Study on time-varying reliability analysis method

Material characteristics, environmental conditions and loading characteristics under the time domain features shall be taken into consideration so as to effectively evaluate the reliability of ship grillage structure. Moreover, the method of time-variant reliability serves as an effective approach to solve the problem. In the paper, based on the loading environmental features of ships during the enlistment, research has been conducted on the changing of material geometrical and mechanical characteristics with time under the corrosive action. Furthermore, on the basis of time-variant theory, the timevariant model of section modulus as well as bending strength concerning the ship grillage structure has been established, thus generating a time-variant reliability analysis method integrated with out-crossing rate and First Order Second Moment(FOSM) method. Besides, the paper analyzes the time consecutiveness of ship grillage structure reliability based on the time-variant reliability cases of certain ship grillage structure under the corrosion environment while the failure probability of the ship during the enlistment has been accurately predicted.

The active-learning Kriging (ALK)–based time-variant system reliability analysis has been widely concentrated. Unfortunately, the current time-variant system reliability methods are mostly focused on the series system, parallel system, or series-parallel system; thus, they cannot efficiently deal with the time-variant reliability problem of a complex system such as bridge system, network system, and so on. In view of this issue, the paper proposes an efficient time-variant reliability method for a complex system by introducing the structure function into the ALK-based time-variant reliability analysis. Firstly, similar to the ALK-based time-variant system reliability method, some extreme values corresponding to the initial input samples are optimized, and thus the initial extremum response surface is constructed based on the Kriging model. Then, considering the epistemic uncertainty of the Kriging predictions, the predicted response of system structure function under a particular input sample is viewed as a random variable, and its mean and variance are computed based on the minimal cut sets of a complex system. Lastly, considering the aleatory uncertainty between the different candidate samples, the point corresponding to the maximum prediction variance is selected, the most important component is decided by introducing the structure importance, and its extreme value is correspondingly optimized to update the initial extremum response surface. The stopping criterion is also provided in this paper and the effectiveness of the proposed method is illustrated by several examples.

This paper discusses the effects of corrosion and slamming on Floating Production Storage and Offloading (FPSO) structures in the North Sea by using a time variant structural reliability based approach. An FPSO structure currently in operation in the North Sea is analysed, an analytical approach is suggested and used to determine the Ultimate Strength of the FPSO structure and compared with other published methods. A non-linear corrosion method is then used to determine the effect of corrosion on the ultimate strength and subsequently in the reliability of the structure. Slamming loads on the midship section of the FPSO are calculated using closed form expressions. The effect of slamming and green water load on the overall vertical bending moment applied on the structure is combined with the vertical wave bending and still water loads using the Ferry Borges- Castanheta method and the SRSS rule, to provide the distribution and variation of a loading component for structural reliability analysis to be performed. Time variant reliability analysis using Monte Carlo Simulation is then used to determine reliability indices and probabilities of failure for the structural system analysed on a component level.

Response uncertainty evaluation and dynamic reliability analysis corresponding to classical stochastic dynamic analysis are usually restricted to the uncertainties of the excitation. The inclusion of the parameter uncertainties contained in structural properties and excitation characteristics has become an increasingly important problem in many areas of dynamics. In the present paper, a point estimate procedure is proposed for the evaluation of stochastic response uncertainty, and a response surface approach procedure in standard normal space is proposed for analysis of time-variant reliability analysis for hysteretic MDF structures having parameter uncertainties. Using the proposed procedures, the response uncertainties and time-variant reliability can be easily obtained by several repetitions of stochastic response analysis under given parameters without conducting sensitivity analysis, which is considered to be one of the primary difficulties associated with conventional methods. In the time-variant reliability analysis, the failure probability can be readily obtained by improving the accuracy of the first-order reliability method using the empirical second-order reliability index. The random variables are divided into two groups, those with CDF and those without CDF. The latter are included via the high-order moment standardization technique. A numerical example of a 15F hysteretic MDF structure that takes into account uncertainties of four structural parameters and three excitation characteristics is performed, based on which the proposed procedures are investigated and the effects of parameter uncertainties are discussed. Copyright © 1999 John Wiley & Sons, Ltd.

Time-variant reliability analysis can effectively estimate the safe state of structures under dynamic uncertainties during their lifecycle. However, one of its key challenging issues is computational efficiency. To improve the efficiency, this paper develops an approximation of the first-crossing probability density function (PDF) method, termed AFC-PDFM, based on the first-crossing theory. The response surface of the first-crossing time point (FCTP) about input variables is first estimated by using the moving least squares method (MLSM) and uniform design. Furthermore, an iterative algorithm is developed to compute the origin moments of the FCTP based on the MLSM response surface. Finally, the PDF of the FCTP is obtained by combining the origin moments and the maximum entropy method to avoid direct calculations of the first-crossing rate, which is often intractable, and then the time-variant reliability is estimated. Three examples are implemented to testify and validate the effectiveness of the proposed method and potential applications to engineering problems.

During the long-term service periods of Prestressed Concrete(PC) continuous girder bridges, structural time-varying reliability will degrade due to cyclic creep induced by dynamic vehicle loading, which increases the risk of structural failure. This paper provided a time-varying reliability prediction method for the prestressed concrete continuous T-girder bridge considering random vehicle load information and cyclic creep information. Firstly, the random vehicle load information is simulated with Monte Carlo random simulation method and MATLAB software based on the monitored data obtained from weigh-in-motion (WIM) system. Then, the concrete shrinkage strain model, concrete static creep strain model, concrete cyclic creep strain model and the overall strain model are respectively provided by combining the CEB-FIP model with concrete cyclic creep theory. Finally, by using a numerical model of prestressed concrete bridge, a time-variant reliability analyzing approach of prestressed concrete T-girder bridge considering the limit state of load carrying capacity and the limit state of serviceability is investigated in detail by integrating the random vehicle loading information with the concrete cyclic creep information.

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

Conditional reliability of bulk carriers damaged by ship collisions

Due 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.

The constitutive equation and carrying capacity of structure will change over time under high temperature conditions. The traditional structural reliability models are inefficient to solve these time-varying structural reliability problems. A time-varying response surface method with thermal response and response threshold value changing over time was proposed. The method can be used for high-temperature structural reliability analysis. Combined with Box-Behnken experimental design,a cross quadratic function of structure's basic variables and time was introduced for establishing a time-varying model of the thermal structural response. The function of structural response threshold value and time was established by using temperature as intermediate variable. The time-varying structural reliability calculation method was proposed when basic variables are normally distributed. A study case was given to demonstrate the applicability of this method and its greatly enhanced effectiveness besides accuracy.

Time-variant reliability-based prediction of COVID-19 spread using extended SEIVR model and Monte Carlo sampling

Formulations are presented for estimating probability of failure considering uncertainty of distribution parameters in time invariant and time variant reliability analyses. Based on the formulations the probability of failure can be calculated by recursively using the first order reliability method. Also, a more efficient approximate analysis procedure by using the point estimate method to estimate the probability of failure is given. In this analysis procedure, the point estimate method is used to discretize the uncertain distribution parameters in the time invariant reliability analysis, and to discretize the time-independent random variables and uncertain distribution parameters in the time variant reliability analysis. The probability of failure is then obtained by weighting the probability of failure conditioned at each of discrete points. The conditional probability of failure can be calculated by using first order reliability method, second order reliability method or any other convenient ...

The application of reliability-based design optimization (RBDO) to degrading systems is challenging because of the continual interplay between calculating time-variant reliability (to ensure reliability policies are met) and moving the design point to optimize various objectives, such as cost, weight, size and so forth. The time needed for Monte Carlo Simulation (MCS) is lengthy when reliability calculations are required for each iteration of the design point. The common methods used to date to improve efficiency have some shortcomings: First, most approaches approximate probability via a method that invokes the most-likely failure point (MLFP), and second, tolerances are almost always excluded from the list of design parameters (hence only so-called parameter design is performed), and, without tolerances, true monetary costs cannot be determined, especially in manufactured systems. Herein, the efficiency of RBDO for degrading systems is greatly improved by essentially uncoupling the time-variant reliability problem from the optimization problem. First, a meta-model is built to relate time-variant reliability to the design space. Design of experiment techniques helps to select a few judicious training sets. Second, the meta-model is accessed to quickly evaluate objectives and reliability constraints in the optimization process. The set-theory approach (with MCS) is invoked to find the system reliability accurately and efficiently for multiple competing performance measures. For a case study, the seminal roller clutch with degradation due to wear is examined. The meta-model method, using both moving least-squares and kriging (using DACE in Matlab), is compared to the traditional approach whereby reliability is determined by MCS at each optimization iteration. The case study shows that both means and tolerances are found that correctly minimize a monetary cost objective and yet ensure that reliability policies are met. The meta-model approach is simple, accurate and very fast, suggesting an attractive means for RBDO of time-variant systems.

Time-variant reliability assessment through equivalent stochastic process transformation

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