Bayesian Model Parameter Estimation for Unknown Probability Distributions
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Solution Overview
Problem
Existing model parameter estimation techniques are limited in accuracy when the distribution profile and statistics for the probability density function are unknown or difficult to estimate, due to insufficient data.
Innovation Solution
A model parameter value estimator system that includes a plant model, a model parameter value estimation section, an accumulation section, and an output section, which performs Bayesian updating on the probability density function using measurement values and process values computed by the plant model, allowing for estimation even in cases where the distribution profile and statistics are unknown or difficult to estimate.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Bayesian updating is performed using a preset probability density function, then estimation accuracy is improved, but the method becomes inapplicable when distribution profile and statistics are unknown or difficult to estimate
Solution Approach 1:
The system performs preliminary actions by automatically acquiring measurement data from the target system and performing initial probability density function estimation before the user needs to make decisions. This preliminary data acquisition and initial estimation enables the system to work even when distribution profiles are unknown, as the necessary statistical information is gathered in advance through automated measurement and initial analysis
Solution Approach 2:
The patent introduces an intermediary estimation result that serves as a bridge between unknown distribution profiles and Bayesian updating. The system first performs probability density function estimation on acquired measurement data to create an intermediate statistical model, which then serves as the basis for subsequent Bayesian updating. This intermediary step enables Bayesian methods to be applied even when original distribution information is unavailable
Solution Approach 3:
The system changes parameters by transitioning from requiring known distribution profiles to using empirically estimated probability density functions. By acquiring measurement data and estimating probability density functions from actual measurements, the system transforms the approach from theory-dependent (requiring known distributions) to data-dependent (using estimated distributions), thereby expanding applicability to unknown distributions
2Measurement precision
If sufficient measurement data is collected to estimate distribution profile and statistics, then estimation accuracy is improved, but data collection time and system complexity increase
Solution Approach 1:
The system performs preliminary probability density function estimation using the measurement data that has been acquired, rather than requiring extensive additional data collection. By establishing the probability density function from available measurement data and then applying Bayesian updating, the system achieves accurate parameter estimation without needing to collect large amounts of additional data, thereby reducing time loss
Solution Approach 2:
The system implements feedback by using acquired measurement data to estimate probability density functions, which then feed into Bayesian updating to refine parameter estimates. This feedback loop allows the system to continuously improve estimation accuracy using available data rather than requiring extensive additional data collection, optimizing the balance between accuracy and data collection time
Data Source
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AI summary
A model parameter value estimator 100 including: a plant model 2 which is a preset physical model simulating an operation of a target product, to which a model parameter value is input, and which computes a process value; a model parameter value estimation section 3 which estimates the model parameter value with a higher likelihood on the basis of the process value; an accumulation section 4 which accumulates a computation result of the model parameter value estimation section 3; and an output section 5 which outputs the computation result of the model parameter value estimation section 3, wherein a measurement value of the target product and a plurality of process values computed by the plant model 2 are input to the model parameter value estimation section 3, and the model parameter value estimation section 3 performs Bayesian updating on a probability density function accumulated in the accumulation section 4 while regarding a function generated on the basis of accuracy evaluation of each of the plurality of process values with respect to the measurement value as a likelihood function. It is thereby possible to provide an estimator and an estimation method for model parameter value estimation capable of estimating a model parameter value even if a distribution profile and statistics for the probability density function are unknown or difficult to estimate.