A Differential Continuation－Regularization Method for Solving Inverse Problems of Acoustic Wave Equations

ＡＤｉｆｆｅｒｅｎｔｉａｌＣｏｎｔｉｎｕａｔｉｏｎ－ＲｅｇｕｌａｒｉｚａｔｉｏｎＭｅｔｈｏｄｆｏｒＳｏｌｖｉｎｇＩｎｖｅｒｓｅＰｒｏｂｌｅｍｓｏｆＡｃｏｕｓｔｉｃＷａｖｅＥｑｕａｔｉｏｎｓ￥（张大力）（韩波）（刘家琦）（姜立功）ＺＨＡＮＧＤａｌｉ；Ｈ...     

A multi-sequential number-theoretic optimization algorithm using clustering methods

A multi-sequential number-theoretic optimization method based on clustering was developed and applied to the optimization of functions with many local extrema. Details of the procedure to generate the clusters and the sequential schedules were given. The algorithm was assessed by comparing its performance with generalized simulated annealing algorithm in a difficult instructive example and a D-optimum experimental design problem. It is shown the presented algorithm to be more effective and reliable based on the two examples. Foundation item: Project supported by the Postdoctoral Science Foundation of Central South University     

Dynamic services selection algorithm in Web services composition supporting cross-enterprises collaboration

Based on the deficiency of time convergence and variability of Web services selection for services composition supporting cross-enterprises collaboration, an algorithm QCDSS (QoS constraints of dynamic Web services selection) to resolve dynamic Web services selection with QoS global optimal path, was proposed. The essence of the algorithm was that the problem of dynamic Web services selection with QoS global optimal path was transformed into a multi-objective services composition optimization problem with QoS constraints. The operations of the cross and mutation in genetic algorithm were brought into PSOA (particle swarm optimization algorithm), forming an improved algorithm (IPSOA) to solve the QoS global optimal problem. Theoretical analysis and experimental results indicate that the algorithm can better satisfy the time convergence requirement for Web services composition supporting cross-enterprises collaboration than the traditional algorithms. Foundation item: Project(70631004) supported by the Key Project of the National Natural Science Foundation of China; Project(20080440988) supported by the Postdoctoral Science Foundation of China; Project(09JJ4030) supported by the Natural Science Foundation of Hunan Province, China; Project supported by the Postdoctoral Science Foundation of Central South University, China     

超声层析成像中的一种非线性反演方法

将模拟退火算法应用于超声层析成像,以避免对初始模型的依赖,并在全局范围内搜寻最优解。为合理确定模拟退火算法的各项参数和规则,在对超声波速进行反演时,进行如下设计：以声波走时误差的二阶范数作为目标函数;以逐渐缩小的邻域对波速向量进行随机扰动,并根据先验信息对新解进行取模约束;以Me-tropolis准则接受新解;通过实验获得合理的初始温度;以指数函数进行降温。为最大程度逼近最优解,需要跟踪保持历史最优解。经过数值模拟及对混凝土桩基的实际测算,证明了该方法的有效性。     

波浪作用下弹性海洋地基的动力反应

基于平面应变条件下的广义Biot理论，提出波浪直接作用下弹性海洋地基有限元分析方法。所提方法能够解决以往弹性海床解析法或各种形式的数值方法无法处理的、包含复杂边界条件的实际工况。以不透水基础下海洋地基为例，分析基础对超静孔隙水压力和有效应力的影响范围与影响程度。     

水工隧洞混凝土衬砌地震动响应过程分析

地震作用下水工隧洞混凝土衬砌结构的动态响应是工程设计和安全评估的重要内容,而建立科学合理的混凝土动力本构模型以及内水与衬砌动力耦合作用分析方法是衬砌结构抗震研究的关键环节。基于应变空间静力损伤本构的基本思路,对三维应力状态下混凝土静态拉、压损伤变量进行定义和求解;在此基础上,考虑静、动态荷载作用下混凝土本构关系曲线的相似性特点,建立了适宜编程的混凝土动态损伤本构模型。基于单相固体介质和流体介质动力分析的显式有限元法,结合耦合界面的边界条件,建立了水工隧洞内水与衬砌耦合作用的动力显式有限元分析模型,该方法可以直接进行逐步积分,无需联立方程组求解,大大简化了计算过程,可以方便地用于分析多种介质的波动传播问题。针对某水电站引水隧洞工程进行了实例分析,计算结果表明：1)各部位混凝土衬砌处于同步震动状态,但腰拱部位位移明显小于顶拱和底拱部位;2)地震作用下混凝土衬砌迅速进入损伤开裂状态,腰拱部位衬砌应力增加明显,损伤破坏严重;3)开裂破坏区由腰拱逐渐向两端扩展,与内水直接作用的内层衬砌结构是抗震设计的薄弱环节。该模型能够合理地反映水工隧洞混凝土衬砌的地震动响应特性,并为水工隧洞抗震设计提供了一种有效的分析方法。     

用于锻压模拟的动力项调整准逆算法

实体成形过程的数值模拟如锻压过程的模拟，由于所采用的算法导致很高计算代价，所以提高计算效率和稳定性，仍然是一个需要努力解决的问题．通常采用的两大类算法，即准静态隐式算法和动力显式算法。难以很有效地应用于这类问题的模拟，基于Newmark类的动力问题算法也会导致庞大的计算量．针对这类问题提出一种特定的算法．该算法基于准静态模型，又加入动力调整项．该方法使用动力项调整加强了刚度矩阵的对角线元素，因而可以使用一种准逆算法代替传统技术求解线性方程组．由于求解代价的显著降低，可以使用显式Runge-Kutta方法进行模拟过程的时间积分．这一方法预计可用于以合理的代价实现锻压过程的稳定和可靠模拟．     

Short-term forecasting optimization algorithms for wind speed along Qinghai-Tibet railway based on different intelligent modeling theories

To protect trains against strong cross-wind along Qinghai-Tibet railway, a strong wind speed monitoring and warning system was developed. And to obtain high-precision wind speed short-term forecasting values for the system to make more accurate scheduling decision, two optimization algorithms were proposed. Using them to make calculative examples for actual wind speed time series from the 18th meteorological station, the results show that: the optimization algorithm based on wavelet analysis method and improved time series analysis method can attain high-precision multi-step forecasting values, the mean relative errors of one-step, three-step, five-step and ten-step forecasting are only 0.30%, 0.75%, 1.15% and 1.65%, respectively. The optimization algorithm based on wavelet analysis method and Kalman time series analysis method can obtain high-precision one-step forecasting values, the mean relative error of one-step forecasting is reduced by 61.67% to 0.115%. The two optimization algorithms both maintain the modeling simple character, and can attain prediction explicit equations after modeling calculation. Foundation item: Project(2006BAC07B03) supported by the National Key Technology R & D Program of China; Project(2006G040-A) supported by the Foundation of the Science and Technology Section of Ministry of Railway: Project(2008yb044) supported by the Foundation of Excellent Doctoral Dissertation of Central South University     

用于锻压模拟的动力项调整准逆算法

实体成形过程的数值模拟如锻压过程的模拟,由于所采用的算法导致很高计算代价,所以提高计算效率和稳定性,仍然是一个需要努力解决的问题.通常采用的两大类算法,即准静态隐式算法和动力显式算法,难以很有效地应用于这类问题的模拟,基于Newmark类的动力问题算法也会导致庞大的计算量.针对这类问题提出一种特定的算法.该算法基于准静态模型,又加入动力调整项.该方法使用动力项调整加强了刚度矩阵的对角线元素,因而可以使用一种准逆算法代替传统技术求解线性方程组.由于求解代价的显著降低,可以使用显式Runge-Kutta方法进行模拟过程的时间积分.这一方法预计可用于以合理的代价实现锻压过程的稳定和可靠模拟.     

Numerical simulation of shock wave interaction with a deformable particle based on the pseudo arc-length method

In this paper, we combine the pseudo arc-length numerical method with the mathematical model of multiphase compressible flow for simulating the shock wave interaction with a deformable particle. Firstly, an arc-length parameter is introduced to weaken the discontinuous singularity of governing equations, and an efficient pseudo arc-length numerical method of multiphase compressible flow is proposed. Then the accuracy and adaptive moving mesh property of this algorithm are tested. Finally, the multiphase pseudo arc-length numerical method is applied to the problem of interaction between shock wave and the deformable particle. Through the flow flied change and data analysis of key points, it can be found the complex wave structures are presented after the interactions between the planar incident shock wave and the metal particle, and all these wave interactions lead to the movement and deformation of metal particle, and then the deformed particle will affect the transmitted shock wave back. According to the discussion, the deformation of particle and shock wave propagation in the particle are determined by the shock wave impedance of each medium and shock speed, so the interaction between shock wave and the deformable particle can be studied on the basis of physical properties of explosive mediums.     

饱和多孔介质散射问题中局部地形影响的显式数值分析法

为了能合理分析局部场地条件对地震波散射波场的影响,基于饱和多孔介质理论的土力学模型,提出了一种显式有限元与黏弹性人工边界相结合的数值波动模拟方法.采用二维模型,以圆弧形凹陷河谷为例,分析了局部地形对饱和多孔介质中散射地震波场的影响,并通过与远置边界结果的对比,说明了该方法的正确性和适用性.     

数控进给伺服系统摩擦补偿控制仿真

针对伺服系统传动机构中摩擦对系统控制精度的影响问题,提出了一种遗传算法与模糊控制复合方法.建立了Stribeck+静摩擦力模型,设计了一种基于遗传算法的模糊补偿控制器,并将模糊补偿控制器应用于伺服系统中进行仿真.仿真结果表明,此方法不仅可有效抑制摩擦力对数控进给伺服系统的非线性作用及系统的低速爬行现象,而且可提高进给伺服系统的动态性能.采用不同的初始控制规则进行分析后发现,设置的初始值对遗传算法的收敛速度和系统的摩擦补偿均具有良好效果.     

半空间内洞室在冲击荷载作用下的瞬态响应

为了研究外界冲击力对地下洞室及周围土体的影响, 对半空间弹性土体圆柱形洞室在突加反平面冲击荷载作用下的瞬态响应进行探讨.将列车急刹车时对隧道产生的冲击力简化为半无限弹性体中突加在圆柱形洞室表面沿轴线方向的均布荷载,利用残余变量法求得频域解,运用Durbin提出的拉普拉斯数值逆变换给出问题的数值解,并将计算结果与静力情况下的结果进行比较,分析土体应力和位移随时间、弹性波的传播距离以及夹角的变化,结果表明：波到达后,该点土体的应力和位移均瞬间增大,随后慢慢减小并逐渐趋于静力值,波向外发散传播,并沿半径方向衰减;对于相同的传播距离上的各点,最大动应力和动位移与夹角无关;应力和位移最后的稳定值随着夹角的增大而增大.     

Speed–density functional relationship for heterogeneous traffic data: a statistical and theoretical investigation

This study is an attempt to establish a suitable speed–density functional relationship for heterogeneous traffic on urban arterials. The model must reproduce the traffic behaviour on traffic stream and satisfy all static and dynamic properties of speed–flow–density relationships. As a first attempt for Indian traffic condition, two behavioural parameters, namely the kinematic wave speed at jam (C_j) and a proposed saturation flow (λ), are estimated using empirical observations. The parameter C_j is estimated by developing a relationship between driver reaction time and vehicle position in the queue at the signalised intersection. Functional parameters are estimated using Levenberg–Marquardt algorithm implemented in the R statistical software. Numerical measures such as root mean squared error, average relative error and cumulative residual plots are used for assessing models fitness. We set out several static and dynamic properties of the flow–speed–density relationships to evaluate the models, and these properties equally hold good for both homogenous and heterogeneous traffic states. From the numerical analysis, it is found that very few models replicate empirical speed–density data traffic behaviour. However, none of the existing functional forms satisfy all the properties. To overcome the shortcomings, we proposed two new speed–density functional forms. The uniqueness of these models is that they satisfy both numerical accuracy and the properties of fundamental diagram. These new forms would certainly improve the modelling accuracy, especially in dynamic traffic studies when coupling with dynamic speed equations.

     

A theory for wave equation inverse problem: The union method for scattered wave extrapolation and velocity imaging

A new theory for inverse problem of wave equation, that is, the union method for scattered wave extrapolation and velocity imaging, is proposed in this paper. This method is very different from the classical wave extrapolation for migration, because we relate directly the scattered wave extrapolation to velocity inversion. And also this method is different from any linearized inverse method of wave equation, because we needn’t use linearized approximation. Because of this, the method can be applied to strong scattering case effectively (i. e. the value of scattered wave is not small, which can not be neglected). This method, of course, is different from nonlinearized optimum inverse method, because in this paper, the nonlinear inverse problem is turned into two steps inverse problem, i. e. scattered wave extrapolated and velocity imaging, which can be solved easily. Hence, the problem how to get the global optimum solution by using the nonlinearized optimum inverse method doesn’t bother us by using the method in this paper. Project supported by the Natural Science Foundation of Hunan Province Synopsis of the first author Song Shougen, professor, born in May 1960, received Ph D degree in Applied Geophysics, majoring in inverse problem in Mathematical Physics.     

Adaptive learning with guaranteed stability for discrete-time recurrent neural networks

To avoid unstable learning, a stable adaptive learning algorithm was proposed for discrete-time recurrent neural networks. Unlike the dynamic gradient methods, such as the backpropagation through time and the real time recurrent learning, the weights of the recurrent neural networks were updated online in terms of Lyapunov stability theory in the proposed learning algorithm, so the learning stability was guaranteed. With the inversion of the activation function of the recurrent neural networks, the proposed learning algorithm can be easily implemented for solving varying nonlinear adaptive learning problems and fast convergence of the adaptive learning process can be achieved. Simulation experiments in pattern recognition show that only 5 iterations are needed for the storage of a 15×15 binary image pattern and only 9 iterations are needed for the perfect realization of an analog vector by an equilibrium state with the proposed learning algorithm.     

Hybrid optimization model of product concepts

Deficiencies of applying the simple genetic algorithm to generate concepts were specified. Based on analyzing conceptual design and the morphological matrix of an excavator, the hybrid optimization model of generating its concepts was proposed, viz. an improved adaptive genetic algorithm was applied to explore the excavator concepts in the searching space of conceptual design, and a neural network was used to evaluate the fitness of the population. The optimization of generating concepts was finished through the ＂evolution - evaluation＂ iteration. The results show that by using the hybrid optimization model, not only the fitness evaluation and constraint conditions are well processed, but also the search precision and convergence speed of the optimization process are greatly improved. An example is presented to demonstrate the advantages of the orooosed method and associated algorithms.     

Some issues on 2.5-D transient electromagnetic forward

Numerical calculation for two integral transforms in 2.5-D transient electromagnetic forward is a difficult and key task, namely, the inverse Fourier transform and the inverse Laplace transform. Some effective algorithms for them were described. Based on the known algorithms in DC resistivity on wave-number distribution and selection, we proposed a principle on how to choose the least wave-number concerning the central-loop transient electromagnetic method. First, observe the behavior of transformation function curve with regard to wave-number in Fourier domain. In the light of its asymptote, ascertain the coverage scope of wave-number. Compared with analytic solution, the least wave-number in Fourier domain can be derived. Furthermore, the Laplace numerical inversion algorithm which needs only a few Laplace variables in pure real domain was also introduced here. The procedure was applied to forward modeling on transient electromagnetic field of a vertical magnetic dipole over uniform half-space to demonstrate them effectiveness and general applicability. Foundation item: Project (40344022) supported by the National Natural Science Foundation of China     

求解有约束非线性规划的混合混沌算法

针对带有约束的非线性规划问题,提出了一种新的算法.首先把有约束的非线性规划转化为含有2个目标的无约束的优化问题,然后利用混沌优化算法和最速下降法来混合求解.数值计算结果显示,该算法是可行有效的.     

一种新的PARAFAC模型拟合算法

为了提高二线性迭代最小二乘（BALS）算法拟合平行因子（PARAFAC）模型的速度,提出了一种新的PARAFAC模型拟合算法. 该算法利用新迭代与旧迭代之间的增量值,来预测下一次迭代的初始值,对BALS中的每次迭代,为2个加载矩阵设置相应的松弛因子,并通过联合优化的方法求得最优松弛因子对,从而加速BALS的收敛速度. 理论分析与仿真结果表明,与已有的BALS算法相比,所提算法在不牺牲性能的条件下,有效地提高了PARAFAC模型的拟合速度.