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An enhanced training algorithm for multilayer neural networks based on reference output of hidden layer

NEURAL COMPUTING & APPLICATIONS 1999年第3期8卷 218-225页

作者： Li, Y Rad, AB Peng, W Hong Kong Polytech Univ Dept Elect Engn Kowloon Peoples R China Flinders Univ S Australia Sch Engn Adelaide SA 5001 Australia

In this paper, the authors propose a new training algorithm which does nor only rely upon the training samples, but also depends upon the output of the hidden layer. We adjust both the connecting weights and outputs of the hidden layer based on Least Square Backpropagation (LSB) algorithm. A set of 'required' outputs of the hidden layer is added to the input sets through a feedback path to accelerate the convergence speed. The numerical simulation results have demonstrated that the algorithm is better than conventional BP, Quasi-Newton BFGS (an alternative to the conjugate gradient methods for fast optimisation) and LSB algorithms in terms of convergence speed and training error. The proposed method does not suffer from the drawback of the LSB algorithm, for which the training error cannot be further reduced after three iterations.

关键词： Backpropagation BFGS Quasi-Newton algorithm conjugate gradient algorithm least squares multilayer neural networks

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FAST TRANSFORM BASED PRECONDITIONERS FOR TOEPLITZ EQUATIONS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1995年第2期16卷 628-645页

作者： BOMAN, E KOLTRACHT, I UNIV CONNECTICUT U9STORRSCT 06269

We present a new preconditioner for n x n symmetric, positive definite Toeplitz, systems. This preconditioner is an element of the n-dimensional vector space of matrices that are diagonalized by the discrete sine transform. Conditions are given for which the preconditioner is positive definite and for which the preconditioned system has asymptotically clustered eigenvalues. The diagonal form of the preconditioner can be calculated in O(n log(n)) operations if n = 2(k) - 1. Thus only n additional parameters need be stored. Moreover, complex arithmetic is not needed. To use the preconditioner effectively, we develop a new technique for computing a fast convolution using the discrete sine transform (also requiring only real arithmetic). The results of numerical experimentation with this preconditioner are presented. Our preconditioner is comparable, and in some cases superior, to the standard circulant preconditioner of Tony Chan. Possible generalizations for other fast transforms are also indicated.

关键词： TOEPLITZ MATRIX conjugate gradient algorithm PRECONDITIONER FAST SINE TRANSFORM

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Inversion of spectral emission measurements to reconstruct the temperature profile along a blackbody optical fiber thermometer

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INVERSE PROBLEMS IN ENGINEERING 2003年第6期11卷 495-513页

作者： Barker, DG Jones, MR Brigham Young Univ Dept Mech Engn CTB 435 Provo UT 84602 USA

A blackbody optical fiber thermometer consists of an optical fiber whose sensing tip is given a metallic coating. The sensing tip of the fiber forms an isothermal cavity, and the emission from this cavity is approximately equal to the emission from a blackbody. Standard two-color optical fiber thermometry involves measuring the spectral intensity at the end of the fiber at two wavelengths. The temperature at the sensing tip of the fiber can then be inferred using Planck's law and the ratio of the spectral intensities. If, however, the length of the optical fiber is exposed to elevated temperatures, erroneous temperature measurements will occur due to emission by the fiber. The results presented in this article show it is possible to use additional spectral measurements to account for emission by the fiber and accurately measure the tip temperature. In addition, the proposed technique can be used to obtain an estimate of the temperature profile along the fiber.

关键词： optical fiber thermometry conjugate gradient algorithm

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An Efficient Phenomenological Inversion Method for Reconstruction of Crack Depth Profile in a Metal From ACFM Probe Output Signals

IEEE OPEN JOURNAL OF INSTRUMENTATION AND MEASUREMENT

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IEEE OPEN JOURNAL OF INSTRUMENTATION AND MEASUREMENT 2022年 1卷

作者： Heidari, Teimour Sadeghi, Seyed Hossein Hesamedin Amirkabir Univ Technol Dept Elect Engn Tehran 15914 Iran

This article proposes an efficient phenomenological inversion method to determine the depth profile of a surface-breaking crack in a metal from the output signal of an alternating current field measurement (ACFM) probe. The proposed method utilizes a conjugate gradient algorithm to minimize an objective function, representing the difference between the probe predicted and actual signals in an iterative manner. The objective function is derived explicitly in terms of crack depth variables by considering a polynomial function for the field distribution in the depth direction and applying appropriate Green's functions. This approach enhances the accuracy and computational efficiency of the inversion process, regardless of the choice of the initial crack depth profile or the presence of noise in the measurement system. The validity and efficiency of the proposed method are demonstrated by comparing the reconstructed depth profiles of several simulated and machine-made cracks with their actual data, and those obtained using the conventional phenomenological approach based on an efficient stochastic optimization scheme along with a fast pseudo-analytic ACFM probe output simulator.

关键词： conjugate gradient algorithm depth profile eddy current (EC) testing fatigue crack phenomenological inversion method

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Application of 3-algorithm ANN programming to predict the strength performance of hydrated-lime activated rice husk ash treated soil

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MULTISCALE AND MULTIDISCIPLINARY MODELING EXPERIMENTS AND DESIGN 2021年第4期4卷 259-274页

作者： Onyelowe, Kennedy C. Iqbal, Mudassir Jalal, Fazal E. Onyia, Michael E. Onuoha, Ifeanyichukwu C. Michael Okpara Univ Agr Dept Civil Engn Umudike Nigeria Kampala Int Univ Dept Civil & Mech Engn Kampala Uganda Shangai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn Shanghai Key Lab Digital Maintenance Bldg & Infra Shanghai Peoples R China Shanghai Jiao Tong Univ Dept Civil Engn Shanghai Peoples R China Univ Nigeria Fac Engn Dept Civil Engn Nsukka Nigeria Fed Univ Technol Owerri Dept Environm Technol Owerri Nigeria

Artificial neural network (ANN) method has been applied in the present work to predict the California bearing ratio (CBR), unconfined compressive strength (UCS), and resistance value (R) of expansive soil treated with recycled and activated composites of rice husk ash. Pavement foundations suffer from poor design and construction, poor material handling and utilization and management lapses. The evolutions of soft computing techniques have produced various algorithms developed to overcome certain lapses in performance. Three of such algorithms from ANN are Levenberg-Muarquardt Backpropagation (LMBP), Bayesian Programming (BP), and conjugate gradient (CG) algorithms. In this work, the expansive soil classified as A-7-6 group soil was treated with hydrated-lime activated rice husk ash (HARHA) in varying proportions between 0.1 and 12% by weight of soil at the rate of 0.1% to produce 121 datasets. These were used to predict the behavior of the soil's strength parameters (CBR, UCS and R) utilizing the evolutionary hybrid algorithms of ANN. The predictor parameters were HARHA, liquid limit (w(L)), (plastic limit (w(P)), plasticity index (I-P), optimum moisture content (w(OMC)), clay activity (A(C)), and (maximum dry density (delta(max)). A multiple linear regression (MLR) was also conducted on the datasets in addition to ANN to serve as a check and linear validation mechanism. MLR and ANN methods agreed in terms of performance and fit at the end of computing and iteration. However, the response validation on the predicted models showed a good correlation above 0.9 and a great performance index. Comparatively, the LMBP algorithm yielded an accurate estimation of the results in lesser iterations than the Bayesian and the CG algorithms, while the Bayesian technique produced the best result with the required number of iterations to minimize the error. And finally, the LMBP algorithm outclassed the other two algorithms in terms of the predicted models' accuracy.

关键词： Soft computing Artificial intelligence Artificial neural network (ANN) Machine learning in geotechnics Back-propagation algorithm Levenberg– muarquardt algorithm Bayesian algorithm conjugate gradient algorithm Sustainable construction materials

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An acceleration algorithm for image reconstruction based on continuous-discrete mapping model

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OPTICAL REVIEW 2000年第2期7卷 132-137页

作者： Yamaya, T Obi, T Yamaguchi, M Ohyama, N Tokyo Inst Technol Imaging Sci & Engn Lab Midori Ku Yokohama Kanagawa 2268503 Japan

In image reconstruction for X-ray computed tomography, images reconstructed by filtered backprojection (FBP) include systematic errors because the FBP method does not take into account some of the properties of the actual imaging system such as the divergence of X-ray beam. One solution to this problem is to use algebraic reconstruction methods, such as generalized analytic reconstruction from discrete samples and natural pixel decomposition. However, in the process of reconstruction using these methods, it is necessary to solve the linear algebraic equations which have a large coefficient matrix. In this paper, we propose a method to accelerate the iteration solving these equations by preconditioning the coefficient matrix using a polynomial function. The results of the computer simulations show the effectiveness of the proposed method.

关键词： computed tomography GARDS NPD continuous-discrete mapping model conjugate gradient algorithm preconditioning acceleration

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An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables

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SIAM JOURNAL ON OPTIMIZATION 1998年第2期8卷 532-560页

作者： Pytlak, R Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn London SW7 2BT England

In this paper we present a new conjugate gradient algorithm for nonlinear programming problems with simple bounds on the variables. The method is an extension of our conjugate gradient algorithm described in [R. Pytlak, IMA J. Numer. Anal., 14 (1994), pp. 443-460]. The simple constraints on the variables are treated by a projection. Under mild assumptions the method is globally convergent. The algorithm has the property whereby many constraints can leave or enter an active set of constraints at one iteration. If the strict complementarity condition is satisfied, the active set at a solution is identified in a finite number of iterations. The algorithm has been tested on problems with more than 10,000 variables.

关键词： conjugate gradient algorithm box constraints projection large-scale problems

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Improved Particle Swarm Optimization-Based Artificial Neural Network for Rainfall-Runoff Modeling

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JOURNAL OF HYDROLOGIC ENGINEERING 2014年第7期19卷 1320-1329页

作者： Asadnia, Mohsen Chua, Lloyd H. C. Qin, X. S. Talei, Amin Nanyang Technol Univ DHI NTU Water & Environm Res Ctr & Educ Hub Singapore 639798 Singapore Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore Monash Univ Sch Engn Bandar Sunway 46150 Selangor Darul Malaysia

This paper presents the application of an improved particle swarm optimization (PSO) technique for training an artificial neural network (ANN) to predict water levels for the Heshui Watershed, China. Daily values of rainfall and water levels from 1988 to 2000 were first analyzed using ANNs trained with the conjugate gradient, gradient descent, and Levenberg-Marquardt neural network (LM-NN) algorithms. The best results were obtained from the LM-NN, and these results were then compared with those from PSO-based ANNs, including the conventional PSO neural network (CPSONN) and the improved PSO neural network (IPSONN) with passive congregation. The IPSONN algorithm improves PSO convergence by using the selfish herd concept in swarm behavior. The results show that the PSO-based ANNs performed better than the LM-NN. For models run using a single parameter (rainfall) as input, the root mean square error (RMSE) of the testing data set for IPSONN was the lowest (0.152 m) compared to those for CPSONN (0.161 m) and LM-NN (0.205 m). For multiparameter (rainfall and water level) inputs, the RMSE of the testing data set for IPSONN was also the lowest (0.089 m) compared to those for CPSONN (0.105 m) and LM-NN (0.145 m). The results also indicate that the LM-NN model performed poorly in predicting the low and peak water levels in comparison to the PSO-based ANNs. Moreover, the IPSONN model was superior to CPSONN in predicting extreme water levels. Lastly, IPSONN had a quicker convergence rate compared to CPSONN. (C) 2014 American Society of Civil Engineers.

关键词： Rainfall-runoff modeling Passive particle swarm optimization Artificial neural network Levenberg-Marquardt algorithm conjugate gradient algorithm gradient descent algorithm

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Classification of GPS Satellites Using Improved Back Propagation Training algorithms

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WIRELESS PERSONAL COMMUNICATIONS 2013年第2期71卷 789-803页

作者： Azami, Hamed Mosavi, Mohammad-Reza Sanei, Saeid Iran Univ Sci & Technol Dept Elect Engn Tehran *** Iran Univ Surrey Fac Engn & Phys Sci Dept Comp Guildford GU2 5XH Surrey England

Factor geometric dilution of precision (GDOP) is an indicator that shows the quality of GPS positioning and has often been used for choosing suitable satellite's subset from at least 24 orbited existing satellites. The calculation of GPS GDOP is a time-consuming task which can be done by solving measurement equations with complicated matrix transformation and inversion. In order to decrease this computational burden, in this research the artificial neural network (ANN) has been used. Although the basic back propagation (BP) is the most popular ANN algorithm and can be used in the estimators, detectors or classifiers, it is too slow for practical problems and its performance is not satisfactory in many cases. To overcome this problem, six algorithms, namely, BP with adaptive learning rate and momentum, Fletcher-Reeves conjugate gradient algorithm (CGA), Polak-Ribikre CGA, Powell-Beale CGA, scaled CGA, and resilient BP have been proposed to reduce the convergence time of the basic BP. The simulation results show that resilient BP, compared with other methods, has greater accuracy and calculation time. The resilient BP can improve the classification accuracy from 93.16 to 98.02 % accuracy by using the GPS GDOP measurement data.

关键词： GPSGDOP Classification Artificial neural network Basic back propagation Resilient back propagation conjugate gradient algorithm

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Numerical Estimation of the Inverse Eigenvalue Problem for a Weighted Helmholtz Equation

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JOURNAL OF SCIENTIFIC COMPUTING 2023年第1期96卷 1-31页

作者： Zhang, Zhengfang Gao, Xiangjing Cheng, Xiaoliang Hangzhou Dianzi Univ Coll Sci Hangzhou 310018 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The inverse eigenvalue problem for a weighted Helmholtz equation is investigated. Based on the finite spectral data, the density function is estimated. The inverse problem is formulated as a least squared functional with respect to the density function, with a L(2 )regularity term. The continuity of the eigenpairs with respect to the density is proved. Mathematical properties of the continuous and the discrete optimization problems are established. A conjugate gradient algorithm is proposed. Numerical results for 1D and 2D inverse eigenvalue problem of the weighted Helmholtz equation are presented to illustrate the effectiveness and efficiency of the proposed algorithm.

关键词： Inverse eigenvalue problem Weighted Helmholtz equation conjugate gradient algorithm Finite element method

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