基于EM算法的極值載荷建模分析與應(yīng)用
本文選題:挖掘機 + 載荷譜 ; 參考:《吉林大學(xué)》2017年碩士論文
【摘要】:對關(guān)鍵機械零部件進行可控疲勞壽命設(shè)計是保證工程機械的使用壽命和可靠性的重要手段。載荷譜的編制是進行疲勞壽命設(shè)計的前提與基礎(chǔ)。機械結(jié)構(gòu)的設(shè)計過程中,只有充分利用了載荷譜提供的實際工況的受載信息,才能保證在節(jié)約成本的情況下最大限度地保證實際使用過程中的可靠性。在航天、水利、建筑等領(lǐng)域,載荷譜的應(yīng)用已經(jīng)比較普遍而且載荷譜的編制流程已經(jīng)比較規(guī)范,一些關(guān)鍵技術(shù)問題的研究已經(jīng)比較深入。而在工程機械領(lǐng)域,載荷譜的編制方法的研究尚未成熟,很多問題仍然需要研究。尤其是關(guān)于載荷的極值部分的度量技術(shù),由于極值載荷對機械結(jié)構(gòu)造成的損傷效果非常顯著,研究極值載荷的度量和統(tǒng)計方法對于可靠性設(shè)計的研究具有非常重要的意義。因此,為了研究工程機械載荷譜編制中極值載荷的統(tǒng)計度量問題,本文提出了一種極值載荷的分布模型,并設(shè)計了相應(yīng)的參數(shù)估計算法,對此模型和方法進行了仿真數(shù)據(jù)分析,驗證了模型和參數(shù)估計算法的有效性,并在試驗載荷數(shù)據(jù)樣本上進一步進行了驗證。本文的主要研究內(nèi)容如下:(1)針對載荷的極值部分,提出了一種統(tǒng)計分布模型。本文根據(jù)對真實的載荷數(shù)據(jù)進行的初步統(tǒng)計學(xué)分析,提出了關(guān)于統(tǒng)計模型的基本假設(shè)。在假設(shè)的基礎(chǔ)之上,結(jié)合極值理論,提出了一種描述極值載荷分布的統(tǒng)計學(xué)模型,并給出了模型的數(shù)學(xué)表達式。(2)基于EM算法的基本思想,設(shè)計了一種應(yīng)用于極值分布模型的參數(shù)估計算法。通過對公式的推導(dǎo)和分析,本文將算法中比較復(fù)雜的似然函數(shù)拆分為簡單似然函數(shù)的組合,簡化了計算過程。之后通過編程實現(xiàn)了算法,并通過并行計算等技術(shù)對程序的計算效率進行了優(yōu)化。介紹了另一種參數(shù)估計算法的原理作對比分析。(3)通過仿真數(shù)據(jù)對算法的性能進行了分析。設(shè)計了仿真數(shù)據(jù)的數(shù)學(xué)模型及程序流程。通過對單組仿真數(shù)據(jù)進行了模型擬合和參數(shù)估計,驗證了模型的擬合效果和參數(shù)估計的無偏性。通過對1000組仿真數(shù)據(jù)對參數(shù)估計算法的有效性進行了分析。并對比了另一種參數(shù)估計算法的效果。結(jié)果表明本文的參數(shù)估計算法計算效果較好,關(guān)鍵參數(shù)的估計誤差在20%以內(nèi),并且偏向于比真值小。(4)在挖掘機斗桿實測載荷數(shù)據(jù)中應(yīng)用本文提出的模型和算法,通過卡方檢驗證明了模型與試驗數(shù)據(jù)是相符合的。并通過采用了自助法進行重抽了 1000組采樣,通過多次重復(fù)試驗再次對參數(shù)估計算法的有效性進行了分析。結(jié)果與仿真數(shù)據(jù)相比基本一致。綜上,本文針對極值載荷提出了一種統(tǒng)計計量模型和一種用于此模型的參數(shù)估計方法,通過仿真數(shù)據(jù)分析和試驗數(shù)據(jù)分析的手段,驗證了模型的適用性和算法的有效性。通過本文的方法,可以方便快速地對工程機械領(lǐng)的極值載荷進行統(tǒng)計度量,建立準確的統(tǒng)計分布模型。本文的研究內(nèi)容對于工程機械載荷譜編制方法的研究具有一定的借鑒和參考意義。
[Abstract]:The design of controllable fatigue life for key mechanical parts is an important means to ensure the service life and reliability of the construction machinery. The compilation of the load spectrum is the prerequisite and foundation for the design of fatigue life. In the process of designing the mechanical structure, only the load information provided in the actual working condition provided by the load spectrum can be guaranteed in the section. In the case of cost, the reliability of practical use is guaranteed to the maximum extent. In space, water conservancy, construction and other fields, the application of load spectrum is more common and the process of compiling load spectrum has been comparatively standardized, and some key technical problems have been studied in depth. In the field of engineering machinery, the method of compiling load spectrum is made. The research is still not mature, and many problems still need to be studied. Especially, the measurement technology of the extreme part of the load is very significant. The measurement and statistical methods of the extreme load are of great significance to the research of reliability design. In this paper, a distributed model of extreme load is proposed in this paper, and a corresponding parameter estimation algorithm is designed. The simulation data analysis of the model and method is carried out to verify the validity of the model and parameter estimation algorithm, and further verification is carried out on the test load data samples. The main contents of this paper are as follows: (1) a statistical distribution model is proposed for the extreme part of the load. Based on the preliminary statistical analysis of the real load data, this paper puts forward the basic hypothesis about the statistical model. On the basis of the hypothesis, a combination of extreme value theory is proposed to describe the distribution of the extreme load distribution. The mathematical expression of the model is given and the mathematical expression of the model is given. (2) based on the basic idea of the EM algorithm, a parameter estimation algorithm applied to the extreme value distribution model is designed. By derivation and analysis of the formula, the complex likelihood function in the algorithm is split into a combination of simple like function, and the calculation process is simplified. After that, the calculation process is simplified. The algorithm is realized by programming, and the computational efficiency of the program is optimized by parallel computing. The principle of another parameter estimation algorithm is introduced and analyzed. (3) the performance of the algorithm is analyzed by the simulation data. The mathematical model and program flow of the simulation data are designed. The simulation data is modeled by a single group of simulation data. The fitting effect and parameter estimation of the model are proved to be unbiased. The effectiveness of the parameter estimation algorithm is analyzed by 1000 groups of simulation data and the effect of the other parameter estimation algorithm is compared. The results show that the calculation results of the parameter estimation algorithm are better and the estimation error of the key parameters is 20. It is less than% and is biased toward the smaller true value. (4) the model and algorithm proposed in this paper are applied to the measured load data of the bucket rod of the excavator. Through the chi square test, it is proved that the model is in accordance with the experimental data. By using the self-help method, 1000 groups of samples are re pumped and the effectiveness of the parameter estimation algorithm is again effective by repeated repeated tests. The results are basically consistent with the simulation data. To sum up, a statistical measurement model and a parameter estimation method for the model are proposed in this paper. The applicability of the model and the effectiveness of the algorithm are verified by means of simulation data analysis and experimental data analysis. It is convenient and quick to measure the extreme load of the engineering mechanical collar and establish an accurate statistical distribution model. The research content of this paper has certain reference and reference significance for the study of the method for compiling the load spectrum of the engineering machinery.
【學(xué)位授予單位】:吉林大學(xué)
【學(xué)位級別】:碩士
【學(xué)位授予年份】:2017
【分類號】:TH122
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