An efficient method for estimating time-dependent global reliability sensitivity

Structural and Multidisciplinary Optimization - Time-dependent global reliability sensitivity can quantify the effect of input variables in their whole distribution ranges on the time-dependent...     

A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability

In estimating the effect of a change in a random variable parameter on the (time-invariant) probability of structural failure estimated through Monte Carlo methods the usual approach is to carry out a duplicate simulation run for each parameter being varied. The associated computational cost may become prohibitive when many random variables are involved. Herein a procedure is proposed in which the numerical results from a Monte Carlo reliability estimation procedure are converted to a form that will allow the basic ideas of the first order reliability method to be employed. Using these allows sensitivity estimates of low computational cost to be made. Illustrative examples with sensitivities computed both by conventional Monte Carlo and the proposed procedure show good agreement over a range of probability distributions for the input random variables and for various complexities of the limit state function.     

Subset simulation method including fitness-based seed selection for reliability analysis

Probability estimation of rare events is a challenging task in the reliability theory. Subset simulation (SS) is a robust simulation technique that transforms a rare event into a sequence of multiple intermediate failure events with large probabilities and efficiently approximates the mentioned probability. Proper handling of a reliability problem by this method requires employing a suitable sampling approach to transmit samples toward the failure set. Markov Chain Monte Carlo (MCMC) is a suitable sampling approach that solves the SS transition phase using the failed sample of each simulation level as the seed of next samples. This paper is aimed to study the seed selection effect on the SS accuracy through several seed selection approaches inspired by the genetic algorithm and particle filter and using the main PDF of the variables to assign a mass function probability to each subset sample in the failure domain. Roulette wheel (I, II), tournament and proportional probability techniques are then employed to choose the weighed samples as seeds to be placed in the MCMC to transmit the samples. To examine the capability of each approach, reliabilities of some engineering problems were investigated and results showed that the proposed approaches could find proper failure sets better than the original SS method, especially in problems with several failure domains.

     

A robust iterative algorithm for structural reliability analysis

In the “first-order reliability method” (FORM), the HL-RF iterative algorithm is a recommended and widely used one to locate the design point and calculate the reliability index. However it may fail to converge if the limit state surface at the design point is highly nonlinear. In this paper, an easy iterative algorithm, which introduces a “new” step length to control the convergence of the sequence and can be named as finite-step-length iterative algorithm, is present. It is proved that the HL-RF method is a special case of this proposed algorithm when the step length tends to infinity and the reason why the HL-RF diverges is illustrated. This proposed algorithm is much easier than other optimization schemes, especially than the modified HL-RF algorithm, because the process of line search for obtaining the step length is not needed. Numerical results indicate that the proposed algorithm is effective and as simple as the HL-RF but more robust.     

A method for solving nonlinear time-dependent drainage model

The purpose of this paper is to present a method for solving nonlinear time-dependent drainage model. This method is based on the perturbation theory and Laplace transformation. The proposed technique allows us to obtain an approximate solution in a series form. The computed results are in good agreement with the results of Adomian decomposition method. Results are presented graphically and in tabulated forms to study the efficiency and accuracy of method. The present approach provides a reliable technique, which avoids the tedious work needed by classical techniques and existing numerical methods. The nonlinear time-dependent drainage model is solved without linearizing or discretizing the nonlinear terms of the equation. The method does not require physically unrealistic assumptions, linearization or discretization in order to find the solutions of the given problems.     

A simnet simulation model for estimating system reliability

A general SIMNET simulation model is developed for estimating system reliability. The input data to the model is comprised of the minimal cut sets of the block diagram representing the system. The time-to-failure of the (parallel-series) components may be descriebd by different distributions. The model can be readily extended to include repair and maintenance of the components.     

A coupled subset simulation and active learning kriging reliability analysis method for rare failure events

Structural and Multidisciplinary Optimization - It is widely recognized that the active learning kriging (AK) combined with Monte Carlo simulation (AK-MCS) is a very efficient strategy for failure...     

Simulation-based time-dependent reliability analysis for composite hydrokinetic turbine blades

The reliability of blades is vital to the system reliability of a hydrokinetic turbine. A time-dependent reliability analysis methodology is developed for river-based composite hydrokinetic turbine blades. Coupled with the blade element momentum theory, finite element analysis is used to establish the responses (limit-state functions) for the failure indicator of the Tsai–Hill failure criterion and blade deflections. The stochastic polynomial chaos expansion method is adopted to approximate the limit-state functions. The uncertainties considered include those in river flow velocity and composite material properties. The probabilities of failure for the two failure modes are calculated by means of time-dependent reliability analysis with joint upcrossing rates. A design example for the Missouri river is studied, and the probabilities of failure are obtained for a given period of operation time.     

An equivalent linear method for structural system reliability with nonlinear safety margins

In Ref. [1 (Comput. Struct.42, 255–262, 1992)], the authors presented the numerical integration method in M space for computing structural system reliability with linear safety margins of the structural system failure modes. It has two advantages over the integration method in the space constructed by the basic variables of the structural system in that: (1) the integral domain is very simple and the integral grid can easily be generated; (2) the computer run time is short. In this paper, an equivalent linear method of the nonlinear safety margins is presented and the integration method in M space is employed in solving the equivalent linear system. Furthermore, for decreasing the computer run time or increasing the computational accuracy, the Gaussian numerical integration method is used for computing the two- and three-order joint failure probabilities of structural failure modes. Several examples illustrate the effectiveness of the method.     

Conditional probability Markov chain simulation based reliability analysis method for nonnormal variables

Based on fast Markov chain simulation for generating the samples distributed in failure region and saddlepoint approximation(SA) technique,an efficient reliability analysis method is presented to evaluate the small failure probability of non-linear limit state function(LSF) with non-normal variables.In the presented method,the failure probability of the non-linear LSF is transformed into a product of the failure probability of the introduced linear LSF and a feature ratio factor.The introduced linear LSF wh...     

A method for improving classification reliability of multilayerperceptrons

Criteria for evaluating the classification reliability of a neural classifier and for accordingly making a reject option are proposed. Such an option, implemented by means of two rules which can be applied independently of topology, size, and training algorithms of the neural classifier, allows one to improve the classification reliability. It is assumed that a performance function P is defined which, taking into account the requirements of the particular application, evaluates the quality of the classification in terms of recognition, misclassification, and reject rates. Under this assumption the optimal reject threshold value, determining the best trade-off between reject rate and misclassification rate, is the one for which the function P reaches its absolute maximum. No constraints are imposed on the form of P, but the ones necessary in order that P actually measures the quality of the classification process. The reject threshold is evaluated on the basis of some statistical distributions characterizing the behavior of the classifier when operating without reject option; these distributions are computed once the training phase of the net has been completed. The method has been tested with a neural classifier devised for handprinted and multifont printed characters, by using a database of about 300000 samples. Experimental results are discussed.     

A discontinuous finite difference streamline diffusion method for time-dependent hyperbolic problems

In this article, a new finite element method, discontinuous finite difference streamline diffusion method (DFDSD), is constructed and studied for first-order linear hyperbolic problems. This method combines the benefit of the discontinuous Galerkin method and the streamline diffusion finite element method. Two fully discrete DFDSD schemes (Euler DFDSD and Crank–Nicolson (CN) DFDSD) are constructed by making use of the difference discrete method for time variables and the discontinuous streamline diffusion method for space variables. The stability and optimal L² norm error estimates are established for the constructed schemes. This method makes contributions to the discontinuous methods. Finally, a numerical example is provided to show the benefit of high efficiency and simple implementation of the schemes.     

A splitting method for a backward parabolic equation with time-dependent coefficients

In this paper we propose a stable numerical method for an ill-posed backward parabolic equation with time-dependent coefficients in a parallelepiped. The problem is reformulated as an ill-posed least squares problem which is solved by the conjugate gradient method with an a posteriori stopping rule. The least squares problem is discretized by a splitting method which reduces the large dimensions of the discretized problem. We calculate the gradient of the objective functional of the discretized least squares problem by the aid of an adjoint discretized problem which enhances its accuracy. The algorithm is tested on several examples, that proves its efficiency.     

A response surface approach for structural reliability analysis using evidence theory

Evidence theory employs a much more general and flexible framework to quantify the epistemic uncertainty, and thereby it is adopted to conduct reliability analysis for engineering structures recently. However, the large computational cost caused by its discrete property significantly influences the practicability of evidence theory. This paper proposes an efficient response surface (RS) method to evaluate the reliability for structures using evidence theory, and hence improves its applicability in engineering problems. A new design of experiments technique is developed, whose key issue is the search of the important control points. These points are the intersections of the limit-state surface and the uncertainty domain, thus they have a significant contribution to the accuracy of the subsequent established RS. Based on them, a high precise radial basis functions RS to the actual limit-state surface is established. With the RS, the reliability interval can be efficiently computed for the structure. Four numerical examples are investigated to demonstrate the effectiveness of the proposed method.     

Hybrid genetic algorithms for structural reliability analysis

The traditional genetic algorithms (GA) involve step-by-step numerical iterations for searching the minimum reliability index of a structural system, and therefore require a relatively long computation time. In practice the size of a design problem can be very large, the limit state functions are usually implicit in terms of the random variables. When using the traditional genetic algorithms, one can encounter problems with the immense effort required in coding ones own finite element code (or for integration with other commercial finite element software) when using the traditional genetic algorithms. For convenient practical applications of the GA in engineering, two new GA methods, namely, a hybrid GA method consisting of artificial neural network (ANN) and a hybrid GA method consisting of ANN and Monte Carlo simulation with importance sampling are proposed in the present study. A distinctive feature of these proposed methods is the introduction of an explicit approximate limit state function. The explicit formulation of the approximate limit state function is derived by using the parameters of the ANN model. By introducing the derived approximate limit state function, the failure probability can be easily calculated, practically when the limit state functions are not explicitly known. These proposed methods are investigated and their accuracy and efficiency are demonstrated using numerical examples. Finally, some important parameters in these proposed methods are also discussed.     

A discrete post-processing method for structural optimization

This paper introduces a discrete variable post-processing method for structural design optimization. The motivation behind the method is to find a good discrete solution at manageable cost while the traditional discrete optimization algorithms are regarded as impractical for large-scale structural design problems. In this paper, the Design of Experiments (DOE) and Conservative Discrete Design (CDD) approaches have been proposed to deal with discrete variables with limited computational cost. Both methods work on the explicit approximate discreteproblem to explore the discrete design. These two approaches, together with engineering rounded-off methods, can be used to process discrete variables at any specified continuous design optimization cycle for structural design problems. Brief background and a theoretical discussion about these approaches are given in this paper. Finally, the methods that have been implemented in MSC.Nastran are demonstrated by academic and real engineering examples.     

A simple method for protein structural classification

Since the concept of structural classes of proteins was proposed, the problem of protein classification has been tackled by many groups. Most of their classification criteria are based only on the helix/strand contents of proteins. In this paper, we proposed a method for protein structural classification based on their secondary structure sequences. It is a classification scheme that can confirm existing classifications. Here a mathematical model is constructed to describe protein secondary structure sequences, in which each protein secondary structure sequence corresponds to a transition probability matrix that characterizes and differentiates protein structure numerically. Its application to a set of real data has indicated that our method can classify protein structures correctly. The final classification result is shown schematically. So it is visual to observe the structural classifications, which is different from traditional methods.     

A pseudo-discrete rounding method for structural optimization

A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denotedselective dynamic rounding, is presented. The method is based on the sequential rounding of a continuous solution and is in its current form used for the optimal discrete sizing design of truss structures. A simple criterion based on discrete variable proximity is proposed for selecting the sequence in which variables are to be rounded, and allowance is made for both upward and downward rounding. While efficient in terms of the required number of function evaluations, the method is also effective in obtaining a low discrete approximation to the global optimum. Numerical results are presented to illustrate the effectiveness and efficiency of the method.