Method and device for providing a sparse Gaussian process model for calculation in an engine control unit

Patent metadata

Field	Value
Publication number	US-9934197-B2
Application number	US-201414581352-A
Country	US
Kind code	B2
Filing date	Dec 23, 2014
Priority date	Dec 27, 2013
Publication date	Apr 3, 2018
Grant date	Apr 3, 2018

Abstract

A method for determining a sparse Gaussian process model to be carried out in a solely hardware-based model calculation unit includes: providing supporting point data points, a parameter vector based thereon, and corresponding hyperparameters; determining or providing virtual supporting point data points for the sparse Gaussian process model; and determining a parameter vector Q y * for the sparse Gaussian process model with the aid of a Cholesky decomposition of a covariant matrix K M between the virtual supporting point data points and as a function of the supporting point data points, the parameter vector based thereon, and the corresponding hyperparameters, which define the sparse Gaussian process model.

First claim

What is claimed is:

1. A method for determining a sparse Gaussian process model, comprising:
providing an internal combustion engine in a test stand;
recording supporting point data points from the test stand into a storage unit, the supporting point data points describing a behavior of the internal combustion engine;
performing, by a hardware-based model calculation unit, the following:
providing the supporting point data points, a parameter vector based on the supporting data points, and corresponding hyperparameters;
determining or providing virtual supporting point data points for the sparse Gaussian process model, wherein the virtual supporting point data points are artificially generated supporting point data points;
determining a parameter vector Q y * for the sparse Gaussian process model by performing a Cholesky decomposition of a covariant matrix K M between the virtual supporting point data points and as a function of the supporting point data points, the parameter vector based thereon, and the corresponding hyperparameters;
ascertaining a covariant matrix K N , the covariant matrix K M , and a covariant matrix K MN , wherein K N is ascertained by determining a covariance of between the supporting point data points, wherein K M is ascertained by determining a covariance between the virtual supporting point data points, and wherein K MN is ascertained by determining a covariance between the supporting point data points and the virtual supporting point data points;
determining a diagonal matrix Λ from K MN T K M −1 K MN , using the Cholesky decomposition of the covariant matrix K M between the virtual supporting point data points;
determining the parameter vector Q y * based on the hyperparameters for the sparse Gaussian process model based on the diagonal matrix;
determining an intermediate variable Q M =K M +K MN (Λ+σ n 2 I) −1 K MN T from the diagonal matrix Λ while using a Cholesky decomposition of the covariant matrix K MN between the conventional and the virtual supporting point data points; and
determining the parameter vector Q y * based on the hyperparameters for the sparse Gaussian process model based on the intermediate variable Q M , wherein the sparse Gaussian process model is determined based on the parameter vector Q y *;

storing the virtual supporting point data points and the hyperparameters for the sparse Gaussian process model on a control unit of a further internal combustion engine; and
operating the further internal combustion engine, by the control unit, using the sparse Gaussian process model, the virtual supporting point data points, and the hyperparameters for the sparse Gaussian process model.

2. The method of claim 1 , wherein the vector Q y * for the sparse Gaussian process model is ascertained as Q y *=L m −T L m −1 +K MN (Λ+σ n 2 I) −1 Y, L M corresponding to the Cholesky decomposition of intermediate variable Q M .

3. The method of claim 1 , wherein a jitter is applied to the hyperparameter vector Q M for the sparse Gaussian process model.

4. A non-transitory computer readable medium having a computer program, which is executable by a processor, comprising:
a program code arrangement having program code for determining a sparse Gaussian process model, which is performed in a hardware-based model calculation unit, by performing the following:
reading supporting point data points from a storage unit, the supporting point data points describing a behavior of an internal combustion engine in a test stand, the test stand providing the supporting point data points to the storage unit;
providing the supporting point data points, a parameter vector based on the supporting point data points, and corresponding hyperparameters;
determining or providing virtual supporting point data points for the sparse Gaussian process model, wherein the virtual supporting point data points are artificially generated supporting data points;
determining a parameter vector Q y * for the sparse Gaussian process model by performing a Cholesky decomposition of a covariant matrix K M between the virtual supporting point data points and as a function of the supporting point data points, the parameter vector based on the supporting point data points, and the corresponding hyperparameters;
ascertaining a covariant matrix K N , the covariant matrix K M , and a covariant matrix K MN , wherein K N is ascertained by determining a covariance of between the supporting point data points, wherein K M is ascertained by determining a covariance between the virtual supporting point data points, and wherein K MN is ascertained by determining a covariance between the supporting point data points and the virtual supporting point data points;
determining a diagonal matrix Λ from K MN T K M −1 K MN , using the Cholesky decomposition of the covariant matrix K M between the virtual supporting point data points; and
determining the parameter vector Q y * based on the hyperparameters for the sparse Gaussian process model based on the diagonal matrix;
determining an intermediate variable Q M =K M +K MN (Λ+σ n 2 I) −1 K MN T from the diagonal matrix Λ while using a Cholesky decomposition of the covariant matrix K MN between the conventional and the virtual supporting point data points; and
determining the parameter vector Q y * based on the hyperparameters for the sparse Gaussian process model based on the intermediate variable Q M Q M , wherein the sparse Gaussian process model is determined based on the parameter vector Q y *;

storing the virtual supporting point data points and the hyperparameters for the sparse Gaussian process model on a control unit of a further internal combustion engine; and
operating the further internal combustion engine, by the control unit, using the sparse Gaussian process model, the virtual supporting point data points, and the hyperparameters for the sparse Gaussian process model.

5. The non-transitory computer-readable medium as recited in claim 4 , wherein the vector Q y * for the sparse Gaussian process model is ascertained as Q y *=L m −T L m −1 +K MN (Λ+σ n 2 I) −1 Y, L M corresponding to the Cholesky decomposition of intermediate variable Q M .

6. The non-transitory computer-readable medium as recited in claim 4 , wherein a jitter is applied to the hyperparameter vector Q M for the sparse Gaussian process model.

Assignees

• Bosch Gmbh Robert

Inventors

• Kloppenburg Ernst
• Hanselmann Michael
• Markert Heiner
• Streichert Felix

Classifications

• G06F17/16

  Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} · CPC title

• G05B2219/40336

  Optimize multiple constraints or subtasks · CPC title

• G06F17/10 Primary

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• G06F17/175 Primary

  of multidimensional data · CPC title