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Surrogate models are extensively used to substitute real models which are expensive to evaluate in the time-dependent reliability analysis. Normally, different surrogate models have different scopes of application. However, information is often insufficient for analysts to select the most appropriate surrogate model for a specific application. Thus, the result precited by individual surrogate model tends to be suboptimal or even inaccurate. Ensemble model can effectively deal with the above concern. This work aims to study the application of ensemble model for reliability analysis of time-independent problems.

In this work, a method of reliability analysis for time-dependent problems based on ensemble learning of surrogate models is developed. The ensemble of surrogate models includes Kriging, radial basis function, and support vector machine. The prediction is approximated by the weighted average model. The ensemble learning of surrogate models is updated by finding and adding the sample points with large prediction errors throughout the entire procedure.

The effectiveness of the proposed method is verified by several examples. The results show that the ensemble of surrogate models can effectively propagate the uncertainty of time-varying problems, and evaluate the reliability with high prediction accuracy and computational efficiency.

This work proposes an adaptive learning framework for the uncertainty propagation of time-dependent problems based on the ensemble of surrogate models. Compared with individual surrogate models, the ensemble model not only saves the effort of selecting an appropriate surrogate model especially when the knowledge of unknown problem is lacking, but also improves the prediction accuracy and computational efficiency.

In the freeze-thaw zone, the pre-stressed concrete of bridge structure will be damaged by freezing-thawing, the bearing capacity of structure will decrease and the safety will be affected. The purpose of this paper is to establish the time-dependent resistance degradation model of structure in the freeze-thaw zone, and analysis the structural reliability and remaining service life in different freeze-thaw zones.

First, according to the theory of structural design, a calculation model of the resistance of pre-stressed concrete structures in f freeze-thaw zone is established. Second, the time-dependent resistance model was verified by the test beam bending failure test results done by the research group, which has been in service for 20 years in freeze-thaw zone. Third, using JC algorithm in MATLAB to calculate the index on the reliability of pre-stressed concrete structure in frozen thawed zones, forecasting the s remaining service life of structure.

First, the calculation model of the resistance of pre-stressed concrete structures in freeze-thaw zone is accurate and it has excellent applicability. Second, the structural resistance deterioration time in Wet-Warm-Frozen Zone is the earliest. Third, once the pre-stressed reinforcement rusts, the structural reliability index will reach limit value quickly. Finally, the remaining service life of structure meets the designed expectation value only in a few of freeze-thaw zones in China.

The research will provide a reference for the design on the durability of a pre-stressed concrete structure in the freeze-thaw zone. In order to verify the security of pre-stressed concrete structures in the freeze-thaw zone, engineers can use the model presented in this paper for durability checking, it has an important significance.

This paper aims to present a novel dynamic reliability model that considers the interval mixed uncertainty for the air-breathing hypersonic flight vehicle (AHFV) to guarantee flight safety and structural reliability.

Initially, the force condition of the fuselage is analyzed based on the longitudinal elastic model of an AHFV. Subsequently, a new high-efficiency dynamic reliability model is presented to describe the failure probability evolution of the fuselage structure. For the random uncertainty problem with interval distribution parameters, the interval PHI2 method of time-dependent reliability is used to obtain the time-dependent reliability interval of the AHFV. Finally, the key variables that affect the failure probability accumulation are determined, which provide an important reference for ensuring structural reliability and improving the life span of AHFVs.

It is demonstrated that the proposed reliability model can obtain more accurate dynamic reliability results for the fuselage, and it is confirmed the key variables that affect the failure probability accumulation. The results also provide an important reference for the reliability analysis of hypersonic vehicles.

The novelty of this work comes from the first application of the PHI2 method (considering the interval mixed uncertainty) in the AHFV and the development of a new reliability model for the entire body of AHFVs. The proposed analysis scheme is implemented on the dynamic model of the AHFV, which provides a more accurate reference for improving the structural reliability and life span of AHFVs.

The purpose of this paper is to analyze the time-dependent reliability of harmonic drive.

The transient finite element analysis (FEA) of harmonic drive is established to calculate the stress under different loads. Combined with the residual strength model and random variables, the time-dependent reliability model of harmonic drive is deduced by the stochastic perturbation method and Edgeworth series. Based on accelerated life tests, the degradation parameters are estimated by maximizing likelihood function. Under variable load, the key stress from transient FEA is transformed into probability density function by kernel density estimation, and the residual strength model is modified by adding adjustment factors to deal with strength degradation under different loads.

The critical position of stress concentration from transient FEA is consistent with the fatigue fracture position at the accelerated life test sample. Compared with the time-dependent reliability method with equivalent circular-shell static stress or empirical degradation parameters, the proposed method has the smallest prediction error of failure life. Under variable load, the state function should be expanded to second-order series for avoiding error items relevant to variance. The failure life expectation under random variable load is smaller than that under constant load.

The time-dependent reliability method of harmonic drive is firstly proposed under constant and variable load. The transient FEA of harmonic drive is established to calculate the stress for strength analysis. The accelerated life test of harmonic drive is conducted for degradation parameters estimation. The adjustment factor is added to the residual strength model for strength degradation under different loads.

Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

The 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.

In 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.

The 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.

The paper provides a useful reference for further theoretical research and engineering application.

Ensuring safe operation of a urea fertilizer plant (UFP) is a vital aspect for its functioning and production. Clearly the safe operation of such systems can only be archived with proper and effective maintenance scheduling and through controlling its failures as well as repairs of the components. Also for this, the concern plant management must have the information regarding the failures that affects the system's performance most/least. The objective of this study is to analyze mathematically the factors that are responsible for the failure/degradation of the decomposition unit of UFP.

The considered system has been modeled by the aid of Markov's birth–death process with two types of failures for its components: variable (which are very similar in practical situations) and constant. The mathematical model is solved by the help of Laplace transform and supplementary variable technique.

In the present paper, the availability, reliability and mean time to failure (MTTF) are computed for the decomposition unit of the UFP. The critical components that affect the reliability and MTTF of the decomposition unit are identified through sensitivity analysis.

In this paper, a mathematical model based on the working of the decomposition unit of a UFP has been developed by considering two types of failure, namely, variable failures rates and constant failure rates (which has not been done in the literature for the decomposition unit). Conclusions in this paper are good references for the improvement of the same.

This paper aims to present a dynamic reliability model of scraper chains based on the fretting wear process and propose a reasonable structural optimization method.

First, the dynamic tension of the scraper chain is modeled by considering the polygon effect of the scraper conveyor. Then, the numerical wear model of the scraper chain is established based on the tangential and radial fretting wear modes. The scraper chain wear process is introduced based on the diameter wear rate. Furthermore, the time-dependent reliability of scraper chains based on the fretting wear process is addressed by the third-moment saddlepoint approximation (TMSA) method. Finally, the scraper chain is optimized based on the reliability optimization design theory.

There is a correlation between the wear and the dynamic tension of the scraper conveyor. The unit sliding distance of fretting wear is affected by the dynamic tension of the scraper conveyor. The reliability estimation of the scraper chain with incomplete probability information is achieved by using the TMSA for the method needs only the first three statistical moments of the state variable. From the perspective of the chain drive system, the reliability-based optimal design of the scraper chain can effectively extend its service life and reduce its linear density.

The innovation of the work is that the physical model of the scraper chain wear is established based on the dynamic analysis of the scraper conveyor. And based on the physical model of wear, the time-dependent reliability and optimal design of scraper chains are carried out.

The aim of this paper is to investigate the failure probability in an irregular area in pipeline (elbow) over its lifetime. The reliability analysis is performed by using of an enhanced first-order reliability method / second-order reliability method (FORM/SORM) and Monte Carlo simulation methods: a numerical model of a corroded pipeline elbow was developed by using finite element method; also, an empirical mechanical behavior model has been proposed. A numerical case with high, moderate and low corrosion rates was conducted to calculate the deferent reliability indexes. The found results can be used in an application case for managing an irregular area in pipeline lifetime. Hence, it is necessary to ensure a rigorous inspection for this part of a pipeline to avoid human and environmental disasters.

The present paper deals a methodology for estimating time-dependent reliability of a corroded pipeline elbow. Firstly, a numerical model of corroded elbow is proposed by using the finite element method. A mechanical behavior under the corrosion defect in time is studied, and an empirical model was also developed.

The result of this paper can be summarized as: a mechanical characterization of the material was carried out experimentally. A numerical model of a corroded pipeline elbow was developed by using the finite element method. An empirical mechanical behavior model has been developed. The reliability of a corroding pipe elbow can be significantly affected by corrosion and residual stress. A proportional relationship has been found between probability of failure and corrosion rate. The yield stress and pressure service have an important sensitivity factor.

Aiming to help Algerian gas and oil companies' decision makers, the present paper illustrates a methodology for estimating time-dependent reliability of a corroded pipeline elbow over its lifetime using numerical models by applying the finite element method. Firstly, a numerical model of a corroded pipe elbow was developed and coupled with an empirical mechanical behavior model, which is also proposed. A probabilistic is then developed to provide realistic corrosion parameters and time modeling, leading to the real impact on the lifetime of an elbow zone in pipeline. The reliability indexes and probability of failure for various corrosion rates with and without issued residual stress are computed using Monte Carlo simulation and FORM.

Performance of the structure depends on design, construction, environment, utilization and reliability aspects. Other factors can be controlled by adopting proper design and construction techniques, but the environmental factors are difficult to control. Hence, mostly in practice, the environmental factors are not considered in the analysis and design appropriately; however, their impact on the performance of the structures is significant along with the design life. It is in this light that this paper aims to perform the time-dependent performance analysis of reinforced concrete structures majorly considering environmental factors.

To achieve the intended objective, a simply supported reinforced concrete beam was designed and detailed as per the Euro Code (EC2). The time-dependent design parameters, corrosion parameters, creep and shrinkage were identified through thorough literature review. The common empirical equations were modified to consider the identified parameters, and finally, the time-dependent performance of reinforced concrete beam was performed.

Findings indicate that attention has to be paid to appropriate consideration of the environmental effect on reinforced concrete structures. In that, the time-dependent performance of reinforced concrete beam significantly decreases with time due to corrosion of reinforcement steel, creep and shrinkage.

However, the Euro code, Ethiopian code and Indian code threat the exposure condition of reinforced concrete by providing corresponding concrete cover that retards the corrosion initiation time but does not eliminate environmental effects. The results of this study clearly indicate that the capacity of reinforced concrete structure degrades with time due to corrosion and creep, whereas the action on the structure due to shrinkage increases. Therefore, appropriate remedial measures have to be taken to control the defects of structures due to the environmental factors to overcome the early failure of the structure.