基于D-S证据理论的信息融合及在可靠性数据处理中的应用研究
|
摘要
随着科学技术的突飞猛进,现代设备和产品朝着大型化、高速化、精密化、一体化的方向快速发展。由于这些设备和产品与人类社会发展及人民生活的联系日益紧密,设备与产品的可靠性越来越受到重视,对可靠性的要求也越来越高。可靠性工程是一个覆盖设备和产品全生命周期的系统工程。可靠性设计、可靠性分配、可靠性评估、可靠性预计、可靠性管理等,都是可靠性工程的范畴。通过几十年的发展,现在已经形成了一整套的可靠性工程方面的理论与方法。传统的可靠性工作是基于可靠性数据的,通过收集的数据,运用以概率论为基础的理论与方法进行分析。
但是,在对一些大型、高精密、复杂设备进行可靠性分析时,却面临可靠性数据缺少的问题。造成可靠性数据缺少的原因主要包括设备本身的高可靠以致可以收集到的失效数据较少,设备的高成本以致无法进行寿命实验收集失效数据,设备的结构复杂以致可靠性实验的进行比较困难,前期可靠性工作的缺失以致可靠性数据积累不足。
可靠性数据不足称为小样本,小样本无法从概率层面上反映设备的失效规律。在小样本情况下,仍然采用以概率论为基础的可靠性理论与方法进行分析与处理,得到的结果将无法让人信服。
其实,在设备和产品的整个生命周期中,除了实验和现场收集的失效数据外,还有很多的数据和信息可以在一定程度上和一定层面上反映设备和产品的可靠性特性。在可靠性数据缺少的情况下,如果能将这些数据和信息进行综合利用,得到的结论将比只利用可靠性数据得到的结论更有说服力。
本文以反映设备和产品可靠性特性的这些数据和信息的综合利用为契机,采用以D-S证据理论信息融合的方法对这些数据和信息进行分析,以期得到更能反映设备和产品可靠性水平和特性的结论。
本文的主要内容如下:
(1)针对现在普遍使用的带权限的D-S证据理论融合算法在证据出现较大冲突时,如果证据权限处于特殊状态,融合结论与常规思维推理结论相悖的问题,通过对证据之间冲突情况的分析,采用集群效应的方法,消弱“坏”对最后融合结论的影响。根据整体冲突程度进行融合权限的再分配。用数值算例对原融合算法和改进后的融合算法的融合结论进行比较分析。
(2)D-S证据理论融合算法研究。当辨识框架的维数和证据数量增加的时候,融合计算量将显著增加,特别是在融合过程中加入了权限之后,计算复杂度也会显著增加,这给工程上应用D-S证据理论融合算法进行信息快速融合带来了困难。针对这一问题,通过向量空间分析,将辨识框架的可能假设转化成向量空间中相互垂直的方向,利用向量空间中向量的相加来处理证据融合问题。
(3)针对D-S证据理论融合算法应用中,基本概率分布的确定时,采用统计数据构造会忽略掉原始统计数据的分布信息问题,将数据分布信息纳入到融合算法中,通过评价融合结论的分布情况来评定融合结论的可信度,并为多层信息融合提供层次间基本概率分配(Basic Probability Assignments,BPAs)和分布信息传递方法。
(4)针对可靠性数据处理中的寿命数据回归分析中原始数据出现明显的分组状况,将分组情况所包含的信息纳入到融合过程中,提出了样本特征预处理方法(Sample Character Preprocess Method,SCPM)。在此基础上提出了可靠性数据和信息融合框架。
(5)以某柴油发动机涡轮增压器的FMECA分析中的风险评估问题为例,在可靠性数据缺少的情况下,以专家评判信息为基础,用风险优先数的方法进行风险评价和排序。分别用D-S证据理论、向量空间分析为基础的简便融合方法和可靠性信息融合框架方法进行计算分析,结果表明,在工程实际中,信息融合可以在不同的层次进行,选择不当可能造成融合结论不可用。
The development of science and technology lead modern device to large-scale, high-speed, precision and integration. Because the relationship between device and human social development and people life, the reliability of equipment and product gets more and more attention, the requirement to reliability are also getting higher.
Reliability engineering is an engineering system through device and produce life cycle. Reliability design, reliability allocation, reliability evaluation, reliability prediction and reliability management are the entire reliability engineering category. With decades of development, people have built a complete reliability theory and method system. Traditional reliability work is based on reliability data, and the theory and method are based on Probability theory.
Unfortunately, we face the problem of lack of reliability data with some large scale, high precision, and complex equipment. The reason of lack of reliability data including high reliability leading lack of failure records, high value leading life experiment hard to be carry on, the defect of reliability work leading reliability data accumulation insufficiency.
The situation of lack of reliability is called small sample, small sample can not reflect the failure regularity and status on the probability level. If we handle the reliability data with traditional reliability theory and method in the situation of small sample, the analysis result is convincing.
In fact, in the whole life cycle of device and product, beside the failure data collected in the experiments and in the using period, there are more data and information which could reflect the device and product’s reliability characters could be got. If we can get these data and information, and make use of these data and information in situation of small sample, we must get more convincing conclusion than the tradition method.
This paper proposes to make use of these useful reliability data and information, and get more convincing conclusion based on D-S evidence theory.
The main work and contribution of this paper is as follow:
(1) Traditional weighted D-S evidence theory combination rule has a unavoidable shortage, when the evidence conflict level is high, and the weight factors of evidence is in a special situation, the fusion result may be contrary to the rational thinking. This paper use cluster effect reduce the influence of“bad”evidence through the analysis to the evidence conflict, reassign weight factor according to the whole conflict level. And compare the fusion result of traditional evidence combination rule and the improved one.
(2) Fusion information with D-S evidence theory combination rules, the computation quantity will increase fast when the number of hypothesis and evidence increase, especially in the weighted evidence theory combination rules. This character lead D-S evidence theory combination rule is hard to be implying in engineering practice in some situation. Through vector space analysis, this paper propose a simple information fusion method, which converse the hypothesis in evidence theory into the vertical directions in vector space, and use the vector adding method the handle the information fusion problem.
In evidence theory, the distribution information will be ignored in the determination of BPAs with statistics data. To avoid this shortage, this paper proposes a method which brings the distribution information into the fusion process, and evaluates the fusion result’s credibility with the distribution of fusion result. This method also gives the BPAs and distribution information transmission way in multilayer fusion structure.
In reliability data analysis practice, we face a situation that the collected data could be grouped in some sets, and there is clear difference among these sets which could not be ignored. This paper proposes a sample character preprocess method, and make use of these sets information in the fusion procedure. And propose the reliability data and information fusion framework on the base of SCPM.
In the FMECA analysis to a diesel turbocharger practice, we can not get enough reliability data, and use experts’judgments to risk analysis. With these expert judgments, we use the traditional D-S evidence theory combination rule, simple information fusion method based on vector space analysis and the reliability data and information fusion framework to handle these expert judgments, compare and analysis the results of these three method.
但是,在对一些大型、高精密、复杂设备进行可靠性分析时,却面临可靠性数据缺少的问题。造成可靠性数据缺少的原因主要包括设备本身的高可靠以致可以收集到的失效数据较少,设备的高成本以致无法进行寿命实验收集失效数据,设备的结构复杂以致可靠性实验的进行比较困难,前期可靠性工作的缺失以致可靠性数据积累不足。
可靠性数据不足称为小样本,小样本无法从概率层面上反映设备的失效规律。在小样本情况下,仍然采用以概率论为基础的可靠性理论与方法进行分析与处理,得到的结果将无法让人信服。
其实,在设备和产品的整个生命周期中,除了实验和现场收集的失效数据外,还有很多的数据和信息可以在一定程度上和一定层面上反映设备和产品的可靠性特性。在可靠性数据缺少的情况下,如果能将这些数据和信息进行综合利用,得到的结论将比只利用可靠性数据得到的结论更有说服力。
本文以反映设备和产品可靠性特性的这些数据和信息的综合利用为契机,采用以D-S证据理论信息融合的方法对这些数据和信息进行分析,以期得到更能反映设备和产品可靠性水平和特性的结论。
本文的主要内容如下:
(1)针对现在普遍使用的带权限的D-S证据理论融合算法在证据出现较大冲突时,如果证据权限处于特殊状态,融合结论与常规思维推理结论相悖的问题,通过对证据之间冲突情况的分析,采用集群效应的方法,消弱“坏”对最后融合结论的影响。根据整体冲突程度进行融合权限的再分配。用数值算例对原融合算法和改进后的融合算法的融合结论进行比较分析。
(2)D-S证据理论融合算法研究。当辨识框架的维数和证据数量增加的时候,融合计算量将显著增加,特别是在融合过程中加入了权限之后,计算复杂度也会显著增加,这给工程上应用D-S证据理论融合算法进行信息快速融合带来了困难。针对这一问题,通过向量空间分析,将辨识框架的可能假设转化成向量空间中相互垂直的方向,利用向量空间中向量的相加来处理证据融合问题。
(3)针对D-S证据理论融合算法应用中,基本概率分布的确定时,采用统计数据构造会忽略掉原始统计数据的分布信息问题,将数据分布信息纳入到融合算法中,通过评价融合结论的分布情况来评定融合结论的可信度,并为多层信息融合提供层次间基本概率分配(Basic Probability Assignments,BPAs)和分布信息传递方法。
(4)针对可靠性数据处理中的寿命数据回归分析中原始数据出现明显的分组状况,将分组情况所包含的信息纳入到融合过程中,提出了样本特征预处理方法(Sample Character Preprocess Method,SCPM)。在此基础上提出了可靠性数据和信息融合框架。
(5)以某柴油发动机涡轮增压器的FMECA分析中的风险评估问题为例,在可靠性数据缺少的情况下,以专家评判信息为基础,用风险优先数的方法进行风险评价和排序。分别用D-S证据理论、向量空间分析为基础的简便融合方法和可靠性信息融合框架方法进行计算分析,结果表明,在工程实际中,信息融合可以在不同的层次进行,选择不当可能造成融合结论不可用。
The development of science and technology lead modern device to large-scale, high-speed, precision and integration. Because the relationship between device and human social development and people life, the reliability of equipment and product gets more and more attention, the requirement to reliability are also getting higher.
Reliability engineering is an engineering system through device and produce life cycle. Reliability design, reliability allocation, reliability evaluation, reliability prediction and reliability management are the entire reliability engineering category. With decades of development, people have built a complete reliability theory and method system. Traditional reliability work is based on reliability data, and the theory and method are based on Probability theory.
Unfortunately, we face the problem of lack of reliability data with some large scale, high precision, and complex equipment. The reason of lack of reliability data including high reliability leading lack of failure records, high value leading life experiment hard to be carry on, the defect of reliability work leading reliability data accumulation insufficiency.
The situation of lack of reliability is called small sample, small sample can not reflect the failure regularity and status on the probability level. If we handle the reliability data with traditional reliability theory and method in the situation of small sample, the analysis result is convincing.
In fact, in the whole life cycle of device and product, beside the failure data collected in the experiments and in the using period, there are more data and information which could reflect the device and product’s reliability characters could be got. If we can get these data and information, and make use of these data and information in situation of small sample, we must get more convincing conclusion than the tradition method.
This paper proposes to make use of these useful reliability data and information, and get more convincing conclusion based on D-S evidence theory.
The main work and contribution of this paper is as follow:
(1) Traditional weighted D-S evidence theory combination rule has a unavoidable shortage, when the evidence conflict level is high, and the weight factors of evidence is in a special situation, the fusion result may be contrary to the rational thinking. This paper use cluster effect reduce the influence of“bad”evidence through the analysis to the evidence conflict, reassign weight factor according to the whole conflict level. And compare the fusion result of traditional evidence combination rule and the improved one.
(2) Fusion information with D-S evidence theory combination rules, the computation quantity will increase fast when the number of hypothesis and evidence increase, especially in the weighted evidence theory combination rules. This character lead D-S evidence theory combination rule is hard to be implying in engineering practice in some situation. Through vector space analysis, this paper propose a simple information fusion method, which converse the hypothesis in evidence theory into the vertical directions in vector space, and use the vector adding method the handle the information fusion problem.
In evidence theory, the distribution information will be ignored in the determination of BPAs with statistics data. To avoid this shortage, this paper proposes a method which brings the distribution information into the fusion process, and evaluates the fusion result’s credibility with the distribution of fusion result. This method also gives the BPAs and distribution information transmission way in multilayer fusion structure.
In reliability data analysis practice, we face a situation that the collected data could be grouped in some sets, and there is clear difference among these sets which could not be ignored. This paper proposes a sample character preprocess method, and make use of these sets information in the fusion procedure. And propose the reliability data and information fusion framework on the base of SCPM.
In the FMECA analysis to a diesel turbocharger practice, we can not get enough reliability data, and use experts’judgments to risk analysis. With these expert judgments, we use the traditional D-S evidence theory combination rule, simple information fusion method based on vector space analysis and the reliability data and information fusion framework to handle these expert judgments, compare and analysis the results of these three method.
引文
[1] http://news.sina.com.cn/z/newyorkoutage/.
[2] http://tech.qq.com/zt/2006/networkFault/.
[3] http://mil.news.sina.com.cn/s/2009-02-12/1032541903.html.
[4] http://news.sina.com.cn/z/japanearthquake0311/.
[5] http://news.sina.com.cn/z/hzdccg2011/.
[6]国家标准GB/T 19000-2008,质量管理体系基础和术语.
[7]王世萍,朱敏波.电子机械可靠性与维修性.北京:清华大学出版社, 2000.
[8]方艮海.产品可靠性评估中的多源信息融合技术研究[博士学位论文].合肥:合肥工业大学, 2006.
[9]李春洋.基于多态系统理论的可靠性分析与优化设计方法研究[博士学位论文],长沙:国防科学技术大学, 2010.
[10]黄洪钟.模糊设计.北京:机械工业出版社, 1999.
[11]周源泉,翁朝曦.可靠性评定.北京:科学出版社, 1990.
[12] Dey D K, Lee T M. Bayes computation for life testing and reliability estimation. IEEE Transactions on Reliability, 1992, 41(4): 621-626.
[13] Thiagarajah K R. Homogeneity tests for scale parameters of 2-parameter exponential populations under time censoring. IEEE Transactions on Reliability, 1995, 44(2): 297-301.
[14] Gibson D. Statistical reliability prediction. International Integrated Reliability Workshop. 1995: 161.
[15] Barnett T S, Grady M, Purdy K. et al. Exploiting defect clustering for yield and reliability prediction. Computers and Digital Techniques. IEE Proceedings. 2005, 152(3): 407-413.
[16] Nelson W B, Meeker W Q. Theory for optimum censored accelerated life test for Weibull and extreme value distributions. Technometrics, 1978, 20(2): 171-177.
[17] Bai D S, Yun H J. Accelerated life tests for products of unequal size. IEEE Transactions on Reliability, 1996, 45(4): 611-618.
[18] Guang-Bin Y. Optimum constant-stress accelerated life-test plans. IEEE Transactions on Reliability, 1994, 43(4): 575-581.
[19] Chaloner K, Larntz K. Bayesian design for accelerated life testing. Journal of StatisticalPlanning and Inference, 1992, 33(2): 245-259.
[20] Nelson W B. Analysis of performance-degradation data from accelerated tests. IEEE Transactions on Reliability, 1981, 30(2): 149-154.
[21] Ioannides E, Beghini E, Bergling G et al. Cleanliness and its importance for bearing performance. Ball Bearing Journal, 1993: 242-248.
[22]庄东辰.退化失效模型及其统计分析[博士学位论文].上海:华东师范大学, 1994.
[23] Wald A. Sequential Analysis. New York: John Wiley & Sons, 1949.
[24] Guikema S D, Pate-Cornell M E. Bayesian analysis of launch vehicle Success rates. Journal of sapcecraft and rockets, 2004, 41(1): 93-102.
[25] Guikema S D, Pate-Cornell Me. Probability of infancy problems for space launch vehicles. Reliability Engineer and System Safety, 2005, 87(3): 303-314.
[26] Guida M, Pulcini G. Automotive reliability inference based on past data and technical knowledge. Reliability Engineer and System Safety, 2002, 76(2): 129-137.
[27] Efron B. Bootstrap methods: another look at the jackknife. The Annals of Statistics, 1979, 7(1): 1-26.
[28] Efron B. Nonparametric estimates of standard error and confidence intervals. The Canadian Journal of Statistics, 1981, 9(2): 137-172.
[29] Efron B. Tibshirani R J. An introduction to the bootsstrap. London: Chapman and Hall, 1993.
[30] Dacision A C, Hinkley D C. Bootstrap methods and their application. Cambridge: Cambridge University Press, 1997.
[31]李洪双.小子样可靠性分析方法及应用研究[硕士学位论文].西安:西北工业大学, 2006.
[32] Rubin D. The Bayesian Bootstrap. Anniversary Statistics, 1981, 9(1): 130-134..
[33] Vapnik V N. The Nature of Statistics Learning Theory. New York: Springer-Verlag, 1995.
[34] Rocco C M, Moreno J A. Fast Monte Carlo reliability evaluation using support vector machine. Reliability Engineer and System Safety, 2002, 76(3): 237-243.
[35] Hurtado J E. An examination of methods for approxinating implicit limit state functions from the viewpoint of statistical learning theory. Structure Safety, 2004, 26(3): 271-293.
[36]唐雪梅,张金槐,邵凤昌,李荣.武器装备小子样试验分析与评估,北京:国防工业出版社, 2001.
[37]张金槐.关于Bayes序贯检验的一些思考.飞行器测控学报, 1992, 11(2): 1-8.
[38]张金槐,蔡洪. Bayes小子样理论的因公研究-回顾与展望.飞行器测控学报, 1998, 17(1): 1-4.
[39]张金槐.可靠性鉴定中利用验前信息的序贯验后加权方法.飞行器测控学报, 1994, 13(1): 1-8.
[40]张金槐,精度评估中的自助法.飞行器测控学报, 2000, 19(3): 61-66.
[41]唐雪梅.小样本场合下相容性检验方法.系统工程与电子技术, 2001, 23(10): 66-68.
[42]唐雪梅.小样本条件下极值分布分位点估计法.战术导弹技术, 2001, 6: 41-45.
[43]尹晓伟,钱文学,谢里阳.贝叶斯网络在机械系统可靠性评估中的应用,东北大学学报(自然科学版). 2008, 29(4): 557-560.
[44]傅惠民,高镇同,徐人平.母体百分位值的置信下限.北京航空航天大学学报, 1990, 11(3): 1-8.
[45]傅惠民.二维单侧容限系数方法.航空学报. 1993, 14(3): 166-172.
[46]傅惠民.正态分布百分位值和百分率的置信限和容忍限公式.航空学报, 1994, 15(1): 94-101.
[47]张士峰,樊树江,张金槐.成败型产品可靠性的Bayes评估.兵工学报, 2001, 22(2): 238-240.
[48]宋保维,秦英孝.小子样产品的可靠性Bayes评定方法.弹箭与制导学报, 1999, (2): 52-57.
[49]郭海涛,阳宪惠.安全系统定量可靠性评估的Markov模型.清华大学学报(自然科学版). 2008, 48(1): 149-152.
[50]周涛,胡昌华,蔡光斌.不完全先验信息条件下的可靠性评估.电光与控制. 2008, 15 (3): 94-96.
[51]边向南,周宇英,马齐爽.多电飞机电气系统可靠性网络拓扑分析法.北京航空航天大学学报. 2008, 34 (10): 1210-1213.
[52]罗吉庭.评估系统可靠性置信下限的随机模拟方法.应用概率统计, 1994, 10(3): 327-332.
[53]盛骤,于渤.对数正态或正态寿命元件及系统的贮存可靠性的近似置信下限.应用数学, 1995, 8(3): 267-272.
[54]肖刚.评估复杂可维修系统可靠性与瞬态可用度的蒙特卡罗方法.兵工学报, 2001, 23(2): 215-218.
[55]陈文华,李奇志,张为鄂.产品可靠性的Bootstrap区间估计方法.机械工程学报, 2003, 6 (3): 106-109.
[56] Ben-Haim Y. Elishakoff I. Convex Models of Unvertainty in Applied Mechanics. Elsevier Science, Amsterdam and New York. 1990.
[57] Elishakoff I.“Are Probalibistic and Anti-Optimization Approaches Compatible?”Whys andHows in Uncertainty Modelling: Probability, Fuzziness and Anti- Optimization. Edited by I. Elishakoff (ed.), Springer, Vienna, 1999: 263-341.
[58]曹鸿钧.基于凸集合模型的结构和多学科系统不确定性分析与设计[博士学位论文].西安:西安电子科技大学. 2005.
[59] Moore R, Yang C. Interval analysis. Technical Document, Lockheed Missiles and Space Division, Number LMSD-285875, 1959.
[60] Ben-Haim Y. A non-Probabilistic concept of reliability. Structure Safety, 1994, 14(4): 227-245.
[61] Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures: from A M Freudenthal’s criticisms to modern convex modeling. Computers & Structures, 1995, 56(6): 871-895.
[62] Rao S S, Berke L. Analysis of uncertain structural system using interval analysis. AIAA Journal, 1997, 35(4): 727-735.
[63]苏静波.工程结构不确定性区间分析方法及其应用研究[博士学位论文].南京:河海大学. 2006.
[64] Kaufmann A. Introduction to the Fuzzy Subsets. New York: Academic Press, 1975.
[65] Dubois D, Prade H. Possibility Theory and Its Applications: A Retrospective and Prospective View. The IEEE International Conference on Fuzzy System. 2003: 3-11.
[66]张池平.多传感器信息融合方法及其在空间目标识别中的应用[博士学位论文].哈尔滨:哈尔滨工业大学, 2006.
[67] Findeisen R L, Allgower F, Foss B A. State and Output Feedback Nonlinear Model Predictive Control: An Overview. European Journal of Control. 2003, (9): 179-195.
[68] Waltz E, Linas L. Multisensor Data Fusion. Boston: Artech House, 1990.
[69] Wald L. A European proposal for terms of reference in data fusion. International Archives of Photogrammetry and Remote Sensing, 1998, 30(7): 651-654.
[70] Yand D Y, Yuzo Y. Multi-sensor Data Fusion and Its Application to Industrial Control. Proceedings of the 39th SCIE Annual Conference. International Session Papers. 2000: 215-220.
[71]马丽娜.基于神经网络的建筑环境信息融合方法研究[硕士学位论文].西安:西安建筑科技大学, 2008.
[72] Dempster A P. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 1967, 38(2): 325-339.
[73] Dempster A P. A Generalization of Bayesian Inference. Journal of the Royal Statistical Society.Series B, 1968, 30(2): 205-247.
[74] Shafer G. A Mathematical Theory of Evidence. New Jersey: Princeton University Press, 1976.
[75] Shafer G. Perspectives on the theory and practice of belief functions. International Journal of Approximate Reasoning, 1990, 4(5-6): 323-362.
[76] Shafer G. Rejoinder to comments on“Perspectives on the theory and practice of belief functions”. International Journal of Approximate Reasoning, 1992, 6(3): 445-480.
[77] Barnett J A. Computational methods for a mathematical theory of evidence. Proceedings of 7th International Joint Conference on Artificial Intelligence(IJCAI-81), Vancouver, B. C., Canada, 1981, 2: 868-875.
[78] Zadeh L A. Review of Shafer’s a mathematical theory of evidence. AI Magazine, 1984, 5(3): 81-83.
[79] Dubois D, Prade H. A SET-THEORETIC VIEW OF BELIEF FUNCTIONS Logical Operations and Approximation by Fuzzy Sets. International journal of general system, 1986, 12(3): 193-226.
[80] Smets P. The combination of evidence in the transferable model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(5): 447-458.
[81] Smets P, Kennes R. The transferable belief model. Artificial Intelligence, 1994, 66(2): 191-234.
[82] Voobraak F. A computationally efficient approximation of Dempster-Shafer theory. International Journal of Man-Machine Study, 1989, 30(5): 525-536.
[83] Dubois D, Prade, H. Consonant approximations of belief functions. International Journal of Approximate Reasoning, 1990, 4(5-6): 410-449.
[84] Tessem B. Approximations for efficient computation in the theory of evidence. Artificial Intelligence, 1993, 61(2):315-329.
[85] Yen J. Generalizing the Dempster-Shafer theory to fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics, 1990, 20(3): 559-570.
[86] Fan X F, Zuo M J. Fault diagnosis of machines based on D-S evidence theory: Part 1. D-S evidence theory and its improvement. Pattern Recognition Letters, 2006, 27(5): 366-376.
[87] Fan X F, Zuo M J. Fault diagnosis of machines based on D-S evidence theory: Part 2. Application of the improved D-S evidence theory in gearbox fault diagnosis. Pattern Recognition Letters, 2006, 27(5): 377-385.
[88] Mathon Bree R, Ozbek Metin M, Pinder George F. Dempster-Shafer Theory Applied toUncertainty Surrounding Permeability. Mathematical Geosciences, 2010, 42(3):293-307.
[89] Tian J F, Zhao W D, Du R Z. D-S Evidence Theory and Its Data Fusion Application in Instrusion Detection. Lecture Notes in Computer Science, 2005, 3802, computational intelligence and security: 244-251.
[90] Marco Paleari, Rachid Benmokhtar, Benoit Huet. Evidence Theory-Based Multimodal Emotion Recongnition. Lecture Notes in Computer Science, 2009, 5371 Advances in Multimedia Modeling: 435-446.
[91] Mohamed Ayman Boujelben, Yves De Smet, Ahmed Frikha, Habib Chabchoub. The First Belief Dominance: A New Approach in Evidence Theory for Comparing Basic Belief Assignments. Lecture Notes in Computer Science, 2009, 5783, Algorithmic Decision Theory: 272-283.
[92]段新生.证据理论与决策,人工智能.北京:中国人民大学出版社, 1993.
[93]刘大有等.广义证据理论的解释.计算机学报, 1997, 20(2): 158-164.
[94]刘大有等.凸函数证据理论模型.计算机研究与发展, 2000, 37(2): 175-181.
[95]刘大有等.一种简化证据理论模型的研究.计算机研究与发展, 1999, 36(2): 134-138.
[96]戴冠中等.证据理论的进展及存在问题.控制理论与应用, 1999, 16(4): 465-469.
[97]张倩生,周作领,贾保国.关于模糊证据理论的一个新解释.中山大学学报(自然科学版), 2003. 42(2): 1-4.
[98]杜文吉,谢维信. D-S证据理论中的证据组合.系统工程与电子技术, 1999. 21(12): 92-94.
[99]张文修.证据理论的随机集表示.模糊系统与数学, 1995, 9(1): 1-6.
[100]苏运霖,管纪文, David A B.证据论与约集论.软件学报, 1999, 10(3): 277-282.
[101]肖人彬等.相关证据合成方法的研究.模式识别与人工智能, 1993, 6(3): 227-234.
[102]曾成,赵保军,何佩昆.不完备框架下的证据组合方法.电子与信息学报, 2005, 27(7): 1043-1046.
[103]徐从富等. Dempster-Shafer证据推理方法理论与应用的综述.模式识别与人工智能, 1999, 12(4): 424-430.
[104]徐从富等.面向数据融合的DS方法综述.电子学报, 2001, 29(3): 393-396.
[105]涂嘉文,徐守时.贝斯方法与Dempster-Shafer证据理论的讨论.红外与激光工程, 2001, 30(2): 139-142.
[106]肖明珠,陈光踽.非精确性中子测量数据的不确定度评定.强激光与离子束, 2005, 17(3): 460-462.
[107]喻永新,费奇,彭祖赠.决策建模支持中的不确定性分析.控制与决策, 1996, 11(5):556-560.
[108]刘大有,杨鲲,唐海鹰.凸函数证据理论模型.计算机研究与发展. 2000, 37(2): 175-181.
[109]肖明珠,陈光踽.一种改进的证据合成公式.数据采集与处理, 2004, 19(4): 467-469.
[110]孙怀江,杨静宇.一种相关证据合成方法.计算机学报, 1999, 22(9): 1004-1007.
[111]杨海峰,侯朝桢.证据理论组合公式的分析与改进.计算机工程, 2005, 31(7): 21-23.
[112]郑东良,杜纯.证据理论在航空装备性能评审中的应用.交通运输工程学报, 2004, 4(3): 114-116.
[113]张东星,罗志增.一种改进的证据算法及其在信息融合中的应用.传感器技术, 2004, 23(4): 56-58.
[114]秦良娟.证据理论在复杂系统可靠性评价中的应用.西安交通大学学报, 1998, 32(8): 100-103.
[115]高洪涛,王敏.证据理论在旋转机械综合故障诊断中的应用.大连理工大学学报. 2001, 41(4): 459-462.
[116]樊红,冯恩德.一种基于证据理论的船舶综合安全评估(FSA)方法.武汉理工大学学报(交通科学与工程版), 2004, 28(4): 546-549.
[117]田亮,曾德良,刘鑫屏等.基于证据融合的球磨机最佳负荷工作点判断.热能动力工程, 2004, 19(2): 198-218.
[118]王鸿飞.基于Dempster-Shafer证据理论的柴油机故障诊断.内燃机学报, 2000, 8(1): 20-23.
[119]刘志言,童树鸿,王艳.基于证据理论的多分类器集成方法研究.电机与控制学报, 2001, 5(3): 208-212.
[120] Mahler R P S. Combining ambiguous evidence with respect to ambiguous a priori knowledge, I: Boolean logic. IEEE Transactions on Systems, Man, and Cybernetics- Part A: Systems and Humans, 1996, 26(1): 27-41.
[121] Fixsen D. Mahler R P S. The modified Dempster- Shafer approach to classification. IEEE Transactions on Systems, Man, and Cybernetics- Part A: Systems and Humans, 1997, 27(1): 27-41
[122] Yen J. GERTIS: a Dempster-Shafer approach to diagnosing hierarchical hypotheses. Communications of the ACM, 1989, 32(5): 573-585.
[123] Yager R R. On the Dempster–Shafer framework and new combination rules. Information Sciences. 1987, 41(2): 93-137.
[124] Philippe Smets. The Combination of Evidence in the Transferable Belief Model. IEEETransactions on Pattern Analysis and Machine Intelligence. 1990, 12(5): 447-458.
[125] Murphy C K. Combining belief functions when evidence conflicts. Decision Support Systems, 2000, 29(1): 1-9.
[126] Kumar K V, Porkodi K, Rocha F. Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: Comparison of various error functions. Journal of Hazardous Materials, 2008, 151(2-3):794–804.
[127] Kumer K V, Sivanesan S. Pseudo second order kinetic models for safranin onto rice husk: Comparison of linear and non-linear regression analysis. Process Biochemistry, 2006, 41(5): 1198–1202.
[128] Cuyt A, Wuytack L. Nonlinear Methods in Numerical Analysis. Elsevier, Amsterdam, 1987.
[129] De Levie Robert. Curve fitting with Least Squares. Critical Reviews in Analytical Chemistry, 2000, 30(1): 59-74.
[130] Philip E Gill, Walter Murray. Algorithms for the solution of the nonlinear least-squares problem. SIAM Journal on Numerical Analysis, 1978, 15(5): 977-992.
[131] Huang Hongzhong, Guan Liwen, Wu Haifan. A study on linear regression model with fuzzy weight and its application to S-N Curve in its regression analysis. Machine Design, 2000, 17(13): 11-12.
[132] Ji Fengxian, Yao Weixing. Weighted least square method for S-N curve fitting. Transaction of Nanjing University of Aeronautics & Astronautics, 2004, 21(1): 53-57.
[133]康锐,石德荣. FMECA技术及其应用.北京:国防工业出版社, 2006.
[134]故障模式影响分析-FMEA教程.北京:北京运通恒达科技有限公司, 2003, 1-4.
[135] GJB1391-92《故障模式、影响及危害性分析程序》.
[136] GB7826-87《系统可靠性分析技术失效模式和效应分析(FMECA)》.
[137] HB6359-89《失效模式、影响及危害性分析程序》.
[138] HB/Z281-95《航空发动机故障模式、影响及危害性分析指南》.
[139]张晗亮.以FMECA为中心的柴油机可靠性研究[硕士学位论文].成都:电子科技大学. 2009.
[140]周俊峰,许乐平,竹建福.故障模式及影响分析方法在船舶主推进系统中的应用.航海工程, 2006, (6): 84-87.
[141]张建国,黄文敏.大型机械产品的FMEA和FTA综合分析方法.机械设计与制造, 2000, (1): 1-3.
[142]贾亚洲,王捷,姜巍巍.国产加工中心故障模式及影响分析(FMEA).江苏机械制造与自动化, 2001,(4): 111-114.
[143]孙有朝,段文颖.一种轻型飞机全动平尾操纵系统的故障模式及影响分析.机械传动, 2000, 24(4): 13-17.
[144]鲍秀峰.浅析失效模式影响分析(FMEA)在电路设计中的应用.集成电路通讯, 2006, 24(3): 49-52.
[145]王辉,闫祥安,王立文.液压机液压系统主缸回路FMEA分析.机床与液压, 2006, (1): 162-164.
[146]洪国钧,常瑞承,李福秋.舰船制造故障模式影响分析技术研究.舰船科学技术, 2006, 28(3): 83-86.
[147]赵雷,韩红新,龚奇勇.基于FTA-FMEA联合法综合诊断电子设备故障.舰船电子工程, 2007, (3): 216-218.
[148]张蓉,王春洁.基于FMEA和FTA的三自由度直角坐标机器人系统可靠性仿真分析.机械科学与技术, 2006, 25(6): 651-654.
[149]陈真,胡宁,许亮.自动变速器液压控制系统FMEA.机床与液压, 2007, 35(4): 212-214.
[150]张日明,孙大文.数控装备故障模式分析.吉林大学学报(工学版). 2008, 38(S1): 123-125.
[151]王晶燕,饶炜,孙泽洲.嫦娥一号卫星飞行事件的系统级FMEA.航天器工程, 2008, 17(2): 90-93.
[152]苗雨奇. FMECA在航空发动机研制工作中的应用.航空发动机, 2000,(3): 56-60.
[153]戴姆勒克莱斯勒,福特,通用汽车公司. QS-9000.失效模式与后果分析(FMEA)参考手册(第三版).北京:北京品士质量管理顾问有限公司, 2001.
[2] http://tech.qq.com/zt/2006/networkFault/.
[3] http://mil.news.sina.com.cn/s/2009-02-12/1032541903.html.
[4] http://news.sina.com.cn/z/japanearthquake0311/.
[5] http://news.sina.com.cn/z/hzdccg2011/.
[6]国家标准GB/T 19000-2008,质量管理体系基础和术语.
[7]王世萍,朱敏波.电子机械可靠性与维修性.北京:清华大学出版社, 2000.
[8]方艮海.产品可靠性评估中的多源信息融合技术研究[博士学位论文].合肥:合肥工业大学, 2006.
[9]李春洋.基于多态系统理论的可靠性分析与优化设计方法研究[博士学位论文],长沙:国防科学技术大学, 2010.
[10]黄洪钟.模糊设计.北京:机械工业出版社, 1999.
[11]周源泉,翁朝曦.可靠性评定.北京:科学出版社, 1990.
[12] Dey D K, Lee T M. Bayes computation for life testing and reliability estimation. IEEE Transactions on Reliability, 1992, 41(4): 621-626.
[13] Thiagarajah K R. Homogeneity tests for scale parameters of 2-parameter exponential populations under time censoring. IEEE Transactions on Reliability, 1995, 44(2): 297-301.
[14] Gibson D. Statistical reliability prediction. International Integrated Reliability Workshop. 1995: 161.
[15] Barnett T S, Grady M, Purdy K. et al. Exploiting defect clustering for yield and reliability prediction. Computers and Digital Techniques. IEE Proceedings. 2005, 152(3): 407-413.
[16] Nelson W B, Meeker W Q. Theory for optimum censored accelerated life test for Weibull and extreme value distributions. Technometrics, 1978, 20(2): 171-177.
[17] Bai D S, Yun H J. Accelerated life tests for products of unequal size. IEEE Transactions on Reliability, 1996, 45(4): 611-618.
[18] Guang-Bin Y. Optimum constant-stress accelerated life-test plans. IEEE Transactions on Reliability, 1994, 43(4): 575-581.
[19] Chaloner K, Larntz K. Bayesian design for accelerated life testing. Journal of StatisticalPlanning and Inference, 1992, 33(2): 245-259.
[20] Nelson W B. Analysis of performance-degradation data from accelerated tests. IEEE Transactions on Reliability, 1981, 30(2): 149-154.
[21] Ioannides E, Beghini E, Bergling G et al. Cleanliness and its importance for bearing performance. Ball Bearing Journal, 1993: 242-248.
[22]庄东辰.退化失效模型及其统计分析[博士学位论文].上海:华东师范大学, 1994.
[23] Wald A. Sequential Analysis. New York: John Wiley & Sons, 1949.
[24] Guikema S D, Pate-Cornell M E. Bayesian analysis of launch vehicle Success rates. Journal of sapcecraft and rockets, 2004, 41(1): 93-102.
[25] Guikema S D, Pate-Cornell Me. Probability of infancy problems for space launch vehicles. Reliability Engineer and System Safety, 2005, 87(3): 303-314.
[26] Guida M, Pulcini G. Automotive reliability inference based on past data and technical knowledge. Reliability Engineer and System Safety, 2002, 76(2): 129-137.
[27] Efron B. Bootstrap methods: another look at the jackknife. The Annals of Statistics, 1979, 7(1): 1-26.
[28] Efron B. Nonparametric estimates of standard error and confidence intervals. The Canadian Journal of Statistics, 1981, 9(2): 137-172.
[29] Efron B. Tibshirani R J. An introduction to the bootsstrap. London: Chapman and Hall, 1993.
[30] Dacision A C, Hinkley D C. Bootstrap methods and their application. Cambridge: Cambridge University Press, 1997.
[31]李洪双.小子样可靠性分析方法及应用研究[硕士学位论文].西安:西北工业大学, 2006.
[32] Rubin D. The Bayesian Bootstrap. Anniversary Statistics, 1981, 9(1): 130-134..
[33] Vapnik V N. The Nature of Statistics Learning Theory. New York: Springer-Verlag, 1995.
[34] Rocco C M, Moreno J A. Fast Monte Carlo reliability evaluation using support vector machine. Reliability Engineer and System Safety, 2002, 76(3): 237-243.
[35] Hurtado J E. An examination of methods for approxinating implicit limit state functions from the viewpoint of statistical learning theory. Structure Safety, 2004, 26(3): 271-293.
[36]唐雪梅,张金槐,邵凤昌,李荣.武器装备小子样试验分析与评估,北京:国防工业出版社, 2001.
[37]张金槐.关于Bayes序贯检验的一些思考.飞行器测控学报, 1992, 11(2): 1-8.
[38]张金槐,蔡洪. Bayes小子样理论的因公研究-回顾与展望.飞行器测控学报, 1998, 17(1): 1-4.
[39]张金槐.可靠性鉴定中利用验前信息的序贯验后加权方法.飞行器测控学报, 1994, 13(1): 1-8.
[40]张金槐,精度评估中的自助法.飞行器测控学报, 2000, 19(3): 61-66.
[41]唐雪梅.小样本场合下相容性检验方法.系统工程与电子技术, 2001, 23(10): 66-68.
[42]唐雪梅.小样本条件下极值分布分位点估计法.战术导弹技术, 2001, 6: 41-45.
[43]尹晓伟,钱文学,谢里阳.贝叶斯网络在机械系统可靠性评估中的应用,东北大学学报(自然科学版). 2008, 29(4): 557-560.
[44]傅惠民,高镇同,徐人平.母体百分位值的置信下限.北京航空航天大学学报, 1990, 11(3): 1-8.
[45]傅惠民.二维单侧容限系数方法.航空学报. 1993, 14(3): 166-172.
[46]傅惠民.正态分布百分位值和百分率的置信限和容忍限公式.航空学报, 1994, 15(1): 94-101.
[47]张士峰,樊树江,张金槐.成败型产品可靠性的Bayes评估.兵工学报, 2001, 22(2): 238-240.
[48]宋保维,秦英孝.小子样产品的可靠性Bayes评定方法.弹箭与制导学报, 1999, (2): 52-57.
[49]郭海涛,阳宪惠.安全系统定量可靠性评估的Markov模型.清华大学学报(自然科学版). 2008, 48(1): 149-152.
[50]周涛,胡昌华,蔡光斌.不完全先验信息条件下的可靠性评估.电光与控制. 2008, 15 (3): 94-96.
[51]边向南,周宇英,马齐爽.多电飞机电气系统可靠性网络拓扑分析法.北京航空航天大学学报. 2008, 34 (10): 1210-1213.
[52]罗吉庭.评估系统可靠性置信下限的随机模拟方法.应用概率统计, 1994, 10(3): 327-332.
[53]盛骤,于渤.对数正态或正态寿命元件及系统的贮存可靠性的近似置信下限.应用数学, 1995, 8(3): 267-272.
[54]肖刚.评估复杂可维修系统可靠性与瞬态可用度的蒙特卡罗方法.兵工学报, 2001, 23(2): 215-218.
[55]陈文华,李奇志,张为鄂.产品可靠性的Bootstrap区间估计方法.机械工程学报, 2003, 6 (3): 106-109.
[56] Ben-Haim Y. Elishakoff I. Convex Models of Unvertainty in Applied Mechanics. Elsevier Science, Amsterdam and New York. 1990.
[57] Elishakoff I.“Are Probalibistic and Anti-Optimization Approaches Compatible?”Whys andHows in Uncertainty Modelling: Probability, Fuzziness and Anti- Optimization. Edited by I. Elishakoff (ed.), Springer, Vienna, 1999: 263-341.
[58]曹鸿钧.基于凸集合模型的结构和多学科系统不确定性分析与设计[博士学位论文].西安:西安电子科技大学. 2005.
[59] Moore R, Yang C. Interval analysis. Technical Document, Lockheed Missiles and Space Division, Number LMSD-285875, 1959.
[60] Ben-Haim Y. A non-Probabilistic concept of reliability. Structure Safety, 1994, 14(4): 227-245.
[61] Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures: from A M Freudenthal’s criticisms to modern convex modeling. Computers & Structures, 1995, 56(6): 871-895.
[62] Rao S S, Berke L. Analysis of uncertain structural system using interval analysis. AIAA Journal, 1997, 35(4): 727-735.
[63]苏静波.工程结构不确定性区间分析方法及其应用研究[博士学位论文].南京:河海大学. 2006.
[64] Kaufmann A. Introduction to the Fuzzy Subsets. New York: Academic Press, 1975.
[65] Dubois D, Prade H. Possibility Theory and Its Applications: A Retrospective and Prospective View. The IEEE International Conference on Fuzzy System. 2003: 3-11.
[66]张池平.多传感器信息融合方法及其在空间目标识别中的应用[博士学位论文].哈尔滨:哈尔滨工业大学, 2006.
[67] Findeisen R L, Allgower F, Foss B A. State and Output Feedback Nonlinear Model Predictive Control: An Overview. European Journal of Control. 2003, (9): 179-195.
[68] Waltz E, Linas L. Multisensor Data Fusion. Boston: Artech House, 1990.
[69] Wald L. A European proposal for terms of reference in data fusion. International Archives of Photogrammetry and Remote Sensing, 1998, 30(7): 651-654.
[70] Yand D Y, Yuzo Y. Multi-sensor Data Fusion and Its Application to Industrial Control. Proceedings of the 39th SCIE Annual Conference. International Session Papers. 2000: 215-220.
[71]马丽娜.基于神经网络的建筑环境信息融合方法研究[硕士学位论文].西安:西安建筑科技大学, 2008.
[72] Dempster A P. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 1967, 38(2): 325-339.
[73] Dempster A P. A Generalization of Bayesian Inference. Journal of the Royal Statistical Society.Series B, 1968, 30(2): 205-247.
[74] Shafer G. A Mathematical Theory of Evidence. New Jersey: Princeton University Press, 1976.
[75] Shafer G. Perspectives on the theory and practice of belief functions. International Journal of Approximate Reasoning, 1990, 4(5-6): 323-362.
[76] Shafer G. Rejoinder to comments on“Perspectives on the theory and practice of belief functions”. International Journal of Approximate Reasoning, 1992, 6(3): 445-480.
[77] Barnett J A. Computational methods for a mathematical theory of evidence. Proceedings of 7th International Joint Conference on Artificial Intelligence(IJCAI-81), Vancouver, B. C., Canada, 1981, 2: 868-875.
[78] Zadeh L A. Review of Shafer’s a mathematical theory of evidence. AI Magazine, 1984, 5(3): 81-83.
[79] Dubois D, Prade H. A SET-THEORETIC VIEW OF BELIEF FUNCTIONS Logical Operations and Approximation by Fuzzy Sets. International journal of general system, 1986, 12(3): 193-226.
[80] Smets P. The combination of evidence in the transferable model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(5): 447-458.
[81] Smets P, Kennes R. The transferable belief model. Artificial Intelligence, 1994, 66(2): 191-234.
[82] Voobraak F. A computationally efficient approximation of Dempster-Shafer theory. International Journal of Man-Machine Study, 1989, 30(5): 525-536.
[83] Dubois D, Prade, H. Consonant approximations of belief functions. International Journal of Approximate Reasoning, 1990, 4(5-6): 410-449.
[84] Tessem B. Approximations for efficient computation in the theory of evidence. Artificial Intelligence, 1993, 61(2):315-329.
[85] Yen J. Generalizing the Dempster-Shafer theory to fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics, 1990, 20(3): 559-570.
[86] Fan X F, Zuo M J. Fault diagnosis of machines based on D-S evidence theory: Part 1. D-S evidence theory and its improvement. Pattern Recognition Letters, 2006, 27(5): 366-376.
[87] Fan X F, Zuo M J. Fault diagnosis of machines based on D-S evidence theory: Part 2. Application of the improved D-S evidence theory in gearbox fault diagnosis. Pattern Recognition Letters, 2006, 27(5): 377-385.
[88] Mathon Bree R, Ozbek Metin M, Pinder George F. Dempster-Shafer Theory Applied toUncertainty Surrounding Permeability. Mathematical Geosciences, 2010, 42(3):293-307.
[89] Tian J F, Zhao W D, Du R Z. D-S Evidence Theory and Its Data Fusion Application in Instrusion Detection. Lecture Notes in Computer Science, 2005, 3802, computational intelligence and security: 244-251.
[90] Marco Paleari, Rachid Benmokhtar, Benoit Huet. Evidence Theory-Based Multimodal Emotion Recongnition. Lecture Notes in Computer Science, 2009, 5371 Advances in Multimedia Modeling: 435-446.
[91] Mohamed Ayman Boujelben, Yves De Smet, Ahmed Frikha, Habib Chabchoub. The First Belief Dominance: A New Approach in Evidence Theory for Comparing Basic Belief Assignments. Lecture Notes in Computer Science, 2009, 5783, Algorithmic Decision Theory: 272-283.
[92]段新生.证据理论与决策,人工智能.北京:中国人民大学出版社, 1993.
[93]刘大有等.广义证据理论的解释.计算机学报, 1997, 20(2): 158-164.
[94]刘大有等.凸函数证据理论模型.计算机研究与发展, 2000, 37(2): 175-181.
[95]刘大有等.一种简化证据理论模型的研究.计算机研究与发展, 1999, 36(2): 134-138.
[96]戴冠中等.证据理论的进展及存在问题.控制理论与应用, 1999, 16(4): 465-469.
[97]张倩生,周作领,贾保国.关于模糊证据理论的一个新解释.中山大学学报(自然科学版), 2003. 42(2): 1-4.
[98]杜文吉,谢维信. D-S证据理论中的证据组合.系统工程与电子技术, 1999. 21(12): 92-94.
[99]张文修.证据理论的随机集表示.模糊系统与数学, 1995, 9(1): 1-6.
[100]苏运霖,管纪文, David A B.证据论与约集论.软件学报, 1999, 10(3): 277-282.
[101]肖人彬等.相关证据合成方法的研究.模式识别与人工智能, 1993, 6(3): 227-234.
[102]曾成,赵保军,何佩昆.不完备框架下的证据组合方法.电子与信息学报, 2005, 27(7): 1043-1046.
[103]徐从富等. Dempster-Shafer证据推理方法理论与应用的综述.模式识别与人工智能, 1999, 12(4): 424-430.
[104]徐从富等.面向数据融合的DS方法综述.电子学报, 2001, 29(3): 393-396.
[105]涂嘉文,徐守时.贝斯方法与Dempster-Shafer证据理论的讨论.红外与激光工程, 2001, 30(2): 139-142.
[106]肖明珠,陈光踽.非精确性中子测量数据的不确定度评定.强激光与离子束, 2005, 17(3): 460-462.
[107]喻永新,费奇,彭祖赠.决策建模支持中的不确定性分析.控制与决策, 1996, 11(5):556-560.
[108]刘大有,杨鲲,唐海鹰.凸函数证据理论模型.计算机研究与发展. 2000, 37(2): 175-181.
[109]肖明珠,陈光踽.一种改进的证据合成公式.数据采集与处理, 2004, 19(4): 467-469.
[110]孙怀江,杨静宇.一种相关证据合成方法.计算机学报, 1999, 22(9): 1004-1007.
[111]杨海峰,侯朝桢.证据理论组合公式的分析与改进.计算机工程, 2005, 31(7): 21-23.
[112]郑东良,杜纯.证据理论在航空装备性能评审中的应用.交通运输工程学报, 2004, 4(3): 114-116.
[113]张东星,罗志增.一种改进的证据算法及其在信息融合中的应用.传感器技术, 2004, 23(4): 56-58.
[114]秦良娟.证据理论在复杂系统可靠性评价中的应用.西安交通大学学报, 1998, 32(8): 100-103.
[115]高洪涛,王敏.证据理论在旋转机械综合故障诊断中的应用.大连理工大学学报. 2001, 41(4): 459-462.
[116]樊红,冯恩德.一种基于证据理论的船舶综合安全评估(FSA)方法.武汉理工大学学报(交通科学与工程版), 2004, 28(4): 546-549.
[117]田亮,曾德良,刘鑫屏等.基于证据融合的球磨机最佳负荷工作点判断.热能动力工程, 2004, 19(2): 198-218.
[118]王鸿飞.基于Dempster-Shafer证据理论的柴油机故障诊断.内燃机学报, 2000, 8(1): 20-23.
[119]刘志言,童树鸿,王艳.基于证据理论的多分类器集成方法研究.电机与控制学报, 2001, 5(3): 208-212.
[120] Mahler R P S. Combining ambiguous evidence with respect to ambiguous a priori knowledge, I: Boolean logic. IEEE Transactions on Systems, Man, and Cybernetics- Part A: Systems and Humans, 1996, 26(1): 27-41.
[121] Fixsen D. Mahler R P S. The modified Dempster- Shafer approach to classification. IEEE Transactions on Systems, Man, and Cybernetics- Part A: Systems and Humans, 1997, 27(1): 27-41
[122] Yen J. GERTIS: a Dempster-Shafer approach to diagnosing hierarchical hypotheses. Communications of the ACM, 1989, 32(5): 573-585.
[123] Yager R R. On the Dempster–Shafer framework and new combination rules. Information Sciences. 1987, 41(2): 93-137.
[124] Philippe Smets. The Combination of Evidence in the Transferable Belief Model. IEEETransactions on Pattern Analysis and Machine Intelligence. 1990, 12(5): 447-458.
[125] Murphy C K. Combining belief functions when evidence conflicts. Decision Support Systems, 2000, 29(1): 1-9.
[126] Kumar K V, Porkodi K, Rocha F. Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: Comparison of various error functions. Journal of Hazardous Materials, 2008, 151(2-3):794–804.
[127] Kumer K V, Sivanesan S. Pseudo second order kinetic models for safranin onto rice husk: Comparison of linear and non-linear regression analysis. Process Biochemistry, 2006, 41(5): 1198–1202.
[128] Cuyt A, Wuytack L. Nonlinear Methods in Numerical Analysis. Elsevier, Amsterdam, 1987.
[129] De Levie Robert. Curve fitting with Least Squares. Critical Reviews in Analytical Chemistry, 2000, 30(1): 59-74.
[130] Philip E Gill, Walter Murray. Algorithms for the solution of the nonlinear least-squares problem. SIAM Journal on Numerical Analysis, 1978, 15(5): 977-992.
[131] Huang Hongzhong, Guan Liwen, Wu Haifan. A study on linear regression model with fuzzy weight and its application to S-N Curve in its regression analysis. Machine Design, 2000, 17(13): 11-12.
[132] Ji Fengxian, Yao Weixing. Weighted least square method for S-N curve fitting. Transaction of Nanjing University of Aeronautics & Astronautics, 2004, 21(1): 53-57.
[133]康锐,石德荣. FMECA技术及其应用.北京:国防工业出版社, 2006.
[134]故障模式影响分析-FMEA教程.北京:北京运通恒达科技有限公司, 2003, 1-4.
[135] GJB1391-92《故障模式、影响及危害性分析程序》.
[136] GB7826-87《系统可靠性分析技术失效模式和效应分析(FMECA)》.
[137] HB6359-89《失效模式、影响及危害性分析程序》.
[138] HB/Z281-95《航空发动机故障模式、影响及危害性分析指南》.
[139]张晗亮.以FMECA为中心的柴油机可靠性研究[硕士学位论文].成都:电子科技大学. 2009.
[140]周俊峰,许乐平,竹建福.故障模式及影响分析方法在船舶主推进系统中的应用.航海工程, 2006, (6): 84-87.
[141]张建国,黄文敏.大型机械产品的FMEA和FTA综合分析方法.机械设计与制造, 2000, (1): 1-3.
[142]贾亚洲,王捷,姜巍巍.国产加工中心故障模式及影响分析(FMEA).江苏机械制造与自动化, 2001,(4): 111-114.
[143]孙有朝,段文颖.一种轻型飞机全动平尾操纵系统的故障模式及影响分析.机械传动, 2000, 24(4): 13-17.
[144]鲍秀峰.浅析失效模式影响分析(FMEA)在电路设计中的应用.集成电路通讯, 2006, 24(3): 49-52.
[145]王辉,闫祥安,王立文.液压机液压系统主缸回路FMEA分析.机床与液压, 2006, (1): 162-164.
[146]洪国钧,常瑞承,李福秋.舰船制造故障模式影响分析技术研究.舰船科学技术, 2006, 28(3): 83-86.
[147]赵雷,韩红新,龚奇勇.基于FTA-FMEA联合法综合诊断电子设备故障.舰船电子工程, 2007, (3): 216-218.
[148]张蓉,王春洁.基于FMEA和FTA的三自由度直角坐标机器人系统可靠性仿真分析.机械科学与技术, 2006, 25(6): 651-654.
[149]陈真,胡宁,许亮.自动变速器液压控制系统FMEA.机床与液压, 2007, 35(4): 212-214.
[150]张日明,孙大文.数控装备故障模式分析.吉林大学学报(工学版). 2008, 38(S1): 123-125.
[151]王晶燕,饶炜,孙泽洲.嫦娥一号卫星飞行事件的系统级FMEA.航天器工程, 2008, 17(2): 90-93.
[152]苗雨奇. FMECA在航空发动机研制工作中的应用.航空发动机, 2000,(3): 56-60.
[153]戴姆勒克莱斯勒,福特,通用汽车公司. QS-9000.失效模式与后果分析(FMEA)参考手册(第三版).北京:北京品士质量管理顾问有限公司, 2001.