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Fatigue life estimation, reliability and durability are important in acquisition, maintenance and operation of vehicle systems. Fatigue life is random because of the stochastic load, the inherent variability of material properties, and the uncertainty in the definition of the S-N curve. The commonly used fatigue life estimation methods calculate the mean (not the distribution) of fatigue life under Gaussian loads using the potentially restrictive narrow-band assumption. In this paper, a general methodology is presented to calculate the statistics of fatigue life for a linear vibratory system under stationary, non-Gaussian loads considering the effects of skewness and kurtosis. The input loads are first characterized using their first four moments (mean, standard deviation, skewness and kurtosis) and a correlation structure equivalent to a given Power Spectral Density (PSD).

Laboratory based durability simulation has become an increasingly important component of vehicle system design validation and production release. It offers several advantages over field testing which has driven its adoption in the automotive and military sectors. Among these advantages are 1) repeatability, 2) earlier testing, 3) isolation of subsystems or components and 4) ability to compress and/or accelerate the testing. In this paper we present time-domain methods and techniques adapted, implemented and used at TARDEC to reduce the time required to perform a laboratory durability test of a full vehicle system, subsystem or component. Specifically, these methods approach a durability schedule holistically by considering all events/surfaces, repeats and channels of interest. They employ the standard Generic Stress Life (GSL) approach, utilizing rain flow cycle counting and a minimum-average method of identifying segments of the events which are less severe.

The United States Army Tank Automotive Research, Development and Engineering Center (TARDEC) built systems to measure the suspension parameters, center of gravity, and moments of inertia of wheeled vehicles. This is part of an ongoing effort to model and predict vehicle dynamic behavior. The new machines, the Suspension Parameter Identification and Evaluation Rig (SPIdER) and the Vehicle Inertia Parameter Evaluation Rig (VIPER), have sufficient capacity to cover most heavy, wheeled vehicles. The SPIdER operates by holding the vehicle sprung mass nominally fixed while hydraulic cylinders move an “axle frame” in bounce or roll under each axle being tested. Up to two axles may be tested at once. Vertical forces at the tires, displacements of the wheel centers in three dimensions, and steer and camber angles are measured.

Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches to calculate the corresponding conditional probability of failure. A Kriging metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure and the failure rate of the dynamic system. The proposed method is demonstrated using a vibratory system.

We propose a new metamodeling method to characterize the output (response) random process of a dynamic system with random parameters, excited by input random processes. The metamodel can be then used to efficiently estimate the time-dependent reliability of a dynamic system using analytical or simulation-based methods. The metamodel is constructed by decomposing the input random processes using principal components or wavelets and then using a few simulations to estimate the distributions of the decomposition coefficients. A similar decomposition is also performed on the output random process. A kriging model is then established between the input and output decomposition coefficients and subsequently used to quantify the output random process corresponding to a realization of the input random parameters and random processes. What distinguishes our approach from others in metamodeling is that the system input is not deterministic but random.

Design optimization often relies on computational models, which are subjected to a validation process to ensure their accuracy. Because validation of computer models in the entire design space can be costly, we have previously proposed an approach where design optimization and model validation, are concurrently performed using a sequential approach with variable-size local domains. We used test data and statistical bootstrap methods to size each local domain where the prediction model is considered validated and where design optimization is performed. The method proceeds iteratively until the optimum design is obtained. This method however, requires test data to be available in each local domain along the optimization path. In this paper, we refine our methodology by using polynomial regression to predict the size and shape of a local domain at some steps along the optimization process without using test data.