A novel and efficient simulation method of structural reliability for Gaussian distributed variables by the introduction of a truncated probability density function

Roudak, Mohammad Amin; Farahani, Melika; Badiezadeh, Sepideh; Amiri Beirami, Mobina; Kiashemshaki, Sheida; Karamloo, Mohammad

doi:10.22059/ceij.2025.392268.2275

A novel and efficient simulation method of structural reliability for Gaussian distributed variables by the introduction of a truncated probability density function

Articles in Press

Authors

Mohammad Amin Roudak ¹

Melika Farahani ²

Sepideh Badiezadeh ²

Mobina Amiri Beirami ²

Sheida Kiashemshaki ²

Mohammad Karamloo ³

¹ Department of Civil Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran.

² Department of Civil Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran

³ Department of Civil Engineering, Shahid Rajaee Teacher Training University, Lavizan, Tehran, Iran

10.22059/ceij.2025.392268.2275

Abstract

In structural reliability analysis, finding an effective way to estimate the probability of failure of structures, is one of the most fundamental challenges. Monte Carlo simulation is recognized as a common method for computing the probability of failure among the various existing approaches. However, its inefficiency is still a significant drawback. Since a large number of samples is required to estimate the probability of failure accurately, the Monte Carlo simulation is a time-consuming process. In this paper, a new method is proposed to improve the efficiency of the Monte Carlo simulation. This is carried out by reducing the number of required samples. The basic concept of the presented method is to generate a smaller number of samples, mostly concentrated on the failure region. To accomplish this goal, a specific distance from the mean of the variables is eliminated from the sample generation space. In fact, the samples are generated based on a truncated joint probability density function. This leads to a significant reduction in the number of generated samples, enhancing the efficiency of the estimation. The accuracy and efficiency of the presented method are validated using various examples.

Keywords

Monte Carlo simulation

Probability of failure

Truncated joint probability density function

Sampling approach

Subjects