Spatial-Temporal Sensitivity Mapping for High-Dimensional Process Parameters
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Solution Overview
Problem
Existing sensitivity analysis techniques focus on local sensitivities and are computationally expensive, often leading to conflicting conclusions and limited scalability, especially when dealing with high-dimensional process parameters in engineering systems.
Innovation Solution
A computer-implemented method for performing global sensitivity analysis in the spatial-temporal domain, which involves receiving process parameters, retrieving historical data, selecting a sampling algorithm to divide the dataset into subspaces, perturbing samples, and computing sensitivity coefficients to identify critical parameters and responses using dynamic estimation of weights.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If local sensitivity analysis techniques are used, then measurement precision is improved, but device complexity and computational cost increase
Solution Approach 1:
The patent segments the high-dimensional parameter space into multiple low-dimensional subspaces using space-filling curves (e.g., Hilbert curve). This segmentation allows sensitivity analysis to be performed independently in each subspace, reducing the computational complexity from exponential in high dimensions to manageable low-dimensional calculations, while maintaining global coverage through the systematic traversal of all subspaces.
Solution Approach 2:
The patent transforms the high-dimensional sensitivity analysis problem into a sequence of low-dimensional problems by mapping the multidimensional parameter space onto a one-dimensional space-filling curve. This dimensionality transformation enables the use of efficient 1D or low-dimensional sensitivity analysis methods while still capturing global sensitivities across all dimensions through the space-filling property of the curve.
2Reliability
If comprehensive global sensitivity analysis is performed, then reliability is improved, but loss of time increases
Solution Approach 1:
The patent performs preliminary action by pre-generating a space-filling curve that systematically covers the entire parameter space before the sensitivity analysis. This pre-computed geometric structure allows the analysis to efficiently traverse all regions of the parameter space in a single pass, ensuring comprehensive global coverage without requiring multiple separate simulations or repeated sampling efforts.
Solution Approach 2:
The patent maintains continuity of useful action by using the space-filling curve to create a continuous traversal path through the parameter space. This continuous traversal ensures that no region is missed and allows for efficient sequential processing of sensitivity calculations across all dimensions, maximizing the information gained per unit of computational time spent.
3Adaptability or versatility
If high-dimensional parameter space is analyzed, then adaptability is improved, but productivity decreases
Solution Approach 1:
The patent segments the high-dimensional parameter space analysis into manageable low-dimensional slices along the space-filling curve. This segmentation allows the analysis to adapt to any number of dimensions by systematically dividing the complex high-dimensional problem into a sequence of simpler low-dimensional problems, maintaining versatility while improving computational productivity through the reduced complexity of each individual calculation.
Data Source
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AI summary
Technical solutions are described for performing sensitivity analysis for engineering systems in spatial-temporal domain. An example method includes receiving a set of process parameters and retrieving a multidimensional dataset containing historical values of the process parameters and corresponding output values. The method further includes selecting a sampling algorithm to divide the multidimensional dataset into multiple subspaces, and selecting multiple samples (xi), one sample from each subspace. The method further includes perturbing the samples, computing a first effect (EEi) on an output value (y), and computing a second effect (SEEii) of perturbing a pair of samples (xi and xj) on the output value. The method further includes computing a sensitivity coefficient of the process parameters on the output value using the second effect for xi and xj, the first effect for xi, and the first effect for xj. An automatic visualization scheme for the global sensitivity results is also provided.