两级敏度分析求解非线性稳态多宗量热传导反问题

提出基于两级敏度分析的稳态非线性热传导反问题的求解策略,建立了便于非线性正演和反演的有限元模型,由此可直接求导进行敏度分析,同时还考虑了非均质和分布参数的影响。对非线性热物性参数和边界条件的反演,进行了数值验证,取得了令人满意的结果,并对信息误差作了初步探讨。     

同伦正则化算法求解多宗量瞬态热传导反问题

以Bregman距离函数作为正则化泛函,建立了多宗量瞬态热传导反演的一种求解模式,可对导热系数和边界条件等进行联合识别.时域上采用精细算法进行离散,并应用同伦算法进行求解.对信息的测量误差和初值选取作了初步探讨,并进行了数值验证.     

共轭梯度法求解多宗量瞬态热传导反问题

提出瞬态热传导反问题中热物性参数和边界条件多宗量反演的一般数值求解模式,导出了敏度计算公式,并用共轭梯度法求解,探讨了测点数目、测量误差和变量初值对反演结果的影响,并进行了数值验证.     

黑体辐射数值反演的快速稳定算法

讨论采用Tikhonov正则化方法进行黑体辐射数值反演的相关技术问题,特别是将双参数模型提供的相当好的正则参数初值与求解Morozov偏差方程的一个三阶收敛格式相结合,给出了一个新的、具有高效稳定等特点的混合数值反演算法,并进行了数值试验.这一算法在原则上也适合其它许多物理参数识别问题(如Fermi体系的反演、各种类型的Abel方程的数值反演等).     

基于机器学习的可燃物热解参数反演研究

数值模拟是研究可燃物热解过程的重要技术手段,但建立数值模型时需要准确的可燃物热解参数,而通过实验手段获得给定材料的全部参数较为困难。针对此问题,本文提出了一种基于机器学习的热解参数反演技术。首先建立了数值模型;然后建立了基于神经网络及遗传算法的混合参数反演模型;最后使用数值模拟数据进行了验证,结果表明提出的参数反演技术可有效兼顾反演效率和反演精度,能够为准确快速获得热解参数提供一种新的工具,具有较好的应用前景。     

热损耗条件下导热系数反演模型及实验研究

通过导热反问题反演求解导热系数通常误差较大,本文构建考虑热损耗条件下的虚拟薄板模型精确求解导热系数。首先通过数值算例验证模型的准确性和稳定性,正向问题使用有限差分法进行求解,反问题求解采用人工蜂群算法进行目标函数最优化。然后搭建第二类边界条件下导热正向装置,进行导热系数实例反演和实验研究,并将新模型与理论模型反演结果对比分析。结果表明理论模型反演结果的相对误差约为-14.76%,而新模型下导热系数反演相对误差达到-4.67%。新模型较理论模型反演结果更精确,有效降低了热损耗对反演的影响,提高了反演精度,更符合实际工况。     

复合介质等效电磁参数的数值研究

利用时域有限差分(FDTD)方法研究了掺杂介质材料等效电磁参数的反演方法.首先用FDTD方法计算掺杂介质的反射、透射系数,然后结合遗传算法和传播矩阵法反演不同掺杂比率的等效电磁参数,得到了等效电磁参数随掺杂比率变化的关系曲线.在复合材料的掺杂比率较低和较高时,等效电磁参数计算公式之间以及数值方法得到的结果比较一致;当掺杂比率处于中间值时,则稍有差别.结果显示用数值方法反演复合材料等效电磁参数具有可行性.     

周期性微结构硅基表面辐射特性数值研究

本文通过时域有限差分法求解 M-well 方程组,分析微结构表面与入射辐射间的相互作用,结合近场 - 远场辐射转换模型,获得了尺寸、温度和入射波长等参数对表面双向反射分布函数的影响规律,研究结果为热辐射的光谱和方向调控技术提供了数值基础.     

用进化策略方法反演二维弹性波动方程的参数

从材料响应的理论合成与实际测量数据相拟合出发,将二维弹性波动方程的参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了进化策略法,并同遗传方法的反演结果进行了比较.数值结果表明,用进化策略方法进行参数反演的精度大大高于用遗传方法进行参数反演的精度,进化策略反演是一种良好的非线性反演方法.     

用改进的遗传算法和高斯牛顿法联合反演三维地下水流模型参数

遗传算法在处理非线性优化问题时具有较好的全局搜索性能,但在局部搜索时搜索效率不高,解的精度亦不高,高斯牛顿法在处理非线性优化问题时的性质正好和遗传算法相反,利用遗传算法和高斯牛顿法的优点,用改进的遗传算法和高斯牛顿法联合反演地下水数值模型参数.首先用遗传算法求出地下水模型参数的初值,然后利用这组初值用高斯牛顿法进行数值模型参数的反演,并以一非均质各向同性三维承压非稳定流理想模型为例,结合有限元法讨论了用遗传算法和高斯牛顿法联合反演地下水数值模型参数的过程.计算结果表明,联合参数反演方法,具有收敛速度快、解的精度高的特点,在地下水渗流和水资源评价等领域可广泛应用.     

Optimization analysis of the thermal cloaking problem for a cylindrical body

The inverse heat transfer problem associated with constructing multilayer material shells cloaking the presence of a cylindrical body in an externally applied temperature field is studied. As the original mathematical model, the steady-state heat equation for an anisotropic shell is used. With the help of the optimization method, this inverse problem is reduced to the corresponding control problem. A numerical algorithm of its solution based on the particle swarm optimization is proposed, and the results of numerical experiments are discussed.     

NON-DESTRUCTIVE EVALUATION OF HORIZONTAL CRACK DETECTION IN BEAMS USING TRANSVERSE IMPACT

Numerical and experimental studies for crack detection in beam employing transverse impact are presented. In the numerical study, a beam model of wave propagation is developed to calculate the time history of beam response before, over and after the crack region. It is expected that the resulting wave in the beam will be scattered by the crack and will carry information on the location and geometry of the crack. Experiments using a scanning laser vibrometer on specimens containing simulated crack are then conducted to verify the numerical results. Comparison study between the numerical results and experimental observations are conducted; good correlation between theory and experiment is observed. The beam model of wave propagation and adaptive multilayer perceptron networks (MLP) are then used for inverse identification of crack parameters (i.e., crack location, depth and length) in the beams. Time-domain displacement responses calculated using the present beam model containing predetermined crack parameters are used as training data for the MLP. Once the MLP is trained, the MLP networks are then employed for inverse determination of an unknown crack in a beam using experimental displacement responses measured with a scanning laser vibrometer. Examples show that the procedure performs well for the determination of a wide range of values for the location, depth and length of the crack.     

广义脉冲谱方法的一个新形式及其应用

构造了一种新的、有一定抗噪能力的广义脉冲谱方法(GPST)的计算格式。设计了选取正则参数过程中节省计算量的技巧.最后探讨了方法在地震勘探一维波方程反问题上的应用,进行了数值模拟。     

The optimization method in design problems of spherical layered thermal shells

The inverse problem of designing multilayered spherical shells, intended for thermal cloaking a spherical body or concentrating heat in it, has been analyzed. The stationary heat conduction equation for an anisotropic medium is applied as an original mathematical model. The optimization method is used to reduce this inverse problem to an extreme problem, where the role of controls is played by the thermal conductivities of shell layers. A numerical algorithm for solving the problem is proposed, and the results of computational experiments are discussed.     

An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

In this paper, an inverse source problem for the time-fractional diffusion equation is investigated. The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure. Here the sparsity is understood with respect to the pixel basis, i.e., the source has a small support. By an elastic-net regularization method, this inverse source problem is formulated into an optimization problem and a semismooth Newton (SSN) algorithm is developed to solve it. A discretization strategy is applied in the numerical realization. Several one- and two- dimensional numerical examples illustrate the efficiency of the proposed method.     

叶栅全三维粘性反问题的数值解

本文发展了一种解叶栅全三维粘性反问题的新的数值方法.基于非正交曲线坐标与相应的非正交速度分量下完全守恒型的Navier－Stokes方程,全三维反问题规定叶片表面的无量纲压力分布反求叶型。计算中叶片表面的边界条件采用一种特殊的方式来处理，即一方面强加给定的压力分布条件,另方面叶面的几何位置在迭代过程中又是可移动的，其移动速度将与Navier—Stokes方程在当地的解联系起来，从而形成一种解定常问题的新的不定常过程.试算证明了本文方法的可行性。     

求解光学CT图象重建问题的广义脉冲谱技术研究

间接法是目前实现医学诊断用近红外光三维成象(光CT)的最有潜力的手段之一.该方法基于以下假设,即给定分别对应于不同点激励源作用下成象组织体表面各点的传输光测量.在组织体内存在着与上述检测量相对应的、唯一的光学参数三维分布.由此,图象重建变成了特定光子传输模型的逆问题.本文提出采用广义脉冲谱技术(Generalized Pulse Spectrum Technique,GPST)进行光学CT图象重建逆问题的求解.给出了GPST在扩散方程光子传输模型逆问题求解中的具体实现,数值实验结果表明,通过选择合适的复频率点,采用GPST算法的图象重建结果优于其它现有算法,且响应时间合理.最后,本文还初步讨论了吸收和散射系数重建中复频率点选择的一些基本原则。     

Impact reduction of the uncertain geometrical parameters on magnetic material identification of an EI electromagnetic inductor using an adaptive inverse algorithm

The magnetic characteristics of the electromagnetic devices' core materials can be recovered by solving an inverse problem, where sets of measurements need to be properly interpreted using a forward numerical model of the device. However, the uncertainties of the geometrical parameter values in the forward model lead to appreciable recovery errors in the recovered values of the material parameters. In this paper, we propose an effective inverse approach technique, in which the influences of the uncertainties in the geometrical model parameters are minimized. In this proposed approach, the cost function that needs to be minimized is adapted with respect to the uncertain geometrical model parameters. The proposed methodology is applied onto the identification of the magnetizing B-H curve of the magnetic material of an EI core inductor. The numerical results show a significant reduction of the recovery errors in the identified magnetic material parameter values. Moreover, the proposed methodology is validated by solving an inverse problem starting from real magnetic measurements.     

辐射传递蒙特卡洛法精度分析及数值试验

本文建立了蒙特卡洛法模拟散射参与性介质内辐射传递计算模型。对蒙特卡洛法的计算精度及运行时间进行了较为详细的分析,提出了几种判断计算精度的方法。同时,借助蒙特卡洛法模拟辐射传递过程,进行数值“辐射实验”。利用该“实验结果”进行了物性反问题研究。在已知光学厚度的前提下,得到散射反照率与后半球辐射热流之间的单值函数关系。