A Comparison of the Estimators of the Scale Parameter of the Errors Distribution in the L1 Regression

The L1 regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L1 estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameterτ. This parameter is such that τ2/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of τ. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model. When the errors follow the Laplace distribution, the maximum likelihood estimator of τ, say , is the mean absolute error, that is, the mean of the absolute residuals. This estimator always decreases when new independent variables are added to the model. Our objective is to develop asymptotic properties of under several errors distributions analytically. We also performed a simulation study to compare the distributions of both estimators in small samples with the objective to establish conditions in which is a good alternative to for such situations.

Integrated Approach of Brain Disorder Analysis by Using Deep Learning Based on DNA Sequence

In order to research brain problems using MRI,PET,and CT neuroimaging,a correct understanding of brain function is required.This has been considered in earlier times with the support of traditional algorithms.Deep learning process has also been widely considered in these genomics data processing system.In this research,brain disorder illness incliding Alzheimer’s disease,Schizophrenia and Parkinson’s diseaseis is analyzed owing to misdetection of disorders in neuroimaging data examined by means fo traditional methods.Moeover,deep learning approach is incorporated here for classification purpose of brain disorder with the aid of Deep Belief Networks(DBN).Images are stored in a secured manner by using DNA sequence based on JPEG Zig Zag Encryption algorithm(DBNJZZ)approach.The suggested approach is executed and tested by using the performance metric measure such as accuracy,root mean square error,Mean absolute error and mean absolute percentage error.Proposed DBNJZZ gives better performance than previously available methods.

Interval Type-2 Fuzzy Model for Intelligent Fire Intensity Detection Algorithm with Decision Making in Low-Power Devices

Local markets in East Africa have been destroyed by raging fires,leading to the loss of life and property in the nearby communities.Electrical circuits,arson,and neglected charcoal stoves are the major causes of these fires.Previous methods,i.e.,satellites,are expensive to maintain and cause unnecessary delays.Also,unit-smoke detectors are highly prone to false alerts.In this paper,an Interval Type-2 TSK fuzzy model for an intelligent lightweight fire intensity detection algorithm with decision-making in low-power devices is proposed using a sparse inference rules approach.A free open–source MATLAB/Simulink fuzzy toolbox integrated into MATLAB 2018a is used to investigate the performance of the Interval Type-2 fuzzy model.Two crisp input parameters,namely:FIT and FIG��are used.Results show that the Interval Type-2 model achieved an accuracy value of FIO�=98.2%,MAE=1.3010,MSE=1.6938 and RMSE=1.3015 using regression analysis.The study shall assist the firefighting personnel in fully understanding and mitigating the current level of fire danger.As a result,the proposed solution can be fully implemented in low-cost,low-power fire detection systems to monitor the state of fire with improved accuracy and reduced false alerts.Through informed decision-making in low-cost fire detection devices,early warning notifications can be provided to aid in the rapid evacuation of people,thereby improving fire safety surveillance,management,and protection for the market community.

Output Linearization of Single-Input Single-Output Fuzzy System to Improve Accuracy and Performance

For fuzzy systems to be implemented effectively,the fuzzy membership function(MF)is essential.A fuzzy system(FS)that implements precise input and output MFs is presented to enhance the performance and accuracy of single-input single-output(SISO)FSs and introduce the most applicable input and output MFs protocol to linearize the fuzzy system’s output.Utilizing a variety of non-linear techniques,a SISO FS is simulated.The results of FS experiments conducted in comparable conditions are then compared.The simulated results and the results of the experimental setup agree fairly well.The findings of the suggested model demonstrate that the relative error is abated to a sufficient range(≤±10%)and that the mean absolute percentage error(MPAE)is reduced by around 66.2%.The proposed strategy to reduceMAPE using an FS improves the system’s performance and control accuracy.By using the best input and output MFs protocol,the energy and financial efficiency of every SISO FS can be improved with very little tuning of MFs.The proposed fuzzy system performed far better than other modern days approaches available in the literature.

A new polar motion prediction method combined with the difference between polar motion series

After the first Earth Orientation Parameters Prediction Comparison Campaign(1 st EOP PCC),the traditional method using least-squares extrapolation and autoregressive(LS+AR)models was considered as one of the polar motion prediction methods with higher accuracy.The traditional method predicts individual polar motion series separately,which has a single input data and limited improvement in prediction accuracy.To address this problem,this paper proposes a new method for predicting polar motion by combining the difference between polar motion series.The X,Y,and Y-X series were predicted separately using LS+AR models.Then,the new forecast value of X series is obtained by combining the forecast value of Y series with that of Y-X series;the new forecast value of Y series is obtained by combining the forecast value of X series with that of Y-X series.The hindcast experimental comparison results from January 1,2011 to April 4,2021 show that the new method achieves a maximum improvement of 12.95%and 14.96%over the traditional method in the X and Y directions,respectively.The new method has obvious advantages compared with the differential method.This study tests the stability and superiority of the new method and provides a new idea for the research of polar motion prediction.

Solutions of Seventh Order Boundary Value Problems Using Ninth Degree Spline Functions and Comparison with Eighth Degree Spline Solutions

In this article, we develop numerical method by constructing ninth degree spline function using extended cubic spline Bickley’s method to find the approximate solution of seventh order linear boundary value problems at different step lengths. The approximate solution is compared with the solution obtained by eighth degree splines and exact solution. It has been observed that the approximate solution is an excellent agreement with exact solution. Low absolute error indicates that our numerical method is effective for solving high order linear boundary value problems.

Chaotic Whale Optimized Fractional Order PID Controller Design for Desalination Process

The main aim of this work is to design a suitable Fractional Order Proportionl Integral Derivative(FOPID)controller with Chaotic Whale Optimization Algorithm(CWOA)for a RO desalination system.Continuous research on Reverse Osmosis(RO)desalination plants is a promising technique for satisfaction with sustainable and efficient RO plants.This work implements CWOA based FOPID for the simulation of reverse osmosis(RO)desalination process for both servo and regulatory problems.Mathematical modeling is a vital constituent of designing advanced and developed engineering processes,which helps to gain a deep study of processes to predict the performance,more efficiently.Numerous approaches have been employed for mathematical models based on mass and heat transfer and concentration of permeable flow rate.Incorporation of FOPID controllers is broadly used to improve the dynamic response of the system,at the same time,to reduce undershoot or overshoot,steady state error and hence improve the response.The performances of the FOPID controller with optimization is compared in terms of measures such as Integral Time Absolute Error(ITAE)and Integral Square Error(ISE).Simulation results with FOPID on desalination process achieved rise time of 0.0311 s,settling time of 0.0489 s and 0.7358%overshoot,better than the existing techniques available in the literatures.

Numerical Solution for Fractional Partial Differential Equation with Bernstein Polynomials

A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient.

Application of Hidden Markov Models in Stock Forecasting

In this paper,we tested our methodology on the stocks of four representative companies:Apple,Comcast Corporation(CMCST),Google,and Qualcomm.We compared their performance to several stocks using the hidden Markov model(HMM)and forecasts using mean absolute percentage error(MAPE).For simplicity,we considered four main features in these stocks:open,close,high,and low prices.When using the HMM for forecasting,the HMM has the best prediction for the daily low stock price and daily high stock price of Apple and CMCST,respectively.By calculating the MAPE for the four data sets of Google,the close price has the largest prediction error,while the open price has the smallest prediction error.The HMM has the largest prediction error and the smallest prediction error for Qualcomm’s daily low stock price and daily high stock price,respectively.

Forecasting Inflation Rate of Zambia Using Holt’s Exponential Smoothing

In this paper, the Holt’s exponential smoothing and Auto-Regressive Integrated Moving Average (ARIMA) models were used to forecast inflation rate of Zambia using the monthly consumer price index (CPI) data from May 2010 to May 2014. Results show that the ARIMA ((12), 1, 0) is an adequate model which best fits the CPI time series data and is therefore suitable for forecasting CPI and subsequently the inflation rate. However, the choice of the Holt’s exponential smoothing is as good as an ARIMA model considering the smaller deviations in the mean absolute percentage error and mean square error. Moreover, the Holt’s exponential smoothing model is less complicated since you do not require specialised software to implement it as is the case for ARIMA models. The forecasted inflation rate for April and May, 2015 is 7.0 and 6.6 respectively.

Tile selection method based on error minimization for photomosaic image creation

Photomosaic images are composite images composed of many small images called tiles.In its overall visual effect,a photomosaic image is similar to the target image,and photomosaics are also called“montage art”.Noisy blocks and the loss of local information are the major obstacles in most methods or programs that create photomosaic images.To solve these problems and generate a photomosaic image in this study,we propose a tile selection method based on error minimization.A photomosaic image can be generated by partitioning the target image in a rectangular pattern,selecting appropriate tile images,and then adding them with a weight coefficient.Based on the principles of montage art,the quality of the generated photomosaic image can be evaluated by both global and local error.Under the proposed framework,via an error function analysis,the results show that selecting a tile image using a global minimum distance minimizes both the global error and the local error simultaneously.Moreover,the weight coefficient of the image superposition can be used to adjust the ratio of the global and local errors.Finally,to verify the proposed method,we built a new photomosaic creation dataset during this study.The experimental results show that the proposed method achieves a low mean absolute error and that the generated photomosaic images have a more artistic effect than do the existing approaches.

PMSM Vector Control Optimization Based on Fractional PI^(λ) of Rotational Speed Outer Loop of Dragonfly Algorithm

Aiming at the problems of slow dynamic response and weak robustness of integer-order proportional integral(PI)controller in double closed loop vector control system of permanent magnet synchronous motor(PMSM),a method of combining dragonfly algorithm with fractional order PI control is proposed for off-line parameter tuning for the outer loop of speed of the system.The parameter to be optimized is used as the spatial position of the optimal individual searching for food sources in the search space,and the error performance index integrated time and absolute error(ITAE)is used as its target fitness function.The motor speed regulation performances of traditional engineering experience setting integer order PI,particle swarm optimization algorithm tuning fractional order PI and dragonfly algorithm tuning fractional order PI are compared,respectively.Results show that the fractional order PI controller optimized by dragonfly algorithm can improve the dynamic response performance of the system,reduce overshoot and enhance robustness,which proves the feasibility and superiority of the optimization strategy.

Prediction and datamining of burned areas of forest fires:Optimized data matching and mining algorithm provides valuable insight

An optimized data-matching machine learning algorithm is developed to provide high-prediction accuracy of total burned areas for specific wildfire incidents.It is applied to a well-studied forest-fire dataset from Portugal Montesinho Natural Park considering 13 input variables.The total burned area distribution of the 517 burn events in that dataset is highly positively skewed.The model is transparent and avoids regressions and hidden layers.This increases its detailed datamining capabilities.It matches the highest burned-area prediction accuracy achieved for this datasetwith a wide range of traditionalmachine learning algorithms.The two-stage prediction process provides informative feature selection that establishes the relative influences of the input variables on burned-area predictions.Optimizing with mean absolute error(MAE)and root mean square error(RMSE)as separate objective functions provides complementary information with which to data mine each total burnedarea incident.Such insight offers potential agricultural,ecological,environmental and forestry benefits by improving the understanding of the key influences associated with each burn event.Data mining the differential trends of cumulative absolute error and squared error also provides detailed insight with which to determine the suitability of each optimized solution to accurately predict burned-areas events of specific types.Such prediction accuracy and insight leads to confidence in how each prediction is derived.It provides knowledge to make appropriate responses and mitigate specific burn incidents,as they occur.Such informed responses should lead to short-term and long-term multi-faceted benefits by helping to prevent certain types of burn incidents being repeated or spread.

Reconstructing Missing Hourly Real-Time Precipitation Data Using a Novel Intermittent Sliding Window Period Technique for Automatic Weather Station Data

Precipitation is the most discontinuous atmospheric parameter because of its temporal and spatial variability. Precipitation observations at automatic weather stations（AWSs） show different patterns over different time periods. This paper aims to reconstruct missing data by finding the time periods when precipitation patterns are similar, with a method called the intermittent sliding window period（ISWP） technique—a novel approach to reconstructing the majority of non-continuous missing real-time precipitation data. The ISWP technique is applied to a 1-yr precipitation dataset（January 2015 to January 2016）, with a temporal resolution of 1 h, collected at 11 AWSs run by the Indian Meteorological Department in the capital region of Delhi. The acquired dataset has missing precipitation data amounting to 13.66%, of which 90.6% are reconstructed successfully. Furthermore, some traditional estimation algorithms are applied to the reconstructed dataset to estimate the remaining missing values on an hourly basis. The results show that the interpolation of the reconstructed dataset using the ISWP technique exhibits high quality compared with interpolation of the raw dataset. By adopting the ISWP technique, the root-mean-square errors（RMSEs）in the estimation of missing rainfall data—based on the arithmetic mean, multiple linear regression, linear regression,and moving average methods—are reduced by 4.2%, 55.47%, 19.44%, and 9.64%, respectively. However, adopting the ISWP technique with the inverse distance weighted method increases the RMSE by 0.07%, due to the fact that the reconstructed data add a more diverse relation to its neighboring AWSs.

Analysis and Design of Scaling Optimal GPM-PID Control with Application to Liquid Level Control

In this paper, a new analysis and design method for proportional-integrative-derivative （PID） tuning is proposed based on controller scaling analysis. Integral of time absolute error （ITAE） index is minimized for specified gain and phase margins （GPM） constraints, so that the transient performance and robustness are both satisfied. The requirements on gain and phase margins are ingeniously formulated by real part constraints （RPC） and imaginary part constraints （IPC）. This set of new constraints is simply related with three parameters and decoupling of the remaining four unknowns, including three controller parameters and the gain margin, in the nonlinear and coupled characteristic equation simultaneously. The formulas of the optimal GPM-PID are derived based on controller scaling analysis. Finally, this method is applied to liquid level control of coke fractionation tower, which demonstrate that the proposed method provides better disturbance rejection and robust tracking performance than some commonly used PID tuning methods.

HIGH ORDER ACCURATE QUINTIC NONPOLYNOMIAL SPLINE FINITE DIFFERENCE APPROXIMATIONS FOR THE NUMERICAL SOLUTION OF NON-LINEAR TWO POINT BOUNDARY VALUE PROBLEMS

We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems.The scheme uses nonpolynomial spline basis and high order finite difference approximations.With the help of spline functions,we derive consistency conditions and it is used to derive high order discretizations of the first derivative.The resulting difference schemes are solved by the standard Newton’s method and have very small computing time.The new method is analyzed for its convergence and the efficiency of the proposed scheme is illustrated by convection-diffusion problem and nonlinear Lotka–Volterra equation.The order of convergence and maximum absolute errors are computed to present the utility of the new scheme.

HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS

In this paper,we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyper-bolic partial differential equation of the form utt=A(x,y,t)uxx+B(x,y,t)uyy+g(x,y,t,u,ux,uy,ut),0<x,y<1,t>0 subject to appropriate initial and Dirichlet boundary conditions.We use only five evaluations of the function g and do not require any fictitious points to discretize the differential equation.The proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally stable.Numerical results are provided to illustrate the usefulness of the proposed method.

Integrated Multi-stage LQR Power Oscillation Damping FACTS Controller

This paper presents an approach for oscillation damping with an integrated multi-stage linear quadratic regulator(MSLQR)FACTS controller combining power oscillation damping(POD)capabilities.The particle swarm optimization(PSO)technique has been used for precise tuning initial control parameters of power system stabilizers(PSS)and FACTS devices(such as STATCOM and UPFC)which results in improved controller performance.It is observed that the proposed control structure damps the oscillations adequately and is modular in design methodology.The sample power system comprising six areas is considered to demonstrate the effectiveness of the proposed concept.The states inter-relation which is shown with eigenvalues reflects better regulation with the proposed controller.The step response also validates the controller performance.

Trio-Geometric mean-based three-stage Runge–Kutta algorithm to solve initial value problem arising in autonomous systems

In the present worldwide scenario,plenty of problems arising in science and engineering which can be modeled as differential equations and out of these,autonomous system has become a subject of great interest.Several laws of physics in which time is considered as an independent variable are expressed as autonomous systems.In this paper,Runge–Kutta(RK)three-stage geometric mean method is used to solve the initial value problem arises in autonomous systems.The method is discussed in detail,convergence of method is discussed,the accuracy and efficiency of the method are proved by considering a numerical example.The result is compared to some other methods and proposed method is found to be more efficient.The detailed analysis of error estimation confirms that proposed method is more efficient as compared to other methods.

A Novel Numerical Method of O(h^(4))for Three-Dimensional Non-Linear Triharmonic Equations

In this article,we present two new novel finite difference approximations of order two and four,respectively,for the three dimensional non-linear triharmonic partial differential equations on a compact stencil where the values of u,δ^(2)u/δn^(2)andδ^(4)u/δn^(4)are prescribed on the boundary.We introduce new ideas to handle the boundary conditions and there is no need to discretize the derivative boundary conditions.We require only 7-and 19-grid points on the compact cell for the second and fourth order approximation,respectively.The Laplacian and the biharmonic of the solution are obtained as by-product of the methods.We require only system of three equations to obtain the solution.Numerical results are provided to illustrate the usefulness of the proposed methods.