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Spatial correlations in time and frequency domains between chlorophyll-a concentration and environmental factors in the Bohai Sea
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作者 Wan XU Di MU +1 位作者 Zhenteng YANG Dekui YUAN 《Journal of Oceanology and Limnology》 SCIE CAS CSCD 2024年第4期1143-1156,共14页
Based on the reconstructed MODIS data and ECMWF reanalysis data from 2003 to 2021,spatial correlations between chlorophyll a(Chl a)and sea surface temperature(SST),photosynthetically available radiation(PAR),aerosol o... Based on the reconstructed MODIS data and ECMWF reanalysis data from 2003 to 2021,spatial correlations between chlorophyll a(Chl a)and sea surface temperature(SST),photosynthetically available radiation(PAR),aerosol optical thickness(AOT),and wind speed(WS)in the Bohai Sea were analyzed from the perspective of time domain and frequency domain.Results indicate that the frequency domain analysis was more conducive to revealing the correlations between Chl a and environmental factors.The spatial pattern of time-domain correlations was similar to the isobaths of the Bohai Sea,which was positive in shallow waters and negative in deep waters for SST,PAR,and AOT,and was reversed for WS.Frequency-domain correlations were obtained by performing Fourier Transform and were higher than correlations in time domain.The spatial distributions indicated that the effects of SST and PAR on Chl a were greater than AOT and WS in the Bohai Sea.Additionally,cross-spectrum analysis was applied to explore the response relationships.A depth-dependent pattern was shown in correlations and time lags,indicating that the influential mechanism of environmental factors on Chl-a concentration is related to seawater depth. 展开更多
关键词 chlorophyll a(Chl a) frequency domain spatial correlation Bohai Sea
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Correlation analysis between fault frequency and service time of underground fluid instruments
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作者 Xiao Tian Guoying Su 《Geodesy and Geodynamics》 EI CSCD 2023年第4期411-418,共8页
In this paper, we make a statistical analysis of the fault information of the underground fluid instruments of 12 models in China from January 2021 to May 2022 based on the Pearson correlation coefficient, and compare... In this paper, we make a statistical analysis of the fault information of the underground fluid instruments of 12 models in China from January 2021 to May 2022 based on the Pearson correlation coefficient, and compare the fault statistics of the meteorological three-element instruments of 3 models during the study period. The results show that:(1) The numbers of faults of the underground fluid instruments of 12models with different service times are basically positively correlated with the numbers of the corresponding instruments, with good consistency. Moreover, the automatic observation instruments(8models) with more than 30 units are significantly correlated at a 0.05 significance level(95% confidence level). Even at a 0.01 significance level(99% confidence level), there are 7 models(7/8) with significant correlation.(2) The positive and negative correlations between the monthly average number of faults and the corresponding service times of the underground fluid instruments of 12 models with different service times are random, and there are 9 models(75%) with no significant correlation at a 0.05 significance level(95% confidence level), while 12 models(100%) with no significant correlation at a 0.01significance level(99% confidence level).(3) The monthly average numbers of faults of the underground fluid instruments of 12 models are basically 0.02-0.05 times/(unit·month), and the overall fault frequency is low.(4) The fault statistics results of the meteorological three-element instruments of 3 models are consistent with the characteristics of the underground fluid instruments of 12 models. In general,there is no significant correlation between the fault frequency and the service time of underground fluid instruments.(5) The results of this paper demonstrate that the service time of underground fluid instruments cannot be taken as the main reason for whether to update the instruments. Similarly, the fault frequency of the instruments cannot be taken as the main reason for the service life of the instruments in the process of formulating the service life standards of underground fluid instruments. 展开更多
关键词 Underground fluid instruments Fault frequency Service time correlation analysis
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Time-and Frequency-Domain Analysis of Ice-Induced Displacement Responses Offshore Fixed Platforms 被引量:3
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作者 Gao, Zhaojie Duan, Menglan 《China Ocean Engineering》 SCIE EI 1998年第4期365-373,共9页
On the basis of ice- induced forced vibration model, ice- induced displacement responses of offshore fixed platforms are investigated in both time domain and frequency domain. The relationships of ice-induced displace... On the basis of ice- induced forced vibration model, ice- induced displacement responses of offshore fixed platforms are investigated in both time domain and frequency domain. The relationships of ice-induced displacement responses with ice breaking modes, ice acting directions and platform structures are analyzed and determined. The results lead to an important conclusion obtained for the first time that ice breaking frequency and the natural frequency of the first mode of the platform are the two main factors that dominate the degree of vibration. The present work provides a firm basis for both design and operation of fixed platforms against ice loading. 展开更多
关键词 offshore fixed platform ice loading CRUSHinG BENDinG BUCKLinG time domain frequency domain DISPLACEMENT power spectral density VIBRATION
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Joint AVO inversion in the time and frequency domain with Bayesian interference 被引量:6
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作者 Zong Zhao-Yun Yin Xing-Yao Li Kun 《Applied Geophysics》 SCIE CSCD 2016年第4期631-640,737,738,共12页
Amplitude variations with offset or incident angle (AVO/AVA) inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion met... Amplitude variations with offset or incident angle (AVO/AVA) inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion method in the time and frequency domain based on Bayesian inversion theory to improve the resolution of the estimated P- and S-wave velocities and density. We initially construct the objective function using Bayesian inference by combining seismic data in the time and frequency domain. We use Cauchy and Gaussian probability distribution density functions to obtain the prior information for the model parameters and the likelihood function, respectively. We estimate the elastic parameters by solving the initial objective function with added model constraints to improve the inversion robustness. The results of the synthetic data suggest that the frequency spectra of the estimated parameters are wider than those obtained with conventional elastic inversion in the time domain. In addition, the proposed inversion approach offers stronger antinoising compared to the inversion approach in the frequency domain. Furthermore, results from synthetic examples with added Gaussian noise demonstrate the robustness of the proposed approach. From the real data, we infer that more model parameter details can be reproduced with the proposed joint elastic inversion. 展开更多
关键词 AVO inversion Bayesian interference time and frequency domain elastic parameters
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Analysis of OSA Syndrome from PPG Signal Using CART-PSO Classifier with Time Domain and Frequency Domain Features 被引量:1
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作者 N.Kins Burk Sunil R.Ganesan B.Sankaragomathi 《Computer Modeling in Engineering & Sciences》 SCIE EI 2019年第2期351-375,共25页
Obstructive Sleep Apnea(OSA)is a respiratory syndrome that occurs due to insufficient airflow through the respiratory or respiratory arrest while sleeping and sometimes due to the reduced oxygen saturation.The aim of ... Obstructive Sleep Apnea(OSA)is a respiratory syndrome that occurs due to insufficient airflow through the respiratory or respiratory arrest while sleeping and sometimes due to the reduced oxygen saturation.The aim of this paper is to analyze the respiratory signal of a person to detect the Normal Breathing Activity and the Sleep Apnea(SA)activity.In the proposed method,the time domain and frequency domain features of respiration signal obtained from the PPG device are extracted.These features are applied to the Classification and Regression Tree(CART)-Particle Swarm Optimization(PSO)classifier which classifies the signal into normal breathing signal and sleep apnea signal.The proposed method is validated to measure the performance metrics like sensitivity,specificity,accuracy and F1 score by applying time domain and frequency domain features separately.Additionally,the performance of the CART-PSO(CPSO)classification algorithm is evaluated through comparing its measures with existing classification algorithms.Concurrently,the effect of the PSO algorithm in the classifier is validated by varying the parameters of PSO. 展开更多
关键词 OBSTRUCTIVE sleep APNEA photoplethysmogram SIGNAL time domain FEATURES frequency domain FEATURES classification and regression tree CLASSIFIER particle swarm optimization algorithm.
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Underdetermined DOA estimation and blind separation of non-disjoint sources in time-frequency domain based on sparse representation method 被引量:9
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作者 Xiang Wang Zhitao Huang Yiyu Zhou 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第1期17-25,共9页
This paper deals with the blind separation of nonstation-ary sources and direction-of-arrival (DOA) estimation in the under-determined case, when there are more sources than sensors. We assume the sources to be time... This paper deals with the blind separation of nonstation-ary sources and direction-of-arrival (DOA) estimation in the under-determined case, when there are more sources than sensors. We assume the sources to be time-frequency (TF) disjoint to a certain extent. In particular, the number of sources presented at any TF neighborhood is strictly less than that of sensors. We can identify the real number of active sources and achieve separation in any TF neighborhood by the sparse representation method. Compared with the subspace-based algorithm under the same sparseness assumption, which suffers from the extra noise effect since it can-not estimate the true number of active sources, the proposed algorithm can estimate the number of active sources and their cor-responding TF values in any TF neighborhood simultaneously. An-other contribution of this paper is a new estimation procedure for the DOA of sources in the underdetermined case, which combines the TF sparseness of sources and the clustering technique. Sim-ulation results demonstrate the validity and high performance of the proposed algorithm in both blind source separation (BSS) and DOA estimation. 展开更多
关键词 underdetermined blind source separation (UBSS)time-frequency (TF) domain sparse representation methoditerative adaptive approach direction-of-arrival (DOA) estimationclustering validation.
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Frequency-time Domain Shielding Effectiveness of Materials and Their Strong Electromagnetic Field Test 被引量:1
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作者 ZHANG Long WEI Guanghui +3 位作者 FAN Lisi HU Xiaofeng ZHAO Yang ZHANG Yongqiang 《高电压技术》 EI CAS CSCD 北大核心 2013年第10期2398-2402,共5页
To describe the shielding ability of materials accurately and comprehensively,the frequency-domain and time-domain shielding effectiveness(SE) of material is investigated.The relevance between them was analyzed based ... To describe the shielding ability of materials accurately and comprehensively,the frequency-domain and time-domain shielding effectiveness(SE) of material is investigated.The relevance between them was analyzed based on the minimum phase method,and the time-domain SE can be derived from frequency-domain SE.The SE of an energy selective surface(ESS) made of a novel material is investigated,and the relationship between SE and radiation field intensity are analyzed.The results show that not only material,but also the intensity of radiation electric field shows influence on SE in its frequency; for some materials,the dependence of SE on radiation electric field intensity needs to be considered.Therefore,it is necessary to research on the SE of shielding material in high-intensity electromagnetic environment. 展开更多
关键词 新型材料 屏蔽效能 磁场测试 时间域 频率 强电 电场强度 遮蔽能力
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Numerical Solution for Fractional-Order Differential Systems with Time-Domain and Frequency-Domain Methods 被引量:1
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作者 Ke Xiao Shang-Bo Zhou Wei-Wei Zhang 《Journal of Electronic Science and Technology of China》 2008年第3期294-298,共5页
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional... For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed. 展开更多
关键词 Analytical solution frequency domain fractional order numerical solution time domain
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Analysis of Time and Frequency Domain of Auditory Brainstem Response in Normal Guinea Pigs
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作者 郭梦和 王锦玲 吴进根 《Journal of Medical Colleges of PLA(China)》 CAS 1990年第2期146-150,共5页
The auditory brainstem response (ABR) was measured for 90 cars of norml gui-nea pigs,from which the mean latency,amplitude and recognition of waves were obtain-ded.The waves were classified into six types,with wave Ⅲ... The auditory brainstem response (ABR) was measured for 90 cars of norml gui-nea pigs,from which the mean latency,amplitude and recognition of waves were obtain-ded.The waves were classified into six types,with wave Ⅲ as the main wave which ac-counted for 77.1% of all the waves.The frequency domain of each type was analysed bymeans of digital filtering and auto-regressive (AR)estimation.The main frequency com-position of ABR in the guinea pigs was restricted within 1600 Hz,in which there werethree peaks at AR spectrum,the mean value of the peaks being 107.33 Hz,566.67 Hzand 1076 Hz respectively.The AR spectrograms of all types waves were very similar toeach other. 展开更多
关键词 AUDITORY brainstern response time domain frequency domain GUinEA PIG
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A Krylov Space-Based Finite Element Time Domain Method for Broadband Frequency Domain Solutions
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作者 Weiyang Lin 《Open Journal of Acoustics》 2017年第4期95-104,共10页
A Krylov space based time domain method for wave propagation problems is introduced. The proposed method uses the Arnoldi algorithm to obtain broad-band frequency domain solutions. This method is especially advantageo... A Krylov space based time domain method for wave propagation problems is introduced. The proposed method uses the Arnoldi algorithm to obtain broad-band frequency domain solutions. This method is especially advantageous in cases where slow convergence is observed when using traditional time domain methods. The efficiency of the method is examined in several test cases to show its fast convergence in such problems. 展开更多
关键词 time domain Method Krylov Space frequency domain Petrov GALERKin
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Linear and Nonlinear Time Domain Block Equalizers on MIMO Frequency Selective Channels
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作者 Cong Li Yasunori Iwanami 《International Journal of Communications, Network and System Sciences》 2013年第3期119-127,共9页
Single-Carrier (SC) transmission with the same bandwidth as Multi-Carrier (MC) transmission (such as OFDM) may have far shorter symbol duration and is considered to be more robust against time selective fading. In thi... Single-Carrier (SC) transmission with the same bandwidth as Multi-Carrier (MC) transmission (such as OFDM) may have far shorter symbol duration and is considered to be more robust against time selective fading. In this paper, we proposed the novel equalization and signal separation schemes in time domain for short block length transmission, i.e., Block Linear Equalization (BLE) and Block Nonlinear Equalization (BNLE) on MIMO frequency selective fading channels. The proposed BLE uses the MMSE based inverse matrix in time domain and the BNLE utilizes the QRD-M (QR Decomposition with M algorithm) with appropriate receiver complexity. We compared the computational complexity among the conventional SC-FDE (Frequency Domain Equalization) scheme and the proposed equalizers. We also used the Low-Density Parity Check (LDPC) decoder concatenated to the proposed BLE and BNLE. 展开更多
关键词 MIMO frequency Selective Fading Channel ISI IAI time domain BLOCK EQUALIZER BLE BNLE
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Hydroelasticity Analysis in Frequency Domain and Time Domain
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作者 Frank Lin 《Journal of Shipping and Ocean Engineering》 2016年第2期65-81,共17页
Hydroelasticity has been introduced in ship seakeeping assessment for more than three decades, and it finally becomes an essential tool in marine industry for design of some types of ship. In the 35 years of evolution... Hydroelasticity has been introduced in ship seakeeping assessment for more than three decades, and it finally becomes an essential tool in marine industry for design of some types of ship. In the 35 years of evolution, hydroelasticity methods applied in industry of marine and offshore energy grown up from two dimensional to three dimensional and now has analysis models of linear model in frequency domain and nonlinear model in time domain. In this paper, we present the three dimensional hydroelasticity theory model in frequency domain and time domain, show the difference in the approach, and discuss their applications in wave-structure interaction. 展开更多
关键词 HYDROELASTICITY SPRinGinG frequency domain time domain boundary element method LinEAR nonlinear.
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Parameters Analysis of Gastric Motility Signals in Time Domain and Frequency Domain
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作者 Zhangyong Li Likun Xu Zhui Xu 《Journal of Life Sciences》 2012年第1期14-19,共6页
In order to assess gastric motility, a new noninvasive method was addressed. Firstly, bio-impedance and stomach electric signals were recorded from the healthy control group and the pathologic stomach group. Wavelet t... In order to assess gastric motility, a new noninvasive method was addressed. Firstly, bio-impedance and stomach electric signals were recorded from the healthy control group and the pathologic stomach group. Wavelet transform was used to remove the influence of the heart activity signals. By analyzing and processing the two signals of the time domain and frequency domain, we get the corresponding parameters of the two groups. According to all the parameters, several verification tests have been carried out, from the result of the statistics, we can find that in both time and frequency domains, impedance signal and synchronize EGG (electrogastrogram) have some similar features. However synchronize EGG cannot be totally instead by gastric motility, especially in morbid state, EGG is not correspondence to impedance signal. The gastric contraction or gastric emptying is a complex procedure including electrical and mechanical activity. Electrical impedance (EIP) and the synchronous EGG should be analyzed together. In conclusion, the parameters have the value to evaluate gastric motility. 展开更多
关键词 Gastric motility SIGNALS wavelet transform time domain frequency domain.
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Integrated Correlation in a Domain with Space and Frequency Axes on a Mobile Radio Channel
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作者 Shigeru Kozono Shota Igarashi Taku Nagashima 《通讯和计算机(中英文版)》 2013年第3期355-366,共12页
关键词 频率相关性 移动无线电 域空间 频道 广播 正交频分复用 分布类型
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A Method in Mixed Frequency-time domain for Fatigue Life Estimation of Steel Girders of Cable-stayed Bridges Due to Buffeting 被引量:1
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作者 顾明 陈礼忠 项海帆 《应用基础与工程科学学报》 EI CSCD 1998年第4期70-79,共10页
发展了斜拉桥钢主梁抖振疲劳寿命的混合时-频域方法.在本方法中,首先建立了桥面处的风速风向概率密度函数,导出的应力谱因其包括背景分量而不再是窄带谱.据应力谱模拟出了疲劳应力的时间历程,并用雨流计数法统计了其幅值特性.基... 发展了斜拉桥钢主梁抖振疲劳寿命的混合时-频域方法.在本方法中,首先建立了桥面处的风速风向概率密度函数,导出的应力谱因其包括背景分量而不再是窄带谱.据应力谱模拟出了疲劳应力的时间历程,并用雨流计数法统计了其幅值特性.基于修正的Miner定理导出了考虑风速风向作用的桥梁主梁抖振疲劳寿命的估算公式,并用此分析了杨浦大桥钢主梁的抖振疲劳寿命.结果表明,风向对抖振疲劳寿命有很大影响;杨浦大桥主梁的疲劳寿命远大于设计寿命. 展开更多
关键词 斜拉桥 钢主梁 抖振 疲劳寿命 混合时-频域
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Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential 被引量:10
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作者 张智勇 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第4期423-436,共14页
Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) do- main technique has some advantages in dealing with nonlinear ... Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis. 展开更多
关键词 fractional exponential nonlinearity harmonic balance method with alter-nating frequency/time (HB-AFT) domain technique global response stability
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Prediction study of hydrocarbon reservoir based on time-frequency domain electromagnetic technique taking Ili Basin as an example 被引量:1
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作者 Tian Yu-Kun Zhou Hui +1 位作者 Ma Yan-Yan Li Juan 《Applied Geophysics》 SCIE CSCD 2020年第5期687-699,900,901,共15页
The time-frequency domain electromagnetic(TFEM)sounding technique can directly detect oil and gas characteristics through anomalies in resistivity and polarizability.In recent years,it has made some breakthroughs in h... The time-frequency domain electromagnetic(TFEM)sounding technique can directly detect oil and gas characteristics through anomalies in resistivity and polarizability.In recent years,it has made some breakthroughs in hydrocarbon detection.TFEM was applied to predict the petroliferous property of the Ili Basin.In accordance with the geological structure characteristics of the study area,a two-dimensional layered medium model was constructed and forward modeling was performed.We used the forward-modeling results to guide fi eld construction and ensure the quality of the fi eld data collection.We used the model inversion results to identify and distinguish the resolution of the geoelectric information and provide a reliable basis for data processing.On the basis of our results,key technologies such as 2D resistivity tomography imaging inversion and polarimetric constrained inversion were developed,and we obtained abundant geological and geophysical information.The characteristics of the TFEM anomalies of the hydrocarbon reservoirs in the Ili Basin were summarized through an analysis of the electrical logging data in the study area.Moreover,the oil-gas properties of the Permian and Triassic layers were predicted,and the next favorable exploration targets were optimized. 展开更多
关键词 timefrequency domain Electromagnetic Hydrocarbon Detection Polarizability Anomaly Favorable Area Prediction
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Aviation multi-station collaborative detecting based on time-frequency correlation of data-link 被引量:1
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作者 Bo Wang Xiaolong Liang +1 位作者 Liang Wei Pingni Liu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第5期827-840,共14页
As an important application research topic of the intelligent aviation multi-station, collaborative detecting must overcome the problem of scouting measurement with status of 'fragmentation', and the NP-hardne... As an important application research topic of the intelligent aviation multi-station, collaborative detecting must overcome the problem of scouting measurement with status of 'fragmentation', and the NP-hardness problem of matching association between target and measurement in the process of scouting to data-link, which has complicated technical architecture of network construction. In this paper, taking advantage of cooperation mechanism on signal level in the aviation multi-station sympathetic network, a method of obtaining target time difference of arrival (TDOA) measurement using multi-station collaborative detecting based on time-frequency association is proposed. The method can not only achieve matching between target and its measurement, but also obtain TDOA measurement by further evolutionary transaction through refreshing sequential pulse time of arrival (TOA) measurement matrix for matching and correlating. Simulation results show that the accuracy of TDOA measurement has significant superiority over TOA, and detection probability of false TDOA measurement introduced by noise and fake measurement can be reduced effectively. 展开更多
关键词 data-link time-frequency correlation aviation multistation synergistic detection time difference of arrival (TDOA)
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Comparison of delay compensation methods for real-time hybrid simulation using frequency-domain evaluation index 被引量:1
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作者 Xu Weijie Guo Tong Chen Cheng 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2016年第1期129-143,共15页
The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenar... The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods (i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation) are selected and compared experimentally using a frequency evaluation index (FEI) method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters. 展开更多
关键词 real-time hybrid simulation frequency domain evaluation index delay compensation methods
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H_∞ fault estimation for a class of linear time-delay systems in finite frequency domain
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作者 Quanchao Dong Maiying Zhong Steven X. Ding 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第5期835-841,共7页
This paper deals with the problem of H∞ fault estimation for linear time-delay systems in finite frequency domain.First a generalized coordinate change is applied to the original system such that in the new coordinat... This paper deals with the problem of H∞ fault estimation for linear time-delay systems in finite frequency domain.First a generalized coordinate change is applied to the original system such that in the new coordinates all the time-delay terms are injected by the system's input and output.Then an observer-based H∞ fault estimator with input and output injections is proposed for fault estimation with known frequency range.With the aid of Generalized Kalman-Yakubovich-Popov lemma,sufficient conditions on the existence of the H∞ fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities.Finally,a numerical example is given to illustrate the effectiveness of the proposed method. 展开更多
关键词 fault estimation time-DELAY generalized coordinate change generalized Kalman-Yakubovich-Popov lemma finite frequency domain.
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