离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改...离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改进K-means聚类算法,提出了一种名为KLOD(local outlier detection based on improved K-means and least-squares methods)的局部离群点检测方法,以实现对局部离群点的精确检测。首先,利用快速搜索和发现密度峰值方法计算数据点的局部密度和相对距离,并将二者相乘得到γ值。其次,将γ值降序排序,利用肘部法则选择γ值最大的k个数据点作为K-means聚类算法的初始聚类中心。然后,通过K-means聚类算法将数据集聚类成k个簇,计算数据点在每个维度上的目标函数值并进行升序排列。接着,确定数据点的每个维度的离散程度并选择适当的拟合函数和拟合点,通过最小二乘法对升序排列的每个簇的每1维目标函数值进行函数拟合并求导,以获取变化率。最后,结合信息熵,将每个数据点的每个维度目标函数值乘以相应的变化率进行加权,得到最终的异常得分,并将异常值得分较高的top-n个数据点视为离群点。通过人工数据集和UCI数据集,对KLOD、LOF和KNN方法在准确度上进行仿真实验对比。结果表明KLOD方法相较于KNN和LOF方法具有更高的准确度。本文提出的KLOD方法能够有效改善K-means聚类算法的聚类效果,并且在局部离群点检测方面具有较好的精度和性能。展开更多
Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity ...Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.展开更多
Quantized kernel least mean square(QKLMS) algorithm is an effective nonlinear adaptive online learning algorithm with good performance in constraining the growth of network size through the use of quantization for inp...Quantized kernel least mean square(QKLMS) algorithm is an effective nonlinear adaptive online learning algorithm with good performance in constraining the growth of network size through the use of quantization for input space. It can serve as a powerful tool to perform complex computing for network service and application. With the purpose of compressing the input to further improve learning performance, this article proposes a novel QKLMS with entropy-guided learning, called EQ-KLMS. Under the consecutive square entropy learning framework, the basic idea of entropy-guided learning technique is to measure the uncertainty of the input vectors used for QKLMS, and delete those data with larger uncertainty, which are insignificant or easy to cause learning errors. Then, the dataset is compressed. Consequently, by using square entropy, the learning performance of proposed EQ-KLMS is improved with high precision and low computational cost. The proposed EQ-KLMS is validated using a weather-related dataset, and the results demonstrate the desirable performance of our scheme.展开更多
A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adap...A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square (MFLMS) algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.展开更多
Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmissio...Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.展开更多
Nano-volt magnetic resonance sounding(MRS) signals are sufficiently weak so that during the actual measurement, they are affected by environmental electromagnetic noise, leading to inaccuracy of the extracted characte...Nano-volt magnetic resonance sounding(MRS) signals are sufficiently weak so that during the actual measurement, they are affected by environmental electromagnetic noise, leading to inaccuracy of the extracted characteristic parameters and hindering effective inverse interpretation. Considering the complexity and non-homogeneous spatial distribution of environmental noise and based on the theory of adaptive noise cancellation, a model system for noise cancellation using multi-reference coils was constructed to receive MRS signals. The feasibility of this system with theoretical calculation and experiments was analyzed and a modified sigmoid variable step size least mean square(SVSLMS) algorithm for noise cancellation was presented. The simulation results show that, the multi-reference coil method performs better than the single one on both signal-to-noise ratio(SNR) improvement and signal waveform optimization after filtering, under the condition of different noise correlations in the reference coils and primary detecting coils and different SNRs. In particular, when the noise correlation is poor and the SNR<0, the SNR can be improved by more than 8 dB after filtering with multi-reference coils. And the average fitting errors for initial amplitude and relaxation time are within 5%. Compared with the normalized least mean square(NLMS) algorithm and multichannel Wiener filter and processing field test data, the effectiveness of the proposed method is verified.展开更多
Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave he...Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper.Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed.It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height.Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys.The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.展开更多
In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
Let be an injective function. For a vertex labeling f, the induced edge labeling is defined by, or;then, the edge labels are distinct and are from . Then f is called a root square mean labeling of G. In this paper, we...Let be an injective function. For a vertex labeling f, the induced edge labeling is defined by, or;then, the edge labels are distinct and are from . Then f is called a root square mean labeling of G. In this paper, we prove root square mean labeling of some degree splitting graphs.展开更多
This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations pro...This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples.展开更多
Visible light communication(VLC) is expected to be a potential candidate of the key technologies in the sixth generation(6G) wireless communication system to support Internet of Things(IoT) applications. In this work,...Visible light communication(VLC) is expected to be a potential candidate of the key technologies in the sixth generation(6G) wireless communication system to support Internet of Things(IoT) applications. In this work, a separate least mean square(S-LMS) equalizer is proposed to compensate lowpass frequency response in VLC system. Joint optimization is employed to realize the proposed S-LMS equalizer with pre-part and post-part by introducing Lagrangian. For verification, the performance of VLC system based on multi-band carrier-less amplitude and phase(m-CAP) modulation with S-LMS equalizer is investigated and compared with that without equalizer,with LMS equalizer and with recursive least squares(RLS)-Volterra equalizer. Results indicate the proposed equalizer shows significant improved bit error ratio(BER) performance under the same conditions. Compared to the RLS-Volterra equalizer, SLMS equalizer achieves better performance under low data rate or high signal noise ratio(SNR) conditions with obviously lower computational complexity.展开更多
Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and ma...Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.展开更多
The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-squ...The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method's overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations(adjacent to the concerning sea area) and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.展开更多
The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for s...The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.展开更多
We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = (a0 - θ0Xt)dt + dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discuss...We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = (a0 - θ0Xt)dt + dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case (a0, θ0) = (0, 0). If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case (θ0 = 0) and for ergodic case (θ0 〉 0) are completely different.展开更多
Advanced processing of lung sound (LS) recording is a significant means to separate heart sounds (HS) and combined low frequency noise from instruments (NI), with saving its characteristics. This paper proposes a new ...Advanced processing of lung sound (LS) recording is a significant means to separate heart sounds (HS) and combined low frequency noise from instruments (NI), with saving its characteristics. This paper proposes a new method of LS filtering which separates HS and NI simultaneously. It focuses on the application of least mean squares (LMS) algorithm with adaptive noise cancelling (ANC) technique. The second step of the new method is to modulate the reference input r1(n) of LMS-ANC to acquiesce combining HS and NI signals. The obtained signal is removed from primary signal (original lung sound recording-LS). The original signal is recorded from subjects and derived HS from it and it is modified by a band pass filter. NI is simulated by generating approximately periodic white gaussian noise (WGN) signal. The LMS-ANC designed algorithm is controlled in order to determine the optimum values of the order L and the coefficient convergence μ. The output results are measured using power special density (PSD), which has shown the effectiveness of our suggested method. The result also has shown visual difference PSD (to) normal and abnormal LS recording. The results show that the method is a good technique for heart sound and noise reduction from lung sounds recordings simultaneously with saving LS characteristics.展开更多
Using the SST data series in tropical ocean (20N ~ 20S, 50E ~ 80W) during 1951 ~ 1997 to calculate its monthly mean square deviation, the work obtains results showing that interannual SST variability of the Pacific is...Using the SST data series in tropical ocean (20N ~ 20S, 50E ~ 80W) during 1951 ~ 1997 to calculate its monthly mean square deviation, the work obtains results showing that interannual SST variability of the Pacific is more significant than that of the Indian Ocean, especially near the central and eastern equatorial Pacific (165W~90W, 6N~6S), where it ranges from 2C to 4C. The interannual SST variability is obvious in November and December but small in March and April. The interannual variability of 搘arm pool?SST is not so obvious as that of the eastern equatorial Pacific. However, interannual SST variability of the Indian Ocean ranges from 1C to 2C or so, being smaller than that of the Pacific. In the Indian Ocean, interannual SST variability of the Southern Hemisphere is more obvious than that of the Northern Hemisphere. According to above characteristics of interannual SST variability, the key sectors are determined.展开更多
文摘离群点检测任务是指检测与正常数据在特征属性上存在显著差异的异常数据。大多数基于聚类的离群点检测方法主要从全局角度对数据集中的离群点进行检测,而对局部离群点的检测性能较弱。基于此,本文通过引入快速搜索和发现密度峰值方法改进K-means聚类算法,提出了一种名为KLOD(local outlier detection based on improved K-means and least-squares methods)的局部离群点检测方法,以实现对局部离群点的精确检测。首先,利用快速搜索和发现密度峰值方法计算数据点的局部密度和相对距离,并将二者相乘得到γ值。其次,将γ值降序排序,利用肘部法则选择γ值最大的k个数据点作为K-means聚类算法的初始聚类中心。然后,通过K-means聚类算法将数据集聚类成k个簇,计算数据点在每个维度上的目标函数值并进行升序排列。接着,确定数据点的每个维度的离散程度并选择适当的拟合函数和拟合点,通过最小二乘法对升序排列的每个簇的每1维目标函数值进行函数拟合并求导,以获取变化率。最后,结合信息熵,将每个数据点的每个维度目标函数值乘以相应的变化率进行加权,得到最终的异常得分,并将异常值得分较高的top-n个数据点视为离群点。通过人工数据集和UCI数据集,对KLOD、LOF和KNN方法在准确度上进行仿真实验对比。结果表明KLOD方法相较于KNN和LOF方法具有更高的准确度。本文提出的KLOD方法能够有效改善K-means聚类算法的聚类效果,并且在局部离群点检测方面具有较好的精度和性能。
基金The authors gratefully acknowledge the support of the National Natural Science Foundation of China(No.11574250).
文摘Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.
基金supported by the National Key Technologies R&D Program of China under Grant No. 2015BAK38B01the National Natural Science Foundation of China under Grant Nos. 61174103 and 61603032+4 种基金the National Key Research and Development Program of China under Grant Nos. 2016YFB0700502, 2016YFB1001404, and 2017YFB0702300the China Postdoctoral Science Foundation under Grant No. 2016M590048the Fundamental Research Funds for the Central Universities under Grant No. 06500025the University of Science and Technology Beijing - Taipei University of Technology Joint Research Program under Grant No. TW201610the Foundation from the Taipei University of Technology of Taiwan under Grant No. NTUT-USTB-105-4
文摘Quantized kernel least mean square(QKLMS) algorithm is an effective nonlinear adaptive online learning algorithm with good performance in constraining the growth of network size through the use of quantization for input space. It can serve as a powerful tool to perform complex computing for network service and application. With the purpose of compressing the input to further improve learning performance, this article proposes a novel QKLMS with entropy-guided learning, called EQ-KLMS. Under the consecutive square entropy learning framework, the basic idea of entropy-guided learning technique is to measure the uncertainty of the input vectors used for QKLMS, and delete those data with larger uncertainty, which are insignificant or easy to cause learning errors. Then, the dataset is compressed. Consequently, by using square entropy, the learning performance of proposed EQ-KLMS is improved with high precision and low computational cost. The proposed EQ-KLMS is validated using a weather-related dataset, and the results demonstrate the desirable performance of our scheme.
基金Project supported by the Higher Education Commission of Pakistan
文摘A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square (MFLMS) algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.
基金supported by the 2011 China Aerospace Science and Technology Foundationthe Certain Ministry Foundation under Grant No.20212HK03010
文摘Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.
基金Projects(41204079,41504086)supported by the National Natural Science Foundation of ChinaProject(20160101281JC)supported by the Natural Science Foundation of Jilin Province,ChinaProjects(2016M590258,2015T80301)supported by the Postdoctoral Science Foundation of China
文摘Nano-volt magnetic resonance sounding(MRS) signals are sufficiently weak so that during the actual measurement, they are affected by environmental electromagnetic noise, leading to inaccuracy of the extracted characteristic parameters and hindering effective inverse interpretation. Considering the complexity and non-homogeneous spatial distribution of environmental noise and based on the theory of adaptive noise cancellation, a model system for noise cancellation using multi-reference coils was constructed to receive MRS signals. The feasibility of this system with theoretical calculation and experiments was analyzed and a modified sigmoid variable step size least mean square(SVSLMS) algorithm for noise cancellation was presented. The simulation results show that, the multi-reference coil method performs better than the single one on both signal-to-noise ratio(SNR) improvement and signal waveform optimization after filtering, under the condition of different noise correlations in the reference coils and primary detecting coils and different SNRs. In particular, when the noise correlation is poor and the SNR<0, the SNR can be improved by more than 8 dB after filtering with multi-reference coils. And the average fitting errors for initial amplitude and relaxation time are within 5%. Compared with the normalized least mean square(NLMS) algorithm and multichannel Wiener filter and processing field test data, the effectiveness of the proposed method is verified.
基金support for this study was provided by the National Natural Science Foundation of China (No.40776006)Research Fund for the Doctoral Program of Higher Education of China (Grant No.20060423009)the Science and Technology Development Program of Shandong Province (Grant No.2008GGB01099)
文摘Significant wave height is an important criterion in designing coastal and offshore structures.Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper.Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed.It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height.Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys.The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
文摘Let be an injective function. For a vertex labeling f, the induced edge labeling is defined by, or;then, the edge labels are distinct and are from . Then f is called a root square mean labeling of G. In this paper, we prove root square mean labeling of some degree splitting graphs.
文摘This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples.
基金supported by National Natural Science Foundation of China (No.61671055)Scientific and Technological Innovation Foundation of Shunde Graduate School, USTB(BK19BF008)。
文摘Visible light communication(VLC) is expected to be a potential candidate of the key technologies in the sixth generation(6G) wireless communication system to support Internet of Things(IoT) applications. In this work, a separate least mean square(S-LMS) equalizer is proposed to compensate lowpass frequency response in VLC system. Joint optimization is employed to realize the proposed S-LMS equalizer with pre-part and post-part by introducing Lagrangian. For verification, the performance of VLC system based on multi-band carrier-less amplitude and phase(m-CAP) modulation with S-LMS equalizer is investigated and compared with that without equalizer,with LMS equalizer and with recursive least squares(RLS)-Volterra equalizer. Results indicate the proposed equalizer shows significant improved bit error ratio(BER) performance under the same conditions. Compared to the RLS-Volterra equalizer, SLMS equalizer achieves better performance under low data rate or high signal noise ratio(SNR) conditions with obviously lower computational complexity.
文摘Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.
基金Supported by National Research Foundation of Singapore (NRF-CRP8-2011-03) and National Natural Science Foundation of China (61120106011, 61034007, 61203045, 61304045)
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51379195 and 41476078)the Natural Science Foundation of Shandong Province(Grant No.ZR2013EEM034)+2 种基金the Scientific Research Foundation of Science Technology Department of Zhejiang Province(Grant No.2015C34013)the Science Research Program of Zhoushan(Grant No.2014C41003)the Innovation Fund for Graduate Student of Shandong Province(Grant No.SDYY12152)
文摘The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method's overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations(adjacent to the concerning sea area) and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
文摘The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.
基金Hu is supported by the National Science Foundation under Grant No.DMS0504783Long is supported by FAU Start-up funding at the C. E. Schmidt College of Science
文摘We study the problem of parameter estimation for mean-reverting α-stable motion, dXt = (a0 - θ0Xt)dt + dZt, observed at discrete time instants. A least squares estimator is obtained and its asymptotics is discussed in the singular case (a0, θ0) = (0, 0). If a0 = 0, then the mean-reverting α-stable motion becomes Ornstein-Uhlenbeck process and is studied in [7] in the ergodic case θ0 〉 0. For the Ornstein-Uhlenbeck process, asymptotics of the least squares estimators for the singular case (θ0 = 0) and for ergodic case (θ0 〉 0) are completely different.
文摘Advanced processing of lung sound (LS) recording is a significant means to separate heart sounds (HS) and combined low frequency noise from instruments (NI), with saving its characteristics. This paper proposes a new method of LS filtering which separates HS and NI simultaneously. It focuses on the application of least mean squares (LMS) algorithm with adaptive noise cancelling (ANC) technique. The second step of the new method is to modulate the reference input r1(n) of LMS-ANC to acquiesce combining HS and NI signals. The obtained signal is removed from primary signal (original lung sound recording-LS). The original signal is recorded from subjects and derived HS from it and it is modified by a band pass filter. NI is simulated by generating approximately periodic white gaussian noise (WGN) signal. The LMS-ANC designed algorithm is controlled in order to determine the optimum values of the order L and the coefficient convergence μ. The output results are measured using power special density (PSD), which has shown the effectiveness of our suggested method. The result also has shown visual difference PSD (to) normal and abnormal LS recording. The results show that the method is a good technique for heart sound and noise reduction from lung sounds recordings simultaneously with saving LS characteristics.
基金Mechanisms of Important Climatic Disasters in China and the Research on Prediction Theory a key national development and planning project for fundamental scientific study Effects of SST Variation in tropical Pacific and Indian Ocean on the Wetness in R
文摘Using the SST data series in tropical ocean (20N ~ 20S, 50E ~ 80W) during 1951 ~ 1997 to calculate its monthly mean square deviation, the work obtains results showing that interannual SST variability of the Pacific is more significant than that of the Indian Ocean, especially near the central and eastern equatorial Pacific (165W~90W, 6N~6S), where it ranges from 2C to 4C. The interannual SST variability is obvious in November and December but small in March and April. The interannual variability of 搘arm pool?SST is not so obvious as that of the eastern equatorial Pacific. However, interannual SST variability of the Indian Ocean ranges from 1C to 2C or so, being smaller than that of the Pacific. In the Indian Ocean, interannual SST variability of the Southern Hemisphere is more obvious than that of the Northern Hemisphere. According to above characteristics of interannual SST variability, the key sectors are determined.