Machine Control Using PCA Variable Grouping for Root Cause Analysis
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Solution Overview
Problem
Current methods for root cause analysis in complex systems, such as production lines, rely on simple correlation statistics and PCA, which fail to capture the underlying dynamics and dependencies between variables, making it difficult to identify the root causes of anomalies and inefficiencies.
Innovation Solution
A computer-implemented method that performs principal component analysis or kernel principal component analysis to identify groups of measurement variables with significant impact on a target variable, allowing for the capture of complex dependencies and non-linear relationships, and uses these groups to control operation parameters and modify the target variable.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If simple correlation statistics and PCA are used for root cause analysis, then the analysis process is simple and fast, but the underlying dynamics and dependencies between variables cannot be captured
Solution Approach 1:
The patent transforms the analysis approach by changing from linear correlation statistics and standard PCA to kernel PCA with non-linear kernels. This parameter change in the mathematical transformation enables capturing non-linear dependencies and complex dynamics while maintaining computational feasibility through the kernel trick, thus resolving the contradiction between analysis simplicity and dynamic capture capability.
Solution Approach 2:
The patent introduces kernel functions as intermediaries that map original variables into higher-dimensional feature spaces where non-linear relationships become linearly separable. This intermediary transformation layer enables the system to capture complex variable dependencies without directly computing complex non-linear relationships, maintaining analytical tractability while improving measurement precision.
2Measurement precision
If kernel PCA is used to capture non-linear relationships, then the capture of underlying dynamics is improved, but the computational complexity increases
Solution Approach 1:
The kernel function serves as a computational intermediary that avoids explicit construction of high-dimensional feature mappings. By computing kernel values directly from input data, the system achieves non-linear relationship capture with computational complexity comparable to linear methods, resolving the contradiction between measurement precision and device complexity.
Solution Approach 2:
The patent uses kernel functions to create implicit copies of data in higher-dimensional spaces without physically transforming the data. This virtual copying through kernel evaluation enables non-linear analysis while maintaining computational efficiency, as the system works with kernel matrices of the same size as the original data matrix.
3Loss of information
If groups of measurement variables are identified to control operation parameters, then the understanding of production processes is improved, but the complexity of control increases
Solution Approach 1:
The patent segments the set of measurement variables into distinct groups based on their relationships captured by kernel PCA. This segmentation identifies which groups of variables jointly influence the target variable, providing process understanding while simplifying control by focusing on variable groups rather than individual variables, thus resolving the contradiction between information retention and control complexity.
Data Source
AI summary
According to various embodiments, a computer-implemented method for controlling a machine is described, the method comprising sensing values of measurement variables for a plurality of measurement events during an operation of the machine, wherein a value is sensed for each measurement variable at each measurement event of the plurality of measurement events, each measurement variable representing an operation parameter of the machine, determining a value of a target variable for each measurement event of the plurality of measurement events, determining, for each measurement event an observation including the sensed values of the measurement variables and the determined value of the target variable, performing a principal component analysis or a kernel principal component analysis for the plurality of observations resulting in loading values and principal components of the observations, determining, for the target variable, one or more principal components for which the absolute value of the loading value is greater than a first predetermined threshold, identifying, for each determined principal component, one or more measurement variables for which the absolute value of the loading value is higher than a second predetermined threshold, grouping the identified measurement variables for each determined principal component into a respective group, and performing joint control of operation parameters represented by measurement variables grouped into the same group to modify the target variable.