【作者】 王穗辉；

【导师】 刘大杰； 刘妙龙；

【作者基本信息】 同济大学 ， 大地测量学与测量工程， 2007， 博士

【摘要】 变形分析及变形趋势预测问题，不仅在工程建设及保障人民生命财产安全方面具有重要意义，就单纯从技术理论的角度而言，它也是一个复杂的系统工程。随着变形监测技术的更新及工程实际的需要，如何引用先进的数学理论和分析方法来深入地了解变形的非线性、复杂性，就是本论文研究的重点所在。本论文围绕变形监测数据处理的各个环节展开。研究成果和具体内容包括：(1)系统归纳了附加基准法进行监测网平差的理论及计算过程，阐述了用该方法取代经典控制网平差的优越性，研究和完善了附加基准法中考虑起算数据带有误差时的平差理论及方法，并推导出了具体的计算公式及进行了实例验算；(2)鉴于非线性监测网平差最好能在非线性系统中进行的需求，本论文深入研究了遗传算法的非线性全局寻优特点及不同遗传算子组合对计算的收敛速度带来的不同影响，提出了最优遗传算子组合的确定方法；此外，提出了用单纯形法取代遗传算法中的交叉操作而形成一种收敛速度更快、计算精度更高的混合遗传算法，并用测试函数及非线性控制网平差实例验证了用混合遗传算法进行非线性优化与传统遗传算法相比较具有的优越性；(3)现代变形数据分析与传统数据处理的重要区别，就是要求建立动态、非线性预报模型。针对动态、非线性的传统人工神经网络建模方法存在的缺陷，本论文研究采用了遗传算法来改进神经网络算法，即用遗传算法来优化网络参数。实例证明：这种改进算法的学习能力很强，可以高精度地逼近训练样本，预测效果好。(4)Kalman滤波在减弱监测数据受噪声的影响、预测系统未来状态方面具有独到优势。论文根据时间序列分析及Kalman滤波均是建立在递推形式上的动态建模方法的情况，推导出两种方法间的相互转换关系，提出可在噪声统计信息缺失的情况下利用观测数据构造时序分析的新息模型，再利用模型参数推求预测增益矩阵和滤波增益矩阵进而建立Kalman滤波模型和预测模型，从而避免了传统Kalman滤波建模中必须知道噪声统计信息、必须进行复杂的Riccati方程解算的过程。更多还原

【Abstract】 Deformation analysis and deformation trend prediction not only has important significance inthe aspects of engineering construction and ensure of people’s life and property safety, but also isa complex systematic engineering, even if purely speaking from the angle of technical theory. Incompany with the update of deformation monitoring technology and the requests of engineeringpractice, this research has focused on how to introduce advanced mathematical theories andanalytic methods to give an insight into the nonlinearity and complexity of deformation.This paper has outspreaded around each step of deformation monitoring data processing.Following are research fmdings and specific contents.(1) This paper has systematically summed up the theory and computational procedure ofmonitoring network adjustment using the method of appending datum, expatiated advantages ofreplacement of classical control network adjustment with this method, investigated and perfectedthe adjustment theory and methodology of the method of appending datum when consideringerrors in initial numerical data. Besides, this paper has deduced concrete computation formulasand checked out it using examples.(2) In view of the request that nonlinear monitoring network adjustment can be used in nonlinearsystem, this paper has indepth researched the nonlinear global optimation characteristics ofgenetic algorithm and effects of different genetic operator combinations to the computationalconvergence rate, proposed a method to confirm the optimal genetic operator combination.Morever, this paper has put forward substitution of the crossover operation with simplex method,shaping a hybrid genetic algorithm which can get higher convergence rate and computationalaccuracy. Besides, using trial functions and examples of nonlinear control network adjustment,this paper has verified the advantages of hybrid genetic algorithm compare to traditional onewhen used in nonlinear optimation.(3) The important difference between modern deformation data analysis and traditionaldeformation data processing lies in the request for the establishment of dynamic and nonlinearprediction models. Aiming at defects exist in artificial neural network which is a dynamic andnonlinear model method, this paper has studied using genetic algorithm to modify neural network algorithm, that is to say using genetic algorithm to optimize network parameters. Examples haveproved that the modified algorithm has good learning capacity, which can approach trainingsamples with high accuracy and can get good predictive validity.(4) Kalman filter has particular advantages when used to weaken the affects of noise inmonitoring data and predict the future state of a system. According that both time serried andKalman filter are dynamic model methods which are established on recursion modal, this paperhas deduced the interconversion relationship between them, and put forward that an innovationmodel of time series analysis using observation data can be utilized when statistical informationof noise is absent. Then the prediction gain matrix and filter gain matrix can be deduced usingmodel parameters. After that, Kalman filter model and prediction model can be established.Consequently, both noise statistical information and complex Riccati formula computation whichare required in the traditional Kalman filter are no longer necessary in the new model.更多还原