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- W3088141884 abstract "One of the requirements of the population-based approach to Structural Health Monitoring (SHM) proposed in the earlier papers in this sequence, is that structures can be represented by points in an abstract space. Furthermore, these spaces should be metric spaces in a loose sense; i.e. there should be some measure of distance applicable to pairs of points; similar structures should then be ‘close’ in the metric. This geometrical structure is not enough for the framing of problems in data-based SHM, as it leaves undefined the notion of feature spaces. Interpreting the feature values on a structure-by-structure basis as a type of field over the space of structures, it seems sensible to borrow an idea from modern theoretical physics, and define feature assignments as sections in a vector bundle over the structure space. With this idea in place, one can interpret the effect of environmental and operational variations as gauge degrees of freedom, as in modern gauge field theories. One can then regard data normalisation procedures like cointegration as gauge-fixing operations. This paper will discuss the various geometrical structures required for an abstract theory of feature spaces in SHM, and will draw analogies with how these structures have shown their power in modern physics." @default.
- W3088141884 created "2020-10-01" @default.
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- W3088141884 date "2020-09-23" @default.
- W3088141884 modified "2023-09-25" @default.
- W3088141884 title "Towards Population-Based Structural Health Monitoring, Part VI: Structures as Geometry" @default.
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- W3088141884 doi "https://doi.org/10.1007/978-3-030-47634-2_26" @default.
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