基于EM算法的极值载荷建模分析与应用

发布时间：2018-04-29 11:40

本文选题：挖掘机 + 载荷谱　；参考：《吉林大学》2017年硕士论文

【摘要】：对关键机械零部件进行可控疲劳寿命设计是保证工程机械的使用寿命和可靠性的重要手段。载荷谱的编制是进行疲劳寿命设计的前提与基础。机械结构的设计过程中,只有充分利用了载荷谱提供的实际工况的受载信息,才能保证在节约成本的情况下最大限度地保证实际使用过程中的可靠性。在航天、水利、建筑等领域,载荷谱的应用已经比较普遍而且载荷谱的编制流程已经比较规范,一些关键技术问题的研究已经比较深入。而在工程机械领域,载荷谱的编制方法的研究尚未成熟,很多问题仍然需要研究。尤其是关于载荷的极值部分的度量技术,由于极值载荷对机械结构造成的损伤效果非常显著,研究极值载荷的度量和统计方法对于可靠性设计的研究具有非常重要的意义。因此,为了研究工程机械载荷谱编制中极值载荷的统计度量问题,本文提出了一种极值载荷的分布模型,并设计了相应的参数估计算法,对此模型和方法进行了仿真数据分析,验证了模型和参数估计算法的有效性,并在试验载荷数据样本上进一步进行了验证。本文的主要研究内容如下:(1)针对载荷的极值部分,提出了一种统计分布模型。本文根据对真实的载荷数据进行的初步统计学分析,提出了关于统计模型的基本假设。在假设的基础之上,结合极值理论,提出了一种描述极值载荷分布的统计学模型,并给出了模型的数学表达式。(2)基于EM算法的基本思想,设计了一种应用于极值分布模型的参数估计算法。通过对公式的推导和分析,本文将算法中比较复杂的似然函数拆分为简单似然函数的组合,简化了计算过程。之后通过编程实现了算法,并通过并行计算等技术对程序的计算效率进行了优化。介绍了另一种参数估计算法的原理作对比分析。(3)通过仿真数据对算法的性能进行了分析。设计了仿真数据的数学模型及程序流程。通过对单组仿真数据进行了模型拟合和参数估计,验证了模型的拟合效果和参数估计的无偏性。通过对1000组仿真数据对参数估计算法的有效性进行了分析。并对比了另一种参数估计算法的效果。结果表明本文的参数估计算法计算效果较好,关键参数的估计误差在20%以内,并且偏向于比真值小。(4)在挖掘机斗杆实测载荷数据中应用本文提出的模型和算法,通过卡方检验证明了模型与试验数据是相符合的。并通过采用了自助法进行重抽了 1000组采样,通过多次重复试验再次对参数估计算法的有效性进行了分析。结果与仿真数据相比基本一致。综上,本文针对极值载荷提出了一种统计计量模型和一种用于此模型的参数估计方法,通过仿真数据分析和试验数据分析的手段,验证了模型的适用性和算法的有效性。通过本文的方法,可以方便快速地对工程机械领的极值载荷进行统计度量,建立准确的统计分布模型。本文的研究内容对于工程机械载荷谱编制方法的研究具有一定的借鉴和参考意义。
[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.

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH122

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