Digital Twin Model Updating for Time-Varying Prediction Error
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Solution Overview
Problem
Current model updating methods in systems engineering are limited by the assumption of prediction error as an independent Gaussian white noise process, leading to biased estimation and incorrect uncertainty quantification due to modeling errors and time-varying uncertainties.
Innovation Solution
An adaptive recursive Bayesian inference framework is employed to jointly estimate model parameters and prediction error characteristics, including a non-stationary Gaussian process with time-variant mean and covariance, allowing for the management of modeling errors and measurement noise.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the prediction error is assumed to be an independent Gaussian white noise process for mathematical simplicity, then the model updating process is computationally tractable, but the estimation becomes biased and uncertainty quantification becomes incorrect due to modeling errors
Solution Approach 1:
The patent transforms the static assumption of independent Gaussian white noise into a dynamic model where prediction error is represented as a non-stationary Gaussian process with time-varying mean and covariance. This dynamic approach allows the model to adapt to changing system conditions and capture temporal correlations in modeling errors, thereby improving estimation accuracy while maintaining computational feasibility through efficient inference algorithms
Solution Approach 2:
The patent changes the parameters of the prediction error model from fixed (independent Gaussian white noise with constant covariance) to time-varying (non-stationary Gaussian process with time-dependent mean and covariance). This parameter transformation enables the model to capture the evolving characteristics of modeling errors throughout the system's operation, resolving the contradiction between mathematical simplicity and estimation accuracy
2Measurement precision
If the prediction error is modeled as a non-stationary Gaussian process with time-variant mean and covariance to account for modeling errors, then estimation accuracy improves, but computational complexity increases
Solution Approach 1:
The patent implements a feedback mechanism where the time-varying mean and covariance of the prediction error are continuously updated based on residual analysis from the model updating process. This feedback loop allows the system to adapt to modeling errors dynamically while using efficient algorithms to maintain computational tractability, balancing accuracy improvements with computational constraints
Solution Approach 2:
The patent introduces an intermediary layer of inference algorithms that bridge the gap between the complex non-stationary Gaussian process model and practical computation. These intermediary algorithms efficiently compute the time-varying parameters without requiring full exploration of the computationally intensive solution space, thereby reducing overall computational complexity while maintaining estimation accuracy
3Ease of operation
If traditional Bayesian model updating is used with zero-mean Gaussian assumption, then the processing is straightforward, but the model updating performance degrades and parameters diverge under real-world conditions
Solution Approach 1:
The patent replaces the static zero-mean Gaussian assumption with a dynamic non-stationary Gaussian process model that adapts to real-world conditions. This dynamic model captures the evolving statistical characteristics of prediction errors, preventing parameter divergence and maintaining reliable model updating performance while preserving reasonable processing simplicity through efficient inference methods
Data Source
AI summary
Systems and methods are provided for creating and using digital models of real-world systems with a learning or data assimilation method. The systems and methods may be used to create and/or use a quantifiable model of a real-world system formed of a variety of sub-systems. and create and/or manage or quantified error or bias of the model. The learning network may be used to jointly estimate model parameters, dynamic input loads, and the statistical characteristics of the prediction error that includes the effects of modeling error and measurement noise. The learning network may be an adaptive recursive Bayesian inference framework. The prediction error may be of the form of a non-stationary Gaussian process with unknown and time-variant mean vector and covariance matrix to be estimated.