Preface

There are two kinds of uncertainties, fussiness and randomness in engineering problems. Several researchers in China and abroad pay attention to the influence of random factors on the structure. In machinery, dam, construction, earthquake and other fields, random factors do have a great impact on the structure. The spatial variability of structural material properties is studied as a random process by many scholars. With the deepening of human understanding, it is not practical to ignore the design of randomness.

In the first chapter, the fuzzy reliability of a single component maintenance system and the repairable series system are studied. Two fuzzy methods for reliability allocation are proposed. The second chapter discusses the reliability of the rigid rotor balance. Based on the sensitivity analysis, a Monte Carlo simulation for the reliability calculation of gears is proposed. Based on the sensitivity analysis, an optimization method for reliability calculation is proposed. The reliability calculation of spring is studied by using the HL-RF method. In the third chapter, optimization design-based HL-RF and IS for the gearbox are proposed. A multi-objective reliability-based fuzzy optimization design for gear box is proposed.

The fourth chapter proposes an improved method of perturbation stochastic finite element to save computational time. In the fifth chapter, differential equations are transformed into linear equations by the Wilson q method. Linear equations are solved by the Successive Over Relaxation method. Anew method of calculating dynamic reliability using the Neumann stochastic finite element is proposed. The sixth chapter discusses the design model of the gearbox established by using the stochastic finite element method. A new method of stochastic finite element for vibration is also proposed. In the last chapter, four stochastic finite element methods are proposed to calculate nonlinear vibration.