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A dimensionality reduction method for probability density evolution method based on manifold learning
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DOI：10.1016/j.ymssp.2026.114617.png)
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Abstract
En 中文
The probability density evolution method and the physical synthesis method provide a scientific approach for calculating the probability density of stochastic system responses and time-varying global reliability. To accelerate the computation, surrogate modeling techniques have been widely adopted. However, the high dimensionality of both input and output variables poses a critical challenge to constructing high-precision surrogate models. A common approach to addressing this issue is low-dimensional feature mapping, which involves simultaneously reducing the dimensionality of input and output variables, establishing a mapping relationship in the reduced low-dimensional space, and then projecting back to the original space. Current low-dimensional feature mapping methods, such as proper orthogonal decomposition, principal component analysis, active subspace method, are primarily limited to capturing linear low-dimensional relationships, often neglecting the intrinsic manifold structure of data points. This paper introduces a nonlinear subspace-based method for input dimensionality reduction, combined with an output dimensionality reduction technique based on manifold learning, to construct a novel class of high-precision low-dimensional feature mapping surrogate models. The proposed framework is successfully applied to probability density evolution method and the physical synthesis method.
Keywords:
Manifold learning
Diffusion maps
High-dimensionality
Dimensionality reduction
Surrogate model
Probability density evolution method
Reliability analysis
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8.9
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