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In recent years, accelerated destructive degradation testing (ADDT) has been applied to obtain the reliability information of an asset (component) at use conditions when the component is highly reliable. In ADDT, degradation data are measured under stress levels more severe than usual so that more component failures can be observed in a short period. In the literature, most application-specific ADDT models assume a parametric degradation process under different accelerating conditions. Models without strong parametric assumptions are desirable to describe the complex ADDT processes. This paper proposes a general ADDT model that consists of a nonparametric part to describe the degradation path and a parametric part to describe the accelerating-variable effect. The proposed model not only provides more model flexibility with few assumptions, but also retains the physical mechanisms of degradation. Due to the complexity of parameter estimation, an efficient method based on self-adaptive differential evolution is developed to estimate model parameters. A simulation study is implemented to verify the developed methods. Two real-world case studies are conducted, and the results show the superior performance of the developed model compared with the existing methods.