Manual inspection and assessment of structures on a large scale is labour intensive and often infeasible, while data-driven machine learning techniques can fail to identify relevant failure mechanisms and suffer from poor generalization to previously unseen conditions, particularly when limited information is available. We propose a physics-informed variational autoencoder formulation for disentangled representation learning of confounding sources in the measurements with the aim of computing the posterior distribution of latent parameters of a physics-based model and predicting the response of a structure when limited measurements are available. The latent space of the autoencoder is augmented with a set of physics-based latent variables that are interpretable and allow for domain knowledge in the form of prior distributions and physics-based models to be included in the autoencoder formulation. To prevent the data-driven components of the model from overriding the known physics, a regularization term is included in the training objective that imposes constraints on the latent space and the generative model prediction. The feasibility of the proposed approach is evaluated on a synthetic case study.

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A method is introduced for the identification of the nonlinear governing equations of dynamical systems in the presence of discontinuous and nonsmooth nonlinear forces, such as the ones generated by frictional contacts, based on noisy measurements. The so-called Physics Encoded Sparse Identification of Nonlinear Dynamics (PhI-SINDy) builds upon the existing RK4-SINDy identification scheme, incorporating known physics and domain knowledge in three different ways (biases). In this way, it addresses the discontinuous behavior of frictional systems when stick–slip phenomena are observed, which can not be captured by existing state-of-the-art approaches. The potential of PhI-SINDy is highlighted through a plethora of case studies, starting from a simple yet representative Single Degree of Freedom (SDOF) oscillator with a Coulomb friction contact under harmonic load, using both synthetic and experimental noisy measurements. An alternative friction law, namely the Dieterich-Ruina one, is also considered as well as a more realistic excitation time series, which was generated based on the Jonswap spectrum. Lastly, a Multi Degree of Freedom system with single and multiple friction contacts is used as a testbed, showcasing the applicability of PhI-SINDy to more complicated systems and/or multiple sources of discontinuous nonlinearities.

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The application of vibration-based Structural Health Monitoring (SHM) for damage detection is characterised by three fundamental aspects: the features extracted as representative of the structural condition that can be directly linked to some form of damage, the metrics selected as novelty or damage index, and the statistical model or classifier built to identify underlying patterns indicative of changes in the structure's state. Focusing on the first step to improve the performance of vibration-based SHM strategies, the extracted features should be robust to noise, sensitive to the presence of a specific type of damage. Further, damage should induce patterns that are distinguishable from environmental and operational variabilities and other forms of damage such as ageing phenomena. In this paper, the problem is framed as an outlier detection problem and the the use of different modal parameters as Damage Sensitive Features (DSFs) is investigated, evaluating them based on the detection performance of an unsupervised One-Class Support Vector Machine (OCSVM) classifier. In particular, an artificial dataset is generated from the calibrated numerical model of a three-storey steel frame structure in different damage scenarios. The methodology is validated against available experimental data. For the case investigated the natural frequencies were sensitive to damage and robust to noise.

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Often overlooked, vibration transmission through the entire body of an animal is an important factor in understanding vibration sensing in animals. To investigate the role of dynamic properties and vibration transmission through the body, we used a modal test and lumped parameter modelling for a spider. The modal test used laser vibrometry data on a tarantula, and revealed five modes of the spider in the frequency range of 20-200 Hz. Our developed and calibrated model took into account the bounce, pitch and roll of the spider body and bounce of all the eight legs. We then performed a parametric study using this calibrated model, varying factors such as mass, inertia, leg stiffness, damping, angle and span to study what effect they had on vibration transmission. The results support that some biomechanical parameters can act as physical constraints on vibration sensing. But also, that the spider may actively control some biomechanical parameters to change the signal intensity it can sense. Furthermore, our analysis shows that the parameter changes in front and back legs have a greater influence on whole system dynamics, so may be of particular importance for active control mechanisms to facilitate biological sensing functions.

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Several on-line identification approaches have been proposed to identify parameters and evolution models of engineering systems and structures when sequential datasets are available via Bayesian inference. In this work, a robust and “tune-free” sampler is proposed to extend one of the sequential Monte Carlo implementations for the identification of time-varying parameters which can be assumed constant within each set of data collected but might vary across different sequences of datasets. The proposed approach involves the implementation of the affine-invariant Ensemble sampler in place of the Metropolis–Hastings sampler to update the samples. An adaptive-tuning algorithm is also proposed to automatically tune the step-size of the affine-invariant ensemble sampler which, in turn, controls the acceptance rate of the samples across iterations. Furthermore, a numerical investigation behind the existence of inherent lower and upper bounds on the acceptance rate, making the algorithm robust by design, is also conducted. The proposed method allows for the off-line and on-line identification of the most probable models under uncertainty. The proposed sampling strategy is first verified against the existing sequential Monte Carlo sampler in a numerical example. Then, it is validated by identifying the time-varying parameters and the most probable model of a nonlinear dynamical system using experimental data.@en

A self-supervised classification algorithm is proposed for detecting and isolating sensor faults of health monitoring devices. This is achieved by automatically extracting information from failure investigations. This approach uses (i) failure reports for extracting comprehensive failure labels; (ii) recorded data of a faulty monitoring device and the information of the failure type for selecting fault-sensitive features. The features-label pairs are then used to train a classification algorithm, so that when a new set of measurements becomes available, the algorithm is capable of identifying with a high accuracy one of the possible failure types included in the training data set. The proposed approach is successfully applied to the failure investigations conducted on a low-cost wearable device, displaying similar challenges encountered in SHM.

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The friction force at joints of engineering structures is usually unknown and not directly identifiable. This contribution explores a procedure for obtaining the governing equation of motion and correctly identifying the unknown Coulomb friction force of a mass-springdashpot system. In particular, a single degree-of-freedom system is investigated both numerically and experimentally. The proposed procedure extends the state-of-the-art datadriven sparse identification of nonlinear dynamics (SINDy) algorithm by developing a methodology that explicitly imposes constraints encoding knowledge of the nonsmooth dynamics experienced during stick-slip phenomena. The proposed algorithm consists of three steps: (i) data segregation of mass-motion from mass-sticking during stick-slip response; (ii) application of SINDy on the mass-motion dataset to obtain the functional form of the governing equation; and (iii) applying sticking and slipping conditions to identify the unknown system parameters. It is shown that the proposed approach yields an improved estimate of the uncertain system parameters such as stiffness, viscous damping, and magnitude of friction force (all mass normalized) for various signal-to-noise ratios compared to SINDy.

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Virtual sensing techniques have gained traction in applications to the structural health monitoring of monopile-based offshore wind turbines, as the strain response below the mudline, which is a primary indicator of fatigue damage accumulation, is impractical to measure directly with physical instrumentation. The Gaussian process latent force model (GPLFM) is a generalized Bayesian virtual sensing technique which combines a physics-driven model of the structure with a data-driven model of latent variables of the system to extrapolate unmeasured strain states. In the GPLFM, unknown sources of excitation are modeled as a Gaussian process (GP) and endowed with a structured covariance relationship with response states, using properties of the GP covariance kernel as well as correlation information supplied by the mechanical model. It is shown that posterior inference of the latent inputs and states is performed by Gaussian process regression of measured accelerations, computed efficiently using Kalman filtering and Rauch–Tung–Striebel smoothing in an augmented state-space model. While the GPLFM has been previously demonstrated in numerical studies to improve upon other virtual sensing techniques in terms of accuracy, robustness, and numerical stability, this work provides one of the first cases of in-situ validation of the GPLFM. The predicted strain response by the GPLFM is compared to subsoil strain data collected from an operating offshore wind turbine in the Westermeerwind Park in the Netherlands. A number of test cases are conducted, where the performance of the GPLFM is evaluated for its sensitivity to varying operational and environmental conditions, to the instrumentation scheme of the turbine, and to the fidelity of the mechanical model. In particular, this paper discusses the capacity of the GPLFM to achieve relatively robust strain predictions under high model uncertainty in the soil-foundation system of the offshore wind turbine by attributing sources of model error to the estimated stochastic input.

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The design of complex engineering systems is an often long and articulated process that highly relies on engineers’ expertise and professional judgment. As such, the typical pitfalls of activities involving the human factor often manifest themselves in terms of lack of completeness or exhaustiveness of the analysis, inconsistencies across design choices or documentation, as well as an implicit degree of subjectivity. An approach is proposed to assist systems engineers in the automatic generation of systems diagrams from unstructured natural language text. Natural Language Processing (NLP) techniques are used to extract entities and their relationships from textual resources (e.g., specifications, manuals, technical reports, maintenance reports) available within an organisation, and convert them into Systems Modelling Language (SysML) diagrams, with particular focus on structure and requirement diagrams. The intention is to provide the users with a more standardised, comprehensive and automated starting point onto which subsequently refine and adapt the diagrams according to their needs. The proposed approach is flexible and open-domain. It consists of six steps which leverage open-access tools, and it leads to an automatic generation of SysML diagrams without intermediate modelling requirement, but through the specification of a set of parameters by the user. The applicability and benefits of the proposed approach are shown through six case studies having different textual sources as inputs, and benchmarked against manually defined diagram elements.

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The decreasing cost and improved sensor and monitoring system technology (e.g., fiber optics and strain gauges) have led to more measurements in close proximity to each other. When using such spatially dense measurement data in Bayesian system identification strategies, the correlation in the model prediction error can become significant. The widely adopted assumption of uncorrelated Gaussian error may lead to inaccurate parameter estimation and overconfident predictions, which may lead to suboptimal decisions. This article addresses the challenges of performing Bayesian system identification for structures when large datasets are used, considering both spatial and temporal dependencies in the model uncertainty. We present an approach to efficiently evaluate the log-likelihood function, and we utilize nested sampling to compute the evidence for Bayesian model selection. The approach is first demonstrated on a synthetic case and then applied to a (measured) real-world steel bridge. The results show that the assumption of dependence in the model prediction uncertainties is decisively supported by the data. The proposed developments enable the use of large datasets and accounting for the dependency when performing Bayesian system identification, even when a relatively large number of uncertain parameters is inferred.

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An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.@en

Multi-modal distributions of some physics-based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and non-linearity. In statistical model updating, for locally identifiable parameters, it can be anticipated that multi-modal posterior distributions would be found. The full characterization of these multi-modal distributions is important as methodologies for structural condition monitoring in structures are frequently based in the comparison of the damaged and healthy models of the structure. The characterization of posterior multi-modal distributions using state-of-the-art sampling techniques would require a large number of simulations of expensive-to-run physics-based models. Therefore, when a limited number of simulations can be run, as it often occurs in engineering, the traditional sampling techniques would not be able to capture accurately the multi-modal distributions. This could potentially lead to large numerical errors when assessing the performance of an engineering structure under uncertainty. Therefore, an approach is proposed for drastically reducing the number of models runs while yielding accurate estimates of highly multi-modal posterior distributions. This approach introduces a cyclical annealing schedule into the Variational Bayes Monte Carlo (VBMC) method to improve the algorithm's phase of exploration and the finding of high probability areas in the multi-modal posteriors throughout the different cycles. Three numerical and one experimental investigations are used to compare the proposed cyclical VBMC with the standard VBMC algorithm, the monotonic VBMC and the Transitional Ensemble Markov Chain Monte Carlo (TEMCMC). It is shown that the standard VBMC fails in capturing multi-modal posteriors as it is unable to escape already found regions of high posterior density. In the presence of highly multi-modal posteriors, the proposed cyclical VBMC algorithm outperforms all the other approaches in terms of accuracy of the resulting posterior, and number of model runs required.

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A key computational challenge in maintenance planning for deteriorating structures is to concurrently secure (i) optimality of decisions over long planning horizons, and (ii) accuracy of realtime parameter updates in high-dimensional stochastic spaces. Both are often encumbered by the presence of discretized continuous-state models that describe the underlying deterioration processes, and the emergence of combinatorial decision spaces due to multi-component environments. Recent advances in Deep Reinforcement Learning (DRL) formulations for inspection and maintenance planning provide us with powerful frameworks to handle efficiently near-optimal decision-making in immense state and action spaces without the need for offline system knowledge. Moreover, Bayesian Model Updating (BMU), aided by advanced sampling methods, allows us to address dimensionality and accuracy issues related to discretized degradation processes. Building upon these concepts, we develop a joint framework in this work, coupling DRL, more specifically deep Q-learning and actor-critic algorithms, with BMU through Hamiltonian Monte Carlo. Single- and multi-component systems are examined, and it is shown that the proposed methodology yields reduced lifelong maintenance costs, and policies of high fidelity and sophistication compared to traditional optimized time- and condition-based maintenance strategies.@en

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These approaches employ a machine learning based optimization strategy, the so-called Bayesian optimization, for evaluating the upper and lower bounds of a generic response variable over the set of possible responses obtained when each interval variable varies independently over its range. The lack of knowledge caused by not evaluating the response function for all the possible combinations of the interval variables is accounted for by developing a probabilistic description of the response variable itself by using a Gaussian Process regression model. An iterative procedure is developed for selecting a small number of simulations to be evaluated for updating this statistical model by using well-established acquisition functions and to assess the response bounds. In both approaches, an initial training dataset is defined. While one approach builds iteratively two distinct training datasets for evaluating separately the upper and lower bounds of the response variable, the other one builds iteratively a single training dataset. Consequently, the two approaches will produce different bound estimates at each iteration. The upper and lower response bounds are expressed as point estimates obtained from the mean function of the posterior distribution. Moreover, a confidence interval on each estimate is provided for effectively communicating to engineers when these estimates are obtained at a combination of the interval variables for which no deterministic simulation has been run. Finally, two metrics are proposed to define conditions for assessing if the predicted bound estimates can be considered satisfactory. The applicability of these two approaches is illustrated with two numerical applications, one focusing on vibration and the other on vibro-acoustics.

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This work presents an application of the recently-developed Sequential Ensemble Monte Carlo sampler in performing on-line Bayesian model updating for the Prognostics Health Management of a passive component of an Advanced Reactor. The passive component involves a stainless-steel material subjected to a thermal creep deformation whose growth rate is modelled by a continuous piece-wise model consisting of 3 models, each representing a creep-growth stage.

There are 2 investigations done in this research. For the first investigation, the model identification capability of the Sequential Monte Carlo sampler is evaluated in identifying the most probable model for each creep-growth stage. For the second investigation, the on-line Bayesian model updating procedure via the aforementioned sampler is then undertaken. In addition, a method is proposed where the model updating approach will be done for each model sequentially across the different creep-growth stage. This process involves utilising information of the boundary conditions obtained from the model output interval at the transition times to determine the prior bounds for each model parameter to be updated. This method seeks to minimise the discontinuity in the updated piece-wise model at the transition times. From there, the Remaining Useful Life analysis on the component is performed.@en

Fatigue assessment in offshore wind turbine support structures requires the monitoring of strains below the mudline, where the highest bending moments occur. However, direct measurement of these strains is generally impractical. This paper presents the validation of a virtual sensing technique based on the Gaussian process latent force model for dynamic strain monitoring. The dataset, taken from an operating near-shore turbine in the Westermeerwind Park in the Netherlands, provides a unique opportunity for validation of strain estimates at locations below the mudline using strain gauges embedded within the monopile foundation.

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An approach is proposed for the evaluation of the probability density functions (PDFs) of the modal parameters for an ensemble of nominally identical structures when there is only access to a single structure and the dispersion parameter is known. The approach combines the Eigensystem realization algorithm on sets of dynamic data, with an explicit nonparametric probabilistic method. A single structure, either a mathematical model or a prototype, is used to obtain simulated data or measurements that are employed to build a discrete time state-space model description. The dispersion parameter is used to describe the uncertainty due to different sources such as the variability found in the population and the identification errors found in the noisy measurements from the experiments. With this approach, instead of propagating the uncertainties through the governing equations of the system, the distribution of the modal parameters of the whole ensemble is obtained by randomizing the matrices in the state-space model with an efficient procedure. The applicability of the approach is shown through the analysis of a two degrees-of-freedom mass-spring-damper system and a cantilever system. The results show that if the source of uncertainty is unknown and it is possible to specify an overall level of uncertainty, by having access to a single system's measurements, it is possible to evaluate the resulting PDFs on the modal parameters. It was also found that high values of the dispersion parameter may lead to nonphysical results such as negative damping ratios values.@en

This paper aims at assessing the effect of dry friction on the dynamic behaviour of a damped mechanical system subject to harmonic forcing. Previous work on friction damped systems highlighted that not including other forms of damping in the dynamic analysis can lead to unrealistic results such as the presence of infinite resonances. In this contribution, an exact solution is derived for the continuous steady-state response of multi-degree-of-freedom systems with a contact between one of the masses and an external wall, using Coulomb’s law to model the friction force and a modal damping model to account for the system’s damping. Closed-form expressions are also derived for the amplitude and phase of the continuous responses, while stick–slip responses are investigated by using an ad-hoc numerical approach. In addition, analytical and numerical results are used for exploring the features and the motion regimes of the dynamic response, leading to the following conclusions: (i) system’s damping has a limited effect on low- and high-frequency behaviours, on the presence of invariant points and inversions across the transmissibility curves and can therefore be neglected, in non-resonant conditions, in the analysis of structures where dry friction is the main source of dissipation; (ii) when the damping of the system is accounted for in the mechanical models along with Coulomb damping, finite resonant peaks are also obtained in continuous sliding regime and their amplitude decreases linearly with the friction force generated in the contact.@en

Bayesian inference is a popular approach towards parameter identification in engineering problems. Such technique would involve iterative sampling methods which are often robust. However, these sampling methods often require significant computational resources and also the tuning of a large number of parameters. This motivates the development of a sampler called the Transitional Ensemble Markov Chain Monte Carlo. The proposed approach implements the Affine-invariant Ensemble sampler in place of the classical Metropolis–Hastings sampler as the Markov chain Monte Carlo move kernel. In doing so, it allows for the sampling of badly-scaled and highly-anisotropic distributions without requiring extra computational costs. This makes the proposed sampler computationally efficient as a result of having less auxiliary parameters to compute per iteration compared to the standard single particle Transitional Markov Chain Monte Carlo. In addition to such change, an adaptive tuning algorithm is also proposed within the new sampler. This algorithm allows for automatic tuning of the step-size of the Affine-invariant Ensemble sampler. Hence, such proposals not only ensure that the new sampler is “tune-free” for the users, but also improves its robustness by ensuring that the acceptance rate of samples is well-controlled within acceptable bounds. As a result, this approach could be significantly faster compared to standard Transitional Markov Chain Monte Carlo methods on badly scaled and highly skewed distributions, which can be encountered when dealing with complex engineering problems. The proposed sampler will be implemented on 2 benchmark numerical examples of varying complexities to demonstrate its strengths and advantages. In addition, the sampler is validated by investigating its parameter identification capability on an Aluminium Frame using experimental data.

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