Time-dependent Limit State Function Research Articles

Multi-objective optimisation of in-service asphalt pavement maintenance schedule considering system reliability estimated via LSTM neural networks

This article presents a novel system reliability-based framework for multi-objective optimisation of preventive maintenance (PM) management of in-service asphalt pavement. To accurately predict the international roughness index (IRI) sequence of pavement sections, a long short-term memory (LSTM) neural network that considers the spatiotemporal correlations between IRI sequences is trained with data retrieved from the long-term pavement performance (LTPP) program. Based on time-dependent limit-state functions (LSFs) incorporating the uncertainty associated with LSTM neural network prediction and the observational error involved in IRI measurement, Monte Carlo simulation (MCS) with importance sampling (IS) is adopted to calculate the reliability of pavement sections. Pavement sections located in New Mexico and Montana are selected as illustrative examples. Tri-objective optimisation processes are investigated by maximising user benefits (i.e. improved system reliability) and agency benefits (i.e. extended service life) while minimising the associated life-cycle cost (LCC) (i.e. user and agency costs) with multi-objective genetic algorithms (GAs). The obtained Pareto solution sets may assist decision-makers in the selection of well-balanced solutions to identify the optimal timing for applying PM treatments to in-service asphalt pavement.

Conditional time-dependent limit state function model considering damages and its application in reliability evaluation of CRTS II track slab

On-site observations show that several damages have occurred in CRTS II slab-type ballastless track system, such as crack and interface debonding between different structural layers, which will trigger the occurrence of some failure modes of CRTS II track slab. As the damages are the prior for specific failure modes, time-dependent reliability of CRTS II track slab should be conducted considering the uncertainties associated with both the failure mode and the damage, which is defined as the conditional time-dependent reliability in this study. To appropriately express the causal relationship among the failure modes and prior damages, a conditional limit state function (LSF) model is proposed with explicit expressions provided. With the aid of the proposed model, conditional time-dependent reliability of CRTS II track slab for two individual failure modes are investigated, which are the steel yielding failure mode under longitudinal cracking, and the vertical instability failure mode under interface debonding. Furthermore, conditional time-dependent system reliability of the track slab has also been analyzed considering four safety failure modes. The advantage of the proposed method is that prior damages have been accounted in establishing the failure criteria and incorporated in the formulation of time-dependent reliability, which provides a general formwork for structural reliability involving the causal relationship among the failure modes and damages.

Active Learning Kriging Model With Adaptive Uniform Design for Time-Dependent Reliability Analysis

Due to uncertainties and time-varying parameters in design, manufacturing, and commissioning, many structural systems often exhibit uncertain and dynamic properties. These systems need time-dependent reliability analysis to help effectively estimate the safe state during their lifecycle. However, one of the challenging issues in doing so lies in computational efficiency. This paper develops an active learning Kriging technique to improve the computational efficiency of time-dependent reliability analysis. The Kriging model is employed first as a response surface to fit the extreme value response of time-dependent limit state functions. The most probable point of the Kriging response surface is then determined by solving an optimization problem in terms of a cumulative distribution function. Further, an adaptive iterative algorithm is developed to prepare the sampling points for updating the Kriging model based on an adaptive uniform design. Monte Carlo simulations are thus performed to facilitate evaluation using the final generated Kriging response surface. Several case studies are undertaken to test and validate the effectiveness of the proposed method and to demonstrate its applicability to engineering problems.

An LSTM-Based Ensemble Learning Approach for Time-Dependent Reliability Analysis

Abstract This paper presents a long short-term memory (LSTM)-based ensemble learning approach for time-dependent reliability analysis. An LSTM network is first adopted to learn system dynamics for a specific setting with a fixed realization of time-independent random variables and stochastic processes. By randomly sampling the time-independent random variables, multiple LSTM networks can be trained and leveraged with the Gaussian process (GP) regression to construct a global surrogate model for the time-dependent limit state function. In detail, a set of augmented data is first generated by the LSTM networks and then utilized for GP modeling to estimate system responses under time-dependent uncertainties. With the GP models, the time-dependent system reliability can be approximated directly by sampling-based methods such as the Monte Carlo simulation (MCS). Three case studies are introduced to demonstrate the efficiency and accuracy of the proposed approach.

Global kriging surrogate modeling for general time-variant reliability-based design optimization problems

While design optimization under uncertainty has been widely studied in the last decades, time-variant reliability-based design optimization (t-RBDO) is still an ongoing research field. The sequential and mono-level approaches show a high numerical efficiency. However, this might be to the detriment of accuracy especially in case of nonlinear performance functions and non-unique time-variant most probable failure point (MPP). A better accuracy can be obtained with the coupled approach, but this is in general computationally prohibitive. This work proposes a new t-RBDO method that overcomes the aforementioned limitations. The main idea consists in performing the time-variant reliability analysis on global kriging models that approximate the time-dependent limit state functions. These surrogates are built in an artificial augmented reliability space and an efficient adaptive enrichment strategy is developed that allows calibrating the models simultaneously. The kriging models are consequently only refined in regions that may potentially be visited by the optimizer. It is also proposed to use the same surrogates to find the deterministic design point with no extra computational cost. Using this point to launch the t-RBDO guarantees a fast convergence of the optimization algorithm. The proposed method is demonstrated on problems involving nonlinear limit state functions and non-stationary stochastic processes.

Maximum probable life time analysis under the required time-dependent failure probability constraint and its meta-model estimation

Time-dependent reliability (failure probability) aims at measuring the probability of the normal (abnormal) operation for structure/mechanism within the given time interval. To analyze the maximum probable life time under a required time-dependent failure probability (TDFP) constraint, an inverse process corresponding to the time-dependent reliability is proposed by taking the randomness of the input variables into consideration. The proposed inverse process employs the monotonicity between the TDFP and the upper boundary of the given time interval which reflects the life time, and an adaptive single-loop sampling meta-model for the time-dependent limit state function is presented to estimate the TDFP at the given time interval flexibly. Since the TDFP is generally monotonic to the upper boundary of the given time interval, thus by adjusting the probable upper and lower boundaries of the time interval in which the corresponding TDFPs include the required TDFP constraint, the proposed approach can always search the maximum probable life time at the required TDFP by the dichotomy. By introducing the time variable as an input which is the same level as the input random variables and constructing the adaptive single-loop sampling meta-model for the time-dependent limit state function in a longer time interval with the TDFP bigger than the required TDFP, the TDFP in any subintervals of the time interval involved in the constructed meta-model can be estimated as a byproduct of the constructed meta-model without any additional actual limit state evaluations. Then the efficiency for analyzing the maximum probable life time is improved by the dichotomy and the unified meta-model of the time-dependent limit state function. Two examples are employed to illustrate the accuracy and the efficiency of the proposed approach.

Corrosion Reliability Analysis Considering the Coupled Effect of Mechanical Stresses

Corrosion is one of the most critical failure mechanisms for engineering structures and systems, as corrosion damages grow with the increase of service time, thus diminish system reliability gradually. Despite tremendous efforts, effectively carrying out reliability analysis considering the complicated coupling effects for corrosion remains to be a grand challenge. There is a substantial need to develop sophisticated corrosion reliability models and effective reliability analysis approaches considering corrosion damage growth under coupled effects such as mechanical stresses. This paper presents a physics-of-failure model for pitting corrosion with the coupled effect of corrosion environment and mechanical stresses. With the developed model, corrosion damage growth can be projected and corrosion reliability can be analyzed. To carry out corrosion reliability analysis, the developed pitting corrosion model can be formulated as time-dependent limit state functions considering pit to crack transition, crack growth, and fracture failure mechanics. A newly developed maximum confidence enhancement (MCE)-based sequential sampling approach is then employed to improve the efficiency of corrosion reliability analysis with the time-dependent limit state functions. A case study is presented to illustrate the efficacy of the developed physics-of-failure model for corrosion considering the coupled mechanical stress effects, and the new corrosion reliability analysis methodology.

Efficient Methods for Time-Dependent Fatigue Reliability Analysis

Two efficient methods for time-dependent fatigue reliability analysis are proposed in this paper based on a random process representation of material fatigue properties and a nonlinear damage accumulation rule. The first method is developed by matching the first two central moments of the accumulated damage to a well-known probability distribution, thus facilitating a direct analytical solution of the time-dependent fatigue reliability. The second method uses the first-order reliability method to calculate the reliability index based on a time-dependent limit state function. These two methods represent different tradeoffs between accuracy and computational efficiency. The proposed methods include the covariance structure of the stochastic damage accumulation process under variable amplitude loading. A wide range of fatigue data available in the literature is used to validate the proposed methods, covering several different types of metallic and composite materials under different variable amplitude loading.

A New Sample-Based Approach to Predict System Performance Reliability

Multiple degradation paths arise when systems operate under uncontrolled, uncertain environmental conditions at customers' hands in the field. This paper presents a design stage method for assessing performance reliability of systems with competing time-variant responses due to components with uncertain degradation rates. Herein, system performance measures (e.g. selected responses) are related to their critical levels by time dependent limit-state functions. System failure is defined as the non-conformance of any response, and hence unions of the multiple failure regions are formed. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region that emerges from a safe region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory is manifest through evaluating probabilities by Monte Carlo simulation. Error analysis suggests ways to predict and minimize errors. An electrical temperature controller shows the details of the method, and the potential of the approach. It is shown that the proposed method provides a more realistic way to predict performance reliability than either worst-case, or simple average-based approaches that are available in the open literature.

QUALITY AND PERFORMANCE RELIABILITY ASSESSMENT OF MULTI-RESPONSE DEGRADING SYSTEMS

This paper presents a non-sampling based method for the simultaneous evaluation of quality and performance reliability of engineering systems with multiple time-variant responses due to multiple degrading components. This work provides a platform for robust design of degrading systems. The system performance degradations are related to component degradations using mechanistic models. The system soft failure is defined as the non-conformance of any response with respect to critical levels and such relations are easily modeled as time dependent limit-state functions. Then, for discrete time it is shown that an incremental failure set that emerges from a safe region can be written using only a pair of successive system instantaneous failure sets. The cumulative distribution function of soft failure is built by summing the incremental failure probabilities. A practical implementation of the proposed method can be manifest by first-order reliability methods (FORM) and second-order bounds. The proposed method can be used to assess initial quality and performance reliability of systems with combinations of designated means and tolerances. Examples of electro mechanical systems show the details of the formulation and the potential of the approach. Error sources and their magnitudes are discussed.

Reliability-based evaluation of automotive wind noise quality

Abstract This paper proposes an efficient method for the reliability analysis of a vehicle body–door subsystem with respect to an important quality issue—wind noise. A nonlinear seal model is constructed for the automotive wind noise problem and the limit state function is evaluated using finite element analysis. A multi-modal adaptive importance sampling (AIS) method is developed for reliability analysis at system level, to improve the efficiency of the Monte Carlo simulation. The method can easily handle implicit and time-dependent limit-state functions, with variables of any statistical distributions. Existing analytical as well as simulation-based methods are also investigated to solve the car door wind noise problem. It is demonstrated through this industrial application problem that the multi-modal AIS method is superior to existing methods in terms of efficiency and accuracy. A generalized framework for reliability estimation is then established for series system reliability problems with large numbers of random variables and complicated, implicit limit states.

Time variant structural reliability analysis using diffusive crack growth models

A procedure to estimate reliabilities of structures under consideration of time variant, deteriorating resistance properties is presented. The deterioration process is confined to the effect of fatigue which is characterized by a diffusive crack growth model leading to a Fokker-Planck equation. The time dependent limit state function is derived from the Burdekin/Stone relation of the Two Criteria Approach. Importance Sampling procedures using the design point are utilized to calculate the failure probabilities in a stepwise procedure. Finally a sensitivity study identifies the initial crack length as the parameter which most significantly affects the reliability estimates.