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ADC border effect and suppression of quantization error in the digital dynamic measurement 被引量:3
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作者 白丽娜 刘海东 +7 位作者 周渭 张勇 翟鸿启 崔震健 赵明英 谷小倩 刘蓓玲 黄李贝 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第9期91-97,共7页
The digital measurement and processing is an important direction in the measurement and control field. The quantization error widely existing in the digital processing is always the decisive factor that restricts the ... The digital measurement and processing is an important direction in the measurement and control field. The quantization error widely existing in the digital processing is always the decisive factor that restricts the development and applications of the digital technology. In this paper, we find that the stability of the digital quantization system is obviously better than the quantization resolution. The application of a border effect in the digital quantization can greatly improve the accuracy of digital processing. Its effective precision has nothing to do with the number of quantization bits, which is only related to the stability of the quantization system. The high precision measurement results obtained in the low level quantization system with high sampling rate have an important application value for the progress in the digital measurement and processing field. 展开更多
关键词 量化误差 边界效应 动态测量 ADC 高精度测量 数字测量 数字处理 测控领域
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Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks
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作者 Lu Wei Zhong Ma Chaojie Yang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第1期981-1000,共20页
The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedd... The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization. 展开更多
关键词 quantization neural network hybrid asymmetric ACCURACY
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In situ calibrated angle between the quantization axis and the propagating direction of the light field for trapping neutral atoms
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作者 郭瑞军 何晓东 +7 位作者 盛诚 王坤鹏 许鹏 刘敏 王谨 孙晓红 曾勇 詹明生 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期318-323,共6页
The recently developed magic-intensity trapping technique of neutral atoms efficiently mitigates the detrimental effect of light shifts on atomic qubits and substantially enhances the coherence time. This technique re... The recently developed magic-intensity trapping technique of neutral atoms efficiently mitigates the detrimental effect of light shifts on atomic qubits and substantially enhances the coherence time. This technique relies on applying a bias magnetic field precisely parallel to the wave vector of a circularly polarized trapping laser field. However, due to the presence of the vector light shift experienced by the trapped atoms, it is challenging to precisely define a parallel magnetic field, especially at a low bias magnetic field strength, for the magic-intensity trapping of85Rb qubits. In this work, we present a method to calibrate the angle between the bias magnetic field and the trapping laser field with the compensating magnetic fields in the other two directions orthogonal to the bias magnetic field direction. Experimentally, with a constantdepth trap and a fixed bias magnetic field, we measure the respective resonant frequencies of the atomic qubits in a linearly polarized trap and a circularly polarized one via the conventional microwave Rabi spectra with different compensating magnetic fields and obtain the corresponding total magnetic fields via the respective resonant frequencies using the Breit–Rabi formula. With known total magnetic fields, the angle is a function of the other two compensating magnetic fields.Finally, the projection value of the angle on either of the directions orthogonal to the bias magnetic field direction can be reduced to 0(4)° by applying specific compensating magnetic fields. The measurement error is mainly attributed to the fluctuation of atomic temperature. Moreover, it also demonstrates that, even for a small angle, the effect is strong enough to cause large decoherence of Rabi oscillation in a magic-intensity trap. Although the compensation method demonstrated here is explored for the magic-intensity trapping technique, it can be applied to a variety of similar precision measurements with trapped neutral atoms. 展开更多
关键词 quantization axis trapping laser ANGLE compensating magnetic fields
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A Combined Antenna Array Deployment with High Positioning Accuracy and Low Angular Measurement Error
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作者 Wangjie Chen Weiqiang Zhu +3 位作者 Zhenhong Fan Li Wu Yi He Yixiao Wang 《Journal of Beijing Institute of Technology》 EI CAS 2024年第2期141-154,共14页
In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution de... In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution design of multi-group baseline clustering.The effectiveness of the antenna array in this paper is verified by sufficient simulation and experiment.After the system deviation correction work,it is found that in the L/S/C/X frequency bands,the ambiguity resolution probability is high,and the phase difference system error between each channel is basically the same.The angle measurement error is less than 0.5°,and the positioning error is less than 2.5 km.Notably,as the center frequency increases,calibration consistency improves,and the calibration frequency points become applicable over a wider frequency range.At a center frequency of 11.5 GHz,the calibration frequency point bandwidth extends to 1200 MHz.This combined antenna array deployment holds significant promise for a wide range of applications in contemporary wireless communication systems. 展开更多
关键词 antenna array deployment ambiguity resolution phase consistency angle measurement error positioning error
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Error field penetration in J-TEXT tokamak based on two-fluid drift-MHD model
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作者 王文 徐涛 +1 位作者 张仪 the J-TEXT team 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期545-551,共7页
An externally generated resonant magnetic perturbation can induce complex non-ideal MHD responses in their resonant surfaces.We have studied the plasma responses using Fitzpatrick's improved two-fluid model and pr... An externally generated resonant magnetic perturbation can induce complex non-ideal MHD responses in their resonant surfaces.We have studied the plasma responses using Fitzpatrick's improved two-fluid model and program LAYER.We calculated the error field penetration threshold for J-TEXT.In addition,we find that the island width increases slightly as the error field amplitude increases when the error field amplitude is below the critical penetration value.However,the island width suddenly jumps to a large value because the shielding effect of the plasma against the error field disappears after the penetration.By scanning the natural mode frequency,we find that the shielding effect of the plasma decreases as the natural mode frequency decreases.Finally,we obtain the m/n=2/1 penetration threshold scaling on density and temperature. 展开更多
关键词 plasma responses drift-MHD model error field penetration
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An Insight Survey on Sensor Errors and Fault Detection Techniques in Smart Spaces
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作者 Sheetal Sharma Kamali Gupta +2 位作者 DeepaliGupta Shalli Rani Gaurav Dhiman 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期2029-2059,共31页
The widespread adoption of the Internet of Things (IoT) has transformed various sectors globally, making themmore intelligent and connected. However, this advancement comes with challenges related to the effectiveness... The widespread adoption of the Internet of Things (IoT) has transformed various sectors globally, making themmore intelligent and connected. However, this advancement comes with challenges related to the effectiveness ofIoT devices. These devices, present in offices, homes, industries, and more, need constant monitoring to ensuretheir proper functionality. The success of smart systems relies on their seamless operation and ability to handlefaults. Sensors, crucial components of these systems, gather data and contribute to their functionality. Therefore,sensor faults can compromise the system’s reliability and undermine the trustworthiness of smart environments.To address these concerns, various techniques and algorithms can be employed to enhance the performance ofIoT devices through effective fault detection. This paper conducted a thorough review of the existing literature andconducted a detailed analysis.This analysis effectively links sensor errors with a prominent fault detection techniquecapable of addressing them. This study is innovative because it paves theway for future researchers to explore errorsthat have not yet been tackled by existing fault detection methods. Significant, the paper, also highlights essentialfactors for selecting and adopting fault detection techniques, as well as the characteristics of datasets and theircorresponding recommended techniques. Additionally, the paper presents amethodical overview of fault detectiontechniques employed in smart devices, including themetrics used for evaluation. Furthermore, the paper examinesthe body of academic work related to sensor faults and fault detection techniques within the domain. This reflectsthe growing inclination and scholarly attention of researchers and academicians toward strategies for fault detectionwithin the realm of the Internet of Things. 展开更多
关键词 error fault detection techniques sensor faults OUTLIERS Internet of Things
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Higher-order expansions of powered extremes of logarithmic general error distribution
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作者 TAN Xiao-feng LI Li-hui 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期47-54,共8页
In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of nor... In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v). 展开更多
关键词 logarithmic general error distribution convergence rate higher-order expansion powered ex-treme
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Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism
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作者 赵润盛 马鸿洋 +2 位作者 程涛 王爽 范兴奎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期285-295,共11页
Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NIS... Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models. 展开更多
关键词 readout errors quantum generative adversarial networks bit-flip averaging method fault tolerant mechanisms
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Single Photon Detection Technology in Underwater Wireless Optical Communication:Modulation Modes and Error Correction Coding Analysis
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作者 GAI Lei LI Wendong WANG Guoyu 《Journal of Ocean University of China》 CAS CSCD 2024年第2期405-414,共10页
This study explores the application of single photon detection(SPD)technology in underwater wireless optical communication(UWOC)and analyzes the influence of different modulation modes and error correction coding type... This study explores the application of single photon detection(SPD)technology in underwater wireless optical communication(UWOC)and analyzes the influence of different modulation modes and error correction coding types on communication performance.The study investigates the impact of on-off keying(OOK)and 2-pulse-position modulation(2-PPM)on the bit error rate(BER)in single-channel intensity and polarization multiplexing.Furthermore,it compares the error correction performance of low-density parity check(LDPC)and Reed-Solomon(RS)codes across different error correction coding types.The effects of unscattered photon ratio and depolarization ratio on BER are also verified.Finally,a UWOC system based on SPD is constructed,achieving 14.58 Mbps with polarization OOK multiplexing modulation and 4.37 Mbps with polarization 2-PPM multiplexing modulation using LDPC code error correction. 展开更多
关键词 error correction coding modulation mode single photon detection underwater communication wireless optical communication
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Efficient unequal error protection for online fountain codes
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作者 SHI Pengcheng WANG Zhenyong +1 位作者 LI Dezhi LYU Haibo 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第2期286-293,共8页
In this paper,an efficient unequal error protection(UEP)scheme for online fountain codes is proposed.In the buildup phase,the traversing-selection strategy is proposed to select the most important symbols(MIS).Then,in... In this paper,an efficient unequal error protection(UEP)scheme for online fountain codes is proposed.In the buildup phase,the traversing-selection strategy is proposed to select the most important symbols(MIS).Then,in the completion phase,the weighted-selection strategy is applied to provide low overhead.The performance of the proposed scheme is analyzed and compared with the existing UEP online fountain scheme.Simulation results show that in terms of MIS and the least important symbols(LIS),when the bit error ratio is 10-4,the proposed scheme can achieve 85%and 31.58%overhead reduction,respectively. 展开更多
关键词 online fountain code random graph unequal error protection(UEP) rateless code
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Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method
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作者 Faming Huang Zuokui Teng +4 位作者 Chi Yao Shui-Hua Jiang Filippo Catani Wei Chen Jinsong Huang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第1期213-230,共18页
In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken a... In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP un-certainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20%are added to these original factors for con-structing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron(MLP),support vector machine(SVM)and random forest(RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2)With the proportions of random errors increasing from 5%to 20%,the LSP uncertainty increases continuously.(3)The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4)The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5)The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide sus-ceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors. 展开更多
关键词 Landslide susceptibility prediction Conditioning factor errors Low-pass filter method Machine learning models Interpretability analysis
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Anomaly-Resistant Decentralized State Estimation Under Minimum Error Entropy With Fiducial Points for Wide-Area Power Systems
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作者 Bogang Qu Zidong Wang +2 位作者 Bo Shen Hongli Dong Hongjian Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第1期74-87,共14页
This paper investigates the anomaly-resistant decentralized state estimation(SE) problem for a class of wide-area power systems which are divided into several non-overlapping areas connected through transmission lines... This paper investigates the anomaly-resistant decentralized state estimation(SE) problem for a class of wide-area power systems which are divided into several non-overlapping areas connected through transmission lines. Two classes of measurements(i.e., local measurements and edge measurements) are obtained, respectively, from the individual area and the transmission lines. A decentralized state estimator, whose performance is resistant against measurement with anomalies, is designed based on the minimum error entropy with fiducial points(MEEF) criterion. Specifically, 1) An augmented model, which incorporates the local prediction and local measurement, is developed by resorting to the unscented transformation approach and the statistical linearization approach;2) Using the augmented model, an MEEF-based cost function is designed that reflects the local prediction errors of the state and the measurement;and 3) The local estimate is first obtained by minimizing the MEEF-based cost function through a fixed-point iteration and then updated by using the edge measuring information. Finally, simulation experiments with three scenarios are carried out on the IEEE 14-bus system to illustrate the validity of the proposed anomaly-resistant decentralized SE scheme. 展开更多
关键词 Decentralized state estimation(SE) measurements with anomalies minimum error entropy unscented Kalman filter wide-area power systems
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Online Capacitor Voltage Transformer Measurement Error State Evaluation Method Based on In-Phase Relationship and Abnormal Point Detection
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作者 Yongqi Liu Wei Shi +2 位作者 Jiusong Hu Yantao Zhao Pang Wang 《Smart Grid and Renewable Energy》 2024年第1期34-48,共15页
The assessment of the measurement error status of online Capacitor Voltage Transformers (CVT) within the power grid is of profound significance to the equitable trade of electric energy and the secure operation of the... The assessment of the measurement error status of online Capacitor Voltage Transformers (CVT) within the power grid is of profound significance to the equitable trade of electric energy and the secure operation of the power grid. This paper advances an online CVT error state evaluation method, anchored in the in-phase relationship and outlier detection. Initially, this method leverages the in-phase relationship to obviate the influence of primary side fluctuations in the grid on assessment accuracy. Subsequently, Principal Component Analysis (PCA) is employed to meticulously disentangle the error change information inherent in the CVT from the measured values and to compute statistics that delineate the error state. Finally, the Local Outlier Factor (LOF) is deployed to discern outliers in the statistics, with thresholds serving to appraise the CVT error state. Experimental results incontrovertibly demonstrate the efficacy of this method, showcasing its prowess in effecting online tracking of CVT error changes and conducting error state assessments. The discernible enhancements in reliability, accuracy, and sensitivity are manifest, with the assessment accuracy reaching an exemplary 0.01%. 展开更多
关键词 Capacitor Voltage Transformer Measurement error Online Monitoring Principal Component Analysis Local Outlier Factor
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Error Analysis of English Pronunciation Acquisition by Chinese Non-English Majors
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作者 Lin Tao Haiying Liang 《Journal of Contemporary Educational Research》 2024年第2期34-47,共14页
Chinese non-English majors are a large group of English learners.In the process of English pronunciation acquisition,issues such as incomplete phonological knowledge,transfer of mother tongue,and overgeneralization,le... Chinese non-English majors are a large group of English learners.In the process of English pronunciation acquisition,issues such as incomplete phonological knowledge,transfer of mother tongue,and overgeneralization,lead to confusion of phonemes and stress,misunderstanding of syllable structure,and errors of assimilation,drop,and epenthesis.The accuracy of English pronunciation can only be improved by knowing both English and Chinese phonological systems,strengthening the teaching of English phonological knowledge,and adopting various phonological training activities. 展开更多
关键词 English pronunciation acquisition Non-English majors error analysis INVESTIGATION Second language acquisition
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Asymptotic uniformity of the quantization error for the Ahlfors-David probability measures 被引量:1
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作者 Sanguo Zhu 《Science China Mathematics》 SCIE CSCD 2020年第6期1039-1056,共18页
Let μ be an Ahlfors-David probability measure on Rq;therefore,there exist some constants s0> 0 and ε0,C1,C2> 0 such that C1εs0≤μ(B(x,ε))≤C2εs0 for all ε∈(0,ε0) and x ∈ supp(μ).For n≥ 1,let αn be a... Let μ be an Ahlfors-David probability measure on Rq;therefore,there exist some constants s0> 0 and ε0,C1,C2> 0 such that C1εs0≤μ(B(x,ε))≤C2εs0 for all ε∈(0,ε0) and x ∈ supp(μ).For n≥ 1,let αn be an n-optimal set for μ of order r;furthermore,let {Pa(αn)}a∈αn be an arbitrary Voronoi partition with respect to αn.The n-th quantization error en,r(μ) for μ of order r can be defined as en,rr(μ):=∫ d(x,αn)r dμ(x).We define Ia(αn,μ):=∫Pa(αn) d(x,αn)r dμ(x),a ∈αn,and prove that,the three quantities ■ are of the same order as that of 1/nen,rr(μ).Thus,our result exhibits that,a weak version of Gersho’s conjecture holds true for the Ahlfors-David probability measures on Rq. 展开更多
关键词 quantization error Ahlfors-David probability measure optimal set Voronoi partition asymptotic uniformity
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Fault Detection of Networked Control Systems with Uncertain Time-Varying Delay and Quantization Error
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作者 李斌 万一鸣 叶昊 《Journal of Shanghai Jiaotong university(Science)》 EI 2011年第5期513-518,共6页
Problems related to fault detection of networked control systems (NCSs) with both uncertain time-varying delay and quantization error are studied in this paper. A novel model with the form of polytopic uncertainty is ... Problems related to fault detection of networked control systems (NCSs) with both uncertain time-varying delay and quantization error are studied in this paper. A novel model with the form of polytopic uncertainty is given to represent the influences of both the time-varying delay and the quantization error, and then the reference model based method is used to design the residual generator that is robust to both unknown network-induced delay and unknown inputs. A numerical example is also given to illustrate the merits of the presented method. The proposed method can be regarded as an extension of the authors' former work, which can only deal with time-varying delay. 展开更多
关键词 fault detection networked control systems (NCSs) DELAY quantization error polytopic uncertainty
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The Effect of Quantization Error on Display Color Gamut Transformation
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作者 Yu Chen, Tiefu Ding Changchun Institute of Optics fine Mechanics and Physics, CAS, P. R. China, 130022,Te1: 86-431-4627053 《光学学报》 EI CAS CSCD 北大核心 2003年第S1期801-802,共2页
Researchers and designers who work with color displays often transform color gamut between two different display devices. This paper demonstrates the effect of quantization error on the transformation based on analyzi... Researchers and designers who work with color displays often transform color gamut between two different display devices. This paper demonstrates the effect of quantization error on the transformation based on analyzing the color gamut deviation profoundly. 展开更多
关键词 EFFECT quantization error Color Gamut
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Quantization error in stereo imaging system with noise distributions
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作者 Deepika Saini Sanjeev Kumar 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2020年第5期86-117,共32页
The problem of estimating quantization error in 2D images is an inherent problem in computer vision.The outcome of this problem is directly related to the error in reconstructed 3D position coordinates of an object.Th... The problem of estimating quantization error in 2D images is an inherent problem in computer vision.The outcome of this problem is directly related to the error in reconstructed 3D position coordinates of an object.Thus estimation of quantization error has its own importance in stereo vision.Although the quantization error cannot be controlled fully,still statistical error analysis helps us to measure the performance of stereo systems that relies on the imaging parameters.Generally,it is assumed that the quantization error in 2D images is distributed uniformly that need not to be true from a practical aspect.In this paper,we have incorporated noise distributions(Triangular and Trapezoidal)for the stochastic error analysis of the quantization error in stereo imaging systems.For the validation of the theoretical analysis,the detailed simulation study is carried out by considering different cases. 展开更多
关键词 quantization error stereo images noise distributions range estimation error range error magnitude relative range error
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On the Asymptotic Uniformity of the Quantization Error for Moran Measures on R^1 被引量:2
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作者 San Guo ZHU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第9期1520-1540,共21页
Let E be a Moran set on R1 associated with a bounded closed interval J and two sequences(nk)k =1 ^∞ and(Ck =(ck,j)j=1)^nk)k≥1. Let μ be the Moran measure on E associated with a sequence(Pk)k≥1 of positive probabil... Let E be a Moran set on R1 associated with a bounded closed interval J and two sequences(nk)k =1 ^∞ and(Ck =(ck,j)j=1)^nk)k≥1. Let μ be the Moran measure on E associated with a sequence(Pk)k≥1 of positive probability vectors with Pk =(pk,j)j =1,^nk, k ≥ 1. We assume that k≥1 1≤j≤nk^inf min Ck,j>0,k≥1 1≤j≤nk^inf minCk,j>0,k≥1 1≤j≤nk ^inf min pk,j>0. For every n ≥ 1, let αn be αn n optimal set in the quantization for μ of order r ∈(0,∞) and{Pa(αn)}a∈α∈an an arbitrary Voronoi partition with respect to αn. We write Iα(α,μ):=∫Pα(αn)^d(x,αn)^τ dμ(x),α∈αn;J(αn,μ):=α∈αn^minⅠα(α,μ),J(αn,μ):=α∈αn^max Ⅰα(α,μ).We show that J(αn,μ),J(αn,μ) and en^r,r(μ)-en^r +1,r(μ) are of the same order as 1/n en^r ,r(μ), where en^r ,r(μ):=∫d(x,αn)^r dμ(x) is the nth quantization error for μ of order r. In particular, for the class of Moran measures on R1, our result shows that a weaker version of Gersho’s conjecture holds. 展开更多
关键词 MORAN measures quantization error VORONOI PARTITION ASYMPTOTIC UNIFORMITY
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The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation 被引量:3
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作者 Leyang Wang Shuhao Han 《Geodesy and Geodynamics》 EI CSCD 2023年第3期244-253,共10页
To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an impr... To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model. 展开更多
关键词 Mixed additive and multiplicative random error Parameter estimation Accuracy evaluation Artificial bee colony algorithm Bootstrap method
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