When implementing structural model updating, whether the model is stochastic or deterministic, the ill‐posed issue is a challenging problem. To effectively address this problem, this paper proposes a new static stochastic model updating method, which combines the homotopy method with the pre‐estimation technique of solution domains of the updating quantities. Firstly, considering the uncertain static measurement displacements, the solution domains of updating factors in structural models such as bridges are derived in terms of the sensitivity of static strain energy. Then the homotopy method is used to transfer the stochastic static model updating equation into a series of deterministic recursive equations about the expansion coefficients of updating factors. Within the pre‐estimated solution domains, the expansion coefficients of the updating factors can be solved by the L‐curve method and the convex optimization. When the measurement positions do not contain the loading points, a model expansion strategy is provided. Two numerical examples demonstrate that the proposed method can offer stable updating results, which coincide very well with those assumed real values, in the cases of high‐dimension and limited measurement points. And when the displacements at the loading points are not directly measured, compared with the Bayesian method with the finite element samples, the proposed method has higher computational efficiency with the equivalent accuracy. When updating a practical continuous box‐girder bridge, the proposed method can efficiently update a large finite element model, and the statistics of updating results agree very well with those of the static measurement data.

This paper presents a Bayesian-based finite element model updating method that integrates static displacement measurements and dynamic modal data to simultaneously identify structural mass and stiffness parameters. By leveraging Bayesian inference, a posterior probability density function (PDF) is constructed by integrating static displacement and modal parameters, thereby effectively decoupling the identification of structural mass and stiffness. The Delayed Rejection Adaptive Metropolis (DRAM) Markov Chain Monte Carlo (MCMC) sampling algorithm is utilized to derive the posterior distributions of the updated parameters. To mitigate the computational burden associated with repetitive finite element (FE) analyses during large-scale MCMC sampling, a Kriging surrogate model is employed to efficiently approximate the time-consuming FE simulations. Numerical examples involving a cantilever beam and an actual concrete three-span single-box girder bridge illustrate that the proposed method accurately identifies simultaneous variations in mass and stiffness at multiple structural locations, effectively addressing parameter coupling and misidentification issues encountered when using either static or dynamic data alone. Moreover, the Kriging surrogate significantly improves computational efficiency. Experimental validation on an aluminum alloy cantilever beam further corroborates the effectiveness and practical applicability of the proposed method.

This paper proposes a new stochastic model updating method to update structural models based on the improved cross-model cross-mode (ICMCM) technique. This new method combines the stochastic hybrid perturbation-Galerkin method with the ICMCM method to solve the model updating problems with limited measurement data and uncertain measurement errors. First, using the ICMCM technique, a new stochastic model updating equation with an updated coefficient vector is established by considering the uncertain measured modal data. Then, the stochastic model updating equation is solved by the stochastic hybrid perturbation-Galerkin method so as to obtain the random updated coefficient vector. Following that, the statistical characteristics of the updated coefficients can be determined. Numerical results of a continuous beam show that the proposed method can effectively cope with relatively large uncertainty in measured data, and the computational efficiency of this new method is several orders of magnitude higher than that of the Monte Carlo simulation method. When considering the rank deficiency, the proposed stochastic ICMCM method can achieve more accurate updating results compared with the cross-model cross-mode (CMCM) method. An experimental example shows that the new method can effectively update the structural stiffness and mass, and the statistics of the frequencies of the updated model are consistent with the measured results, which ensures that the updated coefficients are of practical significance.

The Variational Bayesian Model Updating (VBMU) method employs a variational approach to approximate the posterior distribution of model parameters using a proposal distribution. However, in practical engineering applications, the true posterior distribution of model parameters is often highly complex, multi-modal, and non-Gaussian, making it difficult to approximate accurately using parametric distributions with limited flexibility. To address these challenges, this study proposes a non-parametric variational Bayesian model updating method based on normalizing flows. By leveraging the bijective and information-preserving nature of normalizing flows, the proposed method establishes an expressive transformation between a simple base distribution and a complex target distribution, enabling flexible posterior approximation without sacrificing density tractability. This substantially enhances the expressiveness of the variational posterior, enabling more accurate and efficient posterior inference without the need for manually specifying distribution families or tuning parameter counts. Furthermore, by integrating Approximate Bayesian Computation (ABC) with Gaussian kernel-based Probability Mass Function (PMF) and the intrusive Homotopy Surrogate Model (HSM), an efficiently computable and differentiable Evidence Lower Bound (ELBO) is constructed, which facilitates efficient training of the normalizing flow via stochastic gradient descent type algorithm. The proposed method is validated using a simply supported beam example with a complex, multi-modal parameter distribution, and its performance is benchmarked against the classic VBMU method utilizing the Gaussian Mixture Model (GMM) and an advance Stein Variational Inference method. Finally, the method is applied to update the parameters of a 3 Degree-Of-Freedom (DOF) experimental rig.

Five-hundred-meter Aperture Spherical radio Telescope (FAST) is an important invention in the field of astronomy in China. The active reflector is one of the important components of FAST, which is used to adjust the celestial observation position. This paper is written to address the adjustment problem of the active reflector. The article firstly simplifies the reflecting surface into a two-dimensional model by using the spherical structure characteristic of FAST, and thus establishes the mathematical model of the ideal paraboloid. Secondly, the coordinate system is rotated by using the Rodriguez rotation formula, and the reflecting panel adjustment constraints are taken into account to establish the reflecting panel adjustment model under different azimuth and elevation angles. In this paper, the Particle Swarm Optimization algorithm is also applied to optimize the model so that the working paraboloid is as close as possible to the ideal paraboloid to obtain the best reception effect. This research constructs the working parabolic model of FAST, modifies and optimizes the model to make FAST observes better.