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This paper introduces an efficient methodology for evaluating the first four central moments of performance functions in structural reliability assessment. The procedure of the proposed method is d...

Bayesian updating of the reliability of deteriorating engineering structures based on inspection data has been attracting a lot of attention recently because it can provide more accurate es...

In this paper, a new analytical formula is proposed to determine the mean outcrossing rate of nonstationary non-Gaussian performance functions. The performance function is firstly transform...

Structural reliability analysis involving highly nonnormally distributed performance functions or relatively small failure probabilities is still a challenging problem in engineering practi...

Probability distributions of basic random variables are essential for the accurate evaluation of structural reliability. In engineering practice, the probability distributions of some random variables are often unknown and the only available information about these may be their statistical moments. To conduct structural reliability analysis without the exclusion of random variables with unknown probability distributions, the fourth-moment normal transformation (FMNT) has been proposed. However, the applicability of expression of the FMNT has not been sufficiently investigated. Furthermore, the monotonic regions of the FMNT are not defined without which the application of the transformation is inconvenient, or even unreliable in reliability analysis. In the present paper, a complete expression of the FMNT including six cases with different combinations of skewness and kurtosis is derived, and the monotonicity of each case of the FMNT expression is confirmed. Literature suggests that the complete monotonic expression of the fourth-moment normal transformation is the first time to be successfully accomplished up to date. Through the numerical examples, the FMNT is found to be quite efficient for normal transformation and to be sufficiently accurate to include random variables with unknown probability distributions in structural reliability analysis.

In practical engineering, the probability distributions of some random variables are often unknown, and the only available information about these may be their statistical moments. To conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions, an explicit fourth-moment standardization function has been proposed, and a single expression of its inverse transformation, that is, normal transformation, with limitations of inputting sets of the third and fourth moments (skewness and kurtosis) of random variables was derived. However, the clear definition of the complete expressions of the inverse transformation of fourth-moment standardization function under different combinations of skewness and kurtosis of random variables has not been provided yet. It is in this regard that four criteria are proposed to derive the complete inverse transformation of fourth-moment standardization function, and then the complete expressions of the inverse transformation are formulated. Through the numerical examples presented, the proposed complete expressions are found to be quite efficient for normal transformations and to be sufficiently accurate to include random variables with unknown probability distributions in structural reliability assessment.

The third-moment (3M) method has been considered to be one of the most reliable methods for calculating structural reliability with high computing efficiency. This paper proposes a new 3M reliabili...

In structural reliability analysis, the input variables are often nonnormal and correlated. A procedure for efficient normal transformation, i.e., transforming dependent nonnormal random va...

Estimation of statistical moments of performance functions is one of the main topics in structural reliability analysis by moment methods. It is possible to apply the well-developed multipl...

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 ...

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.