Transition Probability Modeling for Nonlinear Time-Series Diagnosis
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Solution Overview
Problem
Existing dynamic characteristic models for devices in plants, which linearly approximate nonlinearity, result in significant errors between predicted and actual time-series data, making device diagnosis and control inaccurate.
Innovation Solution
An information-processing method that calculates transition probability matrices based on correlated input and output data clusters, allowing for accurate prediction of device operation states without linear approximation, by specifying data clusters, totalizing correspondent data, and counting transition data to estimate future state probabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If nonlinearity is linearly approximated to simplify the dynamic characteristic model, then the model becomes easier to derive and use, but the error between predicted values and actual measured values increases
Solution Approach 1:
The patent changes the fundamental parameter representation from linear coefficients to probability distributions. By representing system states as probability distributions over discrete clusters and using transition probability matrices to model dynamics, the approach captures nonlinear characteristics without requiring linear approximation, thereby maintaining high prediction accuracy while keeping the model computationally tractable.
Solution Approach 2:
The patent segments the continuous state space into discrete clusters. By dividing the range of each state variable into multiple clusters and representing the system state as a probability distribution over these clusters, the method transforms the continuous nonlinear problem into a discrete probabilistic model that can be efficiently computed using transition probability matrices.
2Device complexity
If linear approximation is used to express the dynamic characteristic model, then the computational complexity is reduced, but the error between calculated time-series data and actual time-series data becomes large
Solution Approach 1:
The patent substitutes the traditional mechanical/deterministic dynamic model with a probabilistic model. Instead of using differential equations with linear approximations, the system uses probability distributions and transition probability matrices to model device behavior, replacing the deterministic mechanical approach with a statistical framework that better captures nonlinear realities.
3Device complexity
If the dynamic characteristic model uses linear approximation of nonlinearity, then the model structure is simplified, but the diagnosis and control of devices cannot be appropriately performed
Solution Approach 1:
The patent introduces dynamics into the model by using transition probability matrices that capture temporal evolution of state distributions. The model dynamically updates probability distributions over time based on observed data and transition probabilities, allowing it to adapt to changing device conditions and maintain high diagnosis reliability without requiring complex static model structures.
Data Source
AI summary
An information-processing method is provided, including a step of specifying first data clusters to which the first data each belongs and second data clusters to which the second data each belongs; a step of extracting the first data belonging to one of the first data clusters and the second data acquired at a corresponding time as correspondent data; a step of totalizing the number of pieces of correspondent data included in each of the second data clusters and calculating a total value for each cluster for the second data; and a step of specifying the second data clusters which are transition destinations of the correspondent data in a subsequent time and counting the number of pieces of transition destination data which is the correspondent data transitioning from each of the second data clusters which are transition sources to the second data clusters which are the transition destinations.