Performance Degradation Prediction and Assessment Based on Geometric Space Transformation and Morphology Recognition

Based on the geometric description and conceptual system of performance degradation, this chapter investigates the generalized process and method of performance degradation prediction in a health manifold space. The geometric theories and methods system of performance degradation prediction is preliminarily established, which provides important theoretical and methodological support for further research. Figure 6.1 shows the geometric theories and methods of performance degradation prediction in a health manifold space. Among them, “the intrinsic dimensionality estimation of a health manifold space,” “the dimension determination methods of a high-dimensional background manifold space,” “mappings from a high-dimensional manifold space to a low-dimensional health manifold space,” and “geometric measurement and description methods for performance degradation in a health manifold space” have answered the following questions to be solved by the geometric methods in turn (“What is the dimensionality of performance degradation in a health manifold space and how to determine it?” “How many dimensions of space should we place performance degradation in to best highlight its intrinsic laws and how to determine it?” “How to construct the health manifold space of a specific research object?” “How to describe a constructed manifold space and how to transform information from a specific space into the constructed so that this information can be directly used to reflect the performance degradation status and ultimately support the performance degradation prediction?”).