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Research Papers

Modified Levenberg–Marquardt Algorithm for Backpropagation Neural Network Training in Dynamic Model Identification of Mechanical Systems

[+] Author and Article Information
Ming Li

Laboratory of Intelligent Machines,
School of Energy Systems,
Lappeenranta University of Technology,
Skinnarinlankatu 34,
Lappeenranta 53850, Finland
e-mail: Ming.Li@lut.fi

Huapeng Wu

Laboratory of Intelligent Machines,
School of Energy Systems,
Lappeenranta University of Technology,
Skinnarinlankatu 34,
Lappeenranta 53850, Finland
e-mail: Huapeng.Wu@lut.fi

Yongbo Wang

Laboratory of Intelligent Machines,
School of Energy Systems,
Lappeenranta University of Technology,
Skinnarinlankatu 34,
Lappeenranta 53850, Finland
e-mail: Yongbo.Wang@lut.fi

Heikki Handroos

Laboratory of Intelligent Machines,
School of Energy Systems,
Lappeenranta University of Technology,
Skinnarinlankatu 34,
Lappeenranta 53850, Finland
e-mail: Heikki.Handroos@lut.fi

Giuseppe Carbone

Laboratory of Robotics and Mechatronics,
University of Cassino and South Latium,
Cassino (FR) 03043, Italy
e-mail: carbone@unicas.it

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 5, 2016; final manuscript received October 10, 2016; published online January 25, 2017. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 139(3), 031012 (Jan 25, 2017) (14 pages) Paper No: DS-16-1010; doi: 10.1115/1.4035010 History: Received January 05, 2016; Revised October 10, 2016

For modeling a dynamic system in practice, it often faces the difficulty in improving the accuracy of the constructed analytical model, since some components of the dynamic model are often ignored deliberately due to the difficulty of identification. It is also unwise to apply the neural network to approximate the entire dynamic system as a black box, when the comprehensive knowledge of most components of the dynamics of a large system are available. This paper proposes a method that utilizes the backpropagation (BP) neural network to identify the unknown components of the dynamic system based on the experimental front-end inputs–outputs data of the entire system. It can avoid the difficulty in getting the direct training data for the unknown components, and brings great benefits in the practical application, since to get the front-end inputs–outputs data of the entire dynamic system is easier and cost-effective. In order to train such neural network for the unknown components of dynamics, a modified Levenberg–Marquardt algorithm, which can utilize the front-end inputs–outputs data of the entire dynamic system, has been developed in the paper. Three examples from different application points of view are presented in the paper, and the results show that the proposed modified Levenberg–Marquardt algorithm is efficient to train the neural network for the unknown components of the system based on the data of entire system. The constructed dynamics model, in which the unknown components are substituted by the neural network, can satisfy the requisite accuracy successfully in the computation.

Copyright © 2017 by ASME
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References

Figures

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Fig. 1

Neural network as a dynamic model approximator

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Fig. 2

Neural network as an approximator for part of dynamic system: identification/training process for unknown components/subsystems

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Fig. 3

Neural network training by indirect error propagation

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Fig. 4

Single hidden layer neural network architecture

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Fig. 5

Sinusoidal function approximation of a partially known system

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Fig. 6

Input and Output signal for the actual entire system

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Fig. 7

Root-mean-square of errors between actual and built-up system during neural network training process

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Fig. 8

Comparison between the actual and built-up systems at the 100th iteration of training process

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Fig. 9

Comparison of the actual system and the model built-up based on random inputs: (a) outputs comparison on random inputs between the actual system and the model built-up and (b) errors between the actual system and the model built-up based on random inputs

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Fig. 10

Dynamic model identification of the second-order system: F, target output and F̃, constructed model output

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Fig. 11

Input excitation force of forward dynamics

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Fig. 12

Neural network training process and results of constructed model: (a) root-mean-square of errors between the target output and the constructed model output during neural network training, (b) comparison between targeted output data (F) and constructed model output at the 60th iteration, and (c) errors between the target output data (F) and the constructed model output at the 60th iteration

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Fig. 13

Comparison results between the target data and the constructed model output based on different excitation signals: (a) comparison between the target data and output data of the constructed model based on sinusoidal signal, (b) errors between the target data and output data of the constructed model based on sinusoidal signal, (c) comparison between the target data and output data of the constructed model based on cosine signal, and (d) errors between the target data and output data of the constructed model based on cosine signal

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Fig. 14

Three-dimensional model and kinematic scheme of CaPaMan: 1. end-effector, 2. vertical bar, 3. parallelogram mechanism, 4. driven crank of parallelogram, 5. servo motor, and 6. base I. Passive freedom sliding joint II. Active drive.

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Fig. 15

Inverse dynamic modeling process of Parallel robot with unknown friction model: (a) experimental implementation scheme of getting the training data from entire robotic system point of view and (b) inverse dynamics modeling process incorporating ANN

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Fig. 16

Experimental trajectory

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Fig. 17

Results of constructed inverse dynamic model by incorporating neural network for friction model: (a) root-mean-square of errors between actuator torques and constructed inverse dynamics output during neural network training, (b) comparison between torque of actuator1 (leg1) and the corresponding output of inverse dynamic model, (c) errors between torque of actuator1 (leg1) and the corresponding output of inverse dynamic model, (d) comparison between torque of actuator2 (leg2) and the corresponding output of inverse dynamic model, and (e) errors between torque of actuator2 (leg2) and the corresponding output of inverse dynamic model

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