In structural stochastic analysis, the input can be modeled by random field or stochastic process. In a discrete state, there is randomness between the two input discrete points. For output, can it also be directly characterized by random field or stochastic process? However, for the output, two discrete points in a discrete state appear to be deterministic due to the constraints of the physical system.
In structural stochastic analysis, the output can also be characterized by a random field or stochastic process. This allows for the modeling of uncertainty in the output due to randomness in the input.
One paper that discusses using random fields to model the output of a structural analysis is "Efficient stochastic finite element analysis of irregular wall structures with inelastic random field properties over manifold" by Liang et al. ¹. Another paper that discusses using random fields in structural analysis is "Applications Of Random Field Models In Stochastic Structural Mechanics" by Bucher ².
(1) Efficient stochastic finite element analysis of irregular wall .... https://link.springer.com/article/10.1007/s00466-021-02084-4.
(2) Applications Of Random Field Models In Stochastic Structural ... - Springer. https://link.springer.com/chapter/10.1007/1-4020-4891-2_39.
(3) Stochastic constitutive model of structural steel based on random field .... https://www.sciencedirect.com/science/article/pii/S2214509522001048.
Yes, they can be used for uncertainty modeling and characterization. However, I still have some doubts about this. Taking the input elastic modulus random field as an example, the modulus of one element of a sample is A1, and the element is A2/A3.../An, A1... An is only constrained by the mean, variance and correlation with the random field. There is randomness between any two units. And corresponding to the output response, one element has a modulus of B1 and the other elementis B2, rather than B3... Bn. Because a fixed physical system leads to this determinism, even though the output has randomness across all input samples, it also has determinism with respect to the single sample. This seems different from input input.
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