In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, ...In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.展开更多
In this paper, we propose a novel Residuals-Based Deep Least Squares Support Vector Machine(RBDLSSVM). In the RBD-LSSVM, multiple LSSVMs are sequentially connected. The second LSSVM uses the fitting residuals of the f...In this paper, we propose a novel Residuals-Based Deep Least Squares Support Vector Machine(RBDLSSVM). In the RBD-LSSVM, multiple LSSVMs are sequentially connected. The second LSSVM uses the fitting residuals of the first LSSVM as input time series, and the third LSSVM trains the residuals of the second, and so on. The original time series is the input of the first LSSVM. Additionally, to obtain the best hyper-parameters for the RBD-LSSVM, we propose a model validation method based on redundancy test using Omni-Directional Correlation Function(ODCF). This method is based on the fact when a model is appropriate for a given time series, there should be no information or correlation in the residuals. We propose the use of ODCF as a statistic to detect nonlinear correlation between two random variables. Thus, we can select hyper-parameters without encountering overfitting,which cannot be avoided by only cross validation using the validation set. We conducted experiments on two time series: annual sunspot number series and monthly Total Column Ozone(TCO) series in New Delhi. Analysis of the prediction results and comparisons with recent and past studies demonstrate the promising performance of the proposed RBD-LSSVM approach with redundancy test based model selection method for modeling and predicting nonlinear time series.展开更多
气候系统是典型的非平稳性系统,然而对于气候观测数据的处理通常是在时间序列平稳的假定下完成的,比如气温和降水的多步预报,这通常会导致预报准确度较低。为改进该缺陷,首先将非平稳数据序列分解成平稳的、多尺度特征的本征模态函数分...气候系统是典型的非平稳性系统,然而对于气候观测数据的处理通常是在时间序列平稳的假定下完成的,比如气温和降水的多步预报,这通常会导致预报准确度较低。为改进该缺陷,首先将非平稳数据序列分解成平稳的、多尺度特征的本征模态函数分量(IMF),再使用数值集合预报与逐步回归分析相结合的方式对每一个IMF分量构建不同的预报模型,最后线性拟合成预报结果。通过Visual Studio 2008开发平台使用上述方法建立了一个短期气候预报系统,采用广西区88个气象站1957—2005年的2月距平气温数据进行实际验证。结果表明,相对于普通预测和单一预测方法,加入了EMD和集合预报技术的方法在仅用历史资料进行多步预测的情况下,对于气候的变化趋势以及突发性气候具有更好的预报能力。展开更多
The seasonality and randomness of wind present a significant challenge to the operation of modern power systems with high penetration of wind generation. An effective shortterm wind power prediction model is indispens...The seasonality and randomness of wind present a significant challenge to the operation of modern power systems with high penetration of wind generation. An effective shortterm wind power prediction model is indispensable to address this challenge. In this paper, we propose a combined model, i.e.,a wind power prediction model based on multi-class autoregressive moving average(ARMA). It has a two-layer structure: the first layer classifies the wind power data into multiple classes with the logistic function based classification method;the second layer trains the prediction algorithm in each class. This two-layer structure helps effectively tackle the seasonality and randomness of wind power while at the same time maintaining high training efficiency with moderate model parameters. We interpret the training of the proposed model as a solvable optimization problem. We then adopt an iterative algorithm with a semi-closed-form solution to efficiently solve it. Data samples from open-source projects demonstrate the effectiveness of the proposed model. Through a series of comparisons with other state-of-the-art models, the experimental results confirm that the proposed model improves not only the prediction accuracy,but also the parameter estimation efficiency.展开更多
With the complexity and uncertainty of mobile communication network environment, solving the classical mathematical analysis also becomes more complicated. The model tree of basis function method based on Fourier seri...With the complexity and uncertainty of mobile communication network environment, solving the classical mathematical analysis also becomes more complicated. The model tree of basis function method based on Fourier series is proposed in this paper. Model tree method is the improvement of regression tree analysis. Basis function applied here is four-order Fourier series. When the Fourier coefficients are calculated, the Gauss elimination method is implemented for solving equations. The complexity of the algorithm is n3log(n).展开更多
文摘In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.
文摘In this paper, we propose a novel Residuals-Based Deep Least Squares Support Vector Machine(RBDLSSVM). In the RBD-LSSVM, multiple LSSVMs are sequentially connected. The second LSSVM uses the fitting residuals of the first LSSVM as input time series, and the third LSSVM trains the residuals of the second, and so on. The original time series is the input of the first LSSVM. Additionally, to obtain the best hyper-parameters for the RBD-LSSVM, we propose a model validation method based on redundancy test using Omni-Directional Correlation Function(ODCF). This method is based on the fact when a model is appropriate for a given time series, there should be no information or correlation in the residuals. We propose the use of ODCF as a statistic to detect nonlinear correlation between two random variables. Thus, we can select hyper-parameters without encountering overfitting,which cannot be avoided by only cross validation using the validation set. We conducted experiments on two time series: annual sunspot number series and monthly Total Column Ozone(TCO) series in New Delhi. Analysis of the prediction results and comparisons with recent and past studies demonstrate the promising performance of the proposed RBD-LSSVM approach with redundancy test based model selection method for modeling and predicting nonlinear time series.
文摘气候系统是典型的非平稳性系统,然而对于气候观测数据的处理通常是在时间序列平稳的假定下完成的,比如气温和降水的多步预报,这通常会导致预报准确度较低。为改进该缺陷,首先将非平稳数据序列分解成平稳的、多尺度特征的本征模态函数分量(IMF),再使用数值集合预报与逐步回归分析相结合的方式对每一个IMF分量构建不同的预报模型,最后线性拟合成预报结果。通过Visual Studio 2008开发平台使用上述方法建立了一个短期气候预报系统,采用广西区88个气象站1957—2005年的2月距平气温数据进行实际验证。结果表明,相对于普通预测和单一预测方法,加入了EMD和集合预报技术的方法在仅用历史资料进行多步预测的情况下,对于气候的变化趋势以及突发性气候具有更好的预报能力。
基金supported by the Guangdong-Macao Joint Funding Project(No. 2021A0505080015)Science and Technology Planning Project of Guangdong Province (No. 2019B010137006)Science and Technology Development Fund,Macao SAR (No. SKL-IOTSC(UM)-2021-2023)。
文摘The seasonality and randomness of wind present a significant challenge to the operation of modern power systems with high penetration of wind generation. An effective shortterm wind power prediction model is indispensable to address this challenge. In this paper, we propose a combined model, i.e.,a wind power prediction model based on multi-class autoregressive moving average(ARMA). It has a two-layer structure: the first layer classifies the wind power data into multiple classes with the logistic function based classification method;the second layer trains the prediction algorithm in each class. This two-layer structure helps effectively tackle the seasonality and randomness of wind power while at the same time maintaining high training efficiency with moderate model parameters. We interpret the training of the proposed model as a solvable optimization problem. We then adopt an iterative algorithm with a semi-closed-form solution to efficiently solve it. Data samples from open-source projects demonstrate the effectiveness of the proposed model. Through a series of comparisons with other state-of-the-art models, the experimental results confirm that the proposed model improves not only the prediction accuracy,but also the parameter estimation efficiency.
文摘With the complexity and uncertainty of mobile communication network environment, solving the classical mathematical analysis also becomes more complicated. The model tree of basis function method based on Fourier series is proposed in this paper. Model tree method is the improvement of regression tree analysis. Basis function applied here is four-order Fourier series. When the Fourier coefficients are calculated, the Gauss elimination method is implemented for solving equations. The complexity of the algorithm is n3log(n).
