Parameters Of Gaussian Functions Research Articles

A Sparse Model for Electricity Price Forecasting with LASSO-GRBFN and Brain Storm Optimization

This paper proposes a new method for predicting electricity prices. The method is based on the Generalized Radial Basis Function Network (GRBFN), an extension of the RBFN of Artificial Neural Network (ANN) used for one-step-ahead forecasting. The GRBFN is superior to the RBFN because it evaluates the Gaussian function parameters during learning. Conventional ANN methods consider overfitting with the weight decay method, based on the L2 norm of weights between neurons, but there is still room for improvement. Therefore, the paper proposes using the Least Absolute Shrinkage and Selection Operator (LASSO) to improve the model’s performance. Furthermore, the paper presents the Brain Storm Optimization (BSO) of evolutionary computation to evaluate the cost function with the term of the L1 norm. Conventional methods with the gradient are not suitable for the L1 norm. The proposed method is successfully applied to actual data of ISO New England in the USA.

Probabilistic seismic demand model of UBPRC columns conditioned on Pulse-Structure parameters

Unbonded prestressed reinforced concrete (UBPRC) column has attracted the attention of many researchers in bridge seismic design because of its small residual displacement. However, the research on the mechanism and quantitative method of its seismic response under near-fault impulse ground motions is still insufficient. On this basis, a quantitative probabilistic mathematical model was established to evaluate the seismic demand of UBPRC columns with different structural parameters subjected to earthquakes with varying pulse parameters. Firstly, in order to describe the seismic response of UBPRC columns under pulse-like ground motions accurately and conveniently, a new parameter (xT) composed by fundamental period (T1) and pulse period (Tp) was proposed. It is found that Gaussian function can well describe the relationship between the newly defined parameter and seismic demand, based on a set of seismic response databases of UBPRC columns with different heights under impulse ground motions. Secondly, considering that the peak pulse velocity (Vp) has a significant impact on the seismic response of bridge structures, the influence of Vp on the parameters of Gaussian function was studied, and the functional relationship between these parameters and Vp was established. Finally, a novel probabilistic seismic demand model (PSDM) considering structure parameters and pulse parameters was established, and its accuracy is verified. The quantitative mathematical model with multi pulse-structure coupled parameters can be adopted to conduct the seismic fragility analysis of UBPRC columns. The verification and application indicate that the proposed PSDM model can quickly and accurately estimate the seismic demand of UBPRC column under different near-fault impulse ground motions.

A Novel Structure-Pulse Coupled Model for Quantifying the Column Ductility Demand under Pulse-Like GMs

ABSTRACT A novel model is constructed to investigate the coupling effect of pulse period (Tp ) and peak pulse velocity (Vp ) on structural demands with the varied fundamental period (T1 ) under pulse-like ground motions. The Gaussian function is proposed to quantitatively describe the bell-shape curve of column ductility demand in terms of ln(T1 /Tp ). Further investigation reveals that the two critical parameters of Gaussian function, i.e. the height of the curve’s peak and the position of the center of the peak, are significantly influenced by Vp , and analytically illustrated by Power function and Boltzmann function, respectively. verification of the proposed two-dimensional structure-pulse coupling model exhibits its accuracy and feasibility in predicting the seismic demand conditioned on vector-valued intensity measure ([Vp , ln(T1 /Tp )]) under pulse-like ground motion. Moreover, the coupling model can be used to identify and quantify the response regularity, for instance, the phenomenon that the center position of the peak shifts from 1.0 to 0.5 by increasing Vp is analytically captured in this study. Lastly, the coupling model is also capable to identify the unfavorable range of structural parameters, which is quite practical for near-fault seismic design and risk assessment.

Online Multi-Target Laser Ranging Using Waveform Decomposition on FPGA

To achieve online multi-target laser ranging in full-waveform light detection and ranging (LiDAR), a multi-target laser ranging method using waveform decomposition is proposed and implemented on a field programmable gate array (FPGA). In this method, an emitted laser pulse and the laser echo scattered from multiple targets are decomposed into a set of Gaussian functions, then the distances between the LiDAR and the targets are obtained using the waveform parameters of Gaussian functions. The waveform decomposition method is modified and implemented on a FPGA for online laser ranging. Simulations and experiments were conducted to verify the ranging performances of the proposed method by the comparition with those of a post-processing Gauss-Newton (post-GN) method. The results of simulations show that the proposed method is more efficient compared with the post-GN method. The time cost reduces 79.8% to 91.1% for a laser echo scattered from three close targets. In experiments, a lab-built full-waveform LiDAR system was used to obtain the waveforms of emitted laser pulses and laser echoes scattered from 1, 2, or 3 targets. The results show that the ranging performances of the proposed method are comparable with those of the post-GN method. The proposed method is capable to distinguish close targets with an equivalent time space of 1.8 times pulse width of an emitted laser pulse and decompose laser echo with a signal-to-noise ratio (SNR) higher than 20 dB. The results show that the proposed method can obtain distances of multiple close targets from a laser echo efficiently and accurately.

T-S fuzzy systems optimization identification based on FCM and PSO

The division of fuzzy space is very important in the identification of premise parameters, and the Gaussian membership function is applied to the premise fuzzy set. However, the two parameters of Gaussian membership function, center and width, are not easy to be determined. In this paper, based on Fuzzy c-means (FCM) and particle swarm optimization (PSO) algorithm, a novel T-S fuzzy model optimal identification method of optimizing two parameters of Gaussian function is presented. Firstly, we use FCM algorithm to determine the Gaussian center for rough adjustment. Then, under the condition that the center of Gaussian function is fixed, the PSO algorithm is used to optimize another adjustable parameter, the width of the Gaussian membership function, to achieve fine-tuning, so as to complete the identification of prerequisite parameters of fuzzy model. In addition, the recursive least squares (RLS) algorithm is used to identify the conclusion parameters. Finally, the effectiveness of this method for T-S fuzzy model identification is verified by simulation examples, and the higher identification accuracy can be obtained by using the novel identification method described compared with other identification methods.

СТОХАСТИЧЕСКИЙ АНАЛИЗ ФЛУКТУАЦИЙ ТЕМПЕРАТУРЫ В ЛЕСАХ

When forecasting forest fires, particular importance is attached to the analysis of air temperature changes. Along with data such as precipitation and wind speed, temperature is a basic parameter for determining the drying rate of combustible materials and determining the parameters of the threat of fires (Nesterov index). At the same time, little importance is attached to studies of the patterns of changes in the probability distribution of the temperature fluctuations magnitude during the year. Temperature studies are descriptive, as a rule, estimates diverge, and the boundaries of the given intervals are blurred. The paper has analyzed the nature of the probability distribution of daily temperature fluctuations in the period from January to May. The analysis is based on known and regularly measured data. The results of the analysis of the data of measurements of the temperature of the day and evening showed that the probability distribution can be modeled by the Gaussian function with a sufficient degree of certainty. The parameters of Gaussian function characterize the features of the processes stimulated by temperature changes in the trunks of woody plants. In addition, it turned out that the most likely value of fluctuations is steadily increasing from January to March. It is known that in March intense sap flow occurs in the absence of transpiration currents. Therefore, we can confidently assume that at this time the upward currents in the tree trunks are thermally stimulated.

Vertical Dynamic Loads on Footbridges Generated by People Running

This paper concerns the issue of the dynamic impact of people running on footbridges with particular with attention to various footstrike patterns occurring during the running (i.e. heel strike pattern and forefoot strike pattern). The results of a series of laboratory tests of vertical ground reaction force (VGRF) measurements generated by running people are presented along with the characteristics of the VGRF curves. Based on the results of the tests, a new proposal for a dynamic load model generated by people classified as heel strike runners has been developed, and corrections of the input parameters of two load models proposed by other authors have been performed. Moreover, the VGRF modelling technique using the Gaussian functions is presented along with a set of equations describing the variability of the Gaussian function parameters as a function of the frequency of running. The presented methods of the VGRF modelling allow increasing the accuracy of determining the VGRF values and, consequently, increasing the accuracy of dynamic analyses of footbridges subjected to dynamic loads generated by people running.

Neural networks for 3D temperature field reconstruction via acoustic signals

• A distributed optical fiber sensing system is applied. • Signals will be measured simultaneously by CDMA. • A kernel regression method is used to model the temperature field. • Inversion problem is solved by gradient descent method. • Uncertainty quantification is performed via comparison. Reconstructed 3D temperature field will provide critical input for the control mechanisms to optimize the thermal fluids and combustion process. In this paper, a distributed optical fiber sensing system is used to generate acoustic signals for real-time monitoring and optimization of spatial and temporal distributions of high temperature profile in a boiler furnace in fossil power plants. A code division multiple access (CDMA) based acoustic signal modulation technique for improved signal to noise ratio (SNR) and simultaneous sending/receiving is developed. A kernel regression model which approximates the temperature field as a finite summation of products of space-dependent Gaussian Radial Basis Functions (GRBF) and time-dependent coefficients is established. The inversion problem to estimate the best parameters of Gaussian functions is solved by optimizing a cost function using gradient descent method. Guidance on how to tune design parameters is also given. And regularization is applied for solving the trade-off problem between bias and variance. The numerical simulations show an approximation error less than 5% in 3D temperature field reconstruction. Besides that, the performance of learned model with variation of some relevant design parameters is evaluated, and error analysis for temperature field reconstruction with measurement noise is also given. To validate the availability and efficiency of our proposed 3D temperature field reconstruction mechanism, a 2D temperature field distribution experiment test on microphone is carried out and satisfactory estimation accuracy is achieved.

Leakage detection and calibration of pipe networks by the inverse transient analysis modified by Gaussian functions for leakage simulation

The Inverse Transient Analysis (ITA) is a well known method for leakage detection and calibration of pipe networks. To reduce the problem of dimensionality as well as to allocate candidate leakages everywhere in the network and to handle the simulation and measurement uncertainties, it is assumed that a leakage has a quasi-normal distribution around its true location. Accordingly, a Gaussian function is introduced to simulate each candidate leakage so that the Gaussian function parameters are the ITA decision variables. To manage the ITA process and decrease unnecessary computations, a conceptual step-by-step algorithm is introduced through which the number of candidate leakages is gradually increased until the convergence criteria are met. Solving a benchmark example reveals that the modifications play a significant role in increasing both accuracy and efficiency of the ITA. As compared to the traditional ITA, the new version was successful in solving the example with about 30 times less computation.

GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences

BackgroundAs crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is < 50%, CpG obs/CpG exp varies, and the length of CGI ranges from eight nucleotides to a few thousand of nucleotides. It implies that CGI detection is not just a straightly statistical task and some unrevealed rules probably are hidden.ResultsA novel Gaussian model, GaussianCpG, is developed for detection of CpG islands on human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection.ConclusionsOur Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.

Domestic electricity load modelling by multiple Gaussian functions

Domestic electricity load profile is essential for energy planning and renewable energy system design. This paper presents analysis of domestic electric load characteristics and a method to model domestic and regional load profile. Multiple Gaussian functions are used to express the load characteristics in the proposed model. This is done by associating the Gaussian function parameters with the peak load changes, e.g. changing height parameters to reflect the peak magnitude. The result of the load curve represented with multiple Gaussian functions allows the model to generate a regional load profile using the number of homes, the number of bedrooms (Nr) and the number of occupants (Np). The proposed model simulates domestic load profile by its load demand change characteristics instead of its appliance ownership and use pattern, etc. Data requirement for the proposed method is significantly lower than the previous top-down and bottom-up approaches. Seasonal change is not included in the present paper, but the method is capable of including seasonal changes if each season’s load demand changes in relation to Np and Nr is available. A demonstration of modelling England and Wales’s national hourly load profile in 2001 and 2011 is presented in this paper. Comparison is made of the proposed method with two other published domestic load profile models. Results show that the proposed method improves the mean percentage errors by at least 5.7% on average hourly load profile.

ECG denoising and fiducial point extraction using an extended Kalman filtering framework with linear and nonlinear phase observations

In this paper we propose an efficient method for denoising and extracting fiducial point (FP) of ECG signals. The method is based on a nonlinear dynamic model which uses Gaussian functions to model ECG waveforms. For estimating the model parameters, we use an extended Kalman filter (EKF). In this framework called EKF25, all the parameters of Gaussian functions as well as the ECG waveforms (P-wave, QRS complex and T-wave) in the ECG dynamical model, are considered as state variables. In this paper, the dynamic time warping method is used to estimate the nonlinear ECG phase observation. We compare this new approach with linear phase observation models. Using linear and nonlinear EKF25 for ECG denoising and nonlinear EKF25 for fiducial point extraction and ECG interval analysis are the main contributions of this paper. Performance comparison with other EKF-based techniques shows that the proposed method results in higher output SNR with an average SNR improvement of 12 dB for an input SNR of −8 dB. To evaluate the FP extraction performance, we compare the proposed method with a method based on partially collapsed Gibbs sampler and an established EKF-based method. The mean absolute error and the root mean square error of all FPs, across all databases are 14 ms and 22 ms, respectively, for our proposed method, with an advantage when using a nonlinear phase observation. These errors are significantly smaller than errors obtained with other methods. For ECG interval analysis, with an absolute mean error and a root mean square error of about 22 ms and 29 ms, the proposed method achieves better accuracy and smaller variability with respect to other methods.

Gaussian mixture modeling of hemispheric lateralization for language in a large sample of healthy individuals balanced for handedness.

Hemispheric lateralization for language production and its relationships with manual preference and manual preference strength were studied in a sample of 297 subjects, including 153 left-handers (LH). A hemispheric functional lateralization index (HFLI) for language was derived from fMRI acquired during a covert sentence generation task as compared with a covert word list recitation. The multimodal HFLI distribution was optimally modeled using a mixture of 3 and 4 Gaussian functions in right-handers (RH) and LH, respectively. Gaussian function parameters helped to define 3 types of language hemispheric lateralization, namely “Typical” (left hemisphere dominance with clear positive HFLI values, 88% of RH, 78% of LH), “Ambilateral” (no dominant hemisphere with HFLI values close to 0, 12% of RH, 15% of LH) and “Strongly-atypical” (right-hemisphere dominance with clear negative HFLI values, 7% of LH). Concordance between dominant hemispheres for hand and for language did not exceed chance level, and most of the association between handedness and language lateralization was explained by the fact that all Strongly-atypical individuals were left-handed. Similarly, most of the relationship between language lateralization and manual preference strength was explained by the fact that Strongly-atypical individuals exhibited a strong preference for their left hand. These results indicate that concordance of hemispheric dominance for hand and for language occurs barely above the chance level, except in a group of rare individuals (less than 1% in the general population) who exhibit strong right hemisphere dominance for both language and their preferred hand. They call for a revisit of models hypothesizing common determinants for handedness and for language dominance.

이중게이트 MOSFET의 문턱전압이하 전류에 대한 게이트 산화막 의존성

This paper analyzed the change of subthreshold current for gate oxide thickness of double gate(DG) MOSFET. Poisson's equation had been used to analyze the potential distribution in channel, and Gaussian function had been used as carrier distribution. The potential distribution was obtained as the analytical function of channel dimension, using the boundary condition. The subthreshold current had been analyzed for gate oxide thickness, and projected range and standard projected deviation of Gaussian function. Since this analytical potential model was verified in the previous papers, we used this model to analyze the subthreshold current. Resultly, analytical model showed that subthreshold current was influenced by parameters of Gaussian function and gate oxide thickness of DGMOSFET.

이중게이트 MOSFET의 채널도핑에 다른 문턱전압이하 전류 변화 분석

본 연구에서는 이중게이트 MOSFET의 채널도핑농도의 변화에 따른 문턱전압이하 전류의 변화를 분석하였다. 이를 위하여 이중게이트 MOSFET의 채널 내 전위분포를 구하기 위하여 포아송방정식을 이용하였으며 이때 전하분포함수에 대하여 가우시안 함수를 사용하였다. 전위분포는 경계조건을 이용하여 채널크기에 따른 해석학적인 함수로 구하였다. 가우시안 함수의 변수인 이온주입범위 및 분포편차 그리고 채널도핑농도 등에 대하여 문턱전압 이하 전류 특성의 변화를 관찰하였다. 본 연구의 전위모델에 대한 타당성은 이미 기존에 발표된 논문에서 입증하였으며 본 연구에서는 이 모델을 이용하여 문턱전압이하 전류 특성을 분석하였다. 분석결과, 문턱전압이하 전류는 채널도핑농도 및 가우시안 분포함수의 변수 등에 크게 영향을 받는 것을 관찰할 수 있었다. This paper analyzed the change of subthreshold current for channel doping concentration of double gate(DG) MOSFET. Poisson's equation had been used to analyze the potential distribution in channel, and Gaussian function had been used as carrier distribution. The potential distribution was obtained as the analytical function of channel dimension, using the boundary condition. The subthreshold current had been analyzed for channel doping concentration, and projected range and standard projected deviation of Gaussian function. Since this analytical potential model was verified in the previous papers, we used this model to analyze the subthreshold current. As a result, we know the subthreshold current was influenced on parameters of Gaussian function and channel doping concentration for DGMOSFET.

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.