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Model validation metrics have been developed to provide a quantitative measure that characterizes the agreement between predictions and observations. In engineering design, the metrics become useful for model selection when alternative models are being considered. Additionally, the predictive capability of a computational model needs to be assessed before it is used in engineering analysis and design. Due to the various sources of uncertainties in both computer simulations and physical experiments, model validation must be conducted based on stochastic characteristics. Currently there is no unified validation metric that is widely accepted. In this paper, we present a classification of validation metrics based on their key characteristics along with a discussion of the desired features. Focusing on stochastic validation with the consideration of uncertainty in both predictions and physical experiments, four main types of metrics, namely classical hypothesis testing, Bayes factor, frequentist’s metric, and area metric, are examined to provide a better understanding of the pros and cons of each. Using mathematical examples, a set of numerical studies are designed to answer various research questions and study how sensitive these metrics are with respect to the experimental data size, the uncertainty from measurement error, and the uncertainty in unknown model parameters. The insight gained from this work provides useful guidelines for choosing the appropriate validation metric in engineering applications.

This paper introduces a new phenomenological cumulative damage rule to predict damage and fatigue life under variable amplitude loading. The rule combines a residual S-N curve approach and a material memory concept to describe the damage accumulation behavior. The residual S-N curve slope is regarded as a variable with respect to the loading history. The change in slope is then used as a damage measure and quantified by a material memory degeneration parameter. This model improves the traditional linear damage rule by taking the load-level dependence and loading sequence effect into account, which still preserves its superiority. A series of non-uniform fatigue loading protocols are used to demonstrate the effectiveness of the proposed model. The prediction results using the proposed model are more accurate than those using three popular damage models. Moreover, several common characteristics and fundamental properties of the chosen fatigue models are extracted and discussed.

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Many structures are subjected to variable amplitude loading in engineering practice. The foundation of fatigue life prediction under variable amplitude loading is how to deal with the fatigue damage accumulation. A nonlinear fatigue damage accumulation model to consider the effects of load sequences was proposed in earlier literature, but the model cannot consider the load interaction effects, and sometimes it makes a major error. A modified nonlinear damage accumulation model is proposed in this paper to account for the load interaction effects. Experimental data of two metallic materials are used to validate the proposed model. The agreement between the model prediction and experimental data is observed, and the predictions by proposed model are more possibly in accordance with experimental data than that by primary model and Miner's rule. Comparison between the predicted cumulative damage by the proposed model and an existing model shows that the proposed model predictions can meet the accuracy requirement of the engineering project and it can be used to predict the fatigue life of welded aluminum alloy joint of Electric Multiple Units (EMU); meanwhile, the accuracy of approximation can be obtained from the proposed model though more simple computing process and less material parameters calling for extensive testing than the existing model.

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