility of the measured target values y at the measurement points of the training data, represented as vector Y, given the model parameters H and the measurement points x (represented by the matrix X) of the training data. In model training, p (Y | H, X) is maximized by searching for suitable hyperparameters that lead to a progression of the model function determined by the hyperparameters and the training data or support point data (if different from the training data) and map the training data as accurately as possible. To simplify the calculation, the logarithm of p (Y | H, X) is maximized because the logarithm does not change the continuity of the plausibility function.

The calculation of the Gaussian process model is performed according to the following calculation rule. The input values u ~ _d for a test point u (input quantity vector) are first normalized and centered, according to the following formula:

In each case, m _x the mean value function with respect to an average value corresponding to the input values of the nodes data, s _x the variance of the input values of the nodes data, and d the index for the dimension D of the test point u.

As a result of creating the non-parametric, data-based function model you get:

The thus obtained model value v is normalized by means of an initial normalization, according to the formula: v ~ = vs _y + m _y .

In each case v correspond to a normalized model value (output value) at a normalized test point u (input variable vector of the Dimension D), v ~ a (non-normalized) model value (initial value) at a (non-normalized) test point u ~ (Input variable vector of dimension D), x _{l of} a node of the node data, N of the number of nodes of the node data, D of the dimension of the input data / training data / node data space, and l _d and σ _{f of} the hyperparameters of the model training. The vector Q _y is a quantity calculated from the hyperparameters and the training data. Furthermore, m _{y of} the mean value function correspond to an average value of the output values of the node data and s _{y to} the variance of the output values of the node data.

Starting from the normal operation of the system 1 in which the physical device 3 using the data-based functional model in the control unit 2 operated at certain operating points of the physical device 3 Values of the target size of the function model to be adapted are detected and corresponding measurement point data is provided. The operating points are determined by measuring points that are defined by values of one or more of the control variables A and / or by values of one or more of the state variables Z. The measuring points and the corresponding target quantity are recorded at the same time and thus made available as measuring point data. The format of the measurement point data then corresponds to the format of the support point data points.

Based on the in 2 the flowchart shown, a method is described below, with which in the control unit 2 in the form of hyperparameters and support point data defined data-based function model can be adapted.

As an initial situation, the data-based function model in the form of a Gaussian process model is provided in step S1, where hyperparameters and support point data are stored in the memory unit 23 the control unit 2 are stored. The control of the physical device 3 is using the control unit 2 and performed based on function values determined by the data-based functional model, wherein the function values are operating point-dependent, ie dependent on state variables Z of the physical device 3 , be determined.

wobei K ∈

der Kovarianzmatrix entspricht, die durch die Stützstellendaten und die Kovarianzfunktion definiert ist, wird derjenige Stützstellendatenpunkt mit dem Index i = argmin_j=1,...n(γ_j) bestimmt, der in der bestehenden Menge von Stützstellendaten die geringste Wichtigkeit aufweist. Als Kriterium für die Wichtigkeit kann der Abstand des Zielwerts des betrachteten Stützstellendatenpunkts von den Funktionswerten des datenbasierten Funktionsmodells verwendet werden, der sich aus dem Schurkomplement der reduzierten Kovarianzmatrix γ_j = k_jj – k T / jK –1 / \jk_j mit dem Autokovarianzwert k_jj ergibt, wobei jeweils der Vektor k_j den Kovarianzfunktionswerten zwischen x_j und allen anderen Stützstellendatenpunkten und K_\j der Kovarianzmatrix ohne die dem betrachteten Stützstellenpunkt entsprechende j-te Reihe und Spalte entsprechen.In step S2, the pit data is analyzed to determine which pit point data point has the least importance. This is done as follows. Based on the Gaussian process model provided with the prediction vector, that is, usually trained offline

where K ∈

According to the covariance matrix defined by the landmark data and the covariance function, the node data point with the index i = argmin _{j = 1, ... n} (γ _j ) is determined which has the least importance in the existing set of node data. As a criterion for the importance, the distance of the target value of the considered support point data point from the function values of the data-based function model can be used, which consists of the harmonic complement of the reduced covariance matrix γ _j = k _jj - k T / jK -1 / \ jk _j with the autocovariance value k _jj , where in each case the vector k _j corresponds to the covariance function values between x _j and all other node data points and K _{\ j of} the covariance matrix without the j-th row and column corresponding to the considered node point.

In step S3, for a newly measured measuring point (x _* , y _* ), the projection-indicated error is determined γ _* = k _** - k T / * K ^-1 k _* calculated. In this case, k _** corresponds to an autocovariance of the newly measured measuring point and k _{* to} the vector with covariance function values between the measuring point provided and the current supporting point data points.

In step S4, it is checked whether the projection-induced error of the newly measured measuring point is greater than the distance of the target value of the above-considered supporting point data point from the function values of the least significant data-based operating model. If this is the case (alternative: yes), in step S5 the previously determined support point data point with the least importance is replaced with the index i by the new measurement point, and in step step S6 a new prediction vector α is calculated. Subsequently, it returns to step S2. The updating of the prediction vector can be done by a Cholesky update with LL ^T = σ ² I + K, which is numerically stable and efficient. Furthermore, the average function value m _{i is} replaced by m _* , which results from the mean value function used in training the data-based Gaussian process model and the operating point of the new measurement point (m = 0 in the simplest case) in order to determine the new prediction vector α.

If it is determined in step S4 that the projection-induced error of the newly measured measuring point is smaller than the distance of the target value of the above-considered support point data point from the function values of the data-based function model with the least importance (alternative: no), then the previously determined Leave support point data point with the least importance in the support point data and discard the considered measurement point.

Furthermore, it can be provided to adapt the hyperparameters online after a replacement of a support point data point in step S5 by a measuring point, for. B. using a gradient descent method.

In the case of a Gaussian process model, as described above, the above calculations are based on the covariance matrix K. Therefore, the covariance matrix K must be in the control unit 2 available for the adaptation of the data-based function model. The covariance matrix K can be both in the control unit 2 be saved as well as be calculated online.

To prevent the on-line adaptation from causing the function-based values of the data-based function model to deviate too much from the initial data-based function model, the selection criterion can be further refined to allow a support point data point to be replaced by a measurement point only if it causes it Deviation from the initial data-based function model does not exceed a certain level.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited non-patent literature

• Csato, Lehel; Opper, Manfred, "Sparse On-Line Gaussian Processes"; Neural Computation 14: pp. 641-668, 2002 [0005]
• Smola, AJ, Schölkopf, W., "Sparse Greedy Gaussian Process Regression", Advances in Neural Information Processing Systems 13, p. 619-625, 2001 [0006]
• Seeger, M., Williams, CK, Lawrence, ND, Prospects of the 9th International Workshop on Artificial Intelligence and Statistics, 2003 [0006] "Fast Forward Selection to Speed up Sparse Gaussian Process Regression".
• CE Rasmussen et al., Gaussian Processes for Machine Learning, MIT Press 2006 [0028]

Claims (11)

Method for adapting a data-based function model, in particular a Gaussian process model, comprising the following steps: - providing support point data (S1), by which the data-based function model is defined and the support point data points each having an operating point and a target value of a target variable associated with the operating point; Providing a measuring point and a value of the target variable detected at the measuring point; - determining (S2) that support point data point which has a least importance according to an importance function; and - replacing (S5) the determined support point data point by the measurement point in accordance with a replacement criterion. The method of claim 1, wherein the replacement criterion is satisfied when a projection-induced error of the provided measurement point is greater than the distance of the target value of the least significant support point data point from the function values of the current data-based function model. The method of claim 2, wherein the projection-induced error of the provided measurement point is from γ _* = k _** - k T / * K ^-1 k _* where k _** corresponds to an autocovariance of the provided measurement point and k _* corresponds to a vector with covariance function values between the provided measurement point and the current support point data points. Method according to one of claims 1 to 3, wherein the importance function for the importance of a support point indicates a difference, in particular a distance, of the target value of a support point data point from the function value of the data-based function model at the corresponding support point. The method of claim 4, wherein the importance function γ _j = k _jj - k T / jK -1 / \ jk _j each _kjj corresponds to an autocovariance value of the jth interpolation point of the interpolation point data, the vector _{kj to} the covariance function values between _xj and all other interpolation point data points of the interpolation point data and K _{\ j of} the covariance matrix without the jth row and column corresponding to the considered interpolation point point , Method according to one of claims 1 to 5, wherein the data-based function model corresponds to a Gaussian process model and hyperparameters of the Gaussian process model after a replacement of a support point data point by an optimization method, in particular by means of a gradient descent method, adapted. Device, in particular a control unit ( 2 ), for adapting a data-based function model, in particular a Gaussian process model, the device being designed to: provide support point data by which the data-based function model is defined and the support point data points each having an operating point and a target value of a target variable associated with the operating point include; To provide a measuring point and a value of the target value detected at the measuring point; To determine the support point data point which has a least importance according to an importance function; and - replacing the determined support point data point by the measurement point according to a replacement criterion. System ( 1 ), comprising: - an apparatus according to claim 7; and - a physical device ( 3 ) operated by the device. Computer program adapted to carry out all the steps of the method according to one of claims 1 to 6. An electronic storage medium on which a computer program according to claim 9 is stored. Electronic control unit ( 2 ) comprising an electronic storage medium according to claim 10.

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