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Reliability assessment of dynamic systems with low failure probability can be very expensive. This paper presents and demonstrates a method that uses the Metropolis-Hastings algorithm to sample from an optimal probability density function (PDF) of the random variables. This function is the true PDF truncated over the failure region. For a system subjected to time varying excitation, Shinozuka's method is employed to generate time histories of the excitation. Random values of the frequencies and the phase angles of the excitation are drawn from the optimal PDF. It is shown that running the subset simulation by the proposed approach, which uses Shinozuka's method, is more efficient than the original subset simulation. The main reasons are that the approach involves only 10 to 20 random variables, and it takes advantage of the symmetry of the expression of the displacement as a function of the inputs. The paper demonstrates the method on two examples.

Reliable testing of a mechanical system requires the procedures used for the evaluation to be repeatable and reproducible. However, it is never possible to exactly repeat or reproduce the tests that are used for evaluation. To overcome this limitation, a statistical evaluation procedure can generally be used. However, most of the statistical procedures use scalar values as input without the ability to handle vectors or time-histories. To overcome these limitations, two numerical/statistical methods for determining if the impact time-history response of a mechanical system is repeatable or reproducible are evaluated and elaborated upon. Such a system could be a vehicle, a biological human surrogate, an Anthropometric Test Device (ATD or dummy), etc. The responses could be sets of time-histories of accelerations, forces, moments, etc., of a component or of the system. The example system evaluated is the BioRID II rear impact dummy.

The common practice in finite element based fatigue calculation with multiple channels of road load is to perform a set of unit load static stress analysis and conduct stress time history construction later during fatigue calculation. The main advantage of this so-called quasi-static finite element based fatigue calculation is to avoid time-consuming dynamic stress analysis and also reduce static stress analysis from millions of real load cases to a few dozens unit-load cases. The main disadvantage of this quasi-static finite element based fatigue calculation is the absence of vibration-induced stresses in stress time history construction and fatigue analysis. A decade ago, a modal transient finite element based fatigue calculation was proposed to introduce vibration-induced stresses into finite element based fatigue calculation. The idea is to add vibration-induced modal stresses to load-induced instant stresses in stress time history construction and fatigue calculation.

The Cardan joint of a steerable beam front axle is a complicated mechanical component. It is subjected to drive torque, speed fluctuations, and joint articulation due to powertrain inputs, steering, and suspension kinematics. This combination of high torque and speed fluctuations of the Cardan joint, due to high input drive torque and/or high steer angle maneuvers, can result in premature joint wear. Initially, some observations of premature wear were not well understood based on the existing laboratory and road test data. The present work summarizes a coordinated program of computer modeling, vehicle Rough Road data acquisition, and physical testing used to predict the joint dynamics and to develop advanced testing procedures. Results indicate analytical modeling can predict forces resulting from Cardan joint dynamics for high torque/high turn angle maneuvers, as represented by time history traces recorded in rough road data acquisition.