不完全加速退化的三参数幂模型线性化方法

Method for linearize power function with three parameters of incomplete accelerated degradation data

针对加速度计零偏和标度因数不完全加速退化数据的非线性预测问题,提出一种加速度计加速退化的三参数幂函数模型线性化方法.该方法假设三参数幂函数退化轨迹模型的幂指数与加速应力无关,考虑到不同应力水平的试验时间相当时,较高应力下的参数退化速率较快,其退化轨迹与较低应力水平的相比,退化量更加接近性能参数的失效阈值,而低应力水平下退化量与失效阈值差距较大,因此最高应力水平下的退化轨迹更能反映加速度计性能参数的长期非线性退化规律.据此进一步提出了加速退化数据三参数幂函数模型幂指数确定的均方相关系数最大化原则,该原则通过高应力水平试验数据确定模型的幂指数,由此实现三参数幂函数模型的线性化,克服由于初值敏感而导致模型预测时稳健性较差的问题.为加速退化轨迹非线性模型的预测提供了一种工程化方法.

A method was provided to linearize the power function with three parameters. It was in view of the nonlinear prediction with the incompletely accelerated degradation paths of null bias and scale factor of ac- celerometer. The method was based on the assumption that the exponential parameter of power function is in- dependent with stresses. Due to the degradation rate was faster at the higher stress than that at the lower, and its degradation amount was close to the failure threshold, while the lower were far away from the failure thresh- old. Therefore, the degradation trajectory at the maximum stress level can better reflect the law of the degrada- tion models. Accordingly, a principle called the maximum average correlation coefficient at the maximum stress level to determine the exponential parameter was put forward. Through this principle, the power function with three parameters is linearized, which overcomes the poor robustness of the model prediction due to the sensitive initial value and provides an engineering method for the prediction of nonlinear accelerated degrada- tion paths.