基于正则化SVD算法的三维温度场声学重建

针对电站锅炉炉内三维温度场重建问题,基于声学理论构建数学模型.提出两种基于奇异值分解法(Singular Value Decomposition,SVD)的正则化算法,利用少量声学数据,对炉膛火焰分布的几种典型模型进行仿真重建.采用不同标准差的高斯噪声对两种算法的抗噪声能力进行检验.仿真结果表明,正则化SVD算法可以解决严重不适定的重建问题,重建温度场能够准确反映温度场分布,并且算法具有一定的抗噪声能力.TSVD正则化算法重建速度更快,抗噪声能力更强,适用于燃烧情况复杂的电站锅炉.     

炉膛三维温度场重建中Tikhonov正则化和截断奇异值分解算法比较

在煤粉锅炉诊断中火焰辐射能图像扮演着越来越重要的角色, 通过电荷耦合器件(CCD)获得的辐射能图像可以重建出炉内火焰三维温度场, CCD 用于获取视场角内的辐射能图像. 温度场重建的矩阵方程是一个严重病态的方程, 本文使用两种算法(Tikhonov正则化算法和截断奇异值分解(TSVD)算法)来重建温度场. 应用广义交叉检验算法来选取正确的正则化参数. 数值模拟的环境为一个10 m×10 m×10 m的三维炉膛, 系统被划分为10×10×10的1000个网格, 每个网格单元都是边长为1 m的立方体. 在正问题求解所得到的CCD接受信号基础上加上不同随机误差以模拟测量时的CCD接受信号. 研究两种算法重建后的温度重建误差、两者的重建时间, 以及最高温度的重建效果. 初步的研究结果显示, 一般情况下基于Tikhonov算法重建的温度场比基于TSVD算法重建的温度场误差要小, 计算所需时间短, 最高温度重建更准确.     

在SQUID心磁测量中基于奇异值分解和自适应滤波的噪声消除法

采用矩阵奇异值分解(singular value decomposition, SVD)的方法，对高温射频超导量子干涉仪(HTc rf-SQUID)采集到的单通道心磁信号进行处理.证明了对于近似周期性的心磁信号，在无参考噪声的情况下矩阵奇异值分解的方法与自适应窄带陷波相结合有较好的消除广谱噪声的效果. 关键词： 高温射频超导量子干涉仪 心磁信号 奇异值分解 噪声消除     

基于聚焦型光场相机的火焰温度场重建

光场成像技术可以在一次曝光中,同时记录下入射光线的空间分布信息和传播方向信息,能够得到更丰富的热辐射信号。本文利用聚焦型光场相机对三维火焰进行了光场采集,并利用这些光场信息通过截断奇异值分解(TSVD)重建了不同火焰的三维温度场分布,在重建过程中考虑了光场相机白图像的特点,剔除了对重建不利的无效像素,并且分别对均匀分布、轴对称分布和非轴对称分布的火焰进行了温度场重建,重建结果表明均匀温度分布的重建结果最佳,轴对称分布的重建结果次之,非轴对称分布的重建结果最差。最后考察了不同测量误差下重建结果,重建结果表明在一定的测量误差范围内,TSVD方法的重建效果对测量误差不敏感。     

光偏折层析的Tikhonov正则化重建技术

从不适定问题的求解思想出发,建立了使用Tikhonov正则化方法计算流场参量分布的光偏折层析重建技术。理论上详细讨论了偏折信息的转化、投影方程组的正则化、以及由共轭梯度法实现求解等三个主要步骤。用数值模拟考察该方法对非对称温度分布的重建效果,分别计算了对应不同采样数的欠定与超定投影方程组。结果表明,10次迭代后重建分布的平均误差和峰值误差分别为2.1%和5.2%。使用正则化方法对采集的多方向叠栅偏折投影进行计算,重建出双峰温度场。结果表明,使用正则化方法的双峰值相对误差略高,迭代次数减少,可提高重建效率。     

心磁信号广义S变换域奇异值分解滤波方法

针对心磁信号工频及背景噪声干扰问题, 提出了广义S变换奇异值分解(singular value decomposition, SVD)滤波方法.在离散S变换基础上, 导出了广义矩阵S变换和逆变换公式. 通过对采样信号进行广义S变换, 调节时频分辨率, 利用SVD分解方法确定有效心磁信 号区域, 实现自适应时频滤波. 实验结果表明, 该方法能有效滤除工频及背景噪声干 扰, 且在较少奇异值个数情况下可获得更好的滤波性能. 关键词： 心磁信号 S变换 奇异值分解 时频滤波     

分部优化正则化在近场声全息技术中的应用

在基于等效源法近场声全息技术的基础上,对稳定重建过程不适定性的正则化技术进行深入研究.为改善正则化效果,综合考虑Tikhonov正则化和截断奇异值法,提出一种新的分部优化正则化技术.该技术兼取了两种方法的优点,比Tikhonov正则化稳定,避免了过滤波等正则化失效的情况;比截断奇异值法精度高,包含了更多的细节信息.通过对简支板的数值仿真,分别和Tikhonov正则化和截断奇异值法进行了比较,说明了本文所提方法稳定性较好和精度较高的优点.最后通过实验研究进一步证明了本文方法的有效性和正确性.     

基于积分方程法和奇异值分解的磁性目标磁场延拓技术研究

对磁性目标磁场延拓技术进行了研究,提出了一种基于积分方程法和奇异值分解的新方法.应用该方法只需要采用积分方程法对磁性目标的结构进行较为粗略的单元划分,利用目标下方大平面上的磁场测量值,得到相应的线性方程组.采用基于奇异值分解的截断奇异值方法和修正奇异值方法对该线性方程组进行正则化求解,可实现磁性目标磁场的三维磁场重建、向上或向下延拓.该方法较以前的方法,提高了磁性目标磁场延拓的精度和可靠性,并且解决了磁性目标磁场在一定范围内向上延拓的技术难题. 关键词： 磁性目标磁场 延拓 积分方程法 奇异值分解     

中子深度分析反演算法研究

针对中子深度分析技术,研究几类反演算法：概率迭代法、奇异值分解求解最小二乘法、线性正则化方法及约束线性正则化法.开展相关数值实验,分别在欠定方程、超定方程情况下,对反演算法的结果进行比较.一般情况下几种算法都能得到较为理想的结果,概率迭代法和约束线性正则化法由于有迭代过程,因此在离子源强度发生阶跃处得到的结果并不理想.在超定方程情况下,当选取的反演范围较为随意时,线性正则化方法可能使得解的稳定性较差,而约束线性正则化法能够很好地抑制求解过程中的不稳定性.对实际测量能谱进行反演时,由于能谱有随机误差,线性正则化方法不能很好地抑制误差的影响,反演结果振荡较强,其余方法的结果与参考值符合很好.     

SPSO同时反演乙烯火焰温度和碳黑浓度的实验研究

本文用一台测量范围为500～1100nm的便携式光谱仪对乙烯火焰30mm和50mm两个高度进行扫描,通过黑体炉标定对测量值进行修正得到单色辐射强度,进一步采用随机微粒群算法(SPSO)同时重建出火焰在这两个高度处的温度和碳黑浓度分布.与Abel逆变换以及Tikhonov正则化算法的对比,表明了SPSO方法在同时重建轴对...     

Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method

An efficient numerical inverse radiation analysis based on the backward Monte Carlo (BMC) method is presented to determine the three-dimensional (3-D) temperature distribution in a large rectangular enclosure containing the participating medium, using radiative intensities in the visible range received by charge-coupled device (CCD) cameras. For large radiative sources and small detectors, when the radiation onto a small spot and onto a small direction cone is desired, the BMC method is more efficient than the forward Monte Carlo (FMC) method. Because the temperature reconstruction from the measured radiative intensities is an ill-posed inverse problem, least-square QR decomposition (LSQR) method is introduced to determine the meaningful temperature distribution. In order to gain insight into the effects on the accuracy of temperature distribution reconstruction, the detailed analyses are made using numerical simulations. The results show that the temperature distribution can be reconstructed accurately for the exact and noisy data.     

圆柱壳体瞬态辐射噪声评估算法

通过自身传感器实测振动数据快速评估瞬态辐射噪声,对及时排除故障,保持水下目标隐蔽性具有重要的意义。本文提出一种基于加速度阵列测试数据的圆柱壳体瞬态辐射声场的工程估算方法:借鉴工况传递分析的思路,分析求解瞬态振-声传递率矩阵,将瞬态激励壳体振动的测量数据代入,就可以估算壳体辐射声压级。在振-声传递率求解的过程中引入截断奇异值分解法,改善求逆时的病态矩阵,减少测试中背景干扰带来的估计误差。试验结果证实,该方法可以用来快速评估空气中敲击圆柱壳体所产生的瞬态辐射噪声,大部分频段噪声级估计误差在3 d B以内。本方法可望提供快速估计圆柱形壳体振动水下辐射噪声级借鉴和参考。     

The application of regularization technique based on partial optimization in the nearfield acoustic holography

The regularization technique for stabilizing the reconstruction based on the nearfield acoustic holography(NAH) was investigated on the basis of the equivalent source method.In order to obtain higher regularization effect,a regularization method based on the idea of partial optimization was proposed,which inherits the advantages of the Tikhonov and another regularization method—truncated singular value decomposition(TSVD).Through the numerical simulation,it is proved that the proposed method is stabler than the Tikhonov,and more precise than the TSVD.Finally the validity and the feasibility of the proposed method are demonstrated by an experiment carried out in a semi-anechoic room with two speakers.     

基于非线性光谱字典学习的单幅RGB图像光谱重建方法研究

针对单幅RGB图像重建光谱图像中的病态问题,提出一种基于非线性光谱字典学习的非线性重建方法。为了适应线性和非线性数据,该方法首先改进了基于自联想神经网络模型的非线性主成分分析算法,并利用其从训练光谱集中学习低维光谱字典,用于光谱重建的求逆方程中,以缓解病态状况。再在此光谱字典基础上,利用阻尼高斯牛顿法结合截断奇异值分解的正则化方法,进一步缓解该非线性反演的病态问题,实现单幅RGB图像重建光谱图像。在实验中,采用Munsell以及Munsell+Pantone两个光谱训练集学习光谱字典,同时利用CAVE和UEA光谱图像库进行光谱重建测试。该方法测试结果与现有方法比较发现,该方法在不同光谱训练集下重建CAVE和UEA两库光谱图像的均方根差的平均值最低,分别为0.212 4, 0.255 4, 0.229 4和0.294 9,均方根差的标准偏差接近最好方法的效果,分别为0.068 5, 0.084 7, 0.066 8和0.087 0。此结果表明该方法针对单幅RGB图像重建光谱图像在重建精度和稳定性上均存在优势。     

基于阻尼LSQR-LMBC的火焰三维温度场重建

光场相机可以解决辐射测温多相机系统光路复杂、同步触发难等问题,在辐射成像三维温度重建时有其独特优势. LSQR是求解基于大型稀疏矩阵最小二乘问题的经典算法,该算法用于重建三维温度场时对温度初值依赖较大,在信噪比较低的情况下重建精度不理想.本文提出阻尼LSQR-LMBC重建算法,通过在LSQR方法中添加阻尼正则化项,提高火焰三维温度场重建的抗噪性能,并结合LMBC算法,实现吸收系数和三维温度场同时求解.在数值模拟部分,随着信噪比逐渐降低,阻尼LSQR的重建效果比LSQR更加稳定,在信噪比达到13.86 d B时,重建精度大约提高30%.阻尼LSQR-LMBC的平均重建误差为6.63%.用丁烷火焰进行了实验,重建的丁烷火焰三维温度场分布符合辐射火焰燃烧的特征,和热电偶的测温数据结果进行对比,相对误差在6.8%左右.     

基于迭代TSVD的NMR二维谱反演算法

针对现有基于TSVD的二维反演算法中截断位置判断不准确、容易产生虚假峰等问题,提出了一种改进的方法. 首先,通过逐步求精的方法对L曲线上的拐角位置进行定位,得到迭代的最大截断位置;然后,根据反演核奇异值的集中程度获取迭代的最小截断位置;最后,在给定的截断位置范围内从小到大进行TSVD,每次迭代都以上一次迭代的结果为依据. 对仿真数据和实验数据的反演结果表明,该算法都能够得到比较好的二维反演效果. 与现有基于TSVD的方法相比,该算法具有更高的鲁棒性,能够得到更清晰的二维谱,可满足实际应用需求.     

Application of the nonregularization method to solving the inverse problem of passive acoustic thermotomography on the wavelet basis

A comparative analysis of reconstruction quality is performed for the reconstruction of the temperature distribution under hyperthermia by the regularization and nonregularization methods, which are used for solving the systems of linear equations following from the statement of the ill-posed inverse problem of passive acoustic thermotomography. The basis functions are chosen to be wavelets, which allows a compact representation of the temperature peak under reconstruction. It is shown that, when deep-seated parts of tissue are heated, the nonregularization method gives a much smaller systematic error of temperature reconstruction at the focusing point. At the same time, the random error of reconstruction increases. The nonregularization method of reconstruction can be used in combination with regularization for monitoring hyperthermia procedures in oncology to obtain more detailed information on the in-depth temperature.     

Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies

In this paper, the possibility of visualization of three-dimensional (3-D) temperature distributions in large-scale boiler furnaces from radiative energy images captured by multiple charge-coupled device (CCD) cameras mounted around the furnace is studied numerically. For the calculation of the radiative energy image formation, a fast algorithm proposed by the authors for pinhole imaging is used in this paper, which is based on the Monte Carlo method and combined with a concept of angular factor effective for image formation. This algorithm is applicable for the emitting, absorbing, and isotropic scattering medium. For the inversion of the 3-D temperature distributions which is an ill-posed problem, a modified Tikhonov regularization method is improved, where the finite difference regularizer is defined and can be used in 3-D cases, and the optimal regularization parameter is suggested to be selected by using a post-treatment method. For a 3-D unimodal temperature distribution, the numerical simulation results show that the reconstruction errors for the 3-D temperature distribution can be maintained at levels similar to the measurement error and the visualization quality of the temperature distribution is satisfactory. For a kind of bimodal temperature distribution, the reconstruction errors are higher than those for the unimodal distribution, but the bimodal feature of the temperature distribution can also be reproduced clearly.     

Effect of sensor proximity over the non-conformal hologram plane in the near-field acoustical holography based on the inverse boundary element method

Near-field acoustical holography (NAH) is a useful tool for the identification and visualization of vibro-acoustic sources. In particular, NAH can be applied to many practical sources having irregular shape if the inverse boundary element method (BEM) is employed. Once the relation between the source and the radiated field is defined in the transfer matrix modeled by the BEM, the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface. The usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface, which can be a flat, cylindrical, or spherical shape, for the measurement ease. Then, the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill-posed than the conformal case. To investigate the effect of sensor proximity and distance variability on the reconstruction error, simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate. Flat, tilted, and randomized hologram surfaces were adopted in the test. It was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor. To improve the reconstruction accuracy, an investigation was conducted to find proper field points among a large number of overdetermined field points. The number of field data was reduced gradually under various reduction schemes using condition number, effective independence value, and sensor distance. It was demonstrated that the quality of reconstruction result given by the non-conformal measurement can be improved by removing some field points that contribute to the ill-conditioning of the inverse problem. A small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation. However, further reduction of the field points, becoming an underdetermined situation, yielded a drastic improvement of the reconstruction accuracy.