Uncertain Structural Parameters Research Articles

Mechanical analysis for deepwater drilling riser system with structural parameters uncertainty

Uncertain structural parameters increase the mechanical failure risk of the drilling riser system. The effect of uncertain structural parameters on the mechanical characteristics of the drilling riser system is unclear. Therefore, the mechanical characteristics of the drilling riser system with structural parameter uncertainty are analyzed. A mechanical model with uncertain structural parameters is established based on the basic analysis model and the local average theory. The basic analysis model takes into account the combined effects of platform motion, tensioner, riser string, and marine environment. The local average theory is suitable for situations where there is a lack of uncertainty information. A solution approach is proposed using the second-order central perturbation method and the Newmark-β method. The solution method reduces the load by simplifying degrees of freedom and random variables. The correctness of the solution method is verified using the Monte Carlo method. The analysis results indicate that uncertain structural parameters significantly affect the static response, while the dynamic response is less affected. The failure risk due to static axial stress and static shear stress is heightened by uncertain structural parameters. The failure risk arising from static shear stress at the bottom of the riser system experiences a significant increase.

FAST-AlertNet: Early warning fire-induced collapse of large-span steel truss structures

Large-span steel trusses are often adopted as roof structures of public and industrial buildings. Besides significant property loss, the unexpected and sudden collapse of large-span steel trusses caused by fires also threatens the lives of firefighters and trapped people in fires. To prevent casualties to the greatest extent, real-time evaluation of the structural collapse state of the building at fire rescue scenes is critical. This paper presents a novel framework for early warning the collapse of large-span steel truss structures in fire based on proposing the FAST-AlertNet. The FAST-AlertNet can easily obtain real-time displacements based on easily-measured rotations and temperatures of the steel trusses during fire synchronously. Rotations and temperatures, which reflect uncertain structural parameters of steel trusses and fire scenarios, serve as inputs, while displacements are the outputs. A dynamic weighted loss function is employed in the FAST-AlertNet, yielding better performance reflecting the early-warning points than traditional loss functions. To address the high computational cost of obtaining real spatiotemporal patterns of temperature development inside the building in real fire scenes, transfer learning is utilized to transfer the interlinkage among displacements, temperatures, and rotations established by simplified parametric temperature curves, resulting in improved prediction accuracy in reality. A case study demonstrates the availability of the proposed framework, with the predicted remaining pre-collapse time of a typical steel truss satisfactorily matching the real value. Notably, the proposed framework provides a new methodology for early warning building collapse without requiring the difficultly-measured displacements in fire, which advances its feasibility for practical application.

Predictive probability of detection curves based on data from undamaged structures

This paper develops a model-assisted approach for determining predictive probability of detection curves. The approach is “model-assisted,” as the damage-sensitive features are evaluated in combination with a numerical model of the examined structure. It is “predictive” in the sense that probability of detection (POD) curves can be constructed based on measurement records from the undamaged structure, avoiding any destructive tests. The approach can be applied to a wide range of damage-sensitive features in structural health monitoring and non-destructive testing, provided the statistical distribution of the features can be approximated by a normal distribution. In particular, it is suitable for global vibration-based features, such as modal parameters, and evaluates changes in local structural components, for example, changes in material properties, cross-sectional values, prestressing forces, and support conditions. The approach explicitly considers the statistical uncertainties of the features due to measurement noise, unknown excitation, or other noise sources. Moreover, through confidence intervals, it considers model-based uncertainties due to uncertain structural parameters and a possible mismatch between the modeled and the real structure. Experimental studies based on a laboratory beam structure demonstrate that the approach can predict the POD before damage occurs. Ultimately, several ways to utilize predictive POD curves are discussed, for example, for the evaluation of the most suitable measurement equipment, for quality control, for feature selection, or sensor placement optimization.

Non-probabilistic credible set model for structural uncertainty quantification

A non-probabilistic credible set model for uncertainty quantification structural parameters is proposed in this paper. The developed method surpasses the probabilistic uncertainty quantification method and traditional non-probabilistic uncertainty quantification method by providing both the distribution range of uncertain structural parameters and the corresponding credibility for scant samples, thereby reducing the computation time and improving the credibility of the uncertainty quantification process. The average inverse-distance information entropy, the expanded uncertainty and credibility are introduced to establish a one-dimensional non-probabilistic credible set uncertainty quantification procedure. The basic theory of non-probabilistic sets and a correlation analysis of multidimensional uncertain parameters are reviewed. This theory and analysis are used to develop a multidimensional non-probabilistic credible set uncertainty quantification method. The optimal non-probabilistic set is searched to determine the local coordinate system. The multidimensional uncertainty quantification is subsequently transformed to a one-dimensional uncertainty quantification. A civil aircraft wing structure case, a stiffened plate case and a dynamic case are utilized to verify the feasibility of applying the developed method to various engineering problems.

Reliability-based structural assessment of historical masonry arch bridges: The case study of Cernadela bridge

Nowadays, several historical masonry arch bridges present a deficient state of conservation due to degradation processes induced by natural or human actions. Usually, these constructions have significant economic, cultural, and heritage value. Therefore, they shall be thoroughly assessed to verify their structural integrity and safety condition. For this purpose, reliability-based structural assessments are typically performed. However, the associated outcomes (i.e., reliability index and probability of failure) highly rely on the accuracy of the structural parameters uncertainty quantification. This work presents a study regarding the influence of the scattering of the arches' thickness dimensions in the load-carrying capacity assessment of the Cernadela Bridge, a historical stone bridge located in Galicia, Spain. The study first involved a comprehensive experimental campaign to characterize the outer and inner bridge geometry through geomatic techniques, i.e., terrestrial laser scanning and ground penetrating radar. Subsequently, a limit analysis model was developed, considering only the arches' outer (visible) data. From this initial structural assessment, a reliability index of 2.38 was obtained. The influence of the uncertain structural parameters, both geometric features and material properties, in the collapse load was investigated through a global variance-based sensitivity analysis (i.e., Sobol' indices) complemented by a surrogate modeling strategy based on the Kriging approach. Finally, the measured inner geometry of the arches was introduced in the computational model through Bayesian inference procedures. Thus, two new structural assessments were performed: first, by considering the updated distributions of all arches thicknesses, and second, by considering only the updated distributions of the non-influential ones. Reliability indexes of 1.51 and 2.33 were derived, thus highlighting the importance of a proper uncertainty quantification process and the relevance of the sensitivity analysis outcomes to identify the critical parameters on the bridge mechanical response.

ND testing and establishing models of a multi-span masonry arch bridge

The Olla bridge, built in the second half of the nineteenth century, is an arch bridge consisting of five brick masonry arches with stone masonry piers. The bridge crosses the Stura river along the State Route SS 21, connecting the French border with the South-West part of the Piedmont region, and still represents a crucial node for the local commercial traffic. The paper summarises selected results of the extensive research programme carried out to assess the structural conditions of the historic bridge, which exhibited local damage of the arches and diffused surface decay. After a discussion on the common issues arising in the structural assessment of historical infrastructures, the Olla bridge is described and full details are given on the different steps of the investigation: (a) historical research, geomatic survey, on-site visual inspection and limited local tests on materials; (b) operational modal testing and analysis; (c) development of a FE model based on architectural research and selected modelling assumptions; (d) choice of the uncertain structural parameters and identification of the optimal parameters based on the experimentally obtained data.

Influence of uncertainty of structural parameters on the stochastic dynamic response of asphaltic lining dam-foundation systems to non-stationary random seismic excitation

The present work aims toward the effect of uncertain structural parameters on the stochastic dynamic response of an asphaltic lining dam-foundation system subjected to stationary as well as non-stationary random excitation. Uncertain structural parameters of interest are shear modulus and mass density, modeled using the lognormal distribution. The stochastic seismic response of the dam-foundation system to the random loads with uncertain structural parameters is carried out with the Monte Carlo simulation method. The spatial variability of ground motion is considered with incoherence and wave passage effects as stationary as well as non-stationary random excitation. A time-dependent frequency response function is used throughout the study for non-stationary responses. Obtained results indicate that the variability of shear modulus and mass density can be neglected in stochastic dynamic analysis of an asphaltic lining dam-foundation system. Also, it is seen from the results that stationarity is a reasonable assumption for asphaltic lining dams to typical durations of strong shaking.

An Interval Model Updating Method Based on Meta-Model and Response Surface Reconstruction

In this paper, a new interval finite element model updating method is proposed for interval identification of structural parameters based on meta-model and response surface reconstruction. The lower and upper bounds of the uncertain structural parameters are determined by solving the optimization problem which minimizes the difference between the interval of the predicted and measured responses. The response surface models are reconstructed based on the resampling technique for mapping the relationship between a single input and a single output. Then the accurate interval of the responses during the iteration step can be efficiently estimated using the vertex method. Meanwhile, the Gaussian process regression model (GPRM) is constructed as the meta-model to replace the finite element model for calculating the responses of the system to improve computational efficiency. Several numerical and experimental examples are investigated to elucidate the feasibility of the proposed method in the interval identification of structural parameters. Obtained outcomes have demonstrated that the proposed method outperforms many existing approaches in the literature, especially for the nonlinear monotonously non-increasing problem.

A credible interval analysis method for uncertain structures under nonprobabilistic framework

In this paper, a novel credible structural interval analysis method is proposed. Traditionally, nonprobabilistic uncertainties are modeled as interval or convex models, and no description of their credibility is given. Based on credible nonprobability uncertainty theory, the credible interval and ellipsoid are quantified to model irrelevant and relevant uncertain structural parameters. An efficient adaptive kriging (EAK) method is developed to solve the interval dynamic responses of structures with credible intervals and ellipsoids. In contrast to existing propagation methods, the proposed EAK method shares the samples of different time steps to improve the computational efficiency. A numerical example and two engineering applications are used to show the validity, accuracy and efficiency of the proposed method. Comparisons show that the proposed method can effectively calculate interval dynamic responses with credibility and is competitive when addressing nonlinear or coupled structural systems.

Nonstationary random vibration analysis of structures with uncertain parameters based on a polynomial dimensional decomposition

AbstractBased on polynomial dimensional decomposition (PDD), a novel method for analysing nonstationary random vibration of structures with uncertain parameters is proposed in this paper. The uncertain structural parameters are assumed to be independent random variables, with certain types of probability distributions; thus, the nonstationary random vibration responses of the structures become stochastic functions of these uncertain parameters. A dimensional decomposition and Fourier expansion were applied to calculate the statistical characteristics of the nonstationary random vibration responses of the structures. To calculate the conditional power spectral density (CPSD) and conditional standard deviation (CSD) of the nonstationary random vibration responses, CPSD and CSD were explicitly expressed using expansion coefficients and polynomial basis. Subsequently, the probability distributions of the structural responses can be effectively calculated in terms of these explicit expressions. Dimension‐reduction integration and Gauss numerical integration were applied to calculate expansion coefficients. The validity of the proposed method was verified by numerical examples, including a single‐degree‐of‐freedom system and a multi‐degree‐of‐freedom system (reinforced concrete shear wall). The results indicate that the proposed method is as accurate as Monte Carlo simulation (MCS), whereas the proposed method requires considerably smaller number of nonstationary random vibration analyses than MCS. Moreover, the nonstationary random vibration analysis of a long‐span cable‐stayed bridge demonstrates that the proposed method is feasible for quantifying the uncertainties of the nonstationary random vibration responses of complex engineering structures with uncertain parameters.

Simultaneous layout and size optimization of nonlinear viscous dampers for frame buildings under stochastic seismic excitation

Viscous dampers, as effective energy-dissipation devices, have been widely used for seismic mitigation of building structures. Due to the intrinsic uncertainties of structural parameters and earthquake ground motions, to obtain an optimal performance of structural control, the stochastic design optimization of viscous dampers for buildings is essential. This paper establishes a new dynamic reliability-based optimization framework to address the simultaneous layout and size design of nonlinear viscous dampers in frame buildings, considering the dual randomness of both nonstationary seismic excitations and uncertain structural model parameters. Firstly, a mixed integer optimization problem for nonlinear viscous dampers, including discrete and continuous design variables, is formulated, and the design target is to minimize the cost of the dampers subjected to performance constraints on dynamic reliability of building structures. Then, sequential approximate mixed integer programming with trust region is proposed to solve the optimization problem. Moreover, direct probability integral method is suggested to assess the dynamic reliability and its sensitivity with respect to design variables. Finally, accounting for both stochastic nonstationary seismic excitations and random structural parameters, the optimized results of two numerical examples indicate that the proposed method is a competitive choice for realizing the layout and size optimization of limiting types of nonlinear viscous dampers in frame buildings. To ensure the same target performance of buildings in terms of the probability of exceeding the target value of inter-story drift, the larger peak ground acceleration of stochastic ground motions is, the more cost of dampers is required for seismic protection of buildings.

Reliability-based optimization of structural topologies using artificial neural networks

In this paper, a topology optimization approach is presented, where uncertain load and uncertain material parameters are considered. The concept of compliance minimization, i.e., stiffness maximization, is applied based on a plane stress finite element formulation. In order to take uncertain structural load parameters and uncertain material behavior into account, the topology optimization is embedded into a reliability-based design optimization approach. Uncertain structural parameters and design variables are quantified as random variables, intervals and probability boxes (p-boxes). This allows to consider aleatory and epistemic uncertainties by means of polymorphic uncertainty models within the topology optimization. Solving optimization problems with random variables, intervals and p-boxes leads to a high computational effort, because the objective functions and constraints have to evaluated millions of times. To speed up the optimization process, the finite element simulation of the topology optimization is replaced by artificial neural networks. This includes the topology dependent maximal stresses and displacements of the structure, which are used as constraints, and also the material density distribution inside the design domain. The reliability-based optimization of structural topologies approach is applied to a cantilever structure and a single span girder.

Stochastic Buffeting Analysis of Uncertain Long-Span Bridge Deck with an Optimized Method

The buffeting analysis of an uncertain long-span bridge deck was carried out in this paper. Due to the effect of strong spatial correlation of wind excitation, it should be assumed as partially coherent multiple excitations. The following includes a theoretical formula for the buffeting analysis of a long-span bridge deck with uncertain parameters, which was achieved mainly by a combination of the stochastic pseudo excitation method (SPEM) and response surface method (RSM). The SPEM-RSM was firstly applied to deal with the complicated spectral density function matrix of wind excitation. The buffeting response of the bridge deck was then calculated and verified by the results from the Monte Carlo simulation (MCS). The efficiency and applicability of the hybrid method for strong spatial correlation was proved. After the comparison, the effect of uncertain structural parameters and wind speed on the buffeting performance of the bridge deck were computed. The results showed that the whole uncertainties essentially affected the buffeting response of the deck. The uncertain wind speed played the most significant role in the vertical and lateral motion of the deck. The joint influences between structural uncertainties and uncertain wind speed further affect the random characteristics of the responses. Finally, the effects of different wind speed and wind angle of attack on the aerodynamic performance of the bridge are examined. The variance of the responses increased with the development of wind speed. The effect of different attack angles on the buffeting responses was significant.

Series System Reliability of Uncertain Linear Structures under Gaussian Excitation by Cross Entropy–Based Importance Sampling

We present an adaptive importance sampling (IS) method to estimate the reliability of linear structures with parameter uncertainties that are subjected to Gaussian process excitation. Structural failure is defined as a union of multiple first-passage failure events. The main contribution is the introduction of an efficient IS density for the uncertain structural parameters. This density is determined by minimizing the cross-entropy (CE) between the theoretically optimal IS density of the structural parameters and a chosen parametric family of probability distributions. The CE minimization procedure requires evaluation of the system failure probability conditional on fixed values of the uncertain parameters. A closed-form analytical approximation of this conditional failure probability was derived based on an upper bound on the out-crossing rate. Finally, a joint IS density of the random excitation and the uncertain structural parameters was introduced to estimate the series system failure probability involving parameter uncertainties. The accuracy and efficiency of the proposed method was demonstrated by means of two examples: a Gaussian white noise–excited two-story linear shear frame; and a six-story, three-bay moment-resisting steel frame subjected to a filtered nonstationary Gaussian excitation.

Non-Probabilistic Structural Reliability Analysis Integrating the PSO and the Kriging Model

In view of the problems with implicit performance functions and limited experimental data in the reliability analysis of complex structures, a non-probabilistic reliability method combining the particle swarm optimization (PSO) with the Kriging model was presented. A multidimensional ellipsoid was first used to characterize the uncertain parameters of structures. The Kriging model was then constructed for the implicit performance function, wherein its optimal related parameters was determined through the PSO. Based on the proposed model the reliability analysis was explicitly conducted. The results of 3 numerical examples show that, the proposed method is of effectiveness and feasibility, and has higher accuracy and efficiency than those based on the traditional Kriging model.

Prediction of Squeal Instabilities of a Finite Element Model Automotive Brake With Uncertain Structural and Environmental Parameters With a Hybrid Surrogate Model

Abstract This study focuses on the prediction of the stability behavior of an industrial automotive brake system under structural and environmental uncertainties. Uncertainties are modeled with a random distribution or an interval and are propagated with a hybrid surrogate model associating polynomial chaos and kriging. The objective is to create a surrogate model of each eigenvalue computed with the complex eigenvalue analysis (CEA). As the modes can be tracked only when unstable, the effective size of the training sets can become extremely small. Despite this limitation, it is shown the hybrid meta-model is still able to predict the stability of the brake system. Moreover, the hybrid meta-model gives a direct access to the mean and variance of the eigenvalues with respect to the design parameters without any additional Monte Carlo simulations (MCS). By considering different probability density function for the friction coefficient, it is shown it has a high influence on the stability and the latter should be accurately estimated.

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

Metamodel-based state-dependent fragility modeling for Markovian sequential seismic damage assessment

Accurate characterization of seismic damage accumulation is crucial to reliable seismic risk assessment. Emerging research efforts have been devoted to state-dependent fragility modeling considering the impact of sequential earthquake excitations so as to better inform the management of structure and infrastructure assets. However, the current state-dependent fragility models largely rely on simple functional forms conditioned on only a scalar ground motion intensity measure (IM); fragility models are separately developed for different state-transition scenarios, without any joint modeling mechanism to preserve the multivariate nature among the different damage states; and the lack of parameterization further hinders these models from offering pertinent fragility estimates for structural portfolios with uncertain structural parameters. By leveraging advanced ground motion selection and machine learning techniques, this study proposes a novel metamodel-based state-dependent fragility modeling approach that offers superior parameterization and damage classification capability and can be seamlessly integrated into the Markovian sequential seismic damage assessment (SSDA) framework. The proposed fragility modeling approach features a systematic sequential dynamic analysis procedure that leverages efficient experimental design and hazard-consistent ground motion selection to sufficiently cover the feature space, and an artificial neural network (ANN) classification model conditioned on one-hot encoded initial damage states along with other earthquake and structure-related predictors. Based on generic inelastic single-degree-of-freedom (SDOF) systems with varying structural configurations, damage state classification performance of the proposed fragility model is thoroughly evaluated, and its applicability within the Markovian SSDA framework is elaborated and discussed.

Cross entropy-based importance sampling for first-passage probability estimation of randomly excited linear structures with parameter uncertainty

We propose an efficient importance sampling (IS) method for estimating the first-passage probability of linear structures with uncertain parameters and subjected to Gaussian process excitations. The method evaluates the reliability through integrating the conditional first-passage probability given the uncertain structural parameters. We develop an adaptive IS strategy to efficiently perform this integration based on an IS density that is constructed using the cross entropy (CE) method. The CE method determines the IS density by adaptively minimizing the Kullback–Leibler divergence between the theoretically optimal sampling density and a chosen parametric family of probability distributions. The CE optimization problem is solved for a series of target densities that gradually approach the optimal IS density of the structural parameters. To define the intermediate densities, a smoothening of the conditional first-passage probabilities is employed. Once the IS density of the uncertain structural parameters is obtained, an effective IS density of the random excitations conditional on the structural parameters is introduced to estimate the failure probability of the structure. Unlike other tailored methods for solving this problem, the proposed IS approach does not require any prior analysis of the dynamic system and can be applied as a black-box method. Numerical examples demonstrate that the proposed method can calculate the first-passage probability with remarkable efficiency.

Model-Based Probabilistic Inversion Using Magnetic Data: A Case Study on the Kevitsa Deposit

Structural geological models are widely used to represent relevant geological interfaces and property distributions in the subsurface. Considering the inherent uncertainty of these models, the non-uniqueness of geophysical inverse problems, and the growing availability of data, there is a need for methods that integrate different types of data consistently and consider the uncertainties quantitatively. Probabilistic inference provides a suitable tool for this purpose. Using a Bayesian framework, geological modeling can be considered as an integral part of the inversion and thereby naturally constrain geophysical inversion procedures. This integration prevents geologically unrealistic results and provides the opportunity to include geological and geophysical information in the inversion. This information can be from different sources and is added to the framework through likelihood functions. We applied this methodology to the structurally complex Kevitsa deposit in Finland. We started with an interpretation-based 3D geological model and defined the uncertainties in our geological model through probability density functions. Airborne magnetic data and geological interpretations of borehole data were used to define geophysical and geological likelihoods, respectively. The geophysical data were linked to the uncertain structural parameters through the rock properties. The result of the inverse problem was an ensemble of realized models. These structural models and their uncertainties are visualized using information entropy, which allows for quantitative analysis. Our results show that with our methodology, we can use well-defined likelihood functions to add meaningful information to our initial model without requiring a computationally-heavy full grid inversion, discrepancies between model and data are spotted more easily, and the complementary strength of different types of data can be integrated into one framework.