﻿ BLDC电机温度退化多段Wiener过程建模<sup>*</sup>
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BLDC电机温度退化多段Wiener过程建模

Multistage temperature degradation modeling for BLDC motor based on Wiener process
YUAN Qingyang, YE Jianhua, LI Xiaogang
School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2017-08-31; Accepted: 2017-10-20; Published online: 2017-11-13 13:19
Corresponding author. YE Jianhua, E-mail:yjhuan@buaa.edu.cn
Abstract: Brushless DC(BLDC) motor is widely used and its temperature degradation process is multistage. It is necessary to establish a multistage degradation model. When the model has several parameters, the parameter estimation process is sensitive to the initial value and easy to end up with a local optimization. This study was based on accelerated degradation data of motors. The normal weighted average filter (Gauss filter) was used to improve the results of estimation for the model parameters. A multistage Wiener model was established by using the transition function to modify linear model. Then, to maximize likelihood function for parameter estimation, the numerical optimization method, improved particle swarm optimization (PSO), was used for cycle calculation. The rationality of multistage model is verified by comparison of the normality of residual with widely used nonlinear Wiener model, and by analysis of theoretical life distribution of models and actual failure distribution of this batch. The modeling results show that the degradation mechanism changes at high speed during the degradation of the motor. Finally, prediction for motor life under this stress was gained by life distribution in different moments of time calculated by nonlinear model, which is important for the prognostics and health management (PHM) of motors.
Key words: brushless DC(BLDC) motor     degradation modeling     multistage Wiener process     particle swarm optimization (PSO) algorithm with simplex method     prognostics and health management (PHM)

1 融合加速退化试验

2 Wiener过程 2.1 线性Wiener过程

1) 任意时刻的增量满足正态分布。

2) 任意不相交的时间段内的增量相互独立。

 (1)

 退化增量范围 数量 [-0.1, 0.1) 22 [-0.2, -0.1)∪[0.1, 0.2) 19 [-0.3, -0.2)∪[0.2, 0.3) 8 [-0.4, -0.3)∪[0.3, 0.4) 1 (-∞, -0.4)∪[0.4, -∞) 0

 (2)

 (3)
 (4)
2.2 多段Wiener过程

 (5)

 (6)

 (7)

 (8)

2.3 寿命预测

 (9)

 (10)
3 自优化PSO算法估计模型参数

3.1 单纯形法

1) 在参数空间{u1, u2, γ, c, x0, σ}中建立7个顶点的正则单纯形，顶点为{d1, d2, d3, d4, d5, d6, d7}, 其中，dj=(u1j, u2j, γj, cj, x0j, σj), 下标j表示点序号。

2) 计算正则单纯形顶点的对数似然函数值为{l1, l2, l3, l4, l5, l6, l7}，选择值最小lk的点dk以备删除。

3) 确定备用点：

 (11)

4) 比较备用点与最差点的对数似然函数值{lnew, lk}，若比之较优，更新dk=dnew；较差，缩短步长或满足精度要求计算停止。

3.2 单纯形法自优化PSO算法

PSO算法具有算法简单、搜索效率较高、通用性较强等优势。在该算法中，寻优空间中的每一个个体被抽象为一个粒子，仅考虑其位置属性和运动属性。其运动的速度受自身和群体的历史最优位置的影响，并受到学习因子的协调，从而较好地协调粒子本身和种群之间的关系。本文使用基于单纯形法的PSO算法，将PSO强大的随机全局搜索能力与精确的局部搜索能力结合，算法首先用PSO算法进行全局搜索，当算法陷入局部最优值时用单纯形法快速找出搜索空间的一个最优解，来代替PSO算法中的停止粒子。其流程如下：

1) 初始化每个粒子的当前位置xj，并将当前位置xj记录为自身历史最优位置pj；计算每个粒子自身历史最优位置pj的评价值，将最优评价值所对应的pg记为种群历史最优位置。

2) 将pg进行一次单纯形法优化，将得到的新单纯形中评价值最优的点作为pg

3) 根据PSO算法迭代公式，更新每个粒子的当前位置xj，并计算xj的评价值。

 (12)

4) 对每个粒子，将当前位置xj的评价值与自身历史最优位置pj的评价值进行比较，若优于pj的评价值，则令pj=xj；对每个粒子，将当前位置xi的评价值与种群历史最优位置pg的评价值进行比较，若优于pg的评价值，则令pg=xj

5) 检查终止条件，若未达到终止条件，返回2)。

4 模型结果与分析

 图 1 似然函数值在循环中的优化过程 Fig. 1 Optimization process of likelihood function value in loop
 图 2 不同Wiener模型漂移过程对比 Fig. 2 Comparison of drift processes in different Wiener models

 图 3 不同Wiener模型理论失效分布对比 Fig. 3 Comparison of theoretical failure distribution in different Wiener models

 图 4 不同Wiener模型残差分布对比 Fig. 4 Comparison of residual distributions in different Wiener models

 图 5 多段模型所得剩余寿命分布预测 Fig. 5 Prediction of remaining life distribution by multistage model
5 结论

1) 建立了BLDC电机退化的多段Wiener过程模型，根据本文提出的多段模型理论，电机在性能退化的过程中其机理发生着变化，并且转化速度较快。

2) 在进行加速寿命试验的过程中，应注意其退化机理的变化；而在机理发生改变时，加速寿命试验时应谨慎进行。

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#### 文章信息

YUAN Qingyang, YE Jianhua, LI Xiaogang
BLDC电机温度退化多段Wiener过程建模
Multistage temperature degradation modeling for BLDC motor based on Wiener process

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(7): 1514-1519
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0546