Time-dependent Reliability Analysis Method Research Articles

Time-Dependent Fuzzy Reliability Analysis of Concrete Slab during the Initial Water Storage Period of CFRD: A Case Study

The concrete-faced rockfill dam (CFRD) has been widely constructed worldwide, and the reliability of the concrete panels, the most important containment structure, is critical to the safety of the CFRDs and downstream communities. Several practical projects show that concrete slab cracking usually occurs during the water storage period, which can be attributed to the rapid increase of hydrostatic pressure and uneven settlement of the dam body. In this paper, a time-dependent reliability analysis method considering the fuzziness of the failure criterion is presented to assess the slab cracking risk of the Houziyan CFRD during the water storage period. Based on the observed deformation, the material parameters are calibrated to ensure the fidelity of the numerical simulation. Based on the Drucker–Prager yield criterion and tensile strength criterion, the response surface method is utilized to construct the performance functions at different moments, and then the time-dependent reliability analysis considering the fuzzy failure criteria is implemented for the concrete slab. The case study of the Houziyan CFRD shows that, during the initial period of water storage, the reliability index of the concrete slab decreases with the rise of the water level. With a stable water level, the probability of cracking of the concrete slab slowly decreases as the deformation of the dam body and slab tend to be coordinated. Especially, considering the fuzziness of the failure criteria, the reliability index decreased by about 2%, indicating that the proposed evaluation method is biased toward safety. The method proposed in this paper can reflect the evolution law of concrete slab reliability with the operating environment and provides a new approach to evaluate the performance of the concrete slab during the water storage period.

A novel active learning Gaussian process modeling-based method for time-dependent reliability analysis considering mixed variables

The purpose of time-dependent reliability analysis is evaluating the reliability of a system or component within a specified timeframe. Several approaches have been suggested for addressing time-dependent reliability challenges, including analytical methods and methods based on response surrogate models. As a representative of Machine Learning methods, the Active Learning Gaussian process model has gained more and more popularity in time-dependent reliability analysis. In practical applications, certain uncertainties may not be adequately represented by random variables following deterministic distributions. In contrast, these uncertainties can be easily described by interval variables. This article introduces an innovative method based on Active Learning Gaussian process modeling for time-dependent reliability analysis, encompassing both random and interval variables. The initial step involves transforming stochastic processes into random parameters through spectral decomposition. Moreover, a new sampling strategy to manage mixed uncertainties is proposed, where the candidate samples of mixed variables with positive maximum extreme responses and negative minimum extreme responses are identified. These samples are utilized to construct and renew an extreme Gaussian process model. Lastly, we present an improved confidence-based learning function to accelerate the learning process, which is designed to locate the optimal random input and interval input for updating the extreme Gaussian process model. One mathematical example and two engineering examples are conducted to verify the performance of the proposed method. Results illustrate that our method offers high accuracy while reducing the evaluations of true performance functions in addressing time-dependent reliability issues under mixed uncertainties.

On efficient time-dependent reliability analysis method through most probable point-oriented Kriging model combined with importance sampling

On efficient time-dependent reliability analysis method through most probable point-oriented Kriging model combined with importance sampling

An efficient method for time-dependent reliability problems with high-dimensional outputs based on adaptive dimension reduction strategy and surrogate model

Time-dependent reliability analysis with high dimensional outputs is a challenge because of ‘curse of dimensionality’ and accurate reliability estimation over entire time interval is computationally expensive. In this paper, an efficient time-dependent reliability analysis method is proposed for systems with high dimensional outputs based on adaptive dimension reduction strategy and Kriging. The adaptive Kriging model is constructed in low-dimensional space after performing principal component analysis (PCA) on original time-dependent output. A new learning function and corresponding stopping criterion are developed as the guideline for selecting training samples at each iteration. The proposed learning function focuses on prediction accuracy over the entire time interval and the stopping criterion is directly linked to failure probability. Subsequently, fewer number of function evaluations is required compared with existing competitive works. Moreover, the key advantage of the proposed method is that it is a single-loop process, i.e., the selection of training samples, dimension reduction and Kriging modeling have been combined simultaneously at each iteration with adaptive manner. However, the existing competitive methods, generally, have two independent stages, i.e., stage one is collecting training samples and stage two is performing PCA and Kriging modelling for time-dependent reliability analysis. Thus, these methods cannot fully utilize the information provided by PCA to find optimal training samples. It is noteworthy that the dimension reduction is also an adaptive process in the proposed method, i.e., dimension reduction changes with the training samples at each iteration. The applicability, accuracy and efficiency of the proposed method are validated through three numerical examples and one engineering example.

A time-dependent reliability analysis method based on multi-level meta-models for problems involving interval variables

This paper proposes a new time-dependent reliability analysis method based on a two-level meta-models technique for problems with interval variables, through which the upper and lower bounds of reliability indexes of structures within a given design lifetime period can be obtained efficiently. Firstly, the time parameter, interval and stochastic process parameters in the performance function are transformed into the corresponding random variables. Secondly, the polynomial chaos expansion (PCE) approach is adopted for using an approximate polynomial expression to accurately surrogate the complex original performance function. Thirdly, the Kriging meta-model of time-dependent reliability index about the interval variables is constructed based on the approximate expression, and the upper and lower bounds of the reliability index are calculated with the efficient global optimization (EGO) method. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.

Time-dependent reliability analysis method based on ARBIS and Kriging surrogate model

Time-dependent reliability analysis method based on ARBIS and Kriging surrogate model

Advanced surrogate-based time-dependent reliability analysis method by an effective strategy of reducing the candidate sample pool

Advanced surrogate-based time-dependent reliability analysis method by an effective strategy of reducing the candidate sample pool

Time-Dependent Reliability Analysis of Oil Derrick Structures in Mechanism Failure Mode

Most research studies on the reliability of oil derrick structures have focused on static reliability analysis. Strength degradation with time of oil derrick structures and mechanism failure should also be considered in reliability analysis. In order to address this issue, we propose a new time-dependent reliability analysis method for oil derrick structures in mechanism failure mode and apply it to a tower derrick structure. We used the Monte Carlo finite element method to compute the static failure probability of each derrick component, and steps were employed to determine the main failure mechanisms. The time-dependent failure probabilities of each derrick component in the main failure mechanisms were calculated by the total probability theorem. The time-dependent reliability of a derrick structure system was obtained by considering the system as a series of parallel subsystems. A tower derrick example was used to demonstrate the accuracy and applicability of the proposed method. The results revealed that the proposed method is accurate and reliable.

Developing an improved composite limit state method for time-dependent reliability analysis

Time-dependent reliability analysis remains challenging in practical engineering applications, since the modeling and solution are complicated, resulting in the huge computational burden. The composite limit state (CLS) method can efficiently reduce the computational cost to a certain extent. However, the computational cost is still high. In this article, an improved composite limit state (ICLS) method is proposed for efficient time-dependent reliability analysis, which is based on the original CLS. We propose two enhancements to improve the efficiency of the ICLS approach. First, different from the original method, Kriging surrogate models at all time nodes and one CLS Kriging surrogate model are established in the ICLS method, respectively. In that case, once a new sample is selected, there is no need to evaluate the true limit state function values on the new sample at each time node, leading to a reduction in computational cost. Next, the efficiency is further improved by updating the CLS Kriging surrogate model and the surrogate model at one selected time node simultaneously. Four examples are utilized to demonstrate the efficiency and accuracy of the ICLS method for time-dependent reliability analysis.

Advanced time-dependent reliability analysis based on adaptive sampling region with Kriging model

Aiming at accurately and efficiently estimating the time-dependent failure probability, a novel time-dependent reliability analysis method based on active learning Kriging model is proposed. Although active surrogate model methods have been used to estimate the time-dependent failure probability, efficiently estimating the time-dependent failure probability by a fewer computational time remains an issue because screening all the candidate samples iteratively by the active surrogate model is time-consuming. This article is intended to address this issue by establishing an optimization strategy to search the new training samples for updating the surrogate model. The optimization strategy is performed in the adaptive sampling region which is first proposed. The adaptive sampling region is adjustable by the current surrogate model in order to provide a proper candidate samples region of the input variables. The proposed method employs the optimization strategy to select the optimal sample to be the new training sample point in each iteration, and it does not need to predict the values of all the candidate samples at every time instant in each iterative step. Several examples are introduced to illustrate the accuracy and efficiency of the proposed method for estimating the time-dependent failure probability by simultaneously considering the computational cost and precision.

Kriging Model for Time-Dependent Reliability: Accuracy Measure and Efficient Time-Dependent Reliability Analysis Method

As the performance function of a mechanical structure is usually based on time-consuming computer codes, predicting time-dependent reliability analysis requires a large number of costly simulations in engineering. To reduce the number of evaluations of time-consuming models and enhance efficiency of time-dependent reliability analysis, Kriging is employed as a surrogate of original performance function. Firstly, a quantitative measure of the error of Kriging-based estimation of time-dependent failure probability is obtained by derivation. Dividing the quantitative measure by the Kriging-based estimation, the associated relative error is approximately estimated. Secondly, to construct an accurate Kriging model using fewer samples, a DoE (the design of experiments) strategy is developed. The idea is to adaptively refresh Kriging model with the best next sample that could enhance Kriging model the most with regard to expectation. Finally, a Kriging-based time-dependent reliability analysis method is constructed. In the method, Kriging model is adaptively refreshed according to the proposed DoE strategy, until the relative error of estimated probability of failure below a given threshold. The threshold could be quantitatively adjusted to accuracy requirement of reliability analysis. The proposed method can predict the evolution of failure probability over time. Its advantage is validated by three numerical examples.

A time-dependent reliability analysis method for bearing lubrication

In bearing lubrication, the changes of load, speed, and clearance cause the oil film thickness changes over time. The oil film will rupture when the thickness is insufficient, and the bearing lubrication will fail. In this paper, a novel lubrication reliability estimation method was presented based on the first passage method. The Dowson-Higginson formula was used to calculate the minimum oil film thickness, then the time-dependent reliability was solved by the first passage method (FPM) and first-order reliability method (FORM). The effectiveness of the proposed method was verified by numerical example. This method can be used to analyze the influence of random velocity, load, and time-dependent parameters on lubrication reliability over the whole time domain.

Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis

• A novel active learning and modeling method is proposed for time-dependent reliability analysis. • The real-time estimation error is quantified to measure the prediction accuracy. • A maximum error-guided adaptive refinement strategy is developed to reduce the estimation error. • The propose method is applied to the hydrokinetic turbine blade and self-balancing vehicle. Time-dependent reliability analysis using surrogate model has drawn much attention for avoiding the high computational burden. But the surrogate training strategies of existing methods do not directly consider the estimation error of failure probability, leading to the limitations that some computationally expensive samples are wasted or some algorithms tend to terminate prematurely. To address the challenges, this work proposes a real-time estimation error-guided sampling method. As the classification of random points may be not completely accurate, the wrong-classification probability is calculated by using the mean and variance of Kriging prediction. With this probability, the total numbers of wrongly classified points are obtained. Furthermore, the confidence intervals of the numbers are computed based on the probability theory, and the estimation error of failure probability is calculated through the confidence intervals. Subsequently, the point maximizing the probability is identified as the new sample for decreasing the estimation error, and the maximum error is used to guide when to stop the refinement of Kriging model. Results of three cases demonstrate the performance of the proposed method.

Developing an Instantaneous Response Surface Method t-IRS for Time-Dependent Reliability Analysis

In practical engineering, many uncertain factors in loading or degradation of material properties may vary with time. Stochastic process modeling constitutes a suitable approach for describing these time-dependent uncertainties. By adopting this approach, however, the time-dependent reliability calculation is a great challenge owing to the complexity and the huge computational burden. This paper presents a new instantaneous response surface method t-IRS for time-dependent reliability analysis. Different from the adaptive extreme response surface approach, the proposed method does not need to build and update surrogate models separately at each time node. It first uses the expansion optimal linear estimation method to discretize the stochastic processes into a set of independent standard normal variables together with some deterministic functions of time. Time is then treated as an independent one-dimensional variable. Next, initial samples are generated by Latin hypercube sampling, and the corresponding response values are calculated and utilized to construct an instantaneous response surrogate model of the Kriging type. The active learning method is applied to update the Kriging surrogate model until satisfactory accuracy is achieved. Finally, the instantaneous response surrogate model is used to compute the time-dependent reliability via Monte Carlo simulation. Four case studies are utilized to demonstrate the effectiveness of the t-IRS method for time-dependent reliability analysis.

An active failure-pursuing Kriging modeling method for time-dependent reliability analysis

Abstract Some time-dependent reliability analysis methods use surrogate models to approximate the implicit limit state functions of complex systems. However, the performance of these methods is usually affected by the situations that the used models are not accurate and some samples have no significant contribution to the accuracy improvement. To construct a more suitable model for reliability analysis, this work proposes an active failure-pursuing Kriging modeling method to identify the most valuable samples for improving the accuracy of the predicted failure probability. On the one hand, a global predicted failure probability error index calculated through the real-time reliability result is proposed to pursue the sensitive sample and the corresponding local region that is most likely to maximize the improvement of the accuracy of the reliability result. A fault-tolerant scheme is further applied to ensure the accuracy of the failure-pursuing process. On the other hand, the correlation-based screening and space partition strategy is developed to describe the local regions and avoid the clustering of samples. In each iteration, the Kriging model is updated with the exploitation of new sample from the local regions around the sensitive samples. Additionally, an equivalent stochastic process transformation is developed to form a uniform high probability density sampling space. The results of three cases demonstrate the efficiency, accuracy and stability of the proposed method.

An adaptive multiple-Kriging-surrogate method for time-dependent reliability analysis

• Multiple-Kriging-surrogate is simultaneously constructed for time-dependent structure. • Adaptive strategy is established to identify surrogates and new training samples. • Man-made subjectivity for regression trend is avoided with adaptive selecting procedure. • Time-dependent failure probability can be accurately estimated by the most accurate local model. For accurately and efficiently estimating the time-dependent failure probability (TDFP) of the structure, a novel adaptive multiple-Kriging-surrogate method is proposed. In the proposed method, the multiple Kriging models with different regression trends (i.e., constant, linear and quadratic) are simultaneously constructed with the highest accuracy, on which the TDFP can be obtained. The multiple regression trends are adaptively selected based on the size of sample base, the maximum differences of multiple models and the global accuracy of multiple models. After that, the most suitable multiple regression trends are identified. The proposed method can avoid man-made subjectivity for regression trend in general Kriging surrogate method. Furthermore, better accuracy and efficiency will be obtained by the proposed multiple surrogates than just using a fixed regression model for some engineering applications. Five examples involving four applications with explicit performance function and one tone arch bridge under hurricane load example with implicit performance function are introduced to illustrate the effectiveness of the proposed method for estimating TDFP.

Reliability analysis and optimum maintenance of coastal flood defences using probabilistic deterioration modelling

This paper presents a method for time-dependent reliability analysis, future performance predictions and optimum maintenance strategy of coastal flood defences such as earth sea dykes subjected to changing operation conditions. The reliability analysis takes into account both the changes of hydraulic variables such as water level and wave height due to climate change and the deterioration of structural capacities such as crest freeboard loss and soil seepage length degradation over time. A probabilistic time-dependent semi-Markov process is adopted for estimating the transition probabilities on the basis of available field data through routine inspections and expert judgements. Limit state equations are established for evaluating time-dependent probability of failures associated with wave overtopping through the flood defence crest and piping in the underlying water conductive soils. A multi-objective optimisation method is then employed to find optimum solution space for asset inspection and maintenance by minimising both costs for inspection and annual risk of structural failures. The results for a typical earth sea dyke at Thames Estuary show that the probability of failures associated with wave overtopping and soil piping will increase significantly over time, thus appropriate maintenance strategy is required to reduce the risk caused by changing operating conditions.

An effective approach for kinematic reliability analysis of steering mechanisms

The paper presents an effective surrogate model for system reliability analysis of mechanisms based on an extreme-value kinematic error model and the Kriging approximation. In this regard, two types of kinematic reliability problems are considered, i.e., the system reliability that requires the kinematic error remains within an accuracy threshold along an entire output trajectory, whereas the time-dependent reliability accounts for gradually propagated system failure domain due to the varied pseudo-time parameter from its beginning to the current realization. Both kinematic reliability problems need to evaluate the extreme-valued error function presented in the mixture of absolute and maximum operators. By contrast, the simple position-based error function allows developing accurate surrogate models with a rather small number of training samples. Therefore, an approximation model was proposed to deal with kinematic reliability problems of steering mechanisms. Compared to available reliability methods in the literature, results have demonstrated high accuracy of the proposed method for various kinematic reliability problems. Note that the proposed method for time-dependent reliability analysis requires only one round of design of experiment, rather than repeatedly running the kinematic model like the first-order reliability method. It therefore provides an effective simulation tool for kinematic reliability analysis of mechanisms.

Time-Dependent System Reliability Analysis for Bivariate Responses

Time-dependent system reliability is computed as the probability that the responses of a system do not exceed prescribed failure thresholds over a time duration of interest. In this work, an efficient time-dependent reliability analysis method is proposed for systems with bivariate responses which are general functions of random variables and stochastic processes. Analytical expressions are derived first for the single and joint upcrossing rates based on the first-order reliability method (FORM). Time-dependent system failure probability is then estimated with the computed single and joint upcrossing rates. The method can efficiently and accurately estimate different types of upcrossing rates for the systems with bivariate responses when FORM is applicable. In addition, the developed method is applicable to general problems with random variables, stationary, and nonstationary stochastic processes. As the general system reliability can be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis of general systems with more than two responses. Three examples, including a parallel system, a series system, and a hydrokinetic turbine blade application, are used to demonstrate the effectiveness of the proposed method.

Sequential time-dependent reliability analysis for the lower extremity exoskeleton under uncertainty

This paper proposes a sequential time-dependent reliability analysis method by considering time sequence and correlation of failure processes for the lower extremity exoskeleton under uncertainty, which will provide an approach to improving the comfort and safety for the wearer. A kernel density function based uncertainty quantification method is provided for precisely quantitatively estimating the time-dependent reliability of joints and the position of the end-effector firstly. After decoupling time sequence and failures correlation due to error propagation, the original reliability problem is then transferred to a series time-dependent reliability model. The time-dependent system reliability analysis is finally realized by calculating conditional probability. A case study is implemented to testify the effectiveness of the proposed method.