Time-variant Reliability Analysis Research Articles

Efficient time-variant reliability analysis of Bazimen landslide in the Three Gorges Reservoir Area using XGBoost and LightGBM algorithms

The Three Gorges Reservoir Area (TGRA) is one of the most important areas for landslide prevention and mitigation in China. Rational reliability analysis of reservoir slope stability is a significant prerequisite for designing mitigation measures and preventing landslide disasters. Due to the influences of periodic reservoir water level fluctuation and seasonal rainfall, the reservoir slope reliability may be varying with the external environment. Although geotechnical reliability analysis has been widely applied, how to evaluate the time-variant reliability accurately and efficiently is still a challenging task. This study develops an efficient time-variant reliability analysis approach by integrating the advanced machine learning algorithms of extreme gradient boosting (XGBoost) and light gradient boosting machine (LightGBM). The proposed approach is applied to a practical case adapted from Bazimen landslide in the TGRA. The performances of XGBoost and LightGBM in the evaluation of Bazimen landslide time-variant failure probability are systematically explored. Results show that the proposed approach can evaluate the time-variant failure probability of Bazimen landslide accurately and efficiently, addressing the prohibitive computational cost of conducting a large number of deterministic analyses at each time instant repeatedly. This greatly facilitates the acquisition of time-variant failure probability for geotechnical engineers in practical applications.

Time-variant reliability analysis of underground structures against delayed failure based on the probability density evolution method

The unpredictable delayed failure of underground tunnels may occur after excavation due to the time-dependent behavior of surrounding rock mass, which brings a new consideration to the reliability evaluation of underground structures. In this study, a time-variant reliability analysis procedure via the probability density evolution method (PDEM) is proposed for underground tunnels against delayed failure. The creep-damage theory is introduced to model the time-dependent behavior of rock materials. A new energy-based stability criterion is developed to identify the structural delayed failure. By applying the PDEM with the absorbing boundary condition, the time-varying reliability of underground structures can be obtained. The proposed procedure is applied to a case study involving the deep tunnel with uncertain material parameters. Numerical results demonstrate that the inherent variability of rock properties could result in the large fluctuation of structural delayed responses, which has a significant influence on the time-varying reliability of the tunnels.

An adaptive PC-Kriging method for time-variant structural reliability analysis

The practical application of time-variant reliability analysis is limited by its computationally expensive models which describe the structural system behavior. This paper presents a new adaptive PC-Kriging (APCK) approach to accurately and efficiently assess the time-variant reliabilities. Time interval is firstly discretized with a series of time instants and then the stochastic process is reconstructed by standard normal random variables and deterministic function of time. PC-Kriging (PCK) models are built at each time instant to predict the instantaneous responses of performance function. To improve the accuracy and efficiency, a new update strategy based on the integration of U- and H- learning functions is developed to refine the PCK models of instantaneous responses. One or two best samples are identified by the proposed learning criterion for updating the PCK models. Finally, Monte Carlo simulation (MCS) is used to estimate the time-variant reliability based on the updated PCK models. Four examples are used to validate the accuracy and efficiency of the proposed method.

An estimation variance reduction-guided adaptive Kriging method for efficient time-variant structural reliability analysis

Adaptive Kriging surrogate model is becoming an effective technique to significantly reduce the computational cost for time-variant reliability analysis (TRA). But the existing Kriging adaptive sampling methods for TRA do not consider the correlation between time trajectories and the maximum error-based stopping criterion may be too conservative, both of which will waste some computationally expensive samples. To address the challenges, we propose an estimation variance reduction-guided adaptive Kriging method (VARAK) in this paper. Firstly, we derive the expression for estimation variance of time-variant failure probability and quantify the contribution of a time trajectory to the estimation variance, which includes not only the individual contribution of the time trajectory but also the contribution of correlation between time trajectories. Based on this, the adaptive sampling strategy selects the candidate that has the maximum contribution to the estimation variance as the new training sample, thereby resulting in high efficiency. To accelerate the training approach, the well-known U function is utilized to identify time trajectories with large uncertainty. Moreover, by taking the Kriging prediction uncertainty into account, a new error-based stopping criterion that approximates the relative error between the estimated time-variant failure probability and its expectation is proposed. Since the computation of the proposed stopping criterion may be time-consuming at the initial stage of the adaptive sampling approach, we use the maximum relative error to identify the initial stage and only calculate the stopping criterion after this stage. Four case studies including three numerical examples and an engineering example are presented to demonstrate the good capability and applicability of the proposed VARAK method. The examples illustrate that VARAK can allow the estimated failure probability to converge to the true value at a fast rate with small fluctuations and the procedure can terminate appropriately to avoid oversampling when accuracy is high enough.

Probabilistic analysis of climate change impact on chloride-induced deterioration of reinforced concrete considering Nordic climate

The impact of climate change on the deterioration of reinforced concrete elements have been frequently highlighted as worthy of investigation. This article addresses this important issue by presenting a time-variant reliability analysis to assess the effect of climate change on four limit states; the probabilities of corrosion initiation, crack initiation, severe cracking, and failure of a simply supported beam built in 2020 and exposed to chloride-induced corrosion. The historical and future climate conditions (as projected by three different emission scenarios) for different climate zones in Sweden are considered, including subarctic conditions where the impact of climate change may lead to large increases in temperature. The probabilities of all limit states are found to be: 1) higher for scenarios with higher GHG emissions and 2) higher for southern than for northern climate zones. However, the end-of-century impact of climate change on the probabilities of reaching the different limit states is found to be higher for northern than for southern climate zones. At 2100, the impact of climate change on the probability of failure can reach up to an increase of 123% for the northernmost zone. It is also noted that the end-of-century impact on the probability of failure is significantly higher (ranging from 3.5–4.9 times higher) than on the other limit states in all climate scenarios.

A time-variant reliability analysis framework for selective laser melting fabricated lattice structures with probability and convex hybrid models

ABSTRACT We propose a time-variant reliability analysis framework to quantitatively predict the lifetime of the lattice structures fabricated by selective laser melting (SLM), including confirming hybrid uncertainties, establishing a hybrid model, and proposing an efficient time-variant reliability method. We first design and manufacture a representative and complex L-shaped body-centred cubic (BCC) lattice structure utilising the SLM method, followed by morphology and microstructure observations to indicate the necessity of accounting for material uncertainty. Further considering loading fluctuation, we develop an effective time-variant reliability analysis method utilising the mixed probability and convex set model. One benchmark numerical example has been employed to shed a light on the high computational efficiency and acceptable computational accuracy of the developed time-variant reliability method. Finally, the proposed framework is performed to a real L-shaped BCC lattice structure to predict its lifetime, finding that the failure probability after ten years can reach more than 40 times the initial design.

A unified approach for time-invariant and time-variant reliability-based design optimization with multiple most probable points

Reliability-based design optimization (RBDO) can fulfill performance-based design of static and dynamic structures considering various uncertainties. For time-invariant and time-variant RBDO problems with multiple most probable points (MPPs, also termed as design points), the existing approaches encounter some difficulties in searching for all MPPs and performing time-variant RBDO which requires complicated time-variant reliability analysis. In this paper, the direct probability integral method (DPIM) combining with the change of probability measure (COM), i.e., DPIM-COM approach, is proposed to attack time-invariant and time-variant RBDO problems with multiple MPPs in a unified framework. Firstly, the DPIM in conjunction with Heaviside function is developed to estimate time-invariant and time-variant probabilistic constraints directly and explicitly. Then, an efficient formula for calculating the sensitivity of probabilistic constraints with respect to random design variables is derived based on the DPIM and COM strategy, where the representative points for reliability computation keep unchanged and only the corresponding assigned probabilities need to be updated. Accordingly, the corresponding structural responses of representative points at the current design variables can be reused to evaluate the sensitivity of probabilistic constraints, which saves much computational cost, especially for time-variant RBDO problems. Finally, three numerical examples, including the ten-story building with tuned mass damper under deterministic earthquake ground motion and near-fault stochastic impulsive ground motions, demonstrate the effectiveness and versatility of the proposed DPIM-COM approach for addressing time-invariant and time-variant RBDO problems with multiple MPPs.

Parametric Plots of Limit-State Surfaces as a Design Tool in Time-Variant System Reliability

The ability to accurately determine the temporal safe region in time-variant reliability analysis is seminal for reliability-based design. When stochastic excitations are present and discrete-time approaches are invoked, the errors can be large when one uses only one past safe event (and one new failure event) at each time-step. Furthermore, when all previous safe events are accumulated and used, the calculations can be time consuming and the accuracy not ensured. In this paper, a minimal, or a so-called extreme limit-state, surface is obtained to identify the system temporal safe region in an economical manner. To do this, the limit-state surface motion for each failure mode is recorded as a parametric polar plot that provides both magnitude and relative angle of the vectors from the origin to the most-likely failure points (MLFPs) in standard normal space. The angle differences provide correlation and the magnitude differences provide importance. At the component-level, a few logical policies that compare correlation and the magnitude ensure that the safe region is sufficiently recognized. At the system-level, the temporal average of correlations and the magnitudes at the component-level, along with series or parallel system designations, foretells which failure modes are needed to form the system extreme limit-state surface. The impact of the work includes an immediate recognition of the important failure modes and reduced computation for methods such as multi-normal integration. Case studies of both series-system reliability and parallel-system reliability are presented using structural beams excited by stochastic loads and plagued with degrading material properties and dimensions. The accuracy of the extreme LSS is demonstrated cogently. The use of the polar plots as a design tool becomes evident.

Dynamic response and time-variant reliability analysis of an eight-rod shock isolator

The operation of a warship is commonly affected by shock loads in different directions during sailing in a rough sea, which can decrease the precision of the shipboard equipment. To improve the shock resistance performance of the shipboard equipment, an isolator is usually installed to isolate it from the vibration of the ship deck. The paper proposes a method for dynamic response and time-variant reliability analysis of an eight-rod shock isolator (ERSI). ERSI has a novel symmetrical structure, which can improve the utilization of the isolation rods compared with the classical parallel mechanism. The isolator is modeled using Denavit-Hartenberg (D-H) convention and screw theory. Then, Duhamel integral is employed to derive the dynamic response to the isolator after decoupling the governing equation using the modal analysis method. Considering impacts of uncertain factors, this paper also presents a practical method for time-variant reliability analysis of ERSI. Finally, a discussion of the practical example of this method along with a detailed analysis to evaluate the efficiency of the proposed method is presented.

A review and assessment of importance sampling methods for reliability analysis

This paper reviews the mathematical foundation of the importance sampling technique and discusses two general classes of methods to construct the importance sampling density (or probability measure) for reliability analysis. The paper first explains the failure probability estimator of the importance sampling technique, its statistical properties, and computational complexity. The optimal but not implementable importance sampling density, derived from the variational calculus, is the starting point of the two general classes of importance sampling methods. For time-variant reliability analysis, the optimal but not implementable stochastic control is derived that induces the corresponding optimal importance sampling probability measure. In the first class, the optimal importance sampling density is directly approximated by a member of a family of parametric or nonparametric probability density functions. This approximation requires defining the family of approximating probability densities, a measure of distance between two probability densities, and an optimization algorithm. In the second class, the approximating importance sampling density has the general functional form of the optimal solution. The approximation amounts to replacing the limit-state function with a computationally convenient surrogate. The paper then explores the performances of the two classes of importance sampling methods through several benchmark numerical examples. The challenges and future directions of the importance sampling technique are also discussed.

On High-Dimensional Time-Variant Reliability Analysis with the Maximum Entropy Principle

The structural reliability analysis suffers from the curse of dimensionality if the associated limit state function involves a large number of inputs. This study develops a reliability analysis method that deals with high-dimensional inputs over time. The probability distribution of the structural response is reconstructed by the maximum entropy principle which is achieved by solving an optimization problem derived from the concept of relative entropy. The optimization problem is transformed into a convex one with respect to the orders of fractional moments and the Lagrange multipliers. Additionally, considering the associated computational issues, it is reformulated with side constraints on the parameters of the maximum entropy distribution. Then, a global optimization procedure is performed. The proposed method is successfully applied to the reliability analysis of a linear and a nonlinear structural system, which involves a large number of inputs deriving from the discretization of the input random processes.

Time-variant reliability analysis using moment-based equivalent Gaussian process and importance sampling

Time-variant reliability analysis using moment-based equivalent Gaussian process and importance sampling

A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification

This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the cross-correlation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model, through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.

Time-Variant Reliability Analysis Method for Uncertain Motion Mechanisms Based on Stochastic Process Discretization

The reliability of a motion mechanism is affected by corrosion, wear, aging and other components’ performance degradations with the extension of service time. This paper tackles this problem by proposing a time-varying reliability analysis method for uncertain motion mechanisms. First, a model of motion mechanism error is constructed by assessing the difference between actual and expected motion. A time-varying reliability analysis method for a motion mechanism is proposed. The time-varying performance function is discretized into several static performance functions, which are further approximated with several normal variables. Then, the correlation coefficient matrix and probability density function of these normal variables are calculated, and the time-varying reliability of a motion mechanism is obtained via high-dimensional Gaussian integration. The study demonstrates that the proposed method successfully transforms the time-varying reliability problem into several time-invariant reliability problems for analysis, and handles the time-varying reliability problem of a nonlinear motion mechanism involving random variables and stochastic processes, and significantly increases the computational efficiency. Finally, the proposed method’s effectiveness is verified by two numerical examples and one practical engineering problem.

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.

Variational Bayesian inference-based polynomial chaos expansion: Application to time-variantreliability analysis

In the time-variant systems, random variables, stochastic processes, and time parameter are regarded as the inputs of time-variant computational model. This results in an even more computationally expensive model what makes the time-variant reliability analysis a challenging task. This paper addresses the problem by presenting an active learning strategy using polynomial chaos expansion (PCE) in an augmented reliability space. We first propose a new algorithm that determines the sparse representation applying statistical threshold to determine the significant terms of the PCE model. This adaptive decision test is integrated into the variational Bayesian method, improving its accuracy and reducing convergence time. The proposed method uses a composite criterion to identify the most significant time instants and the associated training points to enrich the experimental design. By simulations, we compare the performance of the proposed method with respect to other existing time-variant reliability analysis methods.

Probabilistic method for time-varying reliability analysis of structure via variational bayesian neural network

This study proposes a novel framework computing the dynamic reliability and associated uncertainty quantification of structures under time-varying excitation with significantly reduced time complexity. For this purpose, the deep neural network’s power and the Bayesian theory’s probabilistic ability are leveraged, forming a Bayesian neural network data-driven model (BNN). The BNN-based surrogate model can yield a probability distribution of outputs of interest, e.g., a limit state function and its derived statistics such as median value, confidence interval rather than only a deterministic quantity. The effectiveness and correctness of the proposed method are reaffirmed via three case studies involving examples from the literature and a 3D numerical model of a prestressed reinforced concrete bridge structure, showing a reduction in time complexity up to three orders of magnitude compared to the Monte Carlo method only using finite element models. As a result, an 11-year maintenance routine is recommended for a marine and chemically aggressive environment to ensure the high reliability of prestressed bridge structures when accounting for uncertainty estimation.

A time-varying mechanical structure reliability analysis method based on performance degradation

In mechanical engineering, most mechanical structural systems are composed of many parts, so their structures are complex. When a mechanical structure fails, it is generally caused by various failure modes. When designers want to improve the quality of mechanical products in the design of mechanical products, reliability analysis can play an important role. It is indispensable in the design and manufacture of mechanical products, engineering use, repair and maintenance. Research on time-varying reliability of mechanical structures is of great significance in improving the quality of mechanical products and bringing more economic benefits to engineering. It has received extensive attention in both academic fields and practical engineering applications. This paper takes the time-varying reliability analysis of mechanical structures based on performance degradation as the research topic, focusing on the reliability analysis methods and techniques of mechanical structures such as Gamma degradation process, material P-S-N curve, mixed Copula function, and nested Copula function. The main research content is divided into three parts. (1) The Gamma degradation process and the P-S-N material probabilistic fatigue life curve are used when establishing the strength degradation random model of the mechanical system. It provides the theoretical basis of strength degradation level for time-varying reliability analysis of mechanical structure based on performance degradation. (2) Combine the mixed Copula function and the nested Copula function to establish a comprehensive failure correlation analysis model of the mechanical system. It provides a theoretical basis for failure correlation for time-varying reliability analysis of mechanical structures based on performance degradation. (3) The time-varying reliability analysis of the one-stage gear transmission system in the engineering example is carried out. Researched and analyzed the time-varying reliability of the large and small gears in the one-stage gear transmission system and the mechanical structure of the system itself under the correlation of strength degradation and failure.

On the use of probabilistic and non-probabilistic super parametric hybrid models for time-variant reliability analysis

Due to having a large number of uncertain variables originating from various sources in time-variant reliability problem, the methods for taking account of these uncertainties are of high significance in engineering. In this study, a novel hybrid time-variant reliability model is established based on a probabilistic model and a super parametric convex model. The probabilistic and non-probabilistic parameters can be addressed simultaneously using this model. The stochastic processes are discretized using the expansion optimal linear estimation method to capture the correlation among different time nodes. In addition, the hybrid reliability iteration method is presented to obtain the upper and lower bounds of failure probability simultaneously. Subsequently, a new relaxed reliability iteration method is proposed to solve the hybrid time-variant reliability model. The relaxed method is adopted to ensure the robustness and efficiency of the proposed method. Three examples are discussed to demonstrate the validity and usage of the presented methodology.

Time-Varying Reliability Analysis of Corroded Bridge Cables Based on Fuzzy Failure Criteria

Time-Varying Reliability Analysis of Corroded Bridge Cables Based on Fuzzy Failure Criteria