Reliability Analysis Of Complex Structures Research Articles

Adaptive directed support vector machine method for the reliability evaluation of aeroengine structure

Machine learning methods have been widely applied to structural reliability analysis, due to the excellent performance in modeling precision and efficiency. In this paper, an adaptive directed support vector machine model (ADSVM) is proposed by integrating the adaptive sampling technology (AST) and the developed directed support vector machine (DSVM), to improve the efficiency and accuracy of turbine blade reliability analysis. In the developed method, the AST is adopted to extract high quality samples, in respect of distributed probability density and the distances between sample values and response values. The DSVM was developed by introducing the penalty coefficients for all the slack variables, to improve the modeling accuracy of SVM approach. One numerical example and the reliability analysis of aeroengine high-pressure turbine blade were performed to validate the developed methods. As illustrated in this numerical investigation, the modeling precision of DSVM is improved by alleviating the lag effect of support vector regression. From the comparison of methods, it is demonstrated that the ADSVM has higher accuracy, efficiency and stability in reliability simulations, which are improved by ∼20 % and ∼46.2 %, respectively. The main efforts of this study are to propose a promising approach, ADSVM, for the reliability analysis of complex structures besides turbine blades, which hold the academical significance in enriching and developing mechanical reliability theory.

A novel adaptive Kriging method combining Hessian matrix and an efficient F-scoreβ-based stopping criterion for structural reliability analysis

Reliability analysis of complex structures or highly nonlinear performance functions generate an enormous computational burden and affects computational efficiency. It is crucial to accurately assess structural reliability. However, current methods do not meet the accuracy and efficiency requirements as the complexity and nonlinearity of the model gradually increase. To address these problems, a novel active learning Kriging method combined with a Hessian matrix was proposed for efficient structural reliability analysis. The predicted mean of the Kriging model was used as an element of the Hessian matrix to describe the degree of nonlinearity of the model. Based on the fact that the iterative process is greatly influenced dramatically by the sample points in proximity to the limit state surface (LSS), a candidate sample pool (CSP) is generated, where the sample points located in the vicinity of the LSS with a larger curvature are chosen to add to the design of experiments (DoE). A stopping criterion about F-scoreβ based on the number of the misclassified points is proposed to judge the model fitting effect, which can be used to effectively identify the LSS. Two mathematical cases and two finite element cases were used to illustrate the high accuracy and efficiency of the method, which a novel manner of the nonlinear reliability calculation is provided.

A RBFNN based active learning surrogate model for evaluating low failure probability in reliability analysis

This paper presents a novel active learning surrogate model for estimating low failure probability in the reliability analysis of complex structures based on a radial basis function neural network (RBFNN). The RBFNN surrogate model, which possesses global approximation capability, is constructed by randomly selecting an initial design of experiments (DoEs) from a Monte Carlo Simulation (MCS) population using the minimax distance method. Furthermore, the RBFNN surrogate model is updated by sequentially adding highly representative samples to improve the local prediction accuracy. The highly representative samples are selected using minimax distance method from each level’s failure region of subset simulation (SS), and are further modified by the calculation of actual limit state function (LSF). Consequently, the low failure probability is obtained through an iterative framework that combines SS and RBFNN surrogate model. The proposed approach significantly reduces the number of experiments required, resulting in lower costs and higher efficiency. Three examples are provided to demonstrate the effectiveness and accuracy of the proposed method.

An efficient time-variant reliability analysis strategy embedding the NARX neural network of response characteristics prediction into probability density evolution method

Stochastic response analysis and first-passage reliability evaluation of multi-degree of freedom nonlinear systems subject to non-stationary seismic excitation have been a critical issue in the field of compound random vibrations, yet remain unsolved. This study extends the time-varying reliability analysis method based on the probability density evolution method, making it applicable to the problem of stochastic response analysis and first-passage reliability evaluation of complex engineering structures. To efficiently represent the response of representative samples, a nonlinear autoregressive with exogenous inputs neural network model is introduced in this study. After comparing three different optimization methods, the neural network model based on the Bayesian regularization algorithm is selected as the predictor for the response of complex nonlinear systems, enabling efficient stochastic response analysis and time-varying reliability evaluation. To this end, leveraging the high efficiency of the probability density evolution method, the analysis of time-varying reliability of large-scale structures has been successfully conducted. Furthermore, the proposed method can be easily expanded to dynamic reliability evaluation problems represented by extreme value theory. Three numerical examples are quoted to demonstrate the applicability and advantages of the proposed method in the field of first-passage and extreme-value problems of systems, which are also compared with PCE, SVR, and Kriging. The results from these numerical examples indicate that the proposed method can effectively reduce the required calculational cost for the reliability analysis of complex structures while maintaining high analytical accuracy.

A dynamic Gaussian process surrogate model based on the grasshopper optimization algorithm for non-probabilistic reliability analysis of complex structures

In practical complex engineering structures, the performance function (PF) for reliability analysis is commonly implicit and highly nonlinear. Commonly used surrogate models are appropriate for structural reliability analysis with an implicit PF. However, these methods require hundreds of PF values, which are time-consuming to obtain by adopting numerical analysis, such as finite element analysis (FEA). Therefore, since non-probabilistic reliability analysis does not require a large number of samples, it has great development potential. In this paper, a dynamic Gaussian process (GP) surrogate model based on the grasshopper optimization algorithm (DGP-GOA) is proposed for the non-probabilistic reliability analysis. First, with the help of the scale factor of the convex set model, the non-probabilistic reliability analysis problem is transformed into an unconstrained optimization problem. Second, the DGP-GOA fits the PF by constructing a GP surrogate model with a small dataset. Third, the GOA is used to search for the global optimal solution to obtain a non-probabilistic reliability index. Then, a dynamic retraining strategy is proposed to improve the fitting accuracy and efficiency. The results demonstrate that the proposed method is highly applicable to the non-probabilistic structural reliability analysis of complex engineering structures.

Application of state‐space models with frequency‐dependent uncertainty for efficient reliability analysis of complex structures

AbstractIn this work, we introduce a commonly used framework to model uncertain dynamical systems and adapt it to propagate both parameters uncertainty and model mismatches through a dynamically excited railway bridge system. The approach considers the system inherent uncertainties in the frequency domain and leads to a significant reduction of the computational effort when performing an uncertainty quantification tasks. In an application example the proposed approach is utilized for efficient reliability analysis of the uncertain railway bridge system. The utilized technique allows for an efficient generation of structural responses, and thus enables a fast evaluation of failure probabilities by crude Monte Carlo sampling. Accuracy of the uncertain prediction model is ensured by comparing the failure probabilities with failure probability simulations based on a semi‐analytical Euler‐Bernoulli bridge beam model.

Reliability analysis of complex structures based on Bayesian inference

This paper outlines a logical process based on Bayesian inference to exploit monitoring observations to improve the accuracy in the reliability estimates of civil structures that are retrofitted during their service lives. The proposed approach is particularly effective for complex structures, whose response prediction is affected by structural parameters with significant uncertainty; typical examples are prestressed concrete bridges, heavily influenced by the inherent uncertainties of the material’s creep and shrinkage. The methodology is applied to a real-life complex bridge in Italy, as opposed to academic problems and laboratory tests; the structural model developed for this study includes the original creep law of the Model B3 proposed by Bazant rather than linear approximation or response surfaces. The Bayesian inference is performed using a Markov Chain Monte Carlo (MCMC) method, while the reliability assessment utilises importance sampling (IS) for computational efficiency. The results show the extent to which structural health monitoring (SHM) and Bayesian inference reduce the uncertainty in structural parameters and the prediction of the structural demand. At the same time, they increase structural reliability. Particular attention is given to computational effort, structural modelling and algorithm optimisation.

Structural dynamic reliability analysis: review and prospects

PurposeThe purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.Design/methodology/approachIn this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.FindingsThe numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.Originality/valueThe paper provides a useful reference for further theoretical research and engineering application.

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.

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.

AKSE: A novel adaptive Kriging method combining sampling region scheme and error-based stopping criterion for structural reliability analysis

The reliability analysis of complex structures usually involves implicit performance function and expensive-to-evaluate computational models, which pose a great challenge for the estimation of failure probability. In this paper, an adaptive Kriging-based method is proposed for the efficient estimation of failure probability with high accuracy. Starting from a small set of initial design of experiments (DoE), a Kriging model is constructed and iteratively refined by adding judiciously selected sample points to the DoE. To effectively select more sample points for updating the Kriging model, a new learning function is proposed for the selection of representative samples following the idea of the penalty function method in optimization. Besides, the inclusion of the term that measures the distance between the candidate samples and those in DoE controls the density of samples, and thus enables efficient exploration of the regions of interest. To improve the efficiency of the algorithm, this learning function is integrated with a sampling region scheme to filter out sample points in regions with rather low probability density from the candidate sampling pool. Moreover, a convergence criterion based on the error-based stopping criterion is developed to terminate the learning process at an appropriate stage. Hence, the proposed method is referred to as the Adaptive Kriging method combining Sampling region scheme and Error-based stopping criterion (AKSE). To further explore the possible schemes for the improvement of the proposed method, the combinations of AKSE with a dynamic Kriging method and the bootstrap variance are also investigated. For rare failure events, the Monte Carlo simulation (MCS) in AKSE is replaced by the importance sampling (IS) to establish an improved version of AKSE, namely the AKSE-IS. The performance of the proposed algorithm is evaluated through five numerical examples and the results demonstrate the superior performance of the proposed method both in terms of accuracy and efficiency.

Time-varying reliability analysis of compressor blisk based on particle swash optimization extreme Kriging model

In order to effectively realize the dynamic time-varying reliability analysis of the radial deformation of the aero-engine low pressure compressor, based on Kriging model combined with particle swarm optimization (PSO) and extreme value idea, a particle swarm optimization extremum Kriging model (PSOEKM) method was proposed. Firstly, the analysis principle of PSOEKM method is expounded. Secondly, the modeling idea of PSOEKM method is discussed. Then, the implementation approach of time-varying reliability analysis based on PSOEKM is explored. Finally, taking the aero-engine low pressure compressor blisk as an example, the dynamic reliability analysis is carried out by using PSOEKM. The analysis results show that the reliability is 99.76% when the allowable value of radial deformation of the compressor blisk is 1.594×10-3 m. Compared with the traditional Kriging model and the extreme response surface model, the PSOEKM method has high analysis accuracy and calculation efficiency. The method presented in this paper provides a new research idea for time-varying reliability analysis of complex structures.

Dimensionality reduction-based extremum surrogate modeling strategy for transient reliability analysis of complex structures

To improve the transient reliability analysis of complex structures, dimensionality reduction (DR)-based extremum surrogate modeling strategy (DRESMS) is developed by absorbing the strengths of DR strategy and extremum response surface method (ERSM). In the proposed method, the DR is applied to find the embedding mapping the input data to high-dimensional space which has the potential to improve the transient reliability model, and the ERSM is used to build the regression relationship between input parameters and output response to establish a reliable surrogate model based on capturing dynamic extreme moments. The transient reliability analysis of turbine blisk is performed to verify the approximate accuracy and simulation performance of the proposed DRESMS with the assist of the comparison of methods. As seen in this study, (i) the reliability degree of turbine blisk fatigue life is 0.9939 when the allowable value of fatigue life is 1.7738×103 cycles (subject to 3 sigma levels), and (ii) the developed DRESMS holds advantages of high-modeling efficiency and low-fitting error, and (iii) the DRESMS holds excellent simulation efficiency and simulation precision. The efforts of this study provide the promising DRESMS to solve the transient probabilistic analysis of complex structures with multi-dimensional input parameters, which is significant in monitoring and maintaining complex structures and mechanical systems with the consideration of large-scale parameters.

An Active Learning Polynomial Chaos Kriging metamodel for reliability assessment of marine structures

Metamodel combined with simulation type reliability method is an effective way to determine the probability of failure (Pf) of complex structural systems and reduce the burden of computational models. However, some existing challenges in structural reliability analysis are minimizing the number of calls to the numerical model and reducing the computational time. Most research work considers adaptive methods based on ordinary Kriging with a single point enrichment of the experimental design (ED). This paper presents an active learning reliability method using a hybrid metamodel with multiple point enrichment of ED for structural reliability analysis. The hybrid method (termed as APCKKm-MCS) takes advantage of the global prediction and local interpolation capability of Polynomial Chaos Expansion (PCE) and Kriging, respectively. The U learning function drives active learning in this approach, while K-means clustering is proposed for multiple point enrichment purposes. Two benchmark functions and two practical marine structural cases validate the performance and efficiency of the method. The results confirm that the APCKKm-MCS approach is efficient and reduces the computational time for reliability analysis of complex structures with nonlinearity, high dimension input random variables, or implicit limit state function.

Efficient and Comprehensive Time-Dependent Reliability Analysis of Complex Structures by a Parameter State Model

AbstractA major challenge in a time-dependent reliability analysis is to find a good balance between computational effort, accuracy, and comprehension of the analysis. In this contribution, computa...

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.

Response surface method based on uniform design and weighted least squares for non‐probabilistic reliability analysis

AbstractThe non‐probabilistic reliability theory is a promising methodology for implementing structural reliability analysis in case of scarce statistical data. One of the main obstacles to implement non‐probabilistic reliability analysis is the implication of the limit state function (LSF) for complex structures. This paper aims to establish a surrogate model of the LSF with higher simulation precision, and whereby proposes a response surface method based on the combination of uniform design (UD) and weighted least squares (WLS). At first, the UD method is selected as the sampling method of interval variables to realize the uniform space‐filling of the initial samples, and the sample set is updated by gradually adding the approximate optimal points to increase the sampling density of critical domain. Then, the WLS method is applied to improve the precision of the response surface by adjusting the importance of samples to the function fitting. Finally, a method of constructing sample weights is developed. Two examples are applied to validate the feasibility and efficiency of the proposed method. Results show that the proposed method is effective for non‐probabilistic reliability analysis of complex structures owning to high computational precision and low computational cost in both numerical and case study.

Creep-Based Reliability Evaluation of Turbine Blade-Tip Clearance with Novel Neural Network Regression.

To reveal the effect of high-temperature creep on the blade-tip radial running clearance of aeroengine high-pressure turbines, a distributed collaborative generalized regression extremum neural network is proposed by absorbing the heuristic thoughts of distributed collaborative response surface method and the generalized extremum neural network, in order to improve the reliability analysis of blade-tip clearance with creep behavior in terms of modeling precision and simulation efficiency. In this method, the generalized extremum neural network was used to handle the transients by simplifying the response process as one extremum and to address the strong nonlinearity by means of its nonlinear mapping ability. The distributed collaborative response surface method was applied to handle multi-object multi-discipline analysis, by decomposing one “big” model with hyperparameters and high nonlinearity into a series of “small” sub-models with few parameters and low nonlinearity. Based on the developed method, the blade-tip clearance reliability analysis of an aeroengine high-pressure turbine was performed subject to the creep behaviors of structural materials, by considering the randomness of influencing parameters such as gas temperature, rotational speed, material parameters, convective heat transfer coefficient, and so forth. It was found that the reliability degree of the clearance is 0.9909 when the allowable value is 2.2 mm, and the creep deformation of the clearance presents a normal distribution with a mean of 1.9829 mm and a standard deviation of 0.07539 mm. Based on a comparison of the methods, it is demonstrated that the proposed method requires a computing time of 1.201 s and has a computational accuracy of 99.929% over 104 simulations, which are improvements of 70.5% and 1.23%, respectively, relative to the distributed collaborative response surface method. Meanwhile, the high efficiency and high precision of the presented approach become more obvious with the increasing simulations. The efforts of this study provide a promising approach to improve the dynamic reliability analysis of complex structures.

Probabilistic analysis method of turbine blisk with multi-failure modes by two-way fluid-thermal-solid coupling

This study develops multi-extremum response surface method (MERSM) for the probabilistic analysis of aeroengine turbine blisk with the coexistence of many failure modes by considering two-way fluid-thermal-solid coupling under complex working condition. The mathematical model of MERSM was established with respect to the random input variables of inlet temperature, inlet velocity, density of material, and rotor speed, and the output responses of the maximum values of deformation, stress, and strain. The comprehensive probabilistic analysis of turbine blisk was completed based on MERSM. The results demonstrate that the comprehensive reliability degree of turbine blisk is 0.9944 when the allowable deformation, stress, and strain are 2.6 × 10−3 m, 1.26 × 109 Pa, and 6.75 × 10−3 m/m, respectively. The main factors influencing the comprehensive reliability degree of turbine blisk are rotor speed and gas temperature. The secondary factors are inlet velocity and density of material. As revealed from the comparison of methods, MERSM improves the computational speed and efficiency with the guarantee of accuracy. The efforts of this paper provide a promising approach for the nonlinear transient reliability analysis of complex structures with multi-failure modes and two-way fluid-thermal-solid coupling.

Hybrid perturbation-Galerkin methods for structural reliability analysis

A major challenge in the reliability analysis of complex structures is to determine the response function or surface from which the limit state function can be established and hence the failure probability of the structure can be predicted. The intention of this paper is to propose a new class of hybrid perturbation-Galerkin methods to determine the response function (surface) of the structure. The proposed methods, mainly including single-variable and double-variable approximations, are based on a combination of the perturbation technique and Bubnov–Galerkin projection, where various orders of summation terms of power polynomial expansions are used as the Galerkin trial functions or basis vectors. A series of examples is provided to demonstrate the accuracy and efficiency of the proposed method by comparison with various existing methods. It is found from the numerical examples that with a significantly lower computational effort with respect to the existing reliability methods, very accurate results can be obtained by the proposed methods.