Improved Tikhonov Regularization Research Articles

Reliability Analysis of Intelligent Electric Energy Meter under Fusion Model Illness Analysis Algorithm

This work is aimed at solving the morbidity problem of the smart meter fusion model and improve the measurement accuracy and reliability of the smart meter. Starting with the topology of the smart meter, the reason for the serious morbidity of the smart meter model is discussed. First, the basic process of power system state estimation of smart meters is introduced, and the concept of error analysis of smart meters is clarified. Then, the causes and mechanisms of the ill-conditioned problems of the smart meter model are analyzed, and methods to reduce the morbidity of the smart meter calculation model are analyzed. Finally, a data optimization algorithm based on a greedy strategy and an improved Tikhonov regularization method is proposed. The model data is processed and optimized to reduce the morbidity of the smart meter measurement model. The results show that the analysis algorithm for reducing the morbidity error of the smart meter proposed in this study can effectively interfere with the morbidity of the smart meter calculation model. The processing effect shows that it can reduce the measurement error of the smart meter to about 5%, which is an order of magnitude lower than the error before processing, and the processing effect of the least square method is improved by more than 70%. From the perspective of processing speed, when the user number is between 50 and 100, the running time of the algorithm ranges between 1.5 and 3.5 s, which can be fully adapted to the actual situation and has strong practicability. In short, this study is helpful in improving the accuracy and reliability of smart meter calculations and provides a certain reference for related research.

Research on tomography algorithm of furnace flame temperature field based on acoustic method in thermal power station

An improved Tikhonov regularization algorithm MCTR based on Markov radial basis function is proposed to obtain the feedback of closed-loop control for pulverized coal injection process in thermal power plant, so as to solve the ill posed problem in temperature field reconstruction in furnace. The algorithm constructs a new regularization matrix to replace the standard Tikhonov regularization element matrix, so as to achieve the correction effect of the new algorithm. MCTR algorithm determines the boundary singular value of small singular value defined in this paper by determining the proportion between the standard deviation component corresponding to small singular value and the sum of standard deviation components corresponding to all singular values after singular value decomposition of coefficient matrix. After determining the boundary, a new regularization matrix is constructed according to the eigenvector corresponding to small singular value. Compared with the MTR algorithm using the identity matrix as the regularization matrix, MCTR algorithm only selectively modifies the parameters corresponding to small singular values after determining the regularization parameters, which improves the stability of the parameter solution and the reconstruction accuracy of the temperature field, and is helpful to the automatic control of thermal power plants and the efficiency of coal combustion.

An Improved Tikhonov-Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares

In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither discards small singular values, nor treats all singular value corrections. By fitting the Mackey–Glass time series in an exponential model, we compare the three regularization methods, and the numerically simulated results indicate that the improved regularization method is more effective at reducing the mean square error of the solution and increasing the accuracy of unknowns.

Reconstruction of energy spectrum of runaway electrons in nanosecond-pulse discharges in atmospheric air

This paper presents an experimental investigation into the runaway electron spectrum with a gas diode composed of a rough spherical cathode and plane anode under the excitation of a nanosecond-pulse generator in atmospheric air. The runaway electron beams are measured by a collector covered with aluminum foil with a thickness from 0 μm (mesh grid) to 50 μm. The energy spectrum is calculated by an improved Tikhonov regularization called the maximum entropy method. The experimental results show that the transition state of the discharge consisted of multiple streamer channels stretched from the cathode with glow-like plasma uniformly distributed over the anode. The number of runaway electrons measured by the collector is in the order of 1010 in atmospheric pressure air with a gap spacing of 5 mm and applied voltages of 70–130 kV. The cathode with a rough surface creates a more inhomogeneous electric field and larger emission site for the runaway electrons around the cathode, providing conditions for the coexistence of filamentary streamer and diffuse discharge. The reconstructed spectra show that the energy distribution of the runaway electrons presents a single-peak profile with energies from eU m/2–2eU m/3 (U m is maximal voltage across the gap).

Reconstruction of complex temperature field based on improved Tikhonov regularization

In order to improve the reconstruction accuracy of complex temperature field by acoustic CT, an improved Tikhonov regularization temperature field reconstruction algorithm is proposed. In this method, the filtering factor of standard Tikhonov regularization method is changed, so that no correction is made for larger singular values, while the correction for smaller singular values will increase with the decrease of singular values. The reconstruction results of typical temperature fields based on simulation data and experiment data verify the the effectiveness of the proposed algorithm on reducing reconstruction errors of temperature fields.

Light extinction spectrometry for determining the size distribution and concentration of polydisperse gold nanospheres

Size-dependent complex refractive index and resonant optical properties of gold nanoparticles make it possible to characterize nanoparticles using the light extinction spectra. In this article, light extinction spectrometry (LES) of resonant particles was presented to determine both the size distribution and concentration of polydisperse gold nanospheres. The inverse problem was solved by using the improved Tikhonov regularization method, and the extinction matrix was calculated by Mie theory. Numerical simulations were performed to investigate the effects of wavelength range, size distribution width, particle number concentration, and random noise on the inverted results. To validate the reliability of LES, several laboratory samples were measured using the LES with a relatively simple and compact experimental setup. The results showed that the error of mean diameter is smaller than 6 % and the error of concentration is smaller than 11 % for the samples of 40, 60, and 80 nm and for appropriate concentrations. This work provides a simple, fast, and low-cost method to measure the size distribution and concentration of polydisperse gold nanospheres.

Application of force reconstruction based on an improved Tikhonov regularization scheme

Application of force reconstruction based on an improved Tikhonov regularization scheme

Three-dimensional transient inverse heat conduction problems in the enhanced pool boiling heat transfer

In this paper, the solution methods of three-dimensional transient inverse heat conduction problems (3D IHCP) arising from pool boiling applications that need to reconstruct Neumann boundary conditions are summarized. Due to their mathematical ill-posedness, it is still non-trivial to solve these 3D IHCP at a reasonable cost. Firstly, we introduce the optimization-based regularization methods, such as Tikhonov regularization and iterative regularization. In general, it requires to solve a large number of optimization problems constrained by 3D partial differential equations (PDE). In this case, an improved Tikhonov regularization method is developed to quickly obtain optimal Tikhonov regularization parameter and thereby can accelerate the entire inverse calculation process. Furthermore, an iterative regularization method that is based on the conjugate gradient method is proposed to handle the high-resolution measurement data and many pointwise measurement data. In pool boiling experiments, they can be obtained by an infrared camera and mirco-thermocouples, respectively. Secondly, a completely different approach, a direct two-step strategy is presented to solve the same 3D transient ICHP on thin-plates that commonly occur in engineering applications. The main idea of the approach is to transform the inverse problem into a forward problem that is easier to solve by replacing the unknown Neumann boundary condition with an approximated Dirichlet boundary condition. The method has great advantage in efficiency compared with the optimization-based method that often requires to solve dozens or hundreds of direct, adjoint and sensitivity PDE problems, and therefore has the potential to be developed as efficient online heat-flux soft sensors for many practical applications. Thirdly, to further speed up the numerical solution procedure we develop a time-space dependent adaptive mesh refinement strategy due to the fact that the heat-flux and temperature dynamics related to bubble structures rapidly change in space and time on the boiling surface. A few classical engineering benchmark problems are considered to validate the aforementioned solution approaches, and the proposed approaches are also successfully applied to reconstruct the transient heat-flux distributions on the boiling surface from the noisy experimental data obtained in a series of real pool boiling experiments along the entire boiling curve. On the one hand, the corresponding research works reviewed can be used to explore the heat-transfer mechanism and establish a more accurate heat transfer model enabling the fast, robust and accurate reconstruction of local heat fluxes, which can be considered as realistic boundary conditions on the boiling surface to further study the two-phase flow and heat transfer process of boiling fluid above the heater. On the other hand, it can be also applied to explore the local details of the enhanced pool boiling heat transfer for the design of new heaters such as micro/nano structured surfaces, provide predictions related to the boiling process and conduct optimal experimental design in a systematic way. In the future work, a large number of 3D IHCP for different test regularization parameters will be calculated through a high-throughput parallel computational strategy. Besides, for thick heaters the direct two-step strategy can be used to solve the 3D ICHP accurately with an initial heat-flux guess obtained by the proposed optimization-based inversion approach. This way, the computational efficiency can be further improved. Furthermore, other new inversion methods, for example, which are based on artificial neural network method are being developed to solve 3D transient IHCP for more complex structured heater surfaces such as the micro/nano structures.

A Generalized Nash Equilibrium Approach for Autonomous Energy Management of Residential Energy Hubs

The development of the cutting-edge technologies in cogeneration and trigeneration has led to a rapid transition toward integrated energy systems and the mushrooming of energy hubs, calling for effective energy management schemes. This paper proposes a distributed algorithm for autonomous energy management (AEM) of a cluster of residential energy hubs. Given the interactive behaviors of energy purchasing at the supply side, we treat each hub as a self-interested agent, and formulate the AEM problem of these hubs as a monotone generalized Nash game (MON-GNG). On one hand, there are global coupling constraints representing the supply limits of the input energy systems, which are imposed by the limited capacities of electrical feeders and natural gas pipelines, thus making it a GNG. On the other hand, the cost function of each hub is merely convex in its actions considering the input-to-output energy transformation inside and the impacts of the energy storage devices, which leads to an MON game. The existence of the generalized Nash equilibria (GNEs) of this MON-GNG can be theoretically guaranteed. Then, by reformulating the MON-GNG as a variational inequality problem with special decomposition structure, an efficient and single-loop distributed algorithm is then proposed for computing a GNE with clear economic interpretation based on an improved Tikhonov regularization technique. Principles of parameter selection that will guarantee convergence are suggested. Numeric simulations validate the convergence performance and effectiveness of the proposed algorithm.

A Novel Method for High Frequency-Resolution Group Delay Acquisition Based on Tikhonov Regularization

Abstract The differential method is extensively adopted in the group delay measurement, where a contradiction between frequency-resolution and precision is present owning to the phase measurement error. This paper proposes a novel method for group delay calculating based on improved Tikhonov regularization that can omit the difference procedure. The comparative analysis demonstrates that the new method is capable of obtaining more precise group delay value along with high frequency-resolution when the measurement error of phase is included.

Compressive Sensing Based SAR Imaging and Autofocus Using Improved Tikhonov Regularization

For synthetic aperture radar (SAR) imaging, the compressive sensing (CS) coupled with total variation (TV)-based algorithm is known as an effective focusing technique using under-sampled dataset. However, the performance of the CS-TV method can be degraded by drawbacks of TV in terms of noise sensitivity and computational efficiency. In this paper, a novel approach to CS-SAR imaging is proposed based on improved Tikhonov regularization (ITR) coupled with an adaptive strategy using iterative reweighted matrix to solve the CS reconstruction problem of SAR images with sparsity. The proposed method can provide different degrees of performance of SAR autofocus with changes to the value of certain parameters of ITR. The proposed scheme outperforms conventional CS-based methods with respect to image quality, noise robustness, and computational complexity of the algorithm owing to the additional sensitivity of the proposed objective function. From the simulation results, we verify that the proposed autofocus method is highly efficient in forming SAR images from non-uniformly under-sampled dataset in terms of both image quality and computational efficiency.

An Improved Tikhonov Regularization Method for Lung Cancer Monitoring Using Electrical Impedance Tomography

Bedside monitoring plays an important role in the treatment of lung cancer. As a mostly used technique, X-ray computed tomography cannot provide medical surveillance for patients suffering from lung cancer in real-time. In comparison, the technique of electrical impedance tomography (EIT) has the potential to solve the issue by visualizing the human respiratory system; however, in most cases, its spatial resolution is too low to locate the real pulmonary lesions. One feasible method to improve the image quality is to incorporate the a priori information into the process of EIT imaging. In this paper, the conductivity distributions of lung tissues from a group of patients were extracted as the a priori information at first. Then, a novel EIT imaging method was proposed for lung cancer monitoring. A series of experiments indicated that the proposed method had potential capacity to identify lung cancer and monitor its metastasis. Besides, EIT can be further developed as a short- or long-term medical monitoring tool based on the proposed method.

Dynamic Force Identification Problem Based on a Novel Improved Tikhonov Regularization Method

The main purpose of this paper is to identify the dynamic forces between the conical pick and the coal-seam. According to the theory of time domain method, the dynamic force identification problem of the system is established. The direct problem is described by Green kernel function method. The dynamic force is expressed by a series of functions superposed by impulses, and the dynamic response of the structure is expressed as a convolution integral form between the input dynamic force and the response of Green kernel function. Because of the ill-conditioned characteristics of the structure matrix and the influence of measurement noise in the process of dynamic force identification, it is difficult to deal with this problem by the usual numerical method. In present content, a novel improved Tikhonov regularization method is proposed to solve ill-posed problems. An engineering example shows that the proposed method is effective and can obtain stable approximate solutions to meet the engineering requirements.

Bandwidth correction of spectral measurement based on Levenberg-Marquardt algorithm with improved Tikhonov regularization.

Spectroscopic data often suffers from spectral distortions due to the broadening effects of the spectrometer. In this paper, the issue of bandwidth correction is transformed into a multiparameter optimization problem, and an improved bandwidth correction method based on the Levenberg-Marquardt algorithm with improved Tikhonov regularization is presented. Example LED, Raman, and compact fluorescent lamp spectra were corrected with the proposed method, the Richardson-Lucy method, and the maximum a posterior method, and the correction errors and runtimes under the same stopping conditions of each method were compared. The experimental results show that the proposed method can be applied to different spectra with excellent correction.

Uncorrelated multi-sources load identification in frequency domain based on improved Tikhonov regularization method

Uncorrelated multi-sources load identification in frequency domain based on improved Tikhonov regularization method

Directly Simulation of Second Order Hyperbolic Systems in Second Order Form via the Regularization Concept

AbstractWe present an efficient and robust method for stress wave propagation problems (second order hyperbolic systems) having discontinuities directly in their second order form. Due to the numerical dispersion around discontinuities and lack of the inherent dissipation in hyperbolic systems, proper simulation of such problems are challenging. The proposed idea is to denoise spurious oscillations by a post-processing stage from solutions obtained from higher-order grid-based methods (e.g., high-order collocation or finite-difference schemes). The denoising is done so that the solutions remain higher-order (here, second order) around discontinuities and are still free from spurious oscillations. For this purpose, improved Tikhonov regularization approach is advised. This means to let data themselves select proper denoised solutions (since there is no pre-assumptions about regularized results). The improved approach can directly be done on uniform or non-uniform sampled data in a way that the regularized results maintenance continuous derivatives up to some desired order. It is shown how to improve the smoothing method so that it remains conservative and has local estimating feature. To confirm effectiveness of the proposed approach, finally, some one and two dimensional examples will be provided. It will be shown how both the numerical (artificial) dispersion and dissipation can be controlled around discontinuous solutions and stochastic-like results.

Improved Tikhonov Regularization Research and Applied in Inverse Problem

The regularization which constructs with the first filter function is precisely the Tikhonov regularization. This article has proven the Tikhonov functional minimization problem is decides suitably, namely satisfies the solution the existence, the solution unique reconciliation to rely on continuously the data stability; and this minimization problem in solves the first class equation equally the normal equation. The numerical simulation experiment's result indicated that distinguishes the inverse with the regular reduction solution parameter to have the numerical precision to be high and the stability is good and convergence rate quick characteristic.

Decoupled Reconstruction Method for Simultaneous Estimation of Temperatures and Radiative Properties in a One-Dimensional, Gray, Participating Medium

In the decoupled reconstruction method, using an improved Tikhonov regularization method, the temperature distribution in a participating medium is reconstructed from the boundary temperature image, and the radiative properties (absorption and scattering coefficients) are updated from the measured radiative intensity image. These two steps are taken alternately until convergence is reached. The distributions of temperature and radiative properties for two one-dimensional cases are reconstructed by the method from the boundary temperature and intensity images disturbed by measuremental errors with standard deviations up to 0.05, and the method shows good accuracy and robustness.

Simultaneous reconstruction of temperature distribution, absorptivity of wall surface and absorption coefficient of medium in a 2-D furnace system

For a 2-D furnace system filled with a gray medium, surrounded by gray emitting/absorpting and diffusely reflecting wall surfaces, the temperature distribution is reconstructed using an improved Tikhonov regularization method with radiative energy images detected from the boundary of the furnace, uniform absorptivity of both the wall surfaces and the medium being updated from the temperature images grasped from the boundary too. These steps are taken alternately till a convergence is reached. The measurement errors with normal distribution of standard square deviation of 0.01 are taken into consideration for the radiative energy image and temperature image data. The reconstruction errors for radiative properties vary from 1.45% to 10.75%, and for the highest temperature are within 2%. Comparatively, the reconstruction result for the sharper temperature distribution is not as good as that for the smoother temperature distribution. The applicability of the proposed method may be practically valuable.