Structural Reliability Estimation Research Articles

Efficient reliability analysis of stochastic dynamic first-passage problems by probability density evolution analysis with subset supported point selection

This study introduces a novel point selection procedure for the Probability Density Evolution Method (PDEM) to estimate time-dependent reliability and failure probabilities in dynamic systems under first-passage failure conditions. The method integrates and modifies features of the Subset simulation procedure to adaptively generate dependent sample sets suitable for a reliability analysis by a direct probability integration approach levering PDEM. Performance function assessments are used as weighting factors in the Subset supported Point Selection (S-PS), enhancing the ultimate failure probability estimation accuracy. The presented approach effectively identifies samples in the failure region, particularly benefiting for dynamic systems under stochastic excitation, tested with random dimensions up to 60. It also offers a computationally efficient structural reliability estimation procedure by analyzing full time–history responses. The proposed method provides deeper insights into rare failure events and mechanisms through the visualization of intermediate results. This research presents an advanced framework for estimating structural reliability and understanding critical events in dynamic systems.

Collaborative modeling-based improved moving Kriging approach for low-cycle fatigue life reliability estimation of mechanical structures

To effectively estimate the reliability level of low-cycle fatigue (LCF) life of mechanical structures, a novel method of collaborative modeling-based improved moving Kriging (IMKCM) approach is proposed by fusing improved moving Kriging method and collaborative modeling strategy. In this method, the improved moving Kriging model is developed by the Kriging model, moving least squares method and artificial hummingbird algorithm, in which the Kriging model is selected as the basis function, the artificial hummingbird algorithm is used to define the optimal radius of compact support region and determine the effective modeling samples, and the moving least squares method is adopted to resolve the unknown coefficients; the collaborative modeling strategy is developed from the decomposition and coordination method, in which the mathematical models of the decomposed sub-objectives are synchronously built by the cell array theory, and the mathematical model between the objective and the sub-objectives is established by the improved moving Kriging model. Furthermore, a numerical example (i.e., nested nonlinear function) and an engineering example (i.e., turbine blisk LCF life reliability estimation) are employed to verify the effectiveness of the IMKCM approach. The results show that the proposed IMKCM method holds excellent abilities in modeling features and simulation performance.

Ensemble deep learning enabled multi-condition generative design of aerial building machine considering uncertainties

The Aerial Building Machine (ABM) is a complex construction equipment used in high-rise building construction, facing challenges due to environmental uncertainties. This paper introduces a multi-condition generative design framework to improve ABM's visualization, operability, and intelligence. It seamlessly integrates real-time data between geometric and physical models and employs an ensemble deep learning model for objective value prediction, using a snapshot strategy. Combining structural reliability concepts with Latin hypercube sampling-based stochastic optimization, an optimal design scheme is obtained for uncertain loads. An ABM case study in China illustrates the approach's feasibility, showing it meets reliability requirements across different conditions and achieves significant improvements (16.59% under normal conditions and 16.91% under extreme wind conditions). Additionally, ensemble deep learning outperforms existing methods for ABM structural reliability estimation. Identifying optimal designs and evaluation options, this paper contributes a multi-condition optimization approach for enhanced structural reliability and establishes an efficient generative design workflow and system for exploring a vast solution space.

Modified replica exchange-based MCMC algorithm for estimation of structural reliability based on particle splitting method

We consider the problem of evaluation of the reliability integral when the limit state functions could have complicating features such as (a) discontinuity/rapid changes in values of GU in the space spanned by U, (b) existence of multiple, possibly unimportant, regions of failure with rapid changes in performance function near one or more of the important regions, and (c) multiple regions of failure with substantial contributions to failure probability. We tackle this problem by using the particle splitting framework and introduce an improved Markov chain Monte Carlo sampler based on replica exchange strategy. This is shown to enhance the capacity of samples to detect and explore important regions of failure. The application of the bootstrap technique to deduce the sampling variance of the estimator of the probability of failure is developed. Also given are a few examples of problems in structural mechanics where limit state functions with the aforementioned difficulties arise. The performance of the proposed method in dealing with these difficulties is compared with those of existing methods.

A Data-Fusion Method for Uncertainty Quantification of Mechanical Property of Bi-Modulus Materials: An Example of Graphite

AbstractThe different elastic properties of tension and compression are obvious in many engineering materials, especially new materials. Materials with this characteristic, such as graphite, ceramics, and composite materials, are called bi-modulus materials. Their mechanical properties such as Young’s modulus have randomness in tension and compression due to different porosity, microstructure, etc. To calibrate the mechanical properties of bi-modulus materials by bridging finite element method (FEM) simulation results and scarce experimental data, the paper presents a data-fusion computational method. The FEM simulation is implemented based on parametric variational principle (PVP), while the experimental result is obtained by digital image correlation (DIC) technology. To deal with scarce experimental data, maximum entropy principle (MEP) is employed for the uncertainty quantification (UQ) and calibration of material parameters and responses, which can retain the original probabilistic property of a priori data. The non-parametric p-box is used as a constraint for data fusion. The method presented in this paper can quantify the mechanical properties of materials with high uncertainty, which is verified by a typical example of bi-modulus graphite. It is possible to find applications in the real-time estimation of structural reliability by combining with digital twin technology in the future.

A two-stage dimension-reduced dynamic reliability evaluation (TD-DRE) method for vibration control structures based on interval collocation and narrow bounds theories

Due to the uncertainties from modeling, manufacturing, and working environments, many vibration active control systems usually show dynamic uncertain properties. Hence structural reliability estimation benchmarking to full-cycle vibratory responses is vitally important. In this study, a novel two-stage dimension-reduced dynamic reliability evaluation (TD-DRE) method for linear quadratic regulator (LQR) controlled structures is developed. This method combines interval uncertainties and the time-variant reliability (TVR) concept. In the first stage, the Taylor series expansion is employed to analyze several typical limit states for definition of the time-discretized dynamic reliability. Then the interval collocation method tackles the solution. In the second stage, the TVR problem is indeed transformed to a time-invariant reliability (TIR) problem. Furthermore, the narrow bounds theorem deduces the presented TD-DRE index. Eventually, two application examples are utilized to verify the effectiveness and accuracy of the proposed method. The proposed TD-DRE is more accurate than the traditional first-order Taylor expansion and more effective than the first-passage reliability evaluation method. This method can provide a reference and an initial value for further design, and improve the efficiency of LQR controller design in practical engineering.

Active learning accelerated Monte-Carlo simulation based on the modified K-nearest neighbors algorithm and its application to reliability estimations

This paper proposes an active learning accelerated Monte-Carlo simulation method based on the modified K-nearest neighbors algorithm. The core idea of the proposed method is to judge whether or not the output of a random input point can be postulated through a classifier implemented through the modified K-nearest neighbors algorithm. Compared to other active learning methods resorting to experimental designs, the proposed method is characterized by employing Monte-Carlo simulation for sampling inputs and saving a large portion of the actual evaluations of outputs through an accurate classification, which is applicable for most structural reliability estimation problems. Moreover, the validity, efficiency, and accuracy of the proposed method are demonstrated numerically. In addition, the optimal value of K that maximizes the computational efficiency is studied. Finally, the proposed method is applied to the reliability estimation of the carbon fiber reinforced silicon carbide composite specimens subjected to random displacements, which further validates its practicability.

Assessment of Damage in Composite Pressure Vessels Using Guided Waves.

This paper deals with guided wave-based structural health monitoring of composite overwrapped pressure vessels adopted for space application. Indeed, they are well suited for this scope thanks to their improved performance compared with metallic tanks. However, they are characterized by a complex damage mechanics and suffer from impact induced damage, e.g., due to space debris. After reviewing the limited progress in this specific application, the paper thoroughly covers all the steps needed to design and verify guided wave structural health monitoring system, including methodology, digital modelling, reliability, and noise estimation for a correct decision-making process in a virtual environment. In particular, propagation characteristics of the fundamental anti-symmetric mode are derived experimentally on a real specimen to validate a variety of finite element models useful to investigate wave interaction with damage. Different signal processing techniques are demonstrated sensitive to defect and linearly dependent upon damage severity, showing promising reliability. Those features can be implemented in a probability-based diagnostic imaging in order to detect and localized impact induce damage. A multi-parameter approach is achieved by metrics fusion demonstrating increased capability in damage detection with promising implication in enhancing probability of detection.

Use of Artificial Neural Networks and Response Surface Methodology for Evaluating the Reliability Index of Steel Wind Towers

The estimation of structural reliability is a process that requires a large number of computational hours when statistical data are not available since it is necessary to perform a large amount of analysis or numerical simulations to estimate parameters related to the reliability. A methodology is proposed for estimating the structural reliability index, as well as the demand and structural capacity factors inherent to the structure, given the fundamental vibration period and the height of the structure, by using artificial neural networks (ANN) and, alternatively, the response surface method (RSM). Both approaches are applied to steel wind turbine towers. For the cases studied, ANN allow evaluating the reliability index and both the demand and structural capacity factors with greater accuracy than when using RSM.

Intelligent moving extremum weighted surrogate modeling framework for dynamic reliability estimation of complex structures

To improve the dynamic reliability analyses of complex structures, intelligent weighted Kriging-based moving extremum framework (IWKMEF) is developed by absorbing moving least squares (MLS) thought, Gaussian weight, particle swarm optimization (PSO) method and Kriging model into extremum response surface method (ERSM). ERSM method is employed to convert the dynamic output response into extremum values. MLS thought is used to find effective samples. Gaussian weight is to improve modeling precision. PSO method is applied to optimize the local compact support region radius of MLS. The radial deformation of turbine blisk is conducted to verify the effectiveness of IWKMEF method. The results show that the reliability degree of turbine blisk is 0.9984 when the allowable value is 1.9217 × 10−3 m; The developed IWKMEF holds high performance by comparing direct simulation, ERSM and traditional Kriging model. The efforts of this study provide a useful insight for the dynamic reliability analysis of complex structure.

A novel hybrid adaptive scheme for Kriging-based reliability estimation – A comparative study

Over the past decade, researches on adaptive Kriging-based reliability estimation have been focused on enhancing its performance from three aspects including the simulation methods, learning functions, and stopping criteria, whereas few efforts have been dedicated to give a comprehensive guidance on design of experiment of the initial sampling methods, which directly influences the performance of the surrogate and surrogate-based reliability estimation. This paper presents a comparative study on the adaptive modeling schemes for Kriging-based reliability estimation. Comparison on six common sampling methods for the single step Kriging is conducted with a typical numerical example, to find an optimal initial sampling scheme for the surrogates. A comparative study on the performance of the hybrid adaptive schemes for the adaptive Kriging, each of which includes the initial sampling method, the learning scheme and the corresponding stop criterion, is then implemented on three typical examples, in order to heuristically provide a unique hybrid adaptive scheme for Kriging-based structural reliability estimation. It can synthetically consider the dimension of the input variables, the nonlinearity of the limit-state function and the application scenarios.

Estimation of High Structural Reliability Involving Nonlinear Dependencies Based on Linear Correlations

Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time or spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating nonlinear dependencies thus needs to be addressed based on the linear correlations. This paper first demonstrates the capture of nonlinear dependency by fitting various bivariate non-Gaussian copulas to limited data samples of structural material properties. The vine copula model is used to enable a flexible modeling of multiple nonlinear dependencies by mapping the linear correlations into the non-Gaussian copula parameters. A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. Two examples including a frame structure with different stochastic material properties and a cantilever beam with spatially variable stochastic modulus are investigated to discuss the possible effects of nonlinear dependency on structural reliability. Since the dependency can be determined qualitatively from limited data, the proposed method provides a feasible way for reliability evaluation with prescriptions on correlated stochastic parameters.

Reliability assessment of marine structures considering multidimensional dependency of the variables

For an improved estimation of marine structural reliability, a consideration of random variable dependency is essential. With a limited study on dependence modelling of marine structures, this study proposes a framework for reliability assessment of ocean structural systems with multidimensional variables. This framework captures possible nonlinearity and tail dependence in the variables using vine copula. The proposed method develops a graphical structure of random variables consisting of nodes, edges, and trees using the Drawable Vine (D-vine) approach. This study demonstrates the developed framework on a jacket support structure subjected to the extreme environmental load conditions at Jeanne D′ Arc basin on Canada's east coast. The structure's reliability is evaluated with optimally selected copulas in the D-vine trees and associated marginal distributions. A comparison between the reliability result using the D-vine copula method, Gaussian coupling assumption, and statistical independence between variables proved its superiority in modelling variable dependence of complex marine systems. The probability of failure (Pf) using D-vine copula was closer to the reference Importance Sampling (IS) results than other methods.

Structural dynamic reliability estimation with advanced extremum Kriging method

To enhance the computational performance of the structural dynamic reliability estimation, advanced extremum Kriging method (AEKM) is proposed fusing Kriging surrogate model, multi-population genetic algorithm and response surface method-based extremum thought (ERSM) in this paper. The applicability of the AEKM is verified via the blisk radial deformation dynamic reliability analysis of an aeroengine high-pressure compressor. The results show that the reliability level of the blisk is 0.9956 as the allowable value of radial running deformation 1.75×10−3 m. Moreover, the developed AEKM is superior to other three surrogate models, including ERSM, K-ERSM and IK-ERSM, in terms of computing precision and analytical efficiency. Besides, the analytical precision of the developed method is basically consistent with the direct simulation, and the analytical time is obviously superior to the direct simulation. Therefore, the AEKM is illustrated to be an effective way for structural dynamic reliability analysis, which enriches complex structural reliability theory.

Moving extremum surrogate modeling strategy for dynamic reliability estimation of turbine blisk with multi-physics fields

To improve the dynamic reliability analysis of complex structures like turbine blisk, moving extremum surrogate modeling strategy (MESMS) is proposed in respect of multi-physics coupling with various dynamics/uncertainties. In this strategy, extremum thought is adopted to handle the dynamic process of input parameters and output response, and the importance sampling (IS) method is utilized to extract efficient samples and improve the efficiency of dynamic reliability estimation, and moving least square (MLS) method is used to select good samples from training samples with local compact support region to establish a precise surrogate model. The dynamic reliability analysis of turbine blisk radial deformation with fluid-thermo-structural interaction is performed to validate the developed MESMS in approximate precision and simulation performance by comparing to other methods. As shown in this study, (i) the reliability degree of turbine blisk is 0.9975 when the allowable value of radial deformation is 2.6856 × 10−3 m subject to 3 sigma levels; (ii) the proposed MESMS processes high modeling accuracy and efficiency due to small error; (iii) the MESMS holds high simulation performance in efficiency and accuracy owing to outstanding computational consumption and simulation. These results demonstrate that the MESMS is effective and applicable in structural reliability estimation regarding dynamics and uncertainties. The efforts of this paper provide a useful insight for performing the reliability-based design optimization of complex structures besides turbine blisk.

THE METHOD OF FORMING THE LOWER BOUND OF THE STRUCTURAL RELIABILITY OF THE INFOCOMMUNICATION NETWORK

It is shown in the article, that the tasks of estimation to reliability of infocommunication network (ICN) acquire all greater actuality both in the sphere of planning and during exploitation ICN. Reliability remains one of requirements to ICN, presented in recommendations of the ITU. ICN behave to the structural systems, that is why the special value for ICN acquire the question of estimation of structural reliability. It is marked, that at the calculation of structural reliability ICN most applied is a method that is based on taking into account of totality of ways and cuts, here a structural reliability of network index probability of faultless work of directions of connection, that is used for an information transfer in ICN, is considered. Insufficient scientific of question of determination of lower bound of structural reliability is shown ICN, that determines the assured level of structural reliability of both separate connections and network on the whole. The method for determining the lower bound of the structural reliability of ICN based on the formation of a set of sections is proposed. The idea of the method is based on binary coding of cuts, which leads to a clear formalization of the procedure for constructing a set of cuts in disjunctive normal form and, as a result, to the practical possibility of using the proposed method to determine the lower bound of structural reliability in modern ICN. An example of application of the proposed method is given, which showed the efficiency of the method in comparison with the known method based on the formation of a dual logical function of a set of paths, and then its transformation into a disjunctive normal form to obtain a set of cuts. Further development of this area of work can be: • search for a set of cuts to assess the lower bound of the structural reliability of individual links and the network as a whole for networks with an uncertain topology; • development of approaches to obtaining weighting factors that determine the importance of the lower and upper boundaries of structural reliability, as well as the importance of individual areas of communication.

Structural Reliability Estimation with Participatory Sensing and Mobile Cyber-Physical Structural Health Monitoring Systems

With the help of community participants, smartphones can become useful wireless sensor network (WSN) components, form a self-governing structural health monitoring (SHM) system, and merge structural mechanics with participatory sensing and server computing. This paper presents a methodology and framework of such a cyber-physical system (CPS) that generates a bridge finite element model (FEM) integrated with vibration measurements from smartphone WSNs and centralized/distributed computational facilities, then assesses structural reliability based on updated FEMs. Structural vibration data obtained from smartphones are processed on a server to identify modal frequencies of an existing bridge. Without design drawings and supportive documentation but field measurements and observations, FEM of the bridge is drafted with uncertainties in the structural mass, stiffness, and boundary conditions (BCs). Then, 2700 FEMs are autonomously generated, and the baseline FEM is updated by minimizing the error between the crowdsourcing-based modal identification results and the FEM analysis. Furthermore, using 151 strong ground motion records from databases, the bridge response time history simulations are conducted to obtain displacement demand distribution. Finally, based on reference performance criteria, structural reliability of the bridge is estimated. Integrating the cyber (FEM analysis) and the physical (the bridge structure and measured vibration characteristics) worlds, this crowdsourcing-based CPS can provide a powerful tool for supporting rapid, remote, autonomous, and objective infrastructure-related decision-making. This study presents a new example of the emerging fourth industrial revolution from structural engineering and SHM perspective.

P–S–N Curve Fitting Method Based on Sample Aggregation Principle

Fatigue life tests play a central role in the design of mechanical systems, as the structural reliability estimation depends heavily on the fatigue strength of material, which need to be determined by experiments. The classical statistical analysis, however, can lead to results of limited usefulness when the number of specimens on test is small. Instead, this approach can potentially give more accurate estimates by applying the overall sample at each stress level. For the case of lognormal distribution, equivalent conversion of fatigue life is presented first. Then, P–S–N curve parameters are obtained based on sample aggregation principle. Furthermore, simulation test and experimental test are conducted to validate the proposed method, respectively, demonstrating that this method can sensibly outperform conventional ones. Finally, determination of minimum number of specimens in fatigue testing is presented, which can obtain P–S–N curves with a certain accuracy.

Features of Estimation of Structural Reliability of Power Supply Systems

Development and operation of modern power supply systems of consumers which are the part of distributed generation (DG) systems with their communication with electric power system (EPS) and renewable energy sources (RES) demand changes in estimation of their reliability indicators on the basis of corresponding mathematical apparatus. It is shown that DG systems refer to structures with several overlapping zones of action, which determines their peculiarities, which are represented by some integral characteristic - efficiency of operation, which characterizes the degree of expediency of use of the DG system in different modes. The approach based on evaluation of effectiveness of such systems is offered. Examples of calculation of relatively simple structures of DG systems performing several tasks simultaneously are given.

Reliability evaluation of continuous beam structures using data concerning the displacement of points in a small region

We analyse the impact on the reliability estimation of multi-span beam continuous structures when data about the displacement of the points contained in a small region is considered. The reliability is estimated by using inverse problems techniques combined with a Bayesian method. Some numerical experiments are performed to obtain conclusions concerning the influence of the extension both in time and space for the displacement field observation, as well as the influence of the distance between measurements and crack location on the reliability estimation.