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A time-domain multi-parameter elastic full waveform inversion with pseudo-Hessian preconditioning
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作者 Huang Jian-ping Liu Zhang +5 位作者 Jin Ke-jie Ba Kai-lun Liu Yu-hang Kong Ling-hang Cui Chao li Chuang 《Applied Geophysics》 2025年第3期660-671,893,共13页
Based on waveform fitting,full waveform inversion(FWI)is an important inversion method with the ability to reconstruct multi-parameter models in high precision.However,the strong nonlinear equation used in FWI present... Based on waveform fitting,full waveform inversion(FWI)is an important inversion method with the ability to reconstruct multi-parameter models in high precision.However,the strong nonlinear equation used in FWI presents the following challenges,such as low convergence efficiency,high dependence on the initial model,and the energy imbalance in deep region of the inverted model.To solve these inherent problems,we develop a timedomain elastic FWI method based on gradient preconditioning with the following details:(1)the limited memory Broyden Fletcher Goldfarb Shanno method with faster convergence is adopted to im-prove the inversion stability;(2)a multi-scaled inversion strategy is used to alleviate the nonlinear inversion instead of falling into the local minimum;(3)in addition,the pseudo-Hessian preconditioned illumination operator is involved for preconditioning the parameter gradients to improve the illumination equilibrium degree of deep structures.Based on the programming implementation of the new method,a deep depression model with five diffractors is used for testing.Compared with the conventional elastic FWI method,the technique proposed by this study has better effectiveness and accuracy on the inversion effect and con-vergence,respectively. 展开更多
关键词 elastic full waveform inversion(EFWI) multi-parameter PRECONDITIONING multiscale limited memory Broy den Fletcher Goldfarb Shanno(L-BFGS)
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Optimal multi-parameter quantum metrology for frequencies of magnetic field
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作者 Zhenhua Long Shengshi Pang 《Chinese Physics B》 2025年第8期465-473,共9页
Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in... Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in time-independent Hamiltonians.Here,our work makes an effort to explore multi-parameter estimation with time-dependent Hamiltonians.In particular,we focus on the discrimination of two close frequencies of a magnetic field by using a single qubit.We optimize the quantum controls by employing both traditional optimization methods and reinforcement learning to improve the precision for estimating the frequencies of the two magnetic fields.In addition to the estimation precision,we also evaluate the robustness of the optimization schemes against the shift of the control parameters.The results demonstrate that the hybrid reinforcement learning approach achieves the highest estimation precision,and exhibits superior robustness.Moreover,a fundamental challenge in multi-parameter quantum estimation stems from the incompatibility of the optimal control strategies for different parameters.We demonstrate that the hybrid control strategies derived through numerical optimization remain effective in enhancing the precision of multi-parameter estimation in spite of the incompatibilities,thereby mitigating incompatibilities between control strategies on the estimation precision.Finally,we investigate the trade-offs in estimation precision among different parameters for different scenarios,revealing the inherent challenges in balancing the optimization of multiple parameters simultaneously and providing insights into the fundamental distinction between quantum single-parameter estimation and multi-parameter estimation. 展开更多
关键词 quantum metrology multi-parameter estimation quantum control
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Some Results on the Multi-Parameters Mittag-Leffler Function
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作者 PAN Yu-mei LI Yu-fen +1 位作者 CAI Dong-xin YAN Xing-jie 《Chinese Quarterly Journal of Mathematics》 2025年第1期82-92,共11页
In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above ... In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed. 展开更多
关键词 multi-parameters Mittag-Leffler function Special functions Riemann-Liouville integral
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THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES 被引量:1
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作者 丁卫 汤彦 朱月萍 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期386-404,共19页
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting... Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition. 展开更多
关键词 weighted multi-parameter local Hardy spaces atomic decomposition BOUNDEDNESS inhomogeneous Journéclass
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Existence and joint continuity of local time of multi-parameter fractional Lévy processes
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作者 林正炎 程宗毛 Xing-ming GUO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第3期381-390,共10页
In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its loca... In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time. 展开更多
关键词 multi-parameter fractional Lévy process fractional Brownian sheet local time Gaussian random field multi-parameter Poisson process multi-parameter Brownian motion
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MULTI-PARAMETER ACCELERATED MODIFIED NEWTON-RAPHSON METHODS FOR RIGIDPLASTIC FE ANALYSIS
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作者 Shi Gang Liu Xiaolin 《Acta Mechanica Solida Sinica》 SCIE EI 2002年第4期323-331,共9页
Applications of certain multi-parameter acceleration techniques used with themodified New-ton-Raphson (mN-R) methods to solve the nonlinear equations arising from rigid-plasticfinite element analysis are investigated.... Applications of certain multi-parameter acceleration techniques used with themodified New-ton-Raphson (mN-R) methods to solve the nonlinear equations arising from rigid-plasticfinite element analysis are investigated. New modified multi-parameter techniques, developed fromCrisfield's multi-parameter methods, are utilized to solve these nonlinear equations. The numericalperformance of these techniques is compared with the standard Newton-Raphson method (sN-R),Crisfield's single parameter method (C1), Crisfield's two parameter method (C2) and Crisfield'sthree parameter method (C3). The new techniques do not involve additional residual force calculationand require little extra computational effort. In addition, they are more robust and efficient thanother existing acceleration techniques. 展开更多
关键词 rigid-plastic FEM standard newton-raphson method modified newton-raphsonmethod crisfield's multi-parameter accelerated techniques modified multi-parameter acceleratedtechniques
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Comprehensive early warning of rock burst utilizing microseismic multi-parameter indices 被引量:21
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作者 Linming Dou Wu Cai +1 位作者 Anye Cao Wenhao Guo 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2018年第5期767-774,共8页
Rock bursts have become one of the most severe risks in underground coal mining and its early warning is an important component in the safety management. Microseismic(MS) monitoring is considered potentially as a powe... Rock bursts have become one of the most severe risks in underground coal mining and its early warning is an important component in the safety management. Microseismic(MS) monitoring is considered potentially as a powerful tool for the early warning of rock burst. In this study, an MS multi-parameter index system was established and the critical values of each index were estimated based on the normalized multi-information warning model of coal-rock dynamic failure. This index system includes bursting strain energy(BSE) index, time-space-magnitude independent information(TSMII) indices and timespace-magnitude compound information(TSMCI) indices. On the basis of this multi-parameter index system, a comprehensive analysis was conducted via introducing the R-value scoring method to calculate the weights of each index. To calibrate the multi-parameter index system and the associated comprehensive analysis, the weights of each index were first confirmed using historical MS data occurred in LW402102 of Hujiahe Coal Mine(China) over a period of four months. This calibrated comprehensive analysis of MS multi-parameter index system was then applied to pre-warn the occurrence of a subsequent rock burst incident in LW 402103. The results demonstrate that this multi-parameter index system combined with the comprehensive analysis are capable of quantitatively pre-warning rock burst risk. 展开更多
关键词 ROCK BURST Microseismic(MS)monitoring multi-parameter indices COMPREHENSIVE EARLY WARNING
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Research on Multi-Parameter Evaluation of Electric Vehicle Power Battery Consistency Based on Principal Component Analysis 被引量:11
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作者 WANG Liye WANG Lifang +1 位作者 LIAO Chenglin ZHANG Wenjie 《Journal of Shanghai Jiaotong university(Science)》 EI 2018年第5期711-720,共10页
Electric vehicle power battery consistency is the key factor affecting the performance of power batteries. it is not scientific to evaluate the consistency of the battery depending on voltage or capacity. In this pape... Electric vehicle power battery consistency is the key factor affecting the performance of power batteries. it is not scientific to evaluate the consistency of the battery depending on voltage or capacity. In this paper, multi- parameter evaluation method for battery consistency based on principal component analysis is proposed. Firstly, the characteristic parameters of battery consistency are analyzed, the principal component score can be used as the basis for evaluating the consistency of the battery. Then, the function that multi-parameter evaluation of battery consistency is established. Finally, battery balancing strategy based on fuzzy control is developed. The basic principle of fuzzy control is to fuzzy the input quantity based on expert knowledge, and the fuzzy control auantitv is obtained bv fuzzy control rule_ Th~ re.~nlt.~ ~ro v^rlfiocl hv t,~t 展开更多
关键词 electric vehicle principal component analysis battery consistency multi-parameter evaluation
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Highly maneuvering target tracking using multi-parameter fusion Singer model 被引量:8
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作者 Shuyi Jia Yun Zhang Guohong Wang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第5期841-850,共10页
An algorithm of highly maneuvering target tracking is proposed to solve the problem of large tracking error caused by strong maneuver. In this algorithm, a new estimator, named as multi-parameter fusion Singer (MF-Sin... An algorithm of highly maneuvering target tracking is proposed to solve the problem of large tracking error caused by strong maneuver. In this algorithm, a new estimator, named as multi-parameter fusion Singer (MF-Singer) model is derived based on the Singer model and the fuzzy reasoning method by using radial acceleration and velocity of the target, and applied to the problem of maneuvering target tracking in strong maneuvering environment and operating environment. The tracking performance of the MF-Singer model is evaluated and compared with other manuevering tracking models. It is shown that the MF-Singer model outperforms these algorithms in several examples. 展开更多
关键词 maneuvering target multi-parameter fusion Singer (MF-Singer) fuzzy reasoning Singer model
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Multi-parameter gene expression profiling of peripheral blood for early detection of hepatocellular carcinoma 被引量:5
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作者 Hui Xie Yao-Qin Xue +5 位作者 Peng Liu Peng-Jun Zhang Sheng-Tao Tian Zhao Yang Zhi Guo Hua-Ming Wang 《World Journal of Gastroenterology》 SCIE CAS 2018年第3期371-378,共8页
AIM In our previous study, we have built a nine-gene(GPC3, HGF, ANXA1, FOS, SPAG9, HSPA1 B, CXCR4, PFN1, and CALR) expression detection system based on the Ge XP system. Based on peripheral blood and Ge XP, we aimed t... AIM In our previous study, we have built a nine-gene(GPC3, HGF, ANXA1, FOS, SPAG9, HSPA1 B, CXCR4, PFN1, and CALR) expression detection system based on the Ge XP system. Based on peripheral blood and Ge XP, we aimed to analyze the results of genes expression by different multi-parameter analysis methods and build a diagnostic model to classify hepatocellular carcinoma(HCC) patients and healthy people.METHODS Logistic regression analysis, discriminant analysis, classification tree analysis, and artificial neural network were used for the multi-parameter gene expression analysis method. One hundred and three patients with early HCC and 54 age-matched healthy normal controls were used to build a diagnostic model. Fiftytwo patients with early HCC and 34 healthy people were used for validation. The area under the curve, sensitivity, and specificity were used as diagnostic indicators.RESULTS Artificial neural network of the total nine genes had the best diagnostic value, and the AUC, sensitivity, and specificity were 0.943, 98%, and 85%, respectively. At last, 52 HCC patients and 34 healthy normal controls were used for validation. The sensitivity and specificity were 96% and 86%, respectively.CONCLUSION Multi-parameter analysis methods may increase the diagnostic value compared to single factor analysis and they may be a trend of the clinical diagnosis in the future. 展开更多
关键词 HEPATOCELLULAR CARCINOMA PERIPHERAL BLOOD Early detection multi-parameter Diagnostic value
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Multi-parameter optimization of machining impeller surface based on the on-machine measuring technique 被引量:4
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作者 Gang WANG Wen-long LI +2 位作者 Fan RAO Zheng-rong HE Zhou-ping YIN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2019年第8期2000-2008,共9页
Selecting the optimal machining parameters for impeller surface is a challenging task in the automatic manufacturing industry, due to its free-form surface and deep-crooked flow channel.Existing experimental methods r... Selecting the optimal machining parameters for impeller surface is a challenging task in the automatic manufacturing industry, due to its free-form surface and deep-crooked flow channel.Existing experimental methods require lots of machining experiments and off-line tests, which may lead to high machining cost and low efficiency. This paper proposes a novel method of machining parameters optimization for an impeller based on the on-machine measuring technique. The absolute average error and standard deviation of the measured points are used to define the grey relational grade for reconstructing the objective function, and the complex problem of multi-objective optimization is simplified into a problem of single-objective optimization. Then, by comparing the values of the defined grey relational grade in a designed orthogonal experiment, the optimal combination of the machining parameters is obtained. The experiment-solving process of the objective function corresponds to the minimization of the used errors, which is advantageous to reducing the machining error. The proposed method is efficient and low-cost, since it does not require re-clamping the workpiece for off-line tests. Its effectiveness is verified by an on-machine inspection experiment of the impeller blade. 展开更多
关键词 GREY RELATIONAL grade IMPELLER SURFACE multi-parameters optimization On-machine measuring ORTHOGONAL experiment
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Study on Environmental Multi-parameter Sensor Based on MEMS 被引量:1
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作者 Hongquan Zhang Tong Zhang +2 位作者 Likai Sun Yunbo Shi Jianying Guo 《稀有金属材料与工程》 SCIE EI CAS CSCD 北大核心 2006年第A03期377-380,共4页
A new membrane type Al_2O_3 micromachining material is used.We develop an environmental multi-parameter detection micro-system,which implements the detection to temperature,humidity,wind speed,and CO.The test results ... A new membrane type Al_2O_3 micromachining material is used.We develop an environmental multi-parameter detection micro-system,which implements the detection to temperature,humidity,wind speed,and CO.The test results illustrate that the heat-release unit in micro-system intercross greatly affects other sensing units on the temperature.We study the method of etching process,which formed cavity to reduce the heat exchange efficiency and decrease temperature intercross effect. 展开更多
关键词 Al2O3 membrane sensing unit environmental multi-parameter MICROSYSTEM
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Multi-Parameter Influence Analysis of Interaction Between Internal Solitary Wave and Fixed Submerged Body 被引量:1
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作者 LIU Shuang HE Guang-hua +4 位作者 ZHANG Zhi-gang HU Chang-hong ZHANG Cheng WANG Zheng-ke XIE Hong-fei 《China Ocean Engineering》 SCIE EI CSCD 2023年第6期934-947,共14页
To obtain the interaction characteristics between Internal solitary waves(ISWs)and submerged bodies,a three-dimensional numerical model for simulating ISWs was established in the present study based on the RANS equati... To obtain the interaction characteristics between Internal solitary waves(ISWs)and submerged bodies,a three-dimensional numerical model for simulating ISWs was established in the present study based on the RANS equation.The velocity entrance method was adopted to generate the ISWs.First,the reliability of this numerical model was validated by comparing it with theoretical and literature results.Then,the influence of environmental and navigation parameters on interactions between ISWs and a fixed SUBOFF-submerged body was studied.According to research,the hydrodynamic performance of the submerged body has been significantly impacted by the ISWs when the body is nearing the central region of the wave.Besides,the pitching moment(y')will predominate when the body encounters the ISWs at a certain angle between 0°and 180°,and the lateral force is larger than the horizontal force.Additionally,the magnitude of the force acting on the body is mostly affected by the wave amplitude.The variation of the vertical force is the main way that ISWs affect the hydrodynamic performance of the bodies.The investigations and findings discussed above can serve as a guide to forecast how ISWs will interact with submerged bodies. 展开更多
关键词 CFD internal solitary waves submerged body multi-parameters influence HYDRODYNAMICS
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Multi-parameter joint optimization for double-strip high-speed pantographs to improve pantograph-catenary interaction quality 被引量:1
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作者 Mengzhen Wu Xianghong Xu +3 位作者 Yongzhao Yan Yi Luo Sijun Huang Jianshan Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第1期137-147,共11页
The significant increase in speed of high-speed train will cause the dynamic contact force of the pantograph-catenary system to fluctuate more severely,which poses a challenge to the study of the pantograph-catenary r... The significant increase in speed of high-speed train will cause the dynamic contact force of the pantograph-catenary system to fluctuate more severely,which poses a challenge to the study of the pantograph-catenary relationship and the design of highspeed pantographs.Good pantograph-catenary coupling quality is the essential condition to ensure safe and efficient operation of high-speed train,stable and reliable current collection,and reduction in the wear of contact wires and pantograph contact strips.Among them,the dynamic parameters of high-speed pantographs are crucial to pantograph-catenary coupling quality.With the reduction of the standard deviation of the pantograph-catenary contact force as the optimization goal,multi-parameter joint optimization designs for the high-speed pantograph with two contact strips at multiple running speeds are proposed.Moreover,combining the sensitivity analysis at the optimal solutions,with the parameters and characteristics of in-service DSA380 highspeed pantograph,the optimization proposal of DSA380 was given. 展开更多
关键词 High-speed pantograph Pantograph-catenary interaction quality multi-parameter joint optimization
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Multi-parameters of Thermal Infrared Remote Sensing Anomalies of the Earthquake 被引量:1
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作者 Lu Xian Meng Qingyan +4 位作者 Gu Xingfa Zhang Xiaodong Xiong Pan Ma Weiyu Xie Tao 《Earthquake Research in China》 CSCD 2016年第4期500-512,共13页
Temporal and spatial anomalies associated with the Yushu earthquake, including the Outgoing Longwave Radiation( OLR), the Land Surface Temperature( LST) and surface temperature from the National Center for Environment... Temporal and spatial anomalies associated with the Yushu earthquake, including the Outgoing Longwave Radiation( OLR), the Land Surface Temperature( LST) and surface temperature from the National Center for Environmental Prediction( NCEP) are studied using thermal infrared remote sensing data in this paper. All results confirmed the previous observations of thermal anomalies in the seismic region prior to this earthquake.Among the multi-parameter anomalies, the underground water temperature anomaly appeared first and lasted for the longest time; OLR anomaly,an infrared parameter which indicates the radiation characteristics of the land surface medium,was the first to be detected; LST anomalies appeared later than OLR. NCEP temperature indicates the average atmosphere temperature with a certain vertical thickness; therefore,it was the last detected anomaly. The anomalies of OLR and LST lasted for a similar time length and were all located in the south or southwest of the epicenter. 展开更多
关键词 Yushu earthquake multi-parameters Thermal anomaly
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Design and Realization of Signal Processing Platform of Multi-Parameter Wearable Medical Devices 被引量:1
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作者 Xin Tan Binfeng Xu Qiancheng Liu 《Journal of Signal and Information Processing》 2013年第2期95-100,共6页
This paper presents a design of new type of multi-parameter wearable medical devices signal processing platform. The signal processing algorithm has a QRS-wave detection algorithm based on LADT, wavelet transformation... This paper presents a design of new type of multi-parameter wearable medical devices signal processing platform. The signal processing algorithm has a QRS-wave detection algorithm based on LADT, wavelet transformation and threshold detection with TMS320VC5509 DSP system. The DSP can greatly increase the speed of QRS-wave detection, and the results can be practical used for multi-parameter wearable device detection of abnormal ECG. 展开更多
关键词 multi-parameter WEARABLE MEDICAL Devices DSP LADT WAVELET TRANSFORM ECG Detection Algorithm
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Case Retrieval Method of Multi-parameter for Customized Product
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作者 DING Junjian TAN Shili SONG Xiaofeng WANG Meiting (School of Mechanical&Electronic Engineering and Automation,Shanghai University,Shanghai 200072,China 《武汉理工大学学报》 CAS CSCD 北大核心 2006年第S2期543-546,共4页
The CBR (Case-Based Reasoning) usually is been used to accomplish customized products by variant design or reusable design.In the CBR,retrieve is very important.A simple case retrieval method is been brought forward t... The CBR (Case-Based Reasoning) usually is been used to accomplish customized products by variant design or reusable design.In the CBR,retrieve is very important.A simple case retrieval method is been brought forward to retrieve a opti- mal prototype based on using inputted multi-parameters,it can be programmed easily.An example has been proved this method can find optimal prototype for new design task efficiently. 展开更多
关键词 case-based REASONING retrieve similar DISTANCE multi-parameter
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Non-relativistic scattering amplitude for a new multi-parameter exponential-type potential
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作者 Yazarloo B H Mehraban H Hassanabadi H 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第8期21-25,共5页
In this paper, we study the scattering properties of s-wave Schrdinger equation for the multi-parameter potential,which can be reduced into four special cases for different values of potential parameters, i.e., Hulthn... In this paper, we study the scattering properties of s-wave Schrdinger equation for the multi-parameter potential,which can be reduced into four special cases for different values of potential parameters, i.e., Hulthn, Manning–Rosen,and Eckart potentials. We also obtain and investigate the scattering amplitudes of these special cases. Some numerical results are also obtained and reported. 展开更多
关键词 scattering amplitude Schrodinger equation multi-parameter potential phase shifts cross section
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Elastic direct envelope inversion based on wave mode decomposition for multi-parameter reconstruction of strong-scattering media
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作者 Pan Zhang Ru-Shan Wu +1 位作者 Li-Guo Han Yong Hu 《Petroleum Science》 SCIE CAS CSCD 2022年第5期2046-2063,共18页
The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures... The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures imaging without the need of low-frequency seismic data.However,the current DEI methods are all based on the acoustic approximation.Whereas,in real cases,seismic records are the combined effects of the subsurface multi-parameters.Therefore,the study of DEI in elastic media is necessary for the accurate inversion of strong-scattering structures,such as salt domes.In this paper,we propose an elastic direct envelope inversion(EDEI)method based on wave mode decomposition.We define the objective function of EDEI using multi-component seismic data and derive its gradient formulation.To reduce the coupling effects of multi-parameters,we introduce the wave mode decomposition method into the gradient calculation of EDEI.The update of Vp is primarily the contributions of decomposed P-waves.Two approaches on Vs gradient calculation are proposed,i.e.using the petrophysical relation and wave mode decomposition method.Finally,we test the proposed method on a layered salt model and the SEG/EAGE salt model.The results show that the proposed EDEI method can reconstruct reliable large-scale Vp and Vs models of strong-scattering salt structures.The successive elastic FWI can obtain high-precision inversion results of the strong-scattering salt model.The proposed method also has a good anti-noise performance in the moderate noise level. 展开更多
关键词 Direct envelope inversion Full waveform inversion Elastic wave Strong-scattering media multi-parameter
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Feedback control and quantum error correction assisted quantum multi-parameter estimation
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作者 洪海源 鲁秀娟 匡森 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第4期260-267,共8页
Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it i... Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols. 展开更多
关键词 quantum multi-parameter estimation feedback control quantum error correction Heisenberg limit
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