Actuator State Prediction Using Sparse Gaussian Process Models
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Solution Overview
Problem
Existing methods for learning nonlinear state space models, particularly in high-dimensional latent state spaces, are inefficient and lack robustness.
Innovation Solution
A Gaussian process state space model is employed, utilizing a parameterizable family of functions and sparse Gaussian processes to describe the behavior of an actuator system, with inducing points reducing computational complexity and allowing for efficient learning of temporal dependencies in latent states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional state space models are used to describe actuator behavior, then the model structure is simple, but the learning efficiency and robustness deteriorate in high-dimensional latent state spaces
Solution Approach 1:
The patent transforms the traditional state space model into a Gaussian process state space model by changing the mathematical parameters and structure. This involves using Gaussian process priors for the transition and observation functions, which fundamentally alters how the model learns from data while maintaining interpretability. The parameterization allows efficient handling of high-dimensional latent states through the specific properties of Gaussian processes.
Solution Approach 2:
The patent introduces inducing points as intermediary elements that mediate between the full dataset and the Gaussian process computation. These pseudo-input points serve as a bridge, allowing the model to capture global patterns without computing over all data points, thus improving learning efficiency in high-dimensional spaces while maintaining model accuracy.
2Measurement precision
If full Gaussian process computation is used, then measurement precision is improved, but computational complexity increases significantly
Solution Approach 1:
The patent segments the computation by dividing the full dataset into two parts: inducing points for global pattern capture and actual data points for local refinement. This segmentation allows the computationally intensive Gaussian process operations to be performed only on the smaller inducing point set, while still maintaining accurate state estimation through the hierarchical structure of the approximation.
Solution Approach 2:
Inducing points act as intermediaries that reduce the computational burden. Instead of computing Gaussian process posteriors over all observed data points, the model computes over the inducing points first, then uses these as a basis for efficient inference on the actual data, dramatically reducing computational complexity while preserving measurement precision.
3Reliability
If more data points are used for training, then model accuracy is improved, but training time increases
Solution Approach 1:
The patent creates a compressed representation of the training data through inducing points, which are pseudo-input points that capture the essential patterns of the full dataset. This copying approach allows the model to learn from the condensed representation rather than processing all original data points during inference, significantly reducing training time while maintaining model accuracy through the careful selection of inducing point locations.
Data Source
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AI summary
A method for ascertaining a time characteristic of a measured variable (y) adjustable by an actuator (20), wherein a time characteristic of a control variable (u) is applied to the actuator (20), wherein the ascertaining is effected by means of a Gaussian process state model of the behaviour of the actuator (20), wherein the time characteristic of the measured variable (y) of the actuator (20) is ascertained on the basis of a parameterizable family of functions (q(x1:T, f2:T, z)), wherein in the parameterizable family of functions (q(x1:T, f2:T, z)) a time dependency of a later latent state (xt), in particular ascertained using a transfer function (ft), of the actuator (20) on an earlier latent state (xt-1) of the actuator (20) and an earlier control variable (ut-1) of the actuator (20) is the same as the applicable dependency of the Gaussian process state model.