An improved third term backpropagation algorithm – inertia expanded chebyshev orthogonal polynomial

2019 ◽  
Vol 37 (3) ◽  
pp. 3795-3804
Author(s):  
Madasamy Sornam ◽  
Venkateswaran Vanitha
Keyword(s):  
Orthogonal Polynomial ◽  
Backpropagation Algorithm ◽  
Chebyshev Orthogonal Polynomial

Probability Function Estimation of Rock Random Variables Using Chebyshev Orthogonal Polynomial

2013 ◽  
Vol 351-352 ◽  
pp. 1673-1676
Author(s):  
Feng Qiang Gong ◽  
Shang Qian Hou ◽  
Ting Yu Wu
Keyword(s):  
Orthogonal Polynomial ◽  
Cumulative Distribution Function ◽  
Probability Function ◽  
Hard Rock ◽  
Cumulative Distribution ◽  
Function Estimation ◽  
Chebyshev Orthogonal Polynomial ◽  
Relative Errors ◽  
Stochastic Reliability ◽  
Probability Density Function Pdf

The Chebyshev orthogonal polynomial with sample moments (the origin moments) were used to approximate the probability density function (PDF) or cumulative distribution function (CDF) of variable (CPA method). Three examples from observed datas of uniaxial compressive strength of a kind of hard rock were presented for illustrative purposes. The results show the PDF or CDF of rock variables can be accurately derived from CPA method with sample moments. The relative errors of estimation by CPA method is much smaller than that of TDF method (PDF fitted by some standard theoretical distributions). It is suggested that the presented method can be used in stochastic reliability analysis of rock engineering.

Pengaruh Pemberian Kunyit (Curcuma domestica) terhadap Beberapa Kualitas Fisik dan Organoleptik Bakso Daging Itik

2013 ◽  
Vol 8 (1) ◽  
pp. 16-24
Author(s):  
Sari Murti ◽  
Suharyanto Suharyanto ◽  
Desia Kaharuddin
Keyword(s):  
Orthogonal Polynomial

ABSTRAKPenelitian ini bertujuan untuk mengevaluasi level kunyit yang tepat sehingga dapat meningkatkan kualitas bakso daging itik. Percobaan ini menggunakan Rancangan Acak Lengkap, yang terdiri dari empat perlakuan yaitu P0 (tanpa pemberian kunyit), P1 (pemberian kunyit taraf 2,5%), P2 (pemberian kunyit taraf 5%), dan P3 (pemberian kunyittaraf 7,5%), masing-masing perlakuan terdiri dari tiga ulangan. Hasil penelitian menunjukkan bahwa pemberian kunyit berpengaruh tidak nyata (P>0,05) terhadap variabel susut masak, daya mengikat air, pH dan tekstur bakso daging itik, tetapi nyata (P<0,05) meningkatkan skor warna, menurunkan derajat keamisan dan variabel sifat organoleptik rasa. Hasil yang berpengaruh nyata diuji lanjut menggunakan Orthogonal polynomial dengan menghasilkan persamaan linear dan kuadratik. Dari hasil penelitian disimpulkan bahwa penambahan kunyit 2,5% hingga 7,5% tidak menurunkan kualitas fisik (susut masak, pH, dan DMA). Penambahan kunyit 2,5% dapat mempertahankan cita rasa dan penerimaan umum panelis terhadap bakso daging itik.Kata kunci : Kunyit (Curcuma domestica), kualitas fisik, daging itik

Rancang Bangun Sistem Pakar Prediksi Stres Belajar Dengan Neural Network Algoritma Backpropagation

2016 ◽  
Vol 7 (2) ◽  
pp. 105-112
Author(s):  
Adhi Kusnadi ◽  
Idul Putra
Keyword(s):  
Neural Network ◽  
Expert System ◽  
Stress Level ◽  
Network Structure ◽  
Human Being ◽  
Accuracy Rate ◽  
Backpropagation Algorithm ◽  
Stress Prediction ◽  
Index Terms ◽  
Hidden Nodes

Stress will definitely be experienced by every human being and the level of stress experienced by each individual is different. Stress experienced by students certainly will disturb their study if it is not handled quickly and appropriately. Therefore we have created an expert system using a neural network backpropagation algorithm to help counselors to predict the stress level of students. The network structure of the experiment consists of 26 input nodes, 5 hidden nodes, and 2 the output nodes, learning rate of 0.1, momentum of 0.1, and epoch of 5000, with a 100% accuracy rate. Index Terms - Stress on study, expert system, neural network, Stress Prediction

A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data

2011 ◽  
Vol 291-294 ◽  
pp. 1015-1020 ◽  
Author(s):  
Chong Jin ◽  
Hong Wang ◽  
Xiao Zhou Xia
Keyword(s):  
Experimental Data ◽  
Orthogonal Polynomial ◽  
Least Square ◽  
Base Function ◽  
Concrete Material ◽  
Fitting Method ◽  
Orthogonal Base ◽  
The Matrix ◽  
Uniform Function ◽  
Curve Fitting Method

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

scholarly journals $q$ -Racah Ensemble and Discrete Painlevé Equation

2019 ◽  
Vol 2020 (24) ◽  
pp. 9797-9843 ◽  
Author(s):  
Anton Dzhamay ◽  
Alisa Knizel
Keyword(s):  
Orthogonal Polynomial ◽  
Lax Pair ◽  
Painlevé Equations ◽  
Painlevé Equation ◽  
Painleve Equations ◽  
Symmetry Structure ◽  
The One ◽  
The Relationship ◽  
Gap Probabilities ◽  
Discrete Painlevé Equation

Abstract The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlevé equations. Namely, we consider the $q$-Racah polynomial ensemble and show that the one-interval gap probabilities in this case can be expressed through a solution of the discrete $q$-P$\left (E_7^{(1)}/A_{1}^{(1)}\right )$ equation. Our approach also gives a new Lax pair for this equation. This Lax pair has an interesting additional involutive symmetry structure.

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