Papers by Keyword: Tikhonov Regularization

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Authors: Yu Yan Chen, Xu Wang, Dan Yang, Yi Lv
Abstract: A new hybrid algorithm is presented in this paper, which solves the ill-posed inverse problem of magnetic induction tomography (MIT) and improves the quality of reconstructed image. The hybrid algorithm firstly produces the preliminary image region using Tikhonov regularization algorithm, and then it obtains the final reconstructed image using variation regularization algorithm. The hybrid algorithm, compared with the Tikhonov regularization algorithm and the variation regularization algorithm, overcomes the numerical instability of MIT image reconstruction and accelerates the convergence speed of image reconstruction, and it also improves the resolving power of targets conductor and the quality of the reconstructed image. Simulation results show that the quality of the reconstructed image obtained using the hybrid algorithm is enhanced, so an effective algorithm for magnetic induction tomography (MIT) is introduced.
Authors: Shi Hong Yue, Jin Xin Zhang, Xiu Juan Bao
Abstract: In electrical resistance tomography (ERT), one of the main reasons for poor quality of reconstructed image is ill-posed property of the inverse problem. In order to improve image quality, one of the feasible methods is to incorporate prior information. Based on conventional Tikhonov regularization method to reconstruct ERT image, the regularization matrix, combined with prior information vector, was proposed. The prior information included the structure property of human thorax, conductivity distribution information of organs and other dynamic information during the respiration process. The research results indicated that the proposed method can enhance the spatial resolution of the reconstructed images, and reduced the trail traces of the investigated objectives. It is promising in detecting and monitoring regional lung ventilation change by means of the ERT system with a proper imaging method.
Authors: Jong Woong Park, Sung Han Sim, Hyung Jo Jung, Billie F. Spencer
Abstract: A displacement measurement provides useful information for structural health monitoring (SHM) as it is directly related to stiffness of the structure. Most existing methods of direct measurement such as the Laser Doppler Vibrometer (LDV) and the Liner Variable Differential Transformer (LVDT) are known to have accurate performance but have difficulties particularly in the use of large-scale civil structures as the methods rely on fixed reference points. Alternatively, indirect methods have been developed and widely used methods are Global Positioning System (GPS), vision-based displacement measurement system and displacement estimation from acceleration record. Among the indirect method, the use of accelerometer provides simple and economical in term of both hardware installation and operation. The major problem using acceleration based displacement estimation is low frequency drift caused by double integration. Recently, dynamic displacement estimation algorithm that addresses low-frequency drift problem has been developed. This study utilizes Wireless Smart Sensor (WSN) for estimating dynamic displacement from acceleration measurement in combination with the recently developed displacement estimation algorithm. Integrated into WSN that are low-cost, wireless, compatible with accelerometers, and capable of onboard computation, the displacement can be measured without limit of location on large-scale civil structures. Thus, this approach has the significant potential to impact many applications that require displacement measurements. With the displacement estimation algorithm embedded, the WSN performs in-network data processing to estimate displacements at each distributed sensor location wirelessly using only measured acceleration data. To experimentally validate the performance of displacement estimation using WSN for the use in structures with multiple-degree of freedom, the random vibration test is conducted on the three-story shear building model. The estimated displacement is compared with the reference displacements measured from the laser displacement sensor and the result shows good agreement.
Authors: Ya Mian Peng, Kai Li Wang, Huan Cheng Zhang
Abstract: 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.
Authors: Michele Barsanti, M. Beghini, Ciro Santus, Alessio Benincasa, Lorenzo Bertelli
Abstract: The ring-core method allows the determination of residual stresses at high depth from the surface. The numerical calculation integral method, commonly used for the hole-drilling, can also be applied to the ring-core. The integral method coefficients were obtained for several depth steps after axial-symmetric FE simulations with harmonic load. These coefficients were then validated with a 3D finite element model. Finally, an application was reported, showing the performance of the Tikhonov regularization on experimental data.
Authors: Abbassia Derouiche, Nacer Hamzaoui, Taoufik Boukharouba
Abstract: Our contribution in this work is to detect, localize and quantify the noise sources radiated by a spur gear transmission mechanism. The imaging technique is used; it is based on the acoustic inverse frequency response function (IFRF). The IFRF is based on the inversion of the transfer matrix built between the source points represented by their complex source strengths and listening points represented by the complex pressures measured by the hologram. The measurements were performed in a semi-anechoic room where the floor is concrete and the walls are covered with glass wool. The complex acoustic pressures are measured by an antenna with microphones regularly spaced; it is placed above the noisy mechanism. The reconstruction problem is therefore an inverse problem and is said ill-posed; thus, regularizations are needed to stabilize and to find the best solutions. As regularization technique, the Tikhonov method is applied and the regularization parameters are chosen according to the L-curve method. The goal is to reconstruct as accurately as possible the acoustic field radiated by the transmission mechanism on a fictive and tangent plane to the noisy mechanism considered open and sometimes closed. The results obtained showed that the sources were located with good approximation. The IFRF method is able to reconstruct the sound sources responsible for the noise radiated by the mechanism without any a priori information of the sources distribution, and the visualization of spatial acoustic fields facilitate the understanding of the complex phenomena of radiation.
Authors: Christina Brandt, Jenny Niebsch, Jost Vehmeyer
Abstract: In order to manufacture optical components or mechanical parts with high surface roughness requirements, diamond machining is used. To achieve the desired surface quality, the understanding of the surface generation process and its influencing parameters is important. Here, the crucial parameter is the residual unbalance of the main spindle. As the residual un-balance affects the process and vice versa, the investigation of the process-machine interaction is necessary. In this paper we present a model describing this interaction between dynamical unbalances that occur during the machining process and the engine-shaft structure at the example of an ultra-precision turning lathe. This model allows the determination of the achievable surface quality of a workpiece for a given balancing state. On the other hand we will present a mathematical method to solve the corresponding inverse problem of computing the necessary residual balancing state and balancing weights for a given desired or given measured surface quality.
Authors: Ya Li He, Ya Mian Peng, Li Chao Feng
Abstract: It is feasible for the inverse problem of research in the very vital significance between in practical application. Genetic algorithm is applied in many aspects, but we are more concerned with the application in mathematics. From the start of genetic algorithm, the collection to search for comprehensive coverage of preferred. Due to genetic algorithm is used to search the information, and does not need such problems with the problem is directly related to the derivative of the information. Finally, the results of numerical simulation show that the GA method has high accuracy and quick convergent speed. And it is easy to program and calculate. It is worth of practical application.
Authors: Ya Li He, Shi Qiu Zheng, Yan Mei Yang
Abstract: This article discussed the partial differential equation inverse problem. Because the partial differential equation inverse is the misalignment improperly posed problem, therefore analyzed has had the improperly posed reason. To process the partial differential equation inverse correctly not well-posed ness this difficulty, obtains relies on continuously the data stable approximate solution, has drawn support from the regularization related concept and the regularization general theory.
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