Yan-Gang Zhao

Moment methods for structural reliability

First-order reliability method (FORM) is considered to be one of the most reliable computational methods. In the last decades, researchers have examined the shortcomings of FORM, primarily accuracy and the difficulties involved in searching for the design point by iteration using the derivatives of the performance function. In order to improve upon FORM, several structural reliability methods have been developed based on FORM, such as second-order reliability method (SORM), importance sampling Monte-Carlo simulation, first-order third-moment reliability method (FOTM), and response surface approach (RSA). In the present paper, moment methods for structural reliability are investigated. Five moment method formulas are presented and investigated, and the accuracy and efficiency of these methods are demonstrated using numerical examples. The moment methods, being very simple, have no shortcomings with respect to design points, and requires neither iteration nor the computation of derivatives, and thus are convenient to be applied to structural reliability analysis.

A general procedure for first/second-order reliabilitymethod (FORM/SORM)

First/second-order reliability method (FORM/SORM) is considered to be one of the most reliable computational methods for structural reliability. Its accuracy is generally dependent on three parameters, i.e. the curvature radius at the design point, the number of random variables and the first-order reliability index. In the present paper, the ranges of the three parameters for which FORM/SORM is accurate enough are investigated. The results can help us to judge when FORM is accurate enough, when SORM is required and when an accurate method such as the inverse fast Fourier transformation (IFFT) method is required. A general procedure for FORM/SORM is proposed which includes three steps: i.e. point fitting limit state surface, computation of the sum of the principal curvatures Ks and failure probability computation according to the range of Ks. The procedure is demonstrated by several examples. # 1999 Elsevier Science Ltd. All rights reserved.

Response uncertainty and time‐variant reliability analysis for hysteretic MDF structures

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

Applicable Range of the Fourth–Moment Method for Structural Reliability

Abstract In this paper, the applicable range of the fourth–moment method for structural reliability is investigated and a simple fourth–moment reliability index is suggested. In the applicable range of the fourth–moment method, the simplicity and efficiency of the simple fourth–moment reliability index are demonstrated through several examples.

A Simple Third-Moment Method for Structural Reliability

Abstract The objectives of the present paper are to investigate the applicable range of the third-moment method for structural reliability and to suggest a simple third-moment method for practical application in engineering. The applicable range of the second-moment method is also given. The applicable range of the third-moment method is obtained through investigation of the differences among several third-moment methods. Within the applicable range, it is found that the simple reliability index has a good agreement with the original one, and it is therefore suggested as a simple third-moment reliability index. Since only the first three central moments of the performance functions are used, and since it is unnecessary to know the probability distribution of the basic random variables, the present method should be practical in engineering. In order to investigate the efficiency of the proposed method, several examples are examined under different conditions.

Dynamic Corrosion-induced Cracking Process of RC Considering Effect of Initial Defects

Abstract In this paper, a model of the dynamic corrosion-induced cracking process of reinforced concrete (RC) structures considering the influence of initial defects in concrete cover caused by settlement of concrete is presented. Formulas for predicting time to initial defects initiation, time to cover cracking, threshold expansive pressure and critical weight loss of reinforcing steel are proposed. Comparisons with published experimental data show that the predictions given by the present model are in a good agreement with the experimental results and have better precision than other existing models. Finally, the influences of initial defects on critical corrosion-induced cracking indexes, such as time to initial defects initiation, time to cover cracking, threshold expansion pressure and critical weight loss of reinforcing steel are investigated. It was found that the initial defects have a great effect on critical corrosion-induced cracking indexes. These critical indexes decrease sharply when the size of initial fine crack is less than 1 mm or its number is smaller than 2 respectively, but tend to moderate when the size of the initial fine crack is more than 1 mm or its number is larger than 2. Therefore, it is important to improve the compactness of concrete in order to improve the durability of RC structures.

Monte Carlo Simulation Using Moments of Random Variables

Abstract In the present study, in order to include the random variables with an unknown cumulative distribution function (CDF) into Monte-Carlo Simulation, an inverse normal transformation is suggested. The random variables with an unknown CDF are expressed as a simple function of a standard normal random variable, and the function is determined using the first few statistical moments which are generally available from the statistical data of the random variables. Using the proposed method, the random numbers of random variables with an unknown CDF can be easily generated utilizing those of a standard normal random variable, which is generally considered to be quite easily generated. Some examples are presented from which the efficiency of the method is investigated. It is found that although the method is quite simple, it is accurate enough to includethe random variables with unknown CDF in the Monte-Carlo Simulation for structural reliability.

On the first-order third-moment reliability method

In this article, the reliability evaluation with inclusion of random variable with unknown probability distribution will be discussed, in which the only information of the first three moments of the random variable will be used instead of probability distribution. The second-order polynomial normal transformation technique using the first three central moments is investigated and a pseudo standard normal space is defined based on the investigation. The first-order third-moment reliability analysis in the reduced space and that in the pseudo standard normal space are compared. Through the numerical examples presented, the proposed methods are found to be sufficiently accurate to include the random variables with unknown cumulative distribution functions in the first-order reliability analysis with little extra computational effort.

Time-variant reliability analysis considering parameter uncertainties

It has been realised that the effect of system parameter uncertainties may be very important, even dominant, in time-variant structural reliability. In this study, currently available methods are reviewed, and general performance functions corresponding to dynamic reliability analysis considering parameter uncertainties are investigated. A moment method for time-variant reliability analysis considering parameter uncertainties is developed, and its application is demonstrated through reliability assessment of a prestressed concrete containment. Point estimation is applied to evaluate the first few moments of the general performance function of a structure, from which the moment-based reliability index based on the fourth moment standardisation function can be evaluated without Monte Carlo simulations. The procedure does not require the computation of derivatives or the determination of the design point; thus, it should be computationally effective for time-variant structural reliability assessment.

A quality evaluation method for existing carbonated reinforced concrete members

Objective evaluation of the current quality of existing carbonated reinforced concrete members is important as time may degrade their bearing capacity and rigidity. In this paper, a method in which the weight coefficients of every evaluation factor are determined from the coefficients of variation (COVs) or coefficients of dispersion (CODs) of the standard values of every evaluation factor is proposed in order to evaluate the quality of existing carbonated reinforced concrete members. Because it is unnecessary to gather many experts for evaluating every structure, the method should be more practical and applicable in engineering. Finally, an engineering example shows that this method is feasible to solve the problem of quality evaluation of existing carbonated reinforced concrete members.