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双语推荐：Tikhonov

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针对Tikhonov正则化算法噪声适应能力差和不便于引进额外的约束对解进行限制等缺点,利用迭代Tik?honov正则化算法对雷达方位超分辨进行研究,证明了迭代Tikhonov正则化反卷积公式的收敛性,分析了迭代Tik?honov正则化算法的频域性质,在存在噪声的情况下,提出相应的噪声抑制方法,得到约束迭代Tikhonov正则化算法。针对不同信噪比情况进行了计算机仿真实验,结果表明,与迭代Tikhonov正则化算法相比,约束迭代Tikhonov正则化算法具有较强的噪声适应能力,与常用的约束迭代方法(CID)算法相比,具有较快的收敛速度,初步验证了算法的有效性。
An iterative Tikhonov regularization algorithm was used based on Tikhonov regularization algorithm, because of its poor noise adoptive ability and without introduction of additional constraints on the solutions. The convergence of the deconvolution formula was proved, the frequency domain characteristics was analyzed, the corresponding noise suppres-sion methods was given, and the constrained iterative Tikhonov regularization algorithm was got. According to the different signal-to-noise ratio(SNR), the computer simulation experiment was made. The result showed that, compared with itera-tive Tikhonov regularization algorithm, it had a strong noise adoptive ability, and it had a faster convergence speed, which verified the algorithm efficiency preliminarily.

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探讨Tikhonov正则化方法以及迭代Tikhonov正则化方法在航空重力数据向下延拓中的应用,指出Tikhonov正则化方法在利用GCV法或L曲线法选取正则化参数时存在的不足以及空间域迭代法迭代不收敛的问题。引入波数域Tikhonov迭代正则化法,有效解决了上述方法存在的问题;针对迭代次数的确定问题,提出基于重力异常差异熵的迭代次数确定方法。算例结果表明,波数域迭代法迭代过程收敛,且计算精度高、速度快,值得广泛应用于航空重力数据的向下延拓。
The application of Tikhonov regularization method and space domain iterative Tikhonov method in the downward continuation was studied in this paper .There were some problems in these two methods . For the former , both the GCV and the L-curve methods showed the unconvergence property during the regularization parameter determinationprocess ,whilefor thelatter ,theRMScurvewasunconvergent .The wave number domain iterative method was introduced ,which showed better behavior in the convergence property than the above two methods .For the determination of iterated times ,a method based on gravity anomaly variance entropy was proposed .An experiment was carried out using four methods and result showed that ,compared to the other three methods ,the wave number domain iterative method was better in precision and efficiency ,which was worth to be wildly used in the downward continuation of airborne gravity data .

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在烷烃类多组分混合气体,尤其轻烷烃类气体傅里叶变换红外光谱定量分析中,其中在红外光谱区域吸收峰严重交叉重叠,不易建立定量分析模型。为此,采用Tikhonov正则化算法对甲烷、乙烷、丙烷、异丁烷、正丁烷、异戊烷和正戊烷等七种轻烷烃类混合气体傅里叶变换红外光谱进行特征波长的选择,以便建立定量分析模型。选择六种各气体浓度组成混合烷烃气体,采用Tikhonov正则化算法,通过对比分析混合气体在中红外全波段、主吸收峰和次吸收峰波段特征波长的选择和TR参数的优化,选择出七种气体成分的傅里叶变换红外光谱的特征波长。利用选择的特征波长和Tikhonov正则化参数对实测甲烷光谱数据进行检验分析,与其他气体成分的交叉灵敏度最大为11.153 7%,最小为1.239 7%,预测均方根误差为0.0048,有效增强了Tikhonov正则化算法在轻烷烃类混合气体定量分析中的实用性,初步验证了利用Tikhonov正则化进行烷烃类混合气体傅里叶变换红外光谱特征波长选择的可行性。
In the multicomponent mixture hydrocarbon gases Fourier transform infrared (FTIR) quantitative analysis ,especially for light alkane gases ,it is not easy to establish the quantitative analysis model because their IR spectra absorption peaks are se-riously overlapped .Aiming at this problem ,the Tikhonov regularization algorithm was used to select the characteristic wave-lengths for seven kinds of light alkane mixture gases FTIR which are composed with methane ,ethane ,propane ,iso-butane , n-butane ,iso-pentane and n-pentane .And then the wavelength selection was used to establish the quantitative analysis model . By comparing the analysis characteristics wavelength selection and TR parameters optimization of the mixed gases in the infrared all wave band ,the first absorption peak band and the second peak band ,the characteristic wavelength of 7 kinds of gases were selected by Tikhonov algorithm .The wavelength selection and Tikhonov regularization parameters were used to test the act

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对统计最优平面近场声全息(SOPNAH)技术进行研究,提出了一种吉洪诺夫(Tikhonov)正则化方法并选择最优正则化参数λ。通过仿真实验验证了结合吉洪诺夫正则化方法的SOPNAH能够对噪声源进行准确定位及实现声场重建,并且重建的精度比传统的方法更高。
Based on the SOPNAH technology research ,a Tikhonov regularization method is proposed ,and the optimal regularization parameter λis selected .Simulation results show the combination of Tikhonov regularization method and SOPNAH can accurately locate the noise source and achieve sound field reconstruction ,has higher reconstruction accuracy than the traditional method .

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针对二维多孔隙介质波动方程的参数孔隙率的识别问题，考虑模拟退火法的全局收敛特性，结合求解不适定问题的Tikhonov正则化方法，构造出正则化模拟退火算法。数值实验的结果表明此算法能够有效地处理参数识别问题。
We constructed a regularization simulated annealing algorithm by considering the characteristics of global convergence from the simulated annealing method,and introducing the Tikhonov regularization method for solving ill- posed problems, aiming at the recognition problem of parameter porosity of two-dimensional porous medium wave equations.The results show that this algorithm can effectively deal with the parameter identification problems.

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运用一种边界型无网格算法——边界粒子法求解Robin反问题,结合Tikhonov正则化技术消除反问题的不适定性。该方法仅需边界测量数据,计算精度高,特别适用于反问题的求解。数值算例显示该方法在求解Robin反问题上具有很好的稳定性和收敛性。
A boundary meshfree-boundary particle method is proposed for the solution of Robin inverse problem,in conj unction with the Tikhonov regularization technique to deal with the ill-posedness of in-verse problem.The present method has the merits of truly boundary meshless and high accuracy,which are particular appealing to solve inverse problem.In this study,numerical results are presented to show its good stability and rapid convergence for Robin inverse problem.

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研究了在实Hilbert空间中,求解非线性不适定问题的方法.通过对修正的三阶牛顿法进行Tikhonov正则化,得到新的迭代格式.在适当的条件下选取正则化参数,应用广义偏差准则,得出该迭代格式是单调的且是收敛性的.结果表明此迭代格式可应用于求解非线性不适定问题.
A method for solving nonlinear ill-posed problems in real Hilbert space was mainly studied . Through Tikhonov regularizing the modified Newton method ,an iterative form was obtained .The regu-larization parameter was chose under suitable conditions ,and the generalized error criterion was used ,so that the iterative scheme is monotone and convergence .From the result it could be seen that the nonlin-ear ill-posed problems can be solved by using the iterative scheme .

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介绍了氚分析的β衰变诱发X射线谱( BIXS)方法的发展历程和研究现状。叙述了刻度曲线法、解析方法和蒙特卡罗模拟结合Tikhonov正则法等三种不同解谱技术的BIXS方法的特点，重点介绍了课题组近年来开展的研究工作和取得的进展，包括蒙特卡罗模拟和Tikhonov正则法的引入，氚β衰变内韧致辐射、样品表面粗糙度、氚含量以及实验装置几何参数误差对分析结果影响的研究和应用等，同时也提出了BIXS方法需进一步开展的研究工作。
This paper presents the status and recent progress onβ-decay induced X-ray spectroscopy (BIXS) for tritium measurements. The development history of BIXS method and its applications on tritium analysis are introduced, and at the same time the characteristics of three kinds of BIXS methods, i.e. calibration curve method, analytical method and Monte Carlo simulations combined with Tikhonov regularization method are also introduced. The recent studies on the BIXS method performed in our group, including the incorporation of Monte Carlo simulation and regularization method, effects of internal bremsstrahlung of tritiumβ-decay, sample surface roughness, tritium content and geometrical parameter’s uncertainty of experimental setup in BIXS method, and the application are mainly presented. Finally, the general comments on the further improvements of the BIXS method are given.

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为了弥补现有GPS单频单历元算法在矿区开采沉降中的不足，更加精确地实时监测煤炭开采引起的地表移动，基于Tikhonov正则化方法及阻尼LAMBDA方法，提出了一种适合矿区沉降实时观测的新方法。首先，根据单频单历元方程的特点，利用Tikhonov正则化方法修正单频单历元法方程矩阵，由最小二乘法得到可靠的模糊度实数解；其次，依据阻尼LAMBDA方法搜索固定整周模糊度，其中阻尼因子可根据矿区首期变形监测结果确定；最后，利用该算法处理某矿区地表沉降的实测GPS数据，得到了测站北、东、天顶三方向的定位精度为毫米级，且单历元解算时间远小于采样率。试验结果表明，该算法在矿区沉降中能满足毫米级的观测，同时可满足矿区沉降实时观测，对于实现对矿区沉降的实时观测具有一定的参考价值。
In order to make up for the shortage of the existing algorithm for mining subsidence by using single epoch and single frequency GPS observation,and realize real-time monitoring of the ground movement caused by coal mining more accu-rately,based on Tikhonov regularization method and damped LAMBDA method,a new algorithm for mining settlement in real time is proposed. Firstly,according to the characteristics of the single-frequency and single-epoch equation,Tikhonov regulari-zation method is adopted to correct the matrix of the equation to obtain the reliable real-number solutions of ambiguity by the least squares method. Secondly,the integer ambiguity is fixed according to damped LAMBDA method,the damped factor is de-termined by the initial observation result. Finally,the actual GPS data in mining area is used to conduct experiment so as to test the performance of the algorithm proposed in this paper. The experimental results show that,three directions accuracy of the station i

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在浅海条件下,子空间相交的方法可以消除多途效应的影响,实现水平长阵的准确目标方位估计,获得比常规波束形成算法更优的性能。然而,该算法在数值计算稳定性上存在问题。在最小二乘子空间相交算法的基础上,提出一种Tikhonov规整化的最小二乘子空间相交算法,该算法在原解向量的基础上,施加了一个滤波因子,滤除了小特征值对应的解向量,使算法的数值计算稳定性大大提高,从而也提高了算法的检测性能。试验数据处理结果表明,该算法是有效的。
Bearing estimation is always a hard work in shallow water due to multimode nature of acoustic propagation in an oceanic waveguide. A new least-square subspace intersection (LSSI) method with Tikhonov’s regularization is pro-posed. Subspace intersection method yields unbiased bearing estimates. But it involves an inverse problem with a highly ill-conditioned coefficient matrix. In order to compute stable solutions it is necessary to apply regularization method. It is shown that Tikhonov’s regularization method is suitable for this problem, which can improve the robustness of LSSI algorithm. Results of processing sea-trial real data are presented.

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