The relationships between the fatigue crack growth rate $\left(da/dN\right)$ and stress intensity factor range $\left(\Delta K\right)$ are not always linear even in the Paris region. The stress ratio effects on fatigue crack growth rate are diverse in different materials. However, most existing fatigue crack growth models cannot handle these nonlinearities appropriately. The machine learning method provides a flexible approach to the modeling of fatigue crack growth because of its excellent nonlinear approximation and multivariable learning ability. In this paper, a fatigue crack growth calculation method is proposed based on three different machine learning algorithms (MLAs): extreme learning machine (ELM), radial basis function network (RBFN) and genetic algorithms optimized back propagation network (GABP). The MLA based method is validated using testing data of different materials. The three MLAs are compared with each other as well as the classical two-parameter model ( $K^{*}$ approach). The results show that the predictions of MLAs are superior to those of $K^{*}$ approach in accuracy and effectiveness, and the ELM based algorithms show overall the best agreement with the experimental data out of the three MLAs, for its global optimization and extrapolation ability.

Lamb waves have been reported to be an efficient tool for non-destructive evaluations (NDE) for various application scenarios. However, accurate and reliable damage quantification using the Lamb wave method is still a practical challenge, due to the complex underlying mechanism of Lamb wave propagation and damage detection. This paper presents a Lamb wave damage quantification method using a least square support vector machine (LS-SVM) and a genetic algorithm (GA). Three damage sensitive features, namely, normalized amplitude, phase change, and correlation coefficient, were proposed to describe changes of Lamb wave characteristics caused by damage. In view of commonly used data-driven methods, the GA-based LS-SVM model using the proposed three damage sensitive features was implemented to evaluate the crack size. The GA method was adopted to optimize the model parameters. The results of GA-based LS-SVM were validated using coupon test data and lap joint component test data with naturally developed fatigue cracks. Cases of different loading and manufacturer were also included to further verify the robustness of the proposed method for crack quantification.

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper, a general ADT model based on the Wiener process is proposed to solve the problem for accelerated degradation data analysis. The general model can consider the unit-to-unit variation and temporal variation of the degradation process, and is suitable for both linear and nonlinear ADT analyses with single or multiple acceleration variables. The statistical inference is given to estimate the unknown parameters in both constant stress and step stress ADT. The simulation example and two real applications demonstrate that the proposed method can yield reliable lifetime evaluation results compared with the existing linear and time-scale transformation Wiener processes in both linear and nonlinear ADT analyses.

Accelerated degradation testing (ADT) is an efficient technique for evaluating the lifetime of a highly reliable product whose underlying failure process may be traced by the degradation of the product’s performance parameters with time. However, most research on ADT mainly focuses on a single performance parameter. In reality, the performance of a modern product is usually characterized by multiple parameters, and the degradation paths are usually nonlinear. To address such problems, this paper develops a new s-dependent nonlinear ADT model for products with multiple performance parameters using a general Wiener process and copulas. The general Wiener process models the nonlinear ADT data, and the dependency among different degradation measures is analyzed using the copula method. An engineering case study on a tuner’s ADT data is conducted to demonstrate the effectiveness of the proposed method. The results illustrate that the proposed method is quite effective in estimating the lifetime of a product with s-dependent performance parameters.

Degradation modeling and remaining useful life (RUL) prediction for products with multiple degradation features are hot topics in the prognostic and health management. The key to this problem is to describe the dependence among multiple degradation features effectively. In this paper, a multivariate degradation modeling approach based on the Bayesian dynamic linear model (BDLM) is proposed to calculate the RULs of degradation features, and the Copula function is employed to capture the dependence among RUL distributions. A combined BDLM is used to establish the multivariate degradation model, which includes two typical BDLMs, namely, the linear growth model and seasonal factors model. After the model parameters get calibrated by the maximum likelihood estimation, the model can predict the degradation process of features. Once the failure thresholds are given, the probability density function and cumulative distribution function (CDF) of RUL for each degradation feature can be obtained. Since these RUL distributions are not independent of each other, the Copula function is adopted herein to couple the CDFs. Finally, some practical testing data of a microwave component, which has two degradation features, are utilized to validate our proposed method. This paper provides a new idea for the multivariate degradation modeling and RUL prediction.