Study On A Method Of Computing Reliability With An Approximation Of Failure Domain Combination

High reliability is an important guarantee to improve product quality and competitiveness. The improvement of the reliability calculation accuracy is an important topic in the reliability theory. So far, the mainstream method of the reliability calculation is the First Order Reliability Method(FORM), Second Order Reliability Method(SORM) and Monte Carlo Simulation Method(MCSM). For a linear performance function, one order reliability method may abtain an exact solution. For a non-linear performance function, second oder reliability can improve precision of reliability calculation, but the improved degree of accuracy is still impossible to estimate. However, Monte Carlo simulation method seems to be a universal approach. In fact, a linear performance function is obtained at design point for one order reliability method, a quadratic performance function is obtained at design point for the second order reliability method, and then the reliability is computated. Although reliability calculation of the linear performance function or the quadratic performance function is easier than the original performance function, but the differences between the failure domains of the two alternative performance functions and the failure domain of original performance function is not ignored, and therefore there must be calculation errors.Obviously, a simple linear performance function or a quadratic performance function is used to replace the original performance function in order to estimate the reliability easily. However, the accuracy of reliability caculation may not be guaranteed. If the multiple linear or quadratic performance functions are applied to replace the original performance function, and the combination failure domain of the approximate functions is sufficiently close to the failure domain of the original performance function, and the probability calculation of combination failure domain is sufficiently close to the failure probability of the original performance function. As a result, the reliability calculation accuracy of the original performance function is improved. The main content and innovation of thesis are as follows:(1) Methods to obtain approximate functionMainly for the most probable failure region of the performance function is convex set, approximation function construction was further discussed and researched to guarantee failure domain of approximation functions can approxiamte the origianl failure domain with high accuracy, which makes a solid foundation for further improving the accuracy of reliability calculation. PSO was uesed to obtain multiple design points and main linear approximation functions. For the performance function with high nonlinearity, the important direction method was proposed to bulid sub-linear approximation function, which makes up for the shortcomings of the existing methods. The improved Chen’s method, hyperspherical polar coordinate method and rotation method were also proposed, as necessary supplement. The parabolic method was proposed to obtain the quadratic approximation function, which is insensitive to the nonlinearity degree of performance function than existing methods. At the same time, the one-step response surface method was put forward as a necessary supplement.(2) Reliability calculation for convex safety or failure domainFocus on the reliability calculation method with high accuracy by combinating failure domain of linear approximation functions. For the equivalent main approximation plane was successive established, the failure area of approximation function can successively approximate the original failure domain. The approximation accuracy can also successively improve. When the failure area of equivalent main approximation plane closes to the original failure domain, reliability is also close to the exact value. In addition, the existing linearization point iterative search direction in the Chen’s method was improved, which improves the method’s generality. Through studying failure region combination of linear approximation function, a linear convex probability integral area combination was put forward to approximate the original failure domain, and then the linear convex method was proposed to calculate the reliability of the original failure domain with high accuracy.(3) Reliability calculation of non-convex safety or failure domainFocus on the reliability calculation of system consisted of multiple most probable failure regions. Multiple design points and the most probable failure regions are first found out, and the structural reliability calculation was transformed into system reliability of multiple most probable failure regions. When the design point is a inflection point, the improved linear convex region method and the improved Feng’s method were developed to construct the main equivalent plane of the most probable failure region. The most probable failure region was approximated by the failure domain of the main equivalent plane. The reliability calculation of the system consisted of multiple most probable failure regions was transformed into reliability calculation of the system consisted of multiple failure domains of the main equivalent plane. The progressive cumulative method and successive equivalent method were put forward to calculate the system reliability. This is a further improvement and development of the existing linear approximation method.(4) Quadratic approximation to calculate the reliabilityAim at the reliability calculation of the performance function with multiple peaks and valleys, the original failure domain was divided into some local failure domains. Taking the original failure domain as the "top event" and the local failure area as the "bottom event", the local failure regions were combined to approximate the original failure domain by using the minimum cut set. The construction of quadratic function failure region is researched to approximate local failure region. The local failure region reliability was estimated by the system reliability-ef-quadratic function failure regions. Finally, the high accurate structural reliability was obtained by the reliability of local failure domain system.(5) Application of approximation method in reliability computationThe reliability calculation for the pull rod, bolt, output shaft and mplitude of the tuning system were used to illustrate the feasibility and effectiveness of the proposed approximation method in reliability calculation. Also, the approximation method in reliability sensitivity calculation and system reliability calculation were discussed.