不完全加速退化的三参数幂模型线性化方法

马小兵; 常士华; 陈云霞

不完全加速退化的三参数幂模型线性化方法

北京航空航天大学可靠性与系统工程学院, 北京 100191

基金项目: 国家自然科学基金资助项目(61104133); 质检公益行业科研专项(201010218)

详细信息

中图分类号: TB 114.3; V 241.4
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出版历程
- 收稿日期: 2012-03-21
- 网络出版日期: 2013-04-30

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

School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 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.
- 非线性 /
- 不完全加速退化 /
- 相关系数 /
- 三参数幂函数
Abstract: 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 accelerometer. The method was based on the assumption that the exponential parameter of power function is independent 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 threshold. Therefore, the degradation trajectory at the maximum stress level can better reflect the law of the degradation 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 degradation paths.
- nonlinear /
- incomplete accelerated degradation /
- correlation coefficient /
- power function with three parameters

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参考文献(14)

[1]	包为民,申功勋,李华滨.惯性平台在系统中多位置翻滚自标定方法[J].北京航空航天大学学报,2011,37(4):462-465 Bao Weimin,Shen Gongxun,Li Huabin.Investigation on inertial platform multi-position rolling self-calibration[J].Journal of Beijing University of Aeronautics and Astronautics,2011,37(4):462-465(in Chinese)
[2]	谢森,王玉.非线性系统完全线性化方法的研究[J].控制理论与应用,1997,14(1):139-143 Xie Sen,Wang Yu.Complete linearization control method for nonlinear system[J].Control Theory and Applications,1997,14(1):139-143(in Chinese)
[3]	Cheng D,Isidori A,Respondek W,et al.Exact linearization of nonlinear systems with outputs[J].Math Systems Theory,1986,21:247-255
[4]	史小平,王子才.非线性系统线性化的一种新方法[J].哈尔滨工业大学学报,1998,30(2):68-71 Shi Xiaoping,Wang Zicai.A new method for liearizing monlinear systems[J].Journal of Harbin Institute of Technology,1998,30(2):68-71(in Chinese)
[5]	陈静,王轶卿.近似线性化与精确线性化的分析与比较[J].机械与电子,2008(5):20-22 Chen Jing,Wang Yiqing.The analysis and comparison between approximate linearization and precise linearization[J].Mechanical and Electronic,2008(5):20-22(in Chinese)
[6]	Marcos A,Balas G J.Development of linear parameter varying models for aircraft .Journal of Guidance,Control,and Dynamics,2004,27(2):218-228
[7]	Sinha P K,Pechev A N.Nonlinear H_∞ controllers for electromagnetic suspension systems [J].IEEE Trans Automatic Control,2004,49 (4):563-568
[8]	Vladimir Balan,Cristina Stefania Stamin.State space exact linearization and stabilization with feedback control in SODE economic models[J].Journal of Applied Mathematics and Computing,2008,28(1):271-281
[9]	陶菊春,吴建民.可线性化非线性回归预测模型的剖析与改进[J].数学的实践与认识,2003(2):7-12 Tao Juchun,Wu Jianmin.Analysis and improvement to linearization nonlinear regression model[J].Mathematics in Practice and Theory,2003(2):7-12(in Chinese)
[10]	佘焱,吴波.一般非线性系统的精确线性化[J].上海交通大学学报,1999,33(12):1599-1601 She Yan,Wu Bo.Exact linearization for general nonlinear control system[J].Journal of Shanghai Jiaotong University,1999,33(12):1599-1601(in Chinese)
[11]	韩志涛,井元伟,段晓东,等.一般非线性系统的相关阶与线性化[J].控制与决策,2006,21(9):1065-1067 Han Zhitao,Jing Yuanwei,Duan Xiaodong,et al.Relative degree and linearization of general nonlinear system[J].Control and Decision,2006,21(9):1065-1067(in Chinese)
[12]	孟范伟,何朕,王毅,等.非线性系统的线性化[J].电机与控制学报,2008,12(1):89-92 Meng Fanwei,He Zhen,Wang Yi,et al.Linerization of a nonlinear system[J].Electric Machines and Control,2008,12(1):89-92(in Chinese)
[13]	Cheng Daizhan,Li Zhiqiang.A survey on linerization of nonlinear systems[J].Journal of Shandong University:Engineering Science,2009,39(2):26-36
[14]	和丽清,孙先仿,邱红专.非线性系统的结构选择及其参数的集员辨识[J].北京航空航天大学学报,2010,36(10):1189-1193 He Liqing,Sun Xianfang,Qiu Hongzhuan.Structure selection and parameter set-membership identification for non linear systems[J].Journal of Beijing University of Aeronautics and Astronautics,2010,36(10):1189-1193(in Chinese)