| CPC G06F 17/16 (2013.01) [G06F 17/18 (2013.01); G06F 30/23 (2020.01); G06Q 50/08 (2013.01)] | 12 Claims |
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1. A computer-implemented method for probabilistic health monitoring of complex engineering structures executed by at least one processor operatively coupled to a plurality of sensors, comprising the following steps:
a data collecting step comprising: acquiring response data from the sensors positioned at measuring points on the complex engineering structure, wherein the response data corresponds to structural responses under loading conditions; and
a plurality of processing steps (1) to (8);
(1) initializing algorithm parameters including the iteration stage of the algorithm as i, the iteration number each stage as Ns, difference constant as c, exponential constant as α, likelihood function as g, the important parameter matrix of a model as θ=[θ1, θ2, . . . , θii, . . . , θn], where ii=1, 2, . . . , n, θii is important parameter ii representing structural parameters determined by sensitivity analysis, the prior distribution of model parameters as π(θ), a proposal distribution for generating candidate parameter values, the number of measuring points as Ny and a measuring point response matrix of test as Y=[y1, y2, . . . , yjj, . . . , yNy], where jj=1, 2, . . . , Ny, yjj is response of measuring point jj, and q0=0;
(2) setting i=1, randomly sampling Ns prior parameter matrices 0= [θ(1), θ(2), . . . , θ(j), . . . , θ(Ns)], where j=1, 2, . . . , Ns, θ(j) is prior parameter matrix j, from the prior distribution π(θ) of model parameters, and calculating the likelihood values of corresponding prior parameter values using a finite element model stored in memory;
(3) calculating adaptive algorithm parameters including a variance constant Ccov, a transition parameter qi, a maximum difference Cmax based on comparison between measured and simulated responses, likelihood weight coefficients w(i,j) for each set of prior parameter values, and a mean value Si of the likelihood weight coefficients w(i,j) to overcome coefficient determination challenges in traditional Bayesian updating methods and reduce computation time for finite element models of complex engineering structures;
(4) calculating a variance matrix Σi of the proposal distribution that adaptively adjusts based on weighted covariance of current parameter values;
(5) generating an intermediate model parameter matrix based on likelihood weight coefficients w(i,j) of prior parameter values, performing random sampling using the intermediate parameter matrix and the variance matrix Σi of the proposal distribution to obtain candidate parameter values, constraining candidate values within the prior distribution range by reducing the variance matrix by a factor of 2 and resampling when candidate values exceed the prior distribution boundaries to ensure engineering feasibility and prevent unrealistic parameter combinations, and calculating likelihood values for both intermediate parameters and candidate values using the finite element model;
(6) performing an acceptance-rejection decision by generating a random value u from [0,1] and comparing u with a likelihood ratio to determine whether to accept the candidate parameter values or retain intermediate parameter values;
(7) updating algorithm parameters including the maximum difference Cmax, likelihood function values g, likelihood weight coefficients w(i,j), and mean value Si based on current iteration results; and
(8) controlling iteration flow by incrementing the iteration stage i, evaluating convergence conditions based on the transition parameter qi-1, repeating steps (4) through (8) for continued iteration when qi-1≤1, and terminating the algorithm when qi-1≥1 to achieve automatic convergence determination for complex engineering structure health detection applications and obtain posterior distribution of model parameters for engineering structure safety assessment and health monitoring.
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