A Computationally-Efficient Probabilistic Approach to Model-Based Damage Diagnosis

This work presents a computationally-efficient inverse approach to probabilistic damage diagnosis. Given strain data at a limited number of measurement locations, Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling are used to estimate probability distributions of the unknown location, size, and orientation of damage. Substantial computational speedup is obtained by replacing a three-dimensional finite element (FE) model with an efficient surrogate model. The approach is experimentally validated on cracked test specimens where full field strains are determined using digital image correlation (DIC). Access to full field DIC data allows for testing of different hypothetical sensor arrangements, facilitating the study of strain-based diagnosis effectiveness as the distance between damage and measurement locations increases. The ability of the framework to effectively perform both probabilistic damage localization and characterization in cracked plates is demonstrated and the impact of measurement location on uncertainty in the predictions is shown. Furthermore, the analysis time to produce these predictions is orders of magnitude less than a baseline Bayesian approach with the FE method by utilizing surrogate modeling and effective numerical sampling approaches.

Bayesian inference for structural damage identification faces prohibitive computational demands due to high-dimensional parameter spaces and repeated evaluations of costly finite element (FE) models during Markov chain Monte Carlo (MCMC) sampling. This study introduces an accelerated Bayesian framework integrating a physics-guided convolutional neural network (PhyCNN) with zero-shot transfer learning to overcome these limitations. The PhyCNN surrogate model embeds fundamental mechanics principles via physics-constrained loss functions, replacing FE simulations to rapidly predict modal parameters for damage states. To address domain discrepancies between simulation (source) and operational (target) environments, an adversarial sparse autoencoder establishes domain-invariant latent representations through sparse feature alignment, enabling training-free adaptation to target tasks. Validated on an experimental three-story frame and a numerical cable-stayed bridge model, the proposed framework achieves an order-of-magnitude computational acceleration over conventional MCMC while maintaining high accuracy. Ablation studies demonstrate that integrating physical constraints reduces damage localization errors by 5.14% compared to purely data-driven models. The methodology’s generality is underscored by its compatibility with diverse sampling-based uncertainty quantification methods and extensibility to systems with computationally intensive likelihoods. By synergizing physics-aware deep learning with cross-domain transfer, this work bridges the gap between simulation-driven training and real-world structural health monitoring, offering a practical pathway for real-time Bayesian diagnostics in large-scale infrastructure.

Context.The characterization of the interior of an exoplanet is an inverse problem. The solution requires statistical methods such as Bayesian inference. Current methods employ Markov chain Monte Carlo (MCMC) sampling to infer the posterior probability of the planetary structure parameters for a given exoplanet. These methods are time-consuming because they require the evaluation of a planetary structure model ~105times.Aims.To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks to calculate the posterior probability of the planetary structure parameters.Methods.Conditional invertible neural networks (cINNs) are a special type of neural network that excels at solving inverse problems. We constructed a cINN following the framework for easily invertible architectures (FreIA). This neural network was then trained on a database of 5.6 × 106internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius, and elemental composition of the host star). We also show how observational uncertainties can be accounted for.Results.The cINN method was compared to a commonly used Metropolis-Hastings MCMC. To do this, we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability distributions of the internal structure parameters from both methods are very similar; the largest differences are seen in the exoplanet water content. Thus, cINNs are a possible alternative to the standard time-consuming sampling methods. cINNs allow infering the composition of an exoplanet that is orders of magnitude faster than what is possible using an MCMC method. The computation of a large database of internal structures to train the neural network is still required, however. Because this database is only computed once, we found that using an invertible neural network is more efficient than an MCMC when more than ten exoplanets are characterized using the same neural network.

This paper presents an enhanced version and the validation of a recently proposed methodology for earthquake-induced damage detection and localization in masonry towers by using long-term vibration monitoring data. The proposed enhanced method is based on continuous operational modal analysis through stochastic subspace identification, dynamic multiple linear regressive analysis to remove the effects of changing environmental conditions and finite element (FE) model updating. Any anomalous frequency deviation from normal conditions resulting from an earthquake triggers the damage localization process. This task is performed by solving an inverse FE model calibration problem, where equivalent elastic properties of macrostructural elements are identified by minimizing an objective function considering experimentally identified and numerically predicted damage-induced decays in natural frequencies and changes in eigenvector components. To minimize the computational effort of this calibration procedure, a quadratic surrogate model is constructed using a tuned numerical FE model of the structure. The methodology is validated through application to the “Sciri Tower”, an historic civic masonry tower located in Perugia, Italy, that has been continuously monitored by the authors for more than 1 year. The validation is carried out by using simulated damage scenarios and a set of real far-field earthquake data and is based on a FE model of the tower including surrounding buildings, calibrated on the basis of the measured data from ambient vibration tests. The results demonstrate that the proposed procedure is capable of correctly detecting and localizing earthquake-induced damages.

Global illumination algorithms using Markov chain Monte Carlo (MCMC) sampling are well-known for their efficiency in scenes with complex light transport. Samples in such algorithms are generated as a history of Markov chain states so that they are distributed according to the contributions to the image. The whole process is done based only on the information of the path contributions and user-defined transition probabilities from one state to the others. In light transport simulation, however, there is more information that can be used to improve the efficiency of path sampling. A notable example is multiple importance sampling (MIS) in bidirectional path tracing, which utilizes the probability densities of constructing a given path with different estimators. While MIS is a powerful ordinary Monte Carlo method, how to incorporate such additional information into MCMC sampling has been an open problem. We introduce a novel MCMC sampling framework, primary space serial tempering , which fuses the ideas of MCMC sampling and MIS for the first time. The key idea is to explore not only the sample space using a Markov chain, but also different estimators to generate samples by utilizing the information already available for MIS. Based on this framework, we also develop a novel rendering algorithm, multiplexed Metropolis light transport , which automatically and adaptively constructs paths with appropriate techniques as predicted by MIS. The final algorithm is very easy to implement, yet in many cases shows comparable (or even better) performance than significantly more complex MCMC rendering algorithms.

Development and calibration of digital twins for human skin growth in tissue expansion.

This article is a review article on the optimal Markov chain Monte Carlo (MCMC) sampling. The focus is on homogeneous Markov chains. This article first reviews the problem of finding the optimal transition matrix, which is defined to minimize the asymptotic variance of MCMC estimators. The article later reviews the locally optimal sampler (LOS), an MCMC sampling that performs local updates based on the optimal transition matrix. We conducted a simulation study to compare the LOS with the Metropolis–Hastings and the Gibbs Sampler. The LOS was shown to provide an improved rate of convergence over these two most popular sampling schemes. The implementation of the LOS requires only minor modifications in existing Gibbs sampling code. WIREs Comput Stat 2013. doi: 10.1002/wics.1265This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

RNA exosomes are large multi-subunit protein complexes involved in controlled and processive 3' to 5' RNA degradation. Exosomes form large molecular chambers and harbor multiple nuclease sites as well as RNA binding regions. This makes a quantitative kinetic analysis of RNA degradation with reliable parameter and error estimates challenging. For instance, recent quantitative biochemical assays revealed that degradation speed and efficiency depend on various factors, such as the type of RNA binding caps and the RNA length. We propose the combination of a differential equation model with Bayesian Markov Chain Monte Carlo (MCMC) sampling for a more robust and reliable analysis of such complex kinetic systems. Using the exosome as a paradigm, it is shown that conventional “best fit” approaches to parameter estimation are outperformed by the MCMC method. The parameter distribution returned by MCMC sampling allows for a reliable and meaningful comparison of the data from different time series. In the case of the exosome, we find that the cap structures of the exosome have a direct effect on the recruitment and degradation of RNA, and that these effects are RNA length-dependent. The described approach can be widely applied to any processive reaction with a similar kinetics like the XRN1-dependent RNA degradation, RNA/DNA synthesis by polymerases, and protein synthesis by the ribosome.

Since the physical structure and mathematical models are more complex, reliability analysis in practical engineering can be expensive and difficult. A two-level multifidelity metamodel method for reliability analysis is introduced. Following the surrogate model in most of the relevant works, low-fidelity data and high-fidelity data are integrated by co-Kriging model. Besides, the co-Kriging model also provide an approximation for initial performance function. Bayesian method is adopted in model solution and a hybrid Markov chain Monte Carlo (MCMC) sampling algorithm is proposed. High-fidelity response of reliability performance function is estimated by the conditional distribution derivation based on Bayesian theory. Failure domain is identified by indicator function in sampling space that consists of samples derived from MCMC. Accordingly, failure probability estimations are obtained using Monte Carlo simulation (MCS). It is demonstrated through an illustrative example that the proposed method is valid and accurate.

The Bayesian framework is commonly used to quantify uncertainty in seismic inversion. To perform Bayesian inference, Markov chain Monte Carlo (MCMC) algorithms are regarded as the gold standard technique for sampling from the posterior probability distribution. Consistent MCMC methods have trouble for complex, high-dimensional models, and most methods scale poorly to large datasets, such as those arising in seismic inversion. As an alternative, approximate MCMC methods based on unadjusted Langevin dynamics offer scalability and more rapid sampling at the cost of biased inference. However, when assessing the quality of approximate MCMC samples for characterizing the posterior distribution, most diagnostics fail to account for these biases. In this work, we introduce the kernel Stein discrepancy (KSD) as a diagnostic tool to determine the convergence of MCMC samples for Bayesian seismic inversion. We demonstrate the use of the KSD for measuring sample quality and selecting the optimal Langevin MCMC algorithm for two Gaussian Bayesian inference problems.

This study investigates the feasibility of an alternative structural health monitoring (SHM) technique for an existing, post-tensioned, prestressed concrete bridge in Niigata, Japan. Currently, a static SHM system is in place to detect the progress of damages within the bridge. However, the existing system cannot properly monitor the structural health of the bridge including the periodic vibration, which is one of the damage-sensitive features of interest. Therefore, to effectively detect the real-time performances of the bridge, a three-dimensional (3D) Finite Element (FE) model was developed as a reference and verified using on-site load-deflection test results. After validating the reference FE model, different damage scenarios, such as degradation of concrete, corrosion & rupture of steel tendons and missing tendons, were incorporated in the FE models. Based on non-linear structural and Eigenvalue analyses, natural frequencies and mode shapes of the bridge remain constant even after careful consideration of all types of damages in the FE model. However, vertical displacements are observed to increase for the damage scenarios. Although the effect of tendon rupture and corrosion showed negligible influences on the vertical displacement, the deterioration of the concrete largely influenced the vertical displacement. Additionally, crack widths were found to vary with damage types. Brifely, this study recommends some effective indicators to monitor the structural conditions of the bridge using FE analysis (FEA).

This chapter provides a brief introduction to the use of Bayesian graphical models in R. In these models, parameters are treated as random quantities on an equal footing with the random variables. This allows complex stochastic systems to modeled, often using Markov chain Monte Carlo (MCMC) sampling methods. We first consider a series of examples, ranging from simple repeated sampling, linear regression models, random coefficient regression models, to the chest clinic example of Chap. 3. We formulate these as Bayesian graphical models, and represent them graphically in a compact form using plates. We then describe a special case, in which the unknown parameters are all discrete, and explain how probability propagation methods described in Chap. 3 may be used to compute the posterior distributions. We then turn to the general case, when MCMC sampling is required, and explain the computations involved in Metropolis-Hastings sampling and Gibbs sampling. Finally we illustrate a Bayesian linear regression analysis using the R2WinBUGS package.

Finite element model updating from full-field vibration measurement using digital image correlation

Bending moment–curvature relations (M-χ) are useful in many beam modelling approaches. It allows describing in a simple way the mechanical behaviour at the cross-section scale and can be used to model continuous beams as single degree of freedom systems dedicated to perform stochastic analysis. This paper focused on tree mechanical charaterisation and presents an identification method for obtaining bending moment–curvature relationships up to failure from Digital Image Correlation (DIC) and experimental three points bending tests. Due to wood intrinsic variability, the proposed identification method has been validated from a Finite Element (FE) model which aims at simulating precisely the bending response of a cylindrical stem. The refined FE model has been developed based on the geometry and the boundary conditions of the experimentally tested stems. M-χ curves are derived from the FE model and used within a Single Degree Of Freedom (SDOF) approach. At the stem scale, the prediction of the SDOF model (Force-Displacement) is compared to the FE model and lead to a good agreement. Then the approach is used to characterise fresh European beech samples allowing deriving their mechanical properties (longitudinal Young modulus, modulus of elasticity and modulus of rupture).

A detailed understanding of the changes in load transfer due to implantation is necessary to identify potential failure mechanisms of orthopedic implants. Computational finite element (FE) models provide full field data on intact and implanted bone structures, but their validity must be assessed for clinical relevance. The aim of this study was to test the validity of FE predicted strain distributions for the intact and implanted pelvis using the digital image correlation (DIC) strain measurement technique. FE models of an in vitro hemipelvis test setup were produced, both intact and implanted with an acetabular cup. Strain predictions were compared to DIC and strain rosette measurements. Regression analysis indicated a strong linear relationship between the measured and predicted strains, with a high correlation coefficient (R = 0.956 intact, 0.938 implanted) and a low standard error of the estimate (SE = 69.53 με, 75.09 με). Moreover, close agreement between the strain rosette and DIC measurements improved confidence in the validity of the DIC technique. The FE model therefore was supported as a valid predictor of the measured strain distribution in the intact and implanted composite pelvis models, confirming its suitability for further computational investigations.