本文關(guān)鍵詞：證據(jù)理論中信任函數(shù)的合成方法研究與應(yīng)用　出處：《中國科學(xué)技術(shù)大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 證據(jù)理論 信任函數(shù) 證據(jù)合成 置信規(guī)則庫 證據(jù)推理 相關(guān)證據(jù) 模糊折扣 證據(jù)沖突

【摘要】：在實際問題中,無論是傳感器測量信息還是專家經(jīng)驗知識,一般都存在定程度的不確定性或不完備性。研究不確定信息的建模和推理決策問題具有重要意義。證據(jù)理論是一種常用的不確定推理方法,其中表征信息的信任函數(shù)是定義在識別框架冪集上的一個置信分布,能夠區(qū)分無知與等可能性,比概率分布的表示更加靈活準(zhǔn)確：并且證據(jù)推理的過程與人類專家的思維方式比較相似。因此,證據(jù)理論已成為一種重要的信息融合方法,在多個領(lǐng)域中得以應(yīng)用。鑒于證據(jù)理論處理不確定知識的能力,許多研究將其與其它理論方法相結(jié)合,置信規(guī)則庫推理方法就是其中之一。經(jīng)典證據(jù)理論中通過Dempster規(guī)則合成多條證據(jù),實現(xiàn)推理決策過程。然而使用Dempster規(guī)則需要滿足一定的前提條件,如證據(jù)獨立性、證據(jù)可靠性等,這些條件在實際問題中不一定能夠滿足；而且Dempster規(guī)則合成沖突證據(jù)時可能出現(xiàn)合成悖論問題。為避免合成悖論,并更好的符合實際應(yīng)用條件,本文對信任函數(shù)的合成方法進(jìn)行研究,主要從沖突證據(jù)的分析與合成、證據(jù)重要性與可靠性的處理、相關(guān)證據(jù)的合成等方面展開。此外,針對置信規(guī)則庫推理方法存在模型訓(xùn)練緩慢、規(guī)則約簡方法復(fù)雜等問題,提出一種新的模型結(jié)構(gòu)以解決這些問題。首先,研究了合成悖論問題,并提出一種新的沖突衡量方法和證據(jù)折扣方法。利用規(guī)范分解對典型合成悖論進(jìn)行了分析,總結(jié)出了它們的共同特點,并證明證據(jù)折扣可以避免這一問題。因此,提出一種模糊折扣方法。該方法考慮了證據(jù)之間的沖突和自身不確定性兩方面因素,不僅能夠取得較快的信度收斂速度,并且對異常證據(jù)也具有較好的魯棒性。為衡量證據(jù)沖突和不確定性,分別定義了基于奇異值的沖突衡量方法和基于pignistic概率的區(qū)分度。其次,研究了證據(jù)推理(ER)規(guī)則的相關(guān)性質(zhì)及其存在的問題,并用其對隔振系統(tǒng)的故障診斷問題進(jìn)行研究。分析了ER規(guī)則與證據(jù)折扣方法之間的關(guān)系、權(quán)重歸一化對其合成結(jié)果的影響,以及它在重要性與可靠性表示上存在的缺陷,并提出一種改進(jìn)的方法。針對隔振系統(tǒng)的故障診斷問題,給出了證據(jù)重要性與可靠性的評估方法,提取了合適的特征參數(shù)并用以生成證據(jù),利用改進(jìn)的ER規(guī)則對多傳感器信息進(jìn)行融合,實現(xiàn)故障的診斷發(fā)現(xiàn)。在多種故障情況下對所提方法進(jìn)行了驗證。然后，研究了相關(guān)源證據(jù)已知和未知兩種情況下的相關(guān)證據(jù)合成問題。在相關(guān)源證據(jù)未知的情況下,借助證據(jù)推理規(guī)則處理相對重要性的能力,將其與謹(jǐn)慎合成規(guī)則相結(jié)合,得到加權(quán)謹(jǐn)慎合成規(guī)則：此外，基于最小承諾準(zhǔn)則和證據(jù)似然排序、眾信度排序,分別提出一種相關(guān)證據(jù)合成方法,設(shè)計優(yōu)化方法求解符合條件的信仟函數(shù)。在相關(guān)源證據(jù)已知情況下,利用合成規(guī)則的眾信度函數(shù)表達(dá)形式,得到一種直接計算合成結(jié)果的方法,該方法對相關(guān)源證據(jù)的形式?jīng)]有要求。最后,研究了基于加權(quán)平均推理的置信規(guī)則庫方法。對已有文獻(xiàn)中一些置信規(guī)則庫的計算表明,被激活規(guī)則的置信分布一般存在較大沖突,而加權(quán)平均比較適合這種情況。因此在推理環(huán)節(jié)使用加權(quán)平均代替ER算法,對相應(yīng)置信規(guī)則庫的基本結(jié)構(gòu)進(jìn)行了推導(dǎo),并證明其仍然具有全局逼近能力。為避免過擬合和降低模型復(fù)雜度,利用新置信規(guī)則庫的特殊結(jié)構(gòu),提出一種簡單有效的前提屬性參考值約簡方法。針對動態(tài)系統(tǒng)的時變特性,在正態(tài)輸出假設(shè)條件下,對新置信規(guī)則庫的參數(shù)在線更新方法進(jìn)行了推導(dǎo)。通過數(shù)值仿真對新置信規(guī)則庫及其屬性約簡方法和參數(shù)更新方法進(jìn)行了驗證。
[Abstract]:In fact, whether sensor information or expertise, generally have the degree of uncertainty or imperfection. Study the uncertainty modeling and reasoning decision-making problems is of great significance. Evidence theory is an uncertainty reasoning method commonly used, the trust function is to define a representation of information in the identification of frame power set confidence distribution, to distinguish between ignorance and possibility, than the probability distribution is more flexible and accurate representation: process and human expert evidence reasoning mode of thinking is similar. Therefore, evidence theory has become an important method of information fusion has been applied in many fields. In view of the evidence theory to deal with the uncertain knowledge, many of its combination with other theories, rimer is one of them. In the classical theory of evidence Dempster rule of combination of multiple evidence reasoning, implementation of the decision-making process. However, the use of Dempster rules to meet certain preconditions, such as evidence of independence, evidence of reliability, these conditions in practical problems can not meet the Dempster rules; and conflicting evidence combination possible synthesis paradox. In order to avoid the synthesis of paradox, and better in line with the actual application conditions, this paper studies the synthesis method of trust function, mainly from the analysis and synthesis of conflicting evidence, evidence the importance and reliability of the evidence combination and other aspects. In addition, the rimer model training is slow, the rules of the complex reduction method, put forward a new models to solve these problems. First, studied the synthesis of paradox, and proposed a new conflict measure and evidence discount The typical synthesis method. Analyzed the canonical paradox, summarizes their common features, and evidence of discount can avoid this problem. Therefore, this paper proposes a fuzzy discount method. This method considers the conflict between the evidence and the uncertainty of the two factors, not only can achieve fast convergence reliability, and also has good robustness to abnormal evidence. As a measure of evidence conflict and uncertainty, defines the measure method based on singular value conflict and discrimination based on the probability of pignistic. Secondly, the study of evidence reasoning (ER) properties of rules and problems, and use it to study the fault diagnosis of vibration isolation system. Analysis of the relationship between the ER rules and evidence discount method, influence of weighting normalization on the synthesis results, and it said in importance and reliability. The existence of defects, and put forward an improved method to solve the problem of fault diagnosis of vibration isolation system, gives the assessment of the importance of evidence and the reliability of the method, feature parameters are extracted and used to generate the appropriate evidence of multi-sensor information fusion based on improved ER rules, realize fault diagnosis found in a variety of fault. The case to verify the proposed method. Then, study the synthesis problems related to evidence of evidence known and unknown in two cases. In the case of unknown source of relevant evidence, the evidence reasoning rules relative importance of ability, combined with the cautious synthesis rules, weighted cautious synthesis in addition, the minimum commitment rules: guidelines and evidence likelihood based sorting, the reliability sorting, put forward a relevant evidence synthesis method respectively, trust function design optimization method in line with the conditions. Relevant evidence is known, the use of the public expression of reliability function synthesis rules, a method of direct calculation result, this method does not require the form of relevant evidence. Finally, study the belief rule base inference based on the weighted average method. The have showed some belief rule base calculation in the literature that is activated confidence distribution rules are generally larger conflict, and the weighted average for this situation. So using the weighted average instead of the ER algorithm in reasoning link, the basic structure of the corresponding belief rule base was deduced, and prove that it still has global approximation ability. In order to avoid overfitting and reduce the complexity of the model, using the the special structure of the new belief rule base, puts forward a simple and effective reference attribute value reduction method. According to the dynamic time-varying characteristic of the systems in the normal output hypothesis Then, the online updating method of the new belief rule base is derived. The new belief rule base and its attribute reduction method and parameter update method are verified by numerical simulation.

【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP202

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