Abnormality Detection via Singular Vector Decomposition
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Solution Overview
Problem
Existing abnormality detection methods, such as the Mahalanobis-Taguchi method, face challenges in accuracy due to strong correlations in reference data and limited data sets, leading to issues with calculating Mahalanobis distances and potentially decreasing sensitivity in abnormality detection.
Innovation Solution
An abnormality detection device and method that acquire an error vector, decompose it into components relative to singular vectors, compare these components with variances, and determine abnormalities based on threshold comparisons, adjusting sensitivity and accuracy by considering the number of exceeding results and using frequency distributions for correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If an approximate inverse matrix is obtained by removing components with small singular values, then the calculation stability is improved, but the sensitivity of abnormality detection decreases
Solution Approach 1:
The patent changes the parameter handling approach by not removing small singular values but instead applying regularization (adding epsilon) to the inverted singular values. This transforms the extreme parameter values (infinities from zero singular values) into controlled finite values, maintaining calculation stability while preserving sensitivity to abnormalities in all components including those with small singular values.
2Measurement precision
If the inverse matrix of covariance matrix is calculated, then the Mahalanobis distance can be calculated, but the accuracy decreases when there is strong correlation between characteristic items or insufficient reference data
Solution Approach 1:
The patent applies beforehand cushioning by adding a regularization term (epsilon) to the diagonal elements of the covariance matrix before inversion. This pre-empts the problem of singular or near-singular matrices by ensuring the matrix is always invertible, even when reference data is limited or characteristics are highly correlated, thus maintaining both accuracy and feasibility.
3Object-affected harmful factors
If components with small singular values are removed, then the influence of noise is reduced, but abnormalities in these components cannot be detected
Solution Approach 1:
The patent applies local quality by treating each singular value component differently through selective regularization. Instead of uniformly removing or keeping all small singular values, the method applies epsilon regularization specifically to inverted singular values, allowing local adjustment that suppresses noise amplification while preserving the ability to detect abnormalities in components that would otherwise be discarded.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enhances the accuracy of abnormality detection by preventing sensitivity decreases and overdetection, while improving statistical reliability and handling dynamic systems with dependent measurement values.
Implementation Method 1
a component acquisition process of acquiring a plurality of components into which the error vector is decomposed with respect to a direction of a singular vector
Data Source
AI summary
An abnormality detection device includes a processor and a storage unit connected to the processor. The processor is configured to execute an error vector acquisition process of acquiring an error vector representing a difference between a measurement value vector having multiple measurement values measured at a determination time as elements and an average value vector having an average value of the measurement values accumulated in the storage unit as an element, a component acquisition process of acquiring a plurality of components into which the error vector is decomposed with respect to a direction of a singular vector, a comparing process of comparing a value obtained by squaring each of the components into which the error vector is decomposed with respect to the direction of the singular vector with corresponding variance in the direction of the singular vector individually with respect to the direction of the singular vector, and a determination process of performing an abnormality determination on the basis of plural compared results in the comparing process.