GARCH based degradation modeling of solder joint under vibration loading

The degradation behavior of the solder joint under constant vibration loading is discussed, the voltage value at both sides of the solder joint is taken as the degradation characteristic. Considering the heteroskedasticity of characteristic signal under the vibration loading, the general time series model cannot describe heteroskedasticity, a Generalized Autoregressive Conditional Heteroskedastic model (GARCH) is proposed. Firstly, the upper and lower quantiles of the voltage signal are extracted. The failure time is determined by using the upper quantile and the degradation process is analyzed by the lower quantile. Secondly, the Auto-Regressive(AR) is built as the regressive basic model. Thirdly, a GARCH(1,1) model is proposed, which is tested by the Autoregressive Conditional Heteroskedastic (ARCH) method, the parameters of the model is estimated by the Maximum Likelihood algorithm. Finally, the performance of the presented GARCH based degradation model is examined by real data from experiment, which is compared with the classical AR model according to Akaike Information Criterion(AIC). The results suggest that GARCH(1,1) is superior to AR model, presented a theoretical foundation for further study about the degradation modeling of solder joint under vibration loading.