A Relative Error Estimation Approach for Multiplicative Single Index Model

As an alternative to absolute error methods, such as the least square and least absolute deviation estimations, a product relative error estimation is proposed for a multiplicative single index regression model. Regression coefficients in the model are estimated via a two-stage procedure and their statistical properties such as consistency and normality are studied. Numerical studies including simulation and a body fat example show that the proposed method performs well.

General relative error criterion and M-estimation

Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.

Software Cost Estimation Using Social Group Optimization

This paper introduces the integration of the Social Group Optimization(SGO)algorithm to enhance the accuracy of software cost estimation using the Constructive Cost Model(COCOMO).COCOMO’s fixed coefficients often limit its adaptability,as they don’t account for variations across organizations.By fine-tuning these parameters with SGO,we aim to improve estimation accuracy.We train and validate our SGO-enhanced model using historical project data,evaluating its performance with metrics like the mean magnitude of relative error(MMRE)and Manhattan distance(MD).Experimental results show that SGO optimization significantly improves the predictive accuracy of software cost models,offering valuable insights for project managers and practitioners in the field.However,the approach’s effectiveness may vary depending on the quality and quantity of available historical data,and its scalability across diverse project types and sizes remains a key consideration for future research.

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

Motor Imagery and Error Related Potential Induced Position Control of a Robotic Arm

The paper introduces an electroencephalography(EEG) driven online position control scheme for a robot arm by utilizing motor imagery to activate and error related potential(ErrP) to stop the movement of the individual links, following a fixed(pre-defined) order of link selection. The right(left)hand motor imagery is used to turn a link clockwise(counterclockwise) and foot imagery is used to move a link forward. The occurrence of ErrP here indicates that the link under motion crosses the visually fixed target position, which usually is a plane/line/point depending on the desired transition of the link across 3D planes/around 2D lines/along 2D lines respectively. The imagined task about individual link's movement is decoded by a classifier into three possible class labels: clockwise, counterclockwise and no movement in case of rotational movements and forward, backward and no movement in case of translational movements. One additional classifier is required to detect the occurrence of the ErrP signal, elicited due to visually inspired positional link error with reference to a geometrically selected target position. Wavelet coefficients and adaptive autoregressive parameters are extracted as features for motor imagery and ErrP signals respectively. Support vector machine classifiers are used to decode motor imagination and ErrP with high classification accuracy above 80%. The average time taken by the proposed scheme to decode and execute control intentions for the complete movement of three links of a robot is approximately33 seconds. The steady-state error and peak overshoot of the proposed controller are experimentally obtained as 1.1% and4.6% respectively.

Relative peripheral refractive errors in Chinese children with myopic anisometropia

AIM:To compare relative peripheral refractive errors(RPREs)in Chinese children with and without myopic anisometropia(MAI)and to explore the relationship between RPRE and myopia.METHODS:This observational cross-sectional study included 160 children divided into two groups according to the interocular spherical equivalent refraction(SER)difference≥1.0 D in the MAI group(n=80)and<1.0 D in the non-MAI group(n=80).The MAI group was further divided into two subgroups:ΔSER<2.0 D group and ΔSER≥2.0 D group.Basic ocular biometric parameters of axial length(AL),average keratometry(Ave K),cylinder(CYL),surface regularity index(SRI),and surface asymmetry index(SAI)were recorded.In addition,multispectral refraction topography was performed to measure RPRE,and the parameters were recorded as total refraction difference value(TRDV),refraction difference value(RDV)0-10,RDV10-20,RDV20-30,RDV30-40,RDV40-53,RDV-superior(RDV-S),RDV-inferior(RDV-I),RDV-temporal(RDV-T)and RDV-nasal(RDV-N).RESULTS:In the non-MAI group,the interocular differences of all parameters of RPRE were not significant.In the MAI group,the interocular differences of TRDV,RDV10-53,RDV-S,RDV-I,RDV-T,and RDV-N were significant.In subgroup analysis,the interocular differences of TRDV,RDV30-53,RDV-I,and RDV-T were significant in ΔSER<2.0 D group and ΔSER≥2.0 D group,but the interocular differences of RDV10-30,RDV-S and RDV-N were only significant in the ΔSER≥2.0 D group.In correlation analysis,ΔTRDV,ΔRDV 10-53,ΔRDV-S,and ΔRDV-N were negatively correlated with ΔSER but positively correlated with ΔAL.CONCLUSION:The more myopic eyes have larger hyperopic RPRE in Chinese children with MAI in certain retinal range,and partialΔRPRE is closely associated with ΔSER and ΔAL.

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.

Energy Efficient and Intelligent Mosquito Repellent Fuzzy Control System

Mosquitoes are of great concern for occasionally carrying noxious diseases(dengue,malaria,zika,and yellow fever).To control mosquitoes,it is very crucial to effectively monitor their behavioral trends and presence.Traditional mosquito repellent works by heating small pads soaked in repellant,which then diffuses a protected area around you,a great alternative to spraying yourself with insecticide.But they have limitations,including the range,turning them on manually,and then waiting for the protection to kick in when the mosquitoes may find you.This research aims to design a fuzzy-based controller to solve the above issues by automatically determining a mosquito repellent’s speed and active time.The speed and active time depend on the repellent cartridge and the number of mosquitoes.The Mamdani model is used in the proposed fuzzy system(FS).The FS consists of identifying unambiguous inputs,a fuzzification process,rule evaluation,and a defuzzification process to produce unambiguous outputs.The input variables used are the repellent cartridge and the number of mosquitoes,and the speed of mosquito repellent is used as the output variable.The whole FS is designed and simulated using MATLAB Simulink R2016b.The proposed FS is executed and verified utilizing a microcontroller using its pulse width modulation capability.Different simulations of the proposed model are performed in many nonlinear processes.Then,a comparative analysis of the outcomes under similar conditions confirms the higher accuracy of the FS,yielding a maximum relative error of 10%.The experimental outcomes show that the root mean square error is reduced by 67.68%,and the mean absolute percentage error is reduced by 52.46%.Using a fuzzy-based mosquito repellent can help maintain the speed of mosquito repellent and control the energy used by the mosquito repellent.

Modeling and Analysis of Airlift System Operating in Three-Phase Flow

Based on the momentum theorem, the fluid governing equation in a lifting pipe is proposed by use of the method combining theoretical analysis with empirical correlations related to the previous research, and the performance of an airlift pump can be clearly characterized by the triangular relationship among the volumetric flux of air, water and solid particles, which are obtained respectively by using numerical calculation. The meso-scale river sand is used as tested particles to examine the theoretical model. Results of the model are compared with the data in three-phase flow obtained prior to the development of the present model, by an independent experimental team that used the physical conditions of the present approach. The analytical error can be controlled within 12% for predicting the volumetric flux of water and is smaller than that （±16%） of transporting solid particles in three-phase flow. The experimental results and computations are in good agreement for air-water two-phase flow within a margin of ±8%. Reasonable agreement justifies the use of the present model for engineering design purposes.

A rigorous criterion to identify the validity of the Born approximation

This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.

Nonlinear combined forecasting model based on fuzzy adaptive variable weight and its application

In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using conceptions of the relative error,the change tendency of the forecasted object,gray basic weight and adaptive control coefficient on the basis of the method of fuzzy variable weight.Based on Visual Basic 6.0 platform,a fuzzy adaptive variable weight combined forecasting and management system was developed.The application results reveal that the forecasting precisions from the new nonlinear combined forecasting model are higher than those of other single combined forecasting models and the combined forecasting and management system is very powerful tool for the required decision in complex industry system.

Reliability Analysis of Numerical Simulation of Sea-Crossing Bridge Deformation Under Wave Forces

To study on the numerical simulation calculation reliability of sea-crossing bridge under complex wave forces,the paper applied GPS deformation monitoring and numerical simulation calculation by researching Qingdao Jiaozhou Bay Sea-Crossing Bridge.The db3 wavelet three-layer decomposition was used on the horizontal movement of the sea-crossing bridge and the wind speed of the waves to analyze their correlation.The complex wave forces value of Qingdao Jiaozhou Bay Sea-Crossing Bridge was loaded on FLAC3D software successfully to make numerical simulation calculation of bridge deformation.Since the accuracy of the GPS deformation monitoring reaches millimeter level,it was used to monitor the exact value of the bridge deformation to judge the reliability of numerical simulation.The relative errors of displacement in X,Y and Z directions were between 33%and 41%through comparison.It could be seen that the numerical simulation error was relatively large,which was mainly due to various environmental factors and the deviation of applied wave forces.However,numerical simulation generally reflects the deformation law of the sea-crossing bridge under complex wave forces,providing an effectively technical support for the safe operation assessment of the sea-crossing bridge.

Explicit Solution to the Wave Dispersion Equation with Higher Accuracy

Based on the previous study results, two higher accuracy explicit solutions to the dispersion equation for wave length are presented in this paper. These two solutions have an accuracy of 0. 1% over all wave lengths, which is sufficiently complete for practical application. At the same time, several previous explicit solutions also have been reviewed and compared herein. In comparison with accuracy, the results show that the present two solutions are as good as Wu and Thornton＇s solution （which has a good accuracy over all wave lengths, but its calculation formula is so complex that it is hard to be used with a hand calculator）, and are better than the other solutions, they may be rather useful in practical calculation with a hand calculator or computer.

Electronic Noses Using Quantitative Artificial Neural Network

The present paper covers a new type of electronic nose (e-nose) with a four-sensor array, which has been applied to detecting gases quantitatively in the presence of interference. This e-nose has adapted fundamental aspects of relative error (RE) in changing quantitative analysis into the artificial neural network (ANN). Thus, both the quantitative and the qualitative requirements for ANN in implementing e-nose can be satisfied. In addition, the e-nose uses only 4 sensors in the sensor array, and can be designed for different usages simply by changing one or two sensor(s). Various gases were tested by this kind of e-nose, including alcohol vapor, CO, iiquefied-petrol-gas and CO2. Satisfactory quantitative results were obtained and no qualitative mistake in prediction was observed for the samples being mixed with interference gases.

Industrial Food Quality Analysis Using New k-Nearest-Neighbour methods

The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of Near-Infrared Reflectance(NIR)analysis is practical,relatively easy to implement,and becoming one of the most popular methods for conducting food quality based on NIR data.The k-NN is often named k nearest neighbor classifier when it is used for classifying categorical variables,while it is called k-nearest neighbor regression when it is applied for predicting noncategorical variables.The objective of this paper is to use the functional Near-Infrared Reflectance(NIR)spectroscopy approach to predict some chemical components with some modern statistical models based on the kernel and k-Nearest Neighbour procedures.In this paper,three NIR spectroscopy datasets are used as examples,namely Cookie dough,sugar,and tecator data.Specifically,we propose three models for this kind of data which are Functional Nonparametric Regression,Functional Robust Regression,and Functional Relative Error Regression,with both kernel and k-NN approaches to compare between them.The experimental result shows the higher efficiency of k-NN predictor over the kernel predictor.The predictive power of the k-NN method was compared with that of the kernel method,and several real data sets were used to determine the predictive power of both methods.

Interval of effective time-step size for the numerical computation of nonlinear ordinary differential equations

The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.

AN IMPROVED AGING-PREDICT SCHEME BASED ON SYMMETRICAL NOR GATE

Transistor aging has become the most important factor affecting the integrated circuit reliability.There is detection error caused by stacking effect in the stability checker in the previous respective aging sensors.An improved prediction aging sensor scheme is proposed using symmetrical NOR gate.Simulation experiments show the improved method eliminates prediction error caused by stacking effect.Layout area overhead is 4.65%and 7.06%compared to two respective sensor structures.

Parametric sensitivity analysis of bearing characteristics of single DOF autonomous system of magnetic-liquid double suspension bearing

The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the method of linear and nonlinear treatment,the mathematical expression and parameters sensitivity of relative error of stiffness and damping are presented.Finally,the main factors of magnetic-liquid double suspension bearing(MLDSB)are analyzed,and the influence on bearing performance indicators of single DOF nonlinear autonomous bearing system of main factors is revealed.The results show that linear stiffness/damping is the first part of equivalent stiffness/damping,and the second and third parts are high order minor term of Tayor series transform.The film thickness,the magnetic-liquid proportionality coefficient,the mass of rotor are the major influence factor of the bearing performance.The research can provide the theoretical reference for the design and nonlinear analysis of MLDSB.

Classification of Coal Resources Using Drill Hole Spacing Analysis （DHSA）

The classification of coal resources generally is based on geometric factors and the complexity of geological structures. The classification has not considered coal quality factors such as ash content, sulphur content, caloric value. The development of international classification standards has required a geostatistical analysis for the estimation and classification of coal resources. The purpose of this research is to apply geostatistics method to determine optimal drill hole distance, and to analyze classification of coal resource based on data of coal quality and quantity. Based on global estimation variance （GEV） approach from geostatistics, relative error value was obtained. Drill hole spacing analysis （DHSA） results in optimal drill hole spacing on each coal seam for the coal resources classification. Estimation using kriging block results in the value of kriging relative error. Coal resources classification was based on relative error of 0-10% for measured resources, 10-20% for indicated resources and 〉 20% for inferred resources. Based on a case study in a coal field consisting of three coal seams, the geostatistical approach produced the smallest distance on seam-3 as the optimal borehole range in the research area. This classification yields a greater area of influence than the SNI standard on simple geological complexity.

Relation between the Actual and Estimated Maximum Ground Level Concentration of Air Pollutant and Its Downwind Locations

In this work we used the Gaussian plume model to calculate the actual maximum ground level concentration (MGLC) of air pollutant and its downwind location by using different systems of dispersion parameters and for different stack heights. An approximate formula for the prediction of downwind position that produces the MGLC of a pollutant based on the Gaussian formula was derived for different diffusion parameters. The derived formula was used to calculate the approximate MGLC. The actual and estimated values are presented in tables. The comparison between the actual and estimated values was investigated through the calculation of the relative errors. The values of the relative errors between the actual and estimated MGLC lie in the range from: 0 to 70.2 and 0 to 1.6 for Pasquill Gifford system and Klug system respectively. The errors between the actual and estimated location of the MGLC lies in the range from: 0.2 to 227 and 0.7 to 9.4 for Pasquill Gifford system and Klug system respectively.