Dynamic Machine Modeling Using CVA for Variable Operating Conditions
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Solution Overview
Problem
Current methods for modeling nonlinear and time-varying dynamic systems face challenges due to exponential growth in dimensionality, leading to inefficient computation and inaccurate results, especially when dealing with large-scale industrial processes and variable structure machines.
Innovation Solution
The development of a method and system using canonical variate analysis (CVA) for nonlinear parameter-varying (NLPV) systems, which transforms machine data into a dynamic state space model, allowing for efficient computation and accurate modeling by reducing the computational requirements and improving numerical stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If direct extensions of linear subspace methods are used for modeling nonlinear systems, then the modeling approach can be implemented, but the dimension of the past and future expands exponentially leading to inefficient computation
Solution Approach 1:
The patent transforms the nonlinear system identification problem into a linear algebra problem by changing the parameter representation. Instead of directly modeling nonlinear relationships which causes exponential dimensionality growth, the invention uses subspace methods with linear parameter variations (LPV) where the system matrices are parameterized by time-varying parameters. This parameter transformation allows the use of efficient linear algebra operations while capturing nonlinear behavior, resolving the contradiction between implementation ease and computational efficiency.
2Measurement precision
If the dimension of past and future variables is increased to improve model accuracy, then modeling precision improves, but the computational dimension expands exponentially to 10^9 or 10^12
Solution Approach 1:
The patent segments the high-dimensional nonlinear problem into lower-dimensional linear subproblems. By using subspace methods, the system decomposes the state space into observable and controllable subspaces, allowing accurate modeling without requiring exponential numbers of variables. The segmentation of the mathematical approach enables achieving high modeling accuracy while keeping computational dimensions manageable through structured matrix operations rather than brute-force variable expansion.
Solution Approach 2:
The invention transitions from thinking in terms of expanding time-lag dimensions (which causes exponential growth) to utilizing matrix space dimensions. By formulating the problem in terms of state-space matrices and using singular value decomposition, the approach captures system dynamics in a compact matrix representation rather than expanding the temporal dimension, effectively changing the dimensional space in which the problem is solved.
3Productivity
If iterative subspace approach is used for estimating nonlinear terms, then computation requirements are modest, but the heuristic algorithm does not substantially improve modeling accuracy for nonrandom scheduling functions
Solution Approach 1:
The patent incorporates feedback mechanisms in the form of parameter-update algorithms that use prediction errors to refine the LPV model parameters. The iterative least-squares or gradient-based optimization adjusts the time-varying parameters to minimize prediction errors, creating a feedback loop that continuously improves model accuracy. This structured feedback approach replaces heuristic methods with systematic optimization, achieving both computational efficiency and high accuracy for nonrandom scheduling functions.
Data Source
AI summary
A method and system for forming a dynamic model for the behavior of machines from sensed data. The method and system generates a dynamic model of the machine by applying a canonical variate analysis (CVA) method to subspace system identification extending to parameter varying (LPV) systems and nonlinear (NL) systems in order to make implementation of the computation feasible and accurate.