A new constrained learning algorithm for function approximation by encoding a priori information into feedforward neural networks

Han, Fei; Huang, De-Shuang

doi:10.1007/s00521-007-0135-5

Cited by 54 publications

(11 citation statements)

References 15 publications

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“…The MLP is used to approximate differential equations [5,6,18,19]. In this paper, weights are denoted by reversed indexes, corresponding respectively to their output and input neuron ordinal number.…”

Section: Algorithm 1: Mlp Neural Network Approximationmentioning

confidence: 99%

Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge

Bellamine

Almansoori

Elkamel

2015

Applied Mathematics and Computation

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Section: Algorithm 1: Mlp Neural Network Approximationmentioning

confidence: 99%

Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge

Bellamine

Almansoori

Elkamel

2015

Applied Mathematics and Computation

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“…We apply the augmented Lagrange multiplier method to solve (18) and construct the augmented performance index φ(ω, b (1) , v, b (2) , λ, σ )…”

Section: B Training Algorithm Of Almnnmentioning

confidence: 99%

“…In Fig. 8(a) and (b), the ALMNN's training errors decrease more rapidly than those of DINN, and the convergent speed of ALMNN is faster because the constraints can narrow the solution space of the performance index expressed by (18) and avoid oscillating in the training process, which can quickly obtain the optimal parameters of the NN.…”

Section: A Training For the Almnn-based Nnmentioning

confidence: 99%

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Nonlinear Error Compensation for Load Cells Based on the Optimal Neural Network With an Augmented Lagrange Multiplier

Lin

Wang

et al. 2015

IEEE Trans. Instrum. Meas.

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This paper presents a new approach for compensating nonlinear errors of a load cell, based on the optimal neural network with an augmented Lagrange multiplier (ALMNN). The load cell has serious nonlinear errors, which lower the accuracy of the weighing results. In this proposed approach, first, we construct the constraints for training the neural network (NN) using the load cell's prior knowledge, i.e., the monotonic increasing property of a load cell's input-output function. Second, we create the augmented Lagrange function with a multiplier and a penalty factor to serve as an NN's performance index, and then deduce the ALMNN's detailed training algorithm. The penalty factor plays an important role in ALMNN, thus the reasonable range of numerical value is discussed in this paper. Meanwhile, the weighing principle of a strain gauge load cell is introduced and its nonlinear error model is established. Finally, the experimental results demonstrate the effectiveness of ALMNN. By comparing with the conventional data induction method (DINN, i.e., the training of NN not with the prior knowledge but only the data samples), ALMNN significantly improves the NN's generalization ability, especially in the case of lacking training samples. In addition, the applicability of ALMNN is verified by three additional experiments.Index Terms-First-order derivative constraint, Lagrange multiplier, load cell, monotonicity, neural networks (NNs), nonlinear error compensation.

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“…Second, it have not considered the network structure features as well as the involved problem properties, thus its generalization capabilities are limited. Finally, since BP algorithms are the gradient-based type learning algorithms, they converge very slowly [2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

An improved approximation approach incorporating particle swarm optimization and a priori information into neural networks

Han

Ling

Huang

2009

Neural Comput & Applic

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In this paper, an improved approach incorporating adaptive particle swarm optimization (APSO) and a priori information into feedforward neural networks for function approximation problem is proposed. It is well known that gradient-based learning algorithms such as backpropagation algorithm have good ability of local search, whereas PSO has good ability of global search. Therefore, in the improved approach, the APSO algorithm encoding the first-order derivative information of the approximated function is used to train network to near global minima. Then, with the connection weights produced by APSO, the network is trained with a modified gradient-based algorithm with magnified gradient function. The modified gradient-based algorithm can reduce inputto-output mapping sensitivity and lessen the chance of being trapped into local minima. By combining APSO with local search algorithm and considering a priori information, the improved approach has better approximation accuracy and convergence rate. Finally, simulation results are given to verify the efficiency and effectiveness of the proposed approach.

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A new constrained learning algorithm for function approximation by encoding a priori information into feedforward neural networks

Cited by 54 publications

References 15 publications

Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge

Modeling of complex dynamic systems using differential neural networks with the incorporation of a priori knowledge

Nonlinear Error Compensation for Load Cells Based on the Optimal Neural Network With an Augmented Lagrange Multiplier

An improved approximation approach incorporating particle swarm optimization and a priori information into neural networks

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