scholarly journals Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1155
Author(s):  
Chen ◽  
Huang
Keyword(s):  
Choquet Integral ◽  
Least Square Method ◽  
Least Square ◽  
Integral Model ◽  
Fuzzy Measures ◽  
Proposed Model ◽  
Choquet Integrals ◽  
The Mean ◽  
Input Variables ◽  
Least Mean Squares Algorithm

: Identifying the fuzzy measures of the Choquet integral model is an important component in resolving complicated multi-criteria decision-making (MCDM) problems. Previous papers solved the above problem by using various mathematical programming models and regression-based methods. However, when considering complicated MCDM problems (e.g., 10 criteria), the presence of too many parameters might result in unavailable or inconsistent solutions. While k-additive or p-symmetric measures are provided to reduce the number of fuzzy measures, they cannot prevent the problem of identifying the fuzzy measures in a high-dimension situation. Therefore, Sugeno and his colleagues proposed a hierarchical Choquet integral model to overcome the problem, but it required the partition information of the criteria, which usually cannot be obtained in practice. In this paper, we proposed a GA-based heuristic least mean-squares algorithm (HLMS) to construct the hierarchical Choquet integral and overcame the above problems. The genetic algorithm (GA) was used here to determine the input variables of the sub-Choquet integrals automatically, according to the objective of the mean square error (MSE), and calculated the fuzzy measures with the HLMS. Then, we summed these sub-Choquet integrals into the final Choquet integral for the purpose of regression or classification. In addition, we tested our method with four datasets and compared these results with the conventional Choquet integral, logit model, and neural network. On the basis of the results, the proposed model was competitive with respect to other models.

Thermal Error Robust Modeling for High-Speed Motorized Spindle

2012 ◽  
Vol 466-467 ◽  
pp. 961-965 ◽  
Author(s):  
Chun Li Lei ◽  
Zhi Yuan Rui ◽  
Jun Liu ◽  
Li Na Ren
Keyword(s):  
High Speed ◽  
Thermal Error ◽  
Least Square Method ◽  
Information Criterion ◽  
Least Square ◽  
Proposed Model ◽  
Nc Machine ◽  
Input Variables ◽  
Thermal Error Model ◽  
Multivariate Autoregressive

To improve the manufacturing accuracy of NC machine tool, the thermal error model based on multivariate autoregressive method for a motorized high speed spindle is developed. The proposed model takes into account influences of the previous temperature rise and thermal deformation (input variables) on the thermal error (output variables). The linear trends of observed series are eliminated by the first difference. The order of multivariate autoregressive (MVAR) model is selected by using Akaike information criterion. The coefficients of the MVAR model are determined by the least square method. The established MVAR model is then used to forecast the thermal error and the experimental results have shown the validity and robustness of this model.

Prediction of Comprehensive Thermal Error of a Preloaded Ball Screw on a Gantry Milling Machine

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Kuo Liu ◽  
Haibo Liu ◽  
Te Li ◽  
Yongqing Wang ◽  
Mingjia Sun ◽  
...  
Keyword(s):  
Thermal Field ◽  
Thermal Characteristics ◽  
Thermal Error ◽  
Least Square Method ◽  
High Accuracy ◽  
Least Square ◽  
Ball Screw ◽  
Milling Machine ◽  
Thermal Fields ◽  
Proposed Model

The conception of the comprehensive thermal error of servo axes is given. Thermal characteristics of a preloaded ball screw on a gantry milling machine is investigated, and the error and temperature data are obtained. The comprehensive thermal error is divided into two parts: thermal expansion error ((TEE) in the stroke range) and thermal drift error ((TDE) of origin). The thermal mechanism and thermal error variation of preloaded ball screw are expounded. Based on the generation, conduction, and convection theory of heat, the thermal field models of screw caused by friction of screw-nut pairs and bearing blocks are derived. The prediction for TEE is presented based on thermal fields of multiheat sources. Besides, the factors influencing TDE are analyzed, and the model of TDE is established based on the least square method. The predicted thermal field of the screw is analyzed. The simulation and experimental results indicate that high accuracy stability can be obtained using the proposed model. Moreover, high accuracy stability can still be achieved even if the moving state of servo axis changes randomly, the screw is preloaded, and the thermal deformation process is complex. Strong robustness of the model is verified.

Application of Photoelectric Sensor in Vehicle Power Control System

2020 ◽  
Vol 15 (6) ◽  
pp. 700-706
Author(s):  
Yifan Zhao ◽  
Mengyu Wang ◽  
Kai Wang
Keyword(s):  
Power Control ◽  
Electric Energy ◽  
Least Square Method ◽  
Least Square ◽  
Motor Speed ◽  
Time Calculation ◽  
The Mean ◽  
The Difference ◽  
Artificial Neural Network Ann ◽  
Mean Square Errors

Due to its characteristics of using clean electric energy and bringing no damage to the environment, electric vehicles (EVs) have become a new developmental direction for the automotive industry. Its reliability issues have also attracted the attention of experts and professionals. In the field of automotive power control, from the perspective of motor control, this study uses the photoelectric sensors (PSs) as the research objects and elaborates on the measurement principles of motor speed with PSs. Meanwhile, a diagnosis scheme is proposed for various faults in the measurement. Among them, the measurement speed is converted by the photoelectric signal, and the measured waveform is amplified. In the fault detection process, the Radial Basis Function (RBF) artificial neural network (ANN) is analyzed. By using this method, the difference in the motor speed detected by the sensor is calculated to determine the cause of the failure. The test uses the least-square method to compare the tested motor speed with the actual motor speed. The results show that PSs can measure the motor speed of EVs. As for the motor failures, the mean square errors (MSEs) of motor speeds generated by different faults are compared to determine the fault points according to the speed changes. In addition, the cause of motor failure can be determined by the real-time calculation of the speed differences. The above tests fully prove the effectiveness of measuring the speed of electric motors by PSs; therefore, PSs have broad application prospects in vehicle power control systems.

scholarly journals Econometric Estimation of Production Function with Applications

2019 ◽  
pp. 57-61 ◽  
Author(s):  
Awoingo Adonijah Maxwell ◽  
Isaac Didi Essi
Keyword(s):  
Monte Carlo ◽  
Mean Square Error ◽  
Production Function ◽  
Least Square ◽  
Production Model ◽  
Mean Square ◽  
Unknown Parameters ◽  
Data Generating Process ◽  
The Mean ◽  
Input Variables

This study focuses on Monte Carlo Methods in parameter estimation of production function. The ordinary least square (OLS) method is used to estimate the unknown parameters. The Monte Carlo simulation methods are used for the data generating process. The Cobb-Douglas production model with multiplicative error term is fitted to the data generated. From tables 1.1 to 1.3, the mean square error (MSE) of 1 are 0.007678, 0.001972 and 0.001253 respectively for sample sizes 20, 40 and 80. Our finding showed that the mean square error (MSE) value varies with the sum of the powers of the input variables.

SIMPLIFIED FUZZY INFERENCE RULE-BASED GENETICALLY OPTIMIZED HYBRID FUZZY NEURAL NETWORKS

2008 ◽  
Vol 16 (02) ◽  
pp. 245-274 ◽  
Author(s):  
BYOUNG-JUN PARK ◽  
WITOLD PEDRYCZ ◽  
SUNG-KWUN OH
Keyword(s):  
Neural Networks ◽  
Fuzzy Inference ◽  
Inference Rule ◽  
Least Square Method ◽  
Fuzzy Neural Networks ◽  
Least Square ◽  
Rule Based ◽  
Fuzzy Partition ◽  
Fuzzy Neural ◽  
Input Variables

In this study, we introduce an advanced architecture of genetically optimized Hybrid Fuzzy Neural Networks (gHFNN) and develop a comprehensive design methodology supporting their construction. A series of numeric experiments is included to illustrate the performance of the networks. The construction of gHFNN exploits fundamental technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the gHFNNs results from a synergistic usage of the genetic optimization-driven hybrid system generated by combining Fuzzy Neural Networks (FNN) with Polynomial Neural Networks (PNN). In this tandem, a FNN supports the formation of the condition part of the rule-based structure of the gHFNN. The conclusion part of the gHFNN is designed using PNNs. We distinguish between two types of the simplified fuzzy inference rule-based FNN structures showing how this taxonomy depends upon the type of a fuzzy partition of input variables. As to the conclusion part of the gHFNN, the development of the PNN dwells on two general optimization mechanisms: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the gHFNN, we experimented with three representative numerical examples. A comparative analysis demonstrates that the proposed gHFNN come with higher accuracy as well as superb predictive capabilities when compared with other neurofuzzy models.

The Research on the Methods of the Aero Engine Blades Evaluation

2013 ◽  
Vol 333-335 ◽  
pp. 322-326
Author(s):  
Wen Qi Ma ◽  
Shu Gui Liu
Keyword(s):  
Engine Performance ◽  
Least Square Method ◽  
Chord Length ◽  
Least Square ◽  
Trailing Edge ◽  
Inspection Method ◽  
Maximum Thickness ◽  
Spline Fitting ◽  
Aero Engine ◽  
The Mean

As an important part of the aero engine, the quality of the blade seriously affects the engine performance, so the inspection method of the blade is significant. Based on the research of the HB 5647-98<<to mark dimensions, tolerances of the vane type and the surface roughness of the blade body>> , this paper concludes different evaluation methods of the blade. The main evaluated parameters include the leading and trailing edge radius, the chord length, the maximum thickness of blade profile, the mean camber line, and the surface twist and so on. Here we mainly discuss the previous three terms. The least square method is adopted to fit the arc of the leading and trailing edge; introduce the projection method to calculate the chord length; at last, we employ the spline fitting method to get the mean line and then obtain the maximum thickness of the blade section.

A Camera Calibration Method Based on Free Points

2011 ◽  
Vol 130-134 ◽  
pp. 1885-1888
Author(s):  
Jing Lei Zhang ◽  
Kai Bo Fan ◽  
Yan Jiao Wang
Keyword(s):  
Standard Deviation ◽  
Ccd Camera ◽  
Least Square Method ◽  
Calibration Method ◽  
Initial Guess ◽  
Least Square ◽  
Camera Model ◽  
Extrinsic Parameters ◽  
The Mean ◽  
Constraint Method

A new accurate calibrating technique for intrinsic parameters and extrinsic parameters of CCD camera is described. The camera model is derived by the pinhole projection theory. Then other parameters of the model are resolved under the radial alignment constraints and orthogonal constraints. In order to get a fine initial guess for the nonlinear searching solution, the least square method is introduced, and finally uses radial alignment constraint method to get the results. The experimental results show that the mean absolute differences in x direction and y direction are 0.0070 and 0.1430 separately while the standard deviation are 0.5006 and 1.2046 separately.

scholarly journals Choquet Integral of Fuzzy-Number-Valued Functions: The Differentiability of the Primitive with respect to Fuzzy Measures and Choquet Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Zengtai Gong ◽  
Li Chen ◽  
Gang Duan
Keyword(s):  
Integral Equations ◽  
Real Line ◽  
Fuzzy Number ◽  
Laplace Transformation ◽  
Choquet Integral ◽  
Fuzzy Measures ◽  
Nonadditive Measure ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Interval Valued

This paper deals with the Choquet integral of fuzzy-number-valued functions based on the nonnegative real line. We firstly give the definitions and the characterizations of the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on the nonadditive measure. Furthermore, the operational schemes of above several classes of integrals on a discrete set are investigated which enable us to calculate Choquet integrals in some applications. Secondly, we give a representation of the Choquet integral of a nonnegative, continuous, and increasing fuzzy-number-valued function with respect to a fuzzy measure. In addition, in order to solve Choquet integral equations of fuzzy-number-valued functions, a concept of the Laplace transformation for the fuzzy-number-valued functions in the sense of Choquet integral is introduced. For distorted Lebesgue measures, it is shown that Choquet integral equations of fuzzy-number-valued functions can be solved by the Laplace transformation. Finally, an example is given to illustrate the main results at the end of the paper.

scholarly journals A regression approach for prediction of Youtube views

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Lau Tian Rui ◽  
Zehan Afizah Afif ◽  
R. D. Rohmat Saedudin ◽  
Aida Mustapha ◽  
Nazim Razali
Keyword(s):  
Least Square Method ◽  
Absolute Error ◽  
Descent Method ◽  
Least Square ◽  
Gradient Descent Method ◽  
Ordinary Least Square ◽  
The Public ◽  
Dependent Variables ◽  
Regression Approach ◽  
The Mean

YouTube has grown to be the number one video streaming platform on Internet and home to millions of content creator around the globe. Predicting the potential amount of YouTube views has proven to be extremely important for helping content creator to understand what type of videos the audience prefers to watch. In this paper, we will be introducing two types of regression models for predicting the total number of views a YouTube video can get based on the statistic that are available to our disposal. The dataset we will be using are released by YouTube to the public. The accuracy of both models are then compared by evaluating the mean absolute error and relative absolute error taken from the result of our experiment. The results showed that Ordinary Least Square method is more capable as compared to the Online Gradient Descent Method in providing a more accurate output because the algorithm allows us to find a gradient that is close as possible to the dependent variables despite having an only above average prediction.

Prediction of Log-Transmissivity

1995 ◽  
Vol 26 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Steen Christensen
Keyword(s):  
Prediction Error ◽  
Regression Line ◽  
Specific Capacity ◽  
Covariance Structure ◽  
Prediction Method ◽  
Least Square Method ◽  
Least Square ◽  
Practical Applications ◽  
Well Efficiency ◽  
The Mean

The log-transmissivity may in many cases be predicted from the log-transformed specific capacity of wells by applying a linear statistical model. The coefficients of the linear equation can be estimated by the least-square method. It is shown that if the estimated slope of the line differs from unity then it may indicate that the specific capacity is correlated with the well efficiency. The above prediction method is applied to case studies of aquifers in three different formations: the prediction should not be used for a homogeneous fluvioglacial formation because the variance of the well efficiency dominates the variance of the transmissivity; the prediction is fair for a heterogeneous fluvioglacial formation; and the prediction is poor for a homogeneous limnic formation. In the study of the first formation a correlation between specific capacity and well efficiency can be identified directly from the slope of the regression line. If the predictor values are taken from the drillers log then the standard error of prediction in all the cases is 0.35. This seems to be unacceptable in most practical applications. However, if one needs to predict the mean of a domain and the domain contains a number of observations of the predictor, then the averaging will reduce the prediction error. The averaging procedure ought to take the covariance structure of the variables into consideration.

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