Time-variant Reliability Analysis Method Research Articles

Time-dependent reliability analysis of flood defenses under cumulative internal erosion

Internal erosion is a significant cause of failure in dams, levees and other hydraulic structures. This article studies the time-dependent reliability of such structures under Backward Erosion Piping (BEP), a form of internal erosion in the foundation. First, a physics-based time-dependent piping failure model is presented. Second, a time-variant reliability analysis method is presented which allows to quantify how the reliability evolves over the years due to cumulative pipe growth over multiple flood events. Finally, these models are used to study the importance of time-dependence for reliability estimates of flood defenses in The Netherlands. The findings show that, particularly in coastal areas, incorporating time-dependence significantly reduces the computed failure probability. Reductions vary widely, ranging from a factor of 5 to more than 10 6 , depending on flood duration and levee properties. Therefore, reliability estimates for levees can be improved by incorporating time-dependent pipe development in the BEP failure model, and thereby contribute to avoiding unnecessary reinforcements.

Time-variant reliability analysis of corroded suspender of suspension bridge based on data-driven

The suspender of a suspension bridge is susceptible to corrosion due to environment, material, load, and other factors, which leads to the reduction of its bearing capacity with time, thus adversely affecting the safety and durability of the suspension bridge. Time-variant reliability analysis can consider the time-variant characteristics and uncertainties of each variable, and can better reveal the degradation of corrosion suspender resistance with time. However, due to the complex and highly nonlinear characteristics of the stress situation, the functional function of the suspender is often implicit, and the traditional time-variant reliability analysis method cannot be directly solved. To solve the problem of the implicit function of the suspender, An Adaptive Support Vector Regression with Extreme Response Surface (ASVR-ERS) method was proposed, and it was applied to the time-variant reliability analysis of corroded suspender of a suspension bridge. According to the corrosion characteristics of steel wire in suspenders, a hybrid constitutive model for calculating the ultimate bearing capacity of corroded suspenders was proposed. Furthermore, the time-variant reliability and residual life of corroded suspenders of a self-anchored suspension bridge were systematically studied. The results show that: Compared with the existing methods, the ASVR-ERS method can use fewer training samples to achieve higher computational accuracy. When calculating the ultimate bearing capacity of a corrosion suspender, the phenomenon of ductility degradation caused by steel wire corrosion in the suspender cannot be ignored, and the mixed constitutive model of the ultimate bearing capacity of a corrosion suspender is more reasonable. When the service time of the bridge is the same, the reliability of the suspender in the middle span of the main span is the smallest, and the reliability of the suspender in the full bridge gradually decreases from the bridge tower position to the middle span direction and the side span direction. The decrease rate of suspender reliability is the fastest at the beginning of corrosion and gradually slows down with the deepening of the corrosion degree. When the sheath has the minimum damage and the maximum circumferential damage and reaches life, the suspender section loss rate is between 10 % and 15 %. Compared with improving the safety factor of the suspender, delaying the breakage time of the sheath can improve the life expectancy of the suspender more obviously.

A novel hybrid time-variant reliability analysis method through approximating bound-most-probable point trajectory

In the engineering field, time-variant reliability analysis (TRA) is used to measure the safety level of structures under time-variant uncertainties. Lacking in information or data, some uncertainties cannot be directly quantified as stochastic models, which results in the simultaneous existence of aleatory and epistemic uncertainties in most of problems. In general, stochastic and interval models are respectively used to describe aleatory and epistemic uncertainties. For the hybrid TRA (HTRA) problem considering the two kinds of uncertainties, the existing method needs to excessively evaluate the original time-variant limit-state function, which is too expensive for engineering problems. To address this issue, we propose the concept of bound-most-probable point trajectory (BMPPT) which can be used to construct the approximation of the limit-state hyper-surface. Moreover, we develop a HTRA method based on approximating BMPPT which can further improve the computational efficiency. First, based on time discretization, we transform the HTRA problem into a time-independent series-system reliability problem which can be solved by searching the bound-most-probable point (BMPP) at all discrete time instants. Then, with the BMPPT, the lower and upper bounds of the time-variant limit-state function are linearized into two Gaussian processes. Finally, the expansion optimal linear estimation and Monte Carlo simulation are performed to estimate the time-variant reliability. To avoid excessive BMPP searches, the active learning Kriging is used to approximate the BMPPT. Two numerical examples including a cantilever beam, and a 10-bar truss, and two engineering applications of the solid rocket engine shell and the rocket inter-stage structure are investigated, and the results reveal that the proposed method can solve the HTRA problems with high accuracy and efficiency.

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.

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.

A stochastic process discretization method combing active learning Kriging model for efficient time-variant reliability analysis

Time-variant reliability analysis (TRA) has attracted tremendous interest for evaluating product reliability in full life cycle. Discretization of stochastic process is considered one of the simplest ways to transform a time-variant problem into a time-invariant problem that becomes easier to handle. Its adoption in time-variant problem, nevertheless, requires overcoming two main issues on (1) the low efficiency of small discrete time interval, and (2) the low accuracy of large discrete time interval. To tackle these two challenges, we propose a Kriging-assisted time-variant reliability analysis method based upon stochastic process discretization (namely, K-TRPD for short). First, a complex time-variant reliability problem is converted into conventional time-invariant problem through discretization of stochastic process. Second, the most probable point (MPP) trajectory is approximated through a Kriging model over the entire time period concerned, whose input is identified from the discrete time points by an active learning approach; and the output is obtained by the first order reliability method (FORM) at the identified time points. Finally, the constructed Kriging model is utilized for time-invariant reliability analysis at each discrete time point, and the time-variant reliability is obtained by using the time-invariant reliability analysis results for analyzing the multivariate normal distribution function. In this study, three numerical analysis examples and one engineering design example are presented to demonstrate the effectiveness of the proposed method.

Developing a method for time-variant reliability assessment of passive heat removal systems in nuclear power plants

Nowadays, the use of passive safety systems is considered as the most important candidate to improve the safety level of new generation nuclear power plants. However, the functioning parameters of the passive systems vary significantly over time and are extremely tied to uncertainty. Time dependency may be due to the changes in certain and uncertain parameters and the mission of the passive systems. In this paper, a time-variant reliability analysis method that combines the out-crossing approach (PHI2) and the first-order reliability method (FORM) is developed and applied to analyze the passive heat removal system (PHRS) of VVER-1000 NPP as a case study. The thermo-hydraulic model of the PHRS and its related parameters besides the solving process of PHRS parameters in the PHI2 method are illustrated. The cumulative failure probability of the PHRS is calculated in terms of the system functioning parameters. The results of this study demonstrate that the failure probability of passive safety systems is significant in terms of amplitude and its variation over time and must be considered in the design and operation of these systems in the nuclear industry.

A Time-Variant Reliability Analysis Method Based on the Stochastic Process Discretization under Random and Interval Variables

In practical engineering, it is a cost-consuming problem to consider the time-variant reliability of both random variables and interval variables, which usually requires a lot of calculation. Therefore, a time-variant reliability analysis approach with hybrid uncertain variables is proposed in this paper. In the design period, the stochastic process is discretized into random variables. Simultaneously, the original random variables and the discrete random variables are converted into independent normal variables, and the interval variables are changed into standard variables. Then it is transformed into a hybrid reliability problem of static series system. At different times, the limited state functions are linearized at the most probable point (MPP) and at the most unfavorable point (MUP). The transformed static system reliability problem with hybrid uncertain variables can be solved effectively by introducing random variables. To solve the double-loop nested optimization in the hybrid reliability calculation, an effective iterative method is proposed. Two numerical examples and an engineering example demonstrate the validity of the present approach.

Efficient time-variant reliability analysis through approximating the most probable point trajectory

Time-variant reliability analysis (TRA) is widely utilized to assess the performance of engineering structures under various time-variant uncertainties. Recently, the time discretization-based TRA (TDTRA) methods have been developed, which can achieve satisfactory accuracy but need to excessively perform most probable point (MPP) searches at many equidistant time instants. To improve the efficiency of TDTRA, this paper proposes a TRA method based on approximating the MPP trajectory, referred to as AMPPT. First, this paper introduces a new concept of the MPP trajectory (MPPT), which is defined as the moving path of the MPP in the U-space when time changes. Then, a one-dimensional Kriging model is constructed to approximate the MPPT by the adaptive sampling method, which only performs MPP searches at several critical time instants. To further improve the computational efficiency, a warm-starting strategy is proposed to accelerate the MPP search. Then, the approximated MPPT is employed to transform the time-variant response into an equivalent Gaussian process. Finally, the spectral decomposition method and Monte Carlo simulation are used to compute the time-variant reliability. Comparative studies on four numerical examples and one practical engineering example of the solid rocket engine shell verify that the proposed AMPPT outperforms TDTRA in terms of both accuracy and efficiency. Test results also indicate that the efficiency gain of the proposed AMPPT comes from not only the reduction in the number of MPP searches but also the acceleration of the MPP search itself.

Interval interference time-variant reliability analysis method for propellant tank

Interval interference time-variant reliability analysis method for propellant tank

A time-variant reliability analysis method for non-linear limit-state functions with the mixture of random and interval variables

Most of the current time-variant reliability analysis methods are applicable for only random variables. However, some of the uncertain parameters can only be easily modeled by interval variables in many engineering applications. The main contribution of this paper is to propose a new time-variant reliability analysis method for nonlinear limit state function with the coexistence of random variables and interval uncertain variables. Three primary strategies are put forward. Firstly, the stochastic process in the time-variant limit-state function is discretized, equivalently gaining several static limit-state functions at different time. Secondly, each static limit-state function is linearized at the most probable point (MPP) and the worst-case point (WCP) of interval variable, by doing which, the ordinary time-dependent reliability problem is equally transformed into a static reliability one with mixed uncertain variables. Finally, complex nested optimization problems using sequential iterations are effectively solved in mixed reliability calculation. The proposed method can obtain structural reliability considering time effects and mixed uncertainties. The effectiveness and the efficiency of the proposed method are demonstrated by four numerical examples.

Time-variant reliability analysis for industrial robot RV reducer under multiple failure modes using Kriging model

This paper proposes a time-variant reliability method for an industrial robot rotate vector (RV) reducer with multiple failure modes using a Kriging model. Firstly, the limit state functions of the industrial robot RV reducer are built by considering time-variant load and material degradation based on the failure physic method. Secondly, a time-variant reliability analysis method for multiple failure modes is proposed based on a double-loop Kriging model. The inner loop is the extremal optimization for each limit state function based on the efficient global optimization (EGO). The outer loop is the active learning reliability analysis by combining multiple response Gaussian process model (MRGP) and the Monte Carlo simulation (MCS). Furthermore, three learning functions (U-function, EFF-function and H-function) are individually adopted to choose a new sample point until the convergence is satisfied. Case studies are finally provided to illustrate the effectiveness of the proposed method.

Time-variant reliability analysis of motor-hanger connecting bolts in electric trains

Due to variables in design, manufacturing and working conditions, the working loads of connecting bolts for motor hangers in electric-multiple-unit trains are uncertain. To reduce this uncertainty and improve the reliability of connecting bolts, a novel time-variant reliability analysis method has been developed. First, a parametric finite-element model of a motor hanger was established. The probability distribution of working loads for connecting bolts was then obtained by Monte Carlo simulation. Second, a one-dimensional Brownian differential equation considering the uncertainty of bolt working loads was derived based on Itō’s lemma, and expressions of the mean and variance of bolt stresses under time-variant conditions were given. The time-variant reliability model of the bolts was then constructed based on a time-variant stress–strength interference model and solved by the most-probable-point method. The results showed that the reliability calculated by this method was lower than that of the traditional method and therefore safer. It was concluded that the uncertainty of the working load has a great impact on reliability.

Time-variant reliability modeling based on hybrid non-probability method

In this paper, an innovative time-variant reliability analysis method based on non-probabilistic theory is developed for structures, which combines the interval model with the elliptical model. The coordinate transformation method is adopted to eliminate the correlation between variables for improving the accuracy of the reliability analysis results. An improved multi-dimensional response surface method is selected to solve the reliability problem based on the hybrid model. Finally, taking the cantilever beam structure as a case study, which is used to shed a light on the validity of the presented measure. The results show that in the early and the middle stage of service period, the dispersion of the uncertainty variable has a significant impact on the reliability. At the later stage, the moment degradation is the main factor affecting the reliability.

An improved TRPD method for time-variant reliability analysis

In this paper, an improved time-variant reliability analysis method based on stochastic process discretization (iTRPD) is proposed. Firstly, the time-variant reliability problem is transformed into a time-invariant series system reliability problem. Then the first order reliability method (FORM) is employed to analyze the reliability of each component of the system, and a corresponding approach is given to calculate the correlation coefficient matrix of all the components’ performance functions. Finally, the target time-variant reliability can be obtained with the reliability index vector and the correlation coefficient matrix of the involved components. In this study, the iTRPD is further applied to the system reliability problems, and hence a corresponding time-variant system reliability analysis method is also developed. Four numerical examples are investigated to demonstrate the effectiveness of the proposed methods.

Time-variant reliability assessment for multiple failure modes and temporal parameters

Multiple failure modes and temporal parameters are usually inherent in the complicated products’ performance, which bring new challenges for conducting time-variant reliability analysis and design. This paper proposes a novel time-variant reliability analysis method for multiple failure modes and temporal parameters based on the combination of the extreme value moment method and improved maximum entropy method. Firstly, a scaling function is established to reduce the integration error of the original maximum entropy method. The improved maximum entropy method can transform an infinite interval to a limited interval for a range of integration. The extreme value moments are then obtained by employing the sparse grid technique and the extreme value theory. Finally, the probability density function (PDF) of responses can be obtained by the combination of the extreme value moment method and the improved maximum entropy method and so the time-variant reliability can be estimated. The effectiveness of the proposed method is illustrated with two examples.

A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures

AbstractDue to the uncertainties and the dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. This paper proposes a novel time-variant reliability analysis method using failure processes decomposition to transform the time-variant reliability problems to the time-invariant problems for dynamic structures under uncertainties. The transformation is achieved via a two-stage failure processes decomposition. First, the limit state function with high dimensional input variables and high order temporal parameters is transformed to a quadratic function of time based on the optimized time point in the first-stage failure processes decomposition. Second, based on the characteristics of the quadratic function and reliability criterion, the time-variant reliability problem is then transformed to a time-invariant system reliability problem in the second-stage failure processes decomposition. Then, the kernel density estimation (KDE) method is finally employed for the system reliability evaluation. Several examples are used to verify the effectiveness of the proposed method to demonstrate its efficiency and accuracy.

FORM and Out-Crossing Combined Time-Variant Reliability Analysis Method for Ship Structures

In view of the varying characteristics of material properties, environmental conditions, and loading effects randomly with long time, the random and temporal characters of different variables should take into account when the structural reliability analysis methods are adopted to estimate the reliability of ship structures. Therefore, a time-variant reliability analysis method combined the out-crossing approach and the first-order reliability method is proposed. In this paper, the research is conducted on the time-variant feature of ship structures under the corrosive action according to the environmental testing data. Furthermore, the limit state function is derived based on the time-variant feature analysis results in which the strength and stress of ship structures are both regarded as variables with respect to time. Then, the time-dependent reliability model of ship structures is established based on this combined method, and the solving process of parameters in this model is illustrated. Finally, a case of a ship grillage structure under marine environment is given to prove that the proposed method has a good application in evaluating the reliability of ship structures. The comparison analysis using different methods is also conducted to study the accuracy and efficiency of this method.

A Single-Loop Approach for Time-Variant Reliability-Based Design Optimization

In the process of long-term use, the uncertainty of an engineering structure often presents time-variant or dynamic characteristics due to the influence of stochastic loads and material performance degradations. In such a situation, the structural design optimization will involve an important problem of time-variant reliability-based design optimization (TRBDO). Performing TRBDO involves a nested optimization, which will lead to extremely low computational efficiency. In this paper, a single-loop approach (SLA) is proposed to convert the nested optimization in TRBDO into a sequence iterative process composed of the time-variant reliability analysis (TRA), constraint discretization, and design optimization. In each iteration step, the TRA method based on stochastic process discretization is first used to calculate the time-variant reliability of constraints; second, through introducing the concept of the target reliability index of discretized time period and proposing the corresponding algorithm, each time-variant constraint is discretized into a series of time-invariant constraints to formulate a conventional reliability-based design optimization problem. The approach exhibits a good comprehensive performance in terms of efficiency and convergence. The validity and practicality of the SLA are validated by two numerical examples and a design problem for the chassis of a self-balancing vehicle.

A time-variant reliability analysis method for structural systems based on stochastic process discretization

In this paper, we propose a new method for analyzing time-variant system reliability based on stochastic process discretization, which provides an effective tool for reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system reliability problem, we can obtain the structural reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the method.