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A CCBM-based generalized GKB iterative regularization algorithm for inverse Cauchy problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2023年第1期432卷

作者： Gong, Rongfang Wang, Min Huang, Qin Zhang, Ye Nanjing Univ Aeronaut & Astronaut Sch Math Nanjing 211106 Peoples R China MIIT Key Lab Math Modelling & High Performance Comp Air Nanjing 211106 Peoples R China Beijing Inst Technol Sch Math & Stat Beijing 100081 Peoples R China Shenzhen MSU BIT Univ Shenzhen 518172 Peoples R China

This paper examines inverse Cauchy problems that are governed by a kind of elliptic partial differential equation. The inverse problems involve recovering the missing data on an inaccessible boundary from the measured data on an accessible boundary, which is severely ill-posed. By using the coupled complex boundary method (CCBM), which integrates both Dirichlet and Neumann data into a single Robin boundary condition, we reformulate the underlying problem into an operator equation. Based on this new formulation, we study the solution existence issue of the reduced problem with noisy data. A Golub-Kahan bidiagonalization (GKB) process together with Givens rotation is employed for iteratively solving the proposed operator equation. The regularizing property of the developed method, called CCBM-GKB, and its convergence rate results are proved under a posteriori stopping rule. Finally, a linear finite element method is used for the numerical realization of CCBM-GKB. Various numerical experiments demonstrate that CCBM-GKB is a kind of accelerated iterative regularization method, as it is much faster than the classic Landweber method.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Cauchy problem Inverse problems Regularization iteration algorithm Golub-Kahan bidiagonalization Givens rotation

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Group decision making based on relative projection between fuzzy preference relations

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期184卷

作者： Liu, Zu-Lin Liu, Fang Zhang, Jia-Wei Chen, Xiao-Hong Guangxi Univ Sch Business Nanning 530004 Guangxi Peoples R China Guangxi Univ Sch Math & Informat Sci Nanning 530004 Guangxi Peoples R China Beibu Gulf Univ Coll Sci Qinzhou 535011 Guangxi Peoples R China

Group decision making (GDM) has been widely focused on for coping with the complexity of a practical decision making problem. This paper proposes a relative projection-driven GDM model with fuzzy preference relations (FPRs). First, a novel additive consistency index of FPRs is constructed using the variance of relative projections between column/row vectors in two FPRs, which is called the relative projection variance consistency index (RPVCI). The thresholds of RPVCI for FPRs with acceptable additive consistency (AAC) are calculated using the simulation method. For improving consistency of FPRs, a convergent iteration algorithm is constructed by equipping subjective and objective adjustment parameters. Second, the group consensus level is captured using relative projections of individual FPRs on the collective one. An iteration model is reported to optimize the consensus degree by combining the weights of experts with a comprehensive adjustment coefficient that depends on both subjective and objective factors. Third, a novel GDM algorithm is proposed by integrating the two proposed iteration models. Comparisons with some existing models are offered by carrying out a case study to show the novelty and advantage of the proposed GDM model.

关键词： Group decision making (GDM) Fuzzy preference relation (FPR) Relative projection Consistency and consensus iteration algorithm

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Zero-sum risk-sensitive stochastic games with unbounded payoff functions and varying discount factors

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2023年第2期519卷

作者： Guo, Xin Chen, Jian Li, Zechao Sun Yat Sen Univ Sch Sci Guangzhou Peoples R China Tsinghua Univ Sch Econ & Management Beijing Peoples R China

This paper is an attempt of studying zero-sum risk-sensitive stochastic games with unbounded payoff functions and varying discount factors. First, we obtain a logarithm growth condition to guarantee the finiteness of the expected risk-sensitive discounted payoffs, which is an extension of the bounded reward/cost functions in the existing literature. Second, an example with unbounded payoff functions is given, where the solution to the (associated) Shapley equation (SE) no longer has the boundaries as in the existing research. This motivates us to replace the boundaries of the SE with new ones. Third, using the new boundaries and novel arguments, we not only establish the existence of a solution to the SE, but also prove the existence of the value of the game and a Nash equilibrium. Furthermore, we develop an iteration algorithm for computing (at least approximating) the value and Nash equilibria of the games. Finally, we use an inventory system to illustrate our results and show the difference between our conditions and those in the existing articles. (c) 2022 Published by Elsevier Inc.

关键词： Stochastic game Unbounded payoff State-dependent discount factor Shapley equation Nash equilibrium iteration algorithm

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Large margin projection-based multi-metric learning for classification

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KNOWLEDGE-BASED SYSTEMS 2022年 243卷 108481-108481页

作者： Yuan, Chao Yang, Liming China Agr Univ Coll Informat & Elect Engn Beijing 100083 Peoples R China China Agr Univ Coll Sci Beijing 100083 Peoples R China

Metric learning has been a promising technology to improve classification performance, which aims to learn a data-dependent distance metric such that the similarity between samples can be more effectively evaluated. Metric plays a significant role in the description of similarity between samples, however, learning a single distance metric is usually inadequate, especially when dealing with the heterogeneously distributed data. Traditional metric learning only considers a global metric, while the local metric, which is critical for heterogeneous data, is ignored. In this paper, we formulate a novel large margin projection-based multi-metric learning (LMML) for the binary classification of heterogeneous data, which constructs a unified framework based on global metric and local metrics, where two local distance metrics are learned, one for each class, so that the covariance of samples is as small as possible, and the sample of another class is as far away as possible from the mean of the sample. Moreover, a global distance metric is introduced to capture the common structure between the two classes, which requires that the distance metric in each class should be as close as possible to the global one. An efficient iterative algorithm is designed to optimize the LMML. We also conduct some insightful analyses on the computational complexity and the convergence of the proposed algorithm. Experiments are conducted on artificial datasets, UCI benchmark datasets and handwritten digit datasets to evaluate the proposed method. Compared with the state-of-the-art approaches, the experiment results demonstrate the feasibility and effectiveness of the proposed method. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Classification Heterogeneously distributed data Multi-metric learning iteration algorithm

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Multi-sensor Distributed Estimation Fusion Based on Minimizing the Bhattacharyya Distance Sum 24

Multi-sensor Distributed Estimation Fusion Based on Minimizi...

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24th IEEE International Conference on Information Fusion (FUSION)

作者： Tang, Qi Duan, Zhansheng Xi An Jiao Tong Univ Ctr Informat Engn Sci Res Xian 710049 Shaanxi Peoples R China

ISBN: (纸本)9781737749714

In multi-sensor distributed estimation fusion, local estimation errors are generally correlated among local estimates. Usually, correlation is known to exist but unavailable or unclear to be how large it is, and needed to be considered. For this situation, a sensible way is to set up an optimality criterion and optimize it over all possible such correlations. Based on the framework of minimizing the statistical distance sum between the fused density and local posterior densities, a new method is proposed by utilizing Bhattacharyya distance, which is commonly used in measuring the closeness or similarity between two densities. First, the objective function is introduced. Then, we investigate the convexity form of the objective function, and separate the solving procedure into two steps during settling the original optimization problem, which benefit us to acquire the solution of that problem. At last, the acquired solution (fused estimate) is given in an implicit form, however, it can be obtained through iterative algorithm. And, it is pessimistic definite in mean square error (MSE). Numerical examples illustrate this and show the effectiveness of the proposed distributed method by comparing with several other fusion methods under the same framework but using other kinds of statistical distance.

关键词： Distributed estimation fusion statistical distance Bhattacharyya distance Gaussian assumption iteration algorithm

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An Indoor UWB 3D Positioning Method for Coplanar Base Stations

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SENSORS 2022年第24期22卷 9634-9634页

作者： Zhou, Ning Si, Minghao Li, Dehai Seow, Chee Kiat Mi, Jinzhong Chinese Acad Surveying & Mapping Beijing 100036 Peoples R China China Univ Min & Technol Sch Environm Sci & Spatial Informat Xuzhou 221116 Peoples R China Univ Glasgow Sch Comp Sci Sir Alwyn Williams Bldg Glasgow G128RZ Scotland

As an indispensable type of information, location data are used in various industries. Ultrawideband (UWB) technology has been used for indoor location estimation due to its excellent ranging performance. However, the accuracy of the location estimation results is heavily affected by the deployment of base stations;in particular, the base station deployment space is limited in certain scenarios. In underground mines, base stations must be placed on the roof to ensure signal coverage, which is almost coplanar in nature. Existing indoor positioning solutions suffer from both difficulties in the correct convergence of results and poor positioning accuracy under coplanar base-station conditions. To correctly estimate position in coplanar base-station scenarios, this paper proposes a novel iterative method. Based on the Newton iteration method, a selection range for the initial value and iterative convergence control conditions were derived to improve the convergence performance of the algorithm. In this paper, we mathematically analyze the impact of the localization solution for coplanar base stations and derive the expression for the localization accuracy performance. The proposed method demonstrated a positioning accuracy of 5 cm in the experimental campaign for the comparative analysis, with the multi-epoch observation results being stable within 10 cm. Furthermore, it was found that, when base stations are coplanar, the test point accuracy can be improved by an average of 63.54% compared to the conventional positioning algorithm. In the base-station coplanar deployment scenario, the upper bound of the CDF convergence in the proposed method outperformed the conventional positioning algorithm by about 30%.

关键词： UWB indoor location iteration algorithm coplanar base station

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An improved meshing stiffness calculation algorithm for gear pair involving fractal contact stiffness based on dynamic contact force

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2022年 94卷 1页

作者： Yu, Xin Sun, Yunyun Li, Hongguang Wu, Shijing Wuhan Univ Sch Power & Mech Engn Wuhan 430072 Peoples R China Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China

The contact stiffness, which is under effects of topography at tooth meshing surface, is determined by the dynamic contact force from the holistic meshing behavior of gears. However, in previous literature, the comprehensive effect of contact force on contact stiffness is often replaced by meshing force, which results in the mismatch between contact stiffness and meshing force. To precisely model contact stiffness and meshing stiffness of gear pair, in this paper, fractal contact stiffness model is first established based on the length scale of microscopic asperities, by which the inherent nonlinear relationship between contact force and contact stiffness is revealed. Subsequently, the improved convergence algorithm based on static and dynamic deformation is applied to calculate the actual contact force. Then the contact stiffness and dynamic response of the system are solved. Based on the proposed method involving fractal contact stiffness, the influences of surface roughness are investigated. The calculation results are also compared with those of traditional method, which reveal that dynamic contact force is irreplaceable in the stiffness modeling.

关键词： Fractal method Contact stiffness Contact force iteration algorithm

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FAST iteration algorithm FOR INTEGRAL EQUATIONS OF THE FIRST KIND ARISING IN 2D DIFFRACTION BY SOFT OBSTACLES

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JOURNAL OF COMPUTATIONAL ACOUSTICS 2013年第3期21卷 1350007-1350016页

作者： Scalia, A. Popuzin, V. Pennisi, M. Univ Catania DMI I-95125 Catania CT Italy

We propose a new iteration numerical algorithm to solve boundary integral equations of the first kind arising in the 2D scattering by soft obstacles. The main idea is to operate on each iteration step with an integral equation, which has a convolution kernel, by changing the full kernel with a special averaging procedure. The practical convergence of the algorithm is demonstrated by some examples for three different geometries. If M is the number of iterations then the computational cost of the algorithm is MN log(N).

关键词： Diffraction boundary integral equation iteration algorithm circulant matrix fast method

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Application of Microwave Transmission Sensors for Water Cut Metering under Varying Salinity Conditions: Device, algorithm and Uncertainty Analysis

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SENSORS 2022年第24期22卷 9746页

作者： Zuo, Kai Hong, Yi Qi, Haitao Li, Yi Li, Baolong China Univ Petr Coll Safety & Ocean Engn Beijing 102249 Peoples R China CNOOC EnerTech Drilling & Prod Co Tianjin 300452 Peoples R China CNOOC Res Inst Co Ltd Beijing 100010 Peoples R China Tsinghua Univ Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China

The measurement of water cut in crude oil is an essential procedure in petroleum production and it is desirable to obtain these data through an automatic and real-time method. Microwave sensors can be used for the task, and they are safe, robust and can cover the whole water cut range. However, they are relatively susceptible to the water conductivity and temperature, and the algorithms for addressing these problems are still rare in the literature. In this paper, a microwave transmission sensor that can measure the water cut under varying salinity conditions is proposed, and the algorithm for solving the water cut and salinity simultaneously with the measured amplitude and phase is described in detail. Experiments under different water cut and salinity conditions are conducted, and the results are used to verify the model and algorithm. Finally, a simplified and fast method for uncertainty analysis is proposed and applied to the iteration algorithm under test conditions. It can be concluded that accuracy higher than 95% in the water cut measurements can be expected under the 0 similar to 100% water cut range, and an error of about 10% in the water conductivity is achievable under water-continuous flow conditions. The uncertainty analysis shows that the calculated water cut and salinity results are negatively correlated, and the water salinity uncertainty tends to be larger than the water cut uncertainty. When the water salinity is high, the water cut uncertainty tends to be high whereas the water salinity uncertainty tends to be low.

关键词： microwave sensors microwave transmission line plane wave theory iteration algorithm uncertainty analysis

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A two-step neutron spectrum unfolding method for fission reactors based on artificial neural network

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ANNALS OF NUCLEAR ENERGY 2020年 139卷 107219-107219页

作者： Cao, Chenglong Gan, Quan Song, Jing Long, Pengcheng Wu, Bin Wu, Yican Chinese Acad Sci Inst Nucl Energy Safety Technol Key Lab Neutron & Radiat Safety Hefei 230031 Anhui Peoples R China Univ Sci & Technol China Hefei 230027 Anhui Peoples R China

Comprehensive knowledge of neutron spectrum is significant in reactor design. Online wide-range neutron spectrum unfolding technology still requires improvement in accuracy and efficiency. In the work, a "two-step" neutron spectrum unfolding method based on artificial neural network (ANN) was developed to unfold spectrum with wide energy range. First, a default spectrum was reconstructed by using the ANN model which had been trained with a large amount of neutron spectra generated from Monte Carlo transport calculation. Second, the default spectrum was optimized by using iteration algorithm. The two-step method was verified with a thermal neutron reactor VENUS-3 and a fast neutron reactor BN-600. Comparison of mean square error (MSE) between this method and the traditional unfolding method showed reduction of 83.4% and 85.6% on VENUS-3 and BN-600 respectively, and average relative deviation (ARD) reduction of 89.3% and 86.1% respectively. Also, comparison of spectrum quality (Qs) showed reduction of 83.4% and 86.0% respectively for the two cases. This work demonstrated that the developed two-step method could obtain the better accuracy than traditional method. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Neutron spectrum unfolding Two-step method Artificial neural network iteration algorithm

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