Influence of the optimization methods on neural state estimation quality of the drive system with elasticity

Neural Computing and Applications, Jul 2013

The paper deals with the implementation of optimized neural networks (NNs) for state variable estimation of the drive system with an elastic joint. The signals estimated by NNs are used in the control structure with a state-space controller and additional feedbacks from the shaft torque and the load speed. High estimation quality is very important for the correct operation of a closed-loop system. The precision of state variables estimation depends on the generalization properties of NNs. A short review of optimization methods of the NN is presented. Two techniques typical for regularization and pruning methods are described and tested in detail: the Bayesian regularization and the Optimal Brain Damage methods. Simulation results show good precision of both optimized neural estimators for a wide range of changes of the load speed and the load torque, not only for nominal but also changed parameters of the drive system. The simulation results are verified in a laboratory setup.

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Influence of the optimization methods on neural state estimation quality of the drive system with elasticity

Teresa Orlowska-Kowalska 0 Marcin Kaminski 0 Electrical Bayesian 0 0 T. Orlowska-Kowalska (&) M. Kaminski Institute of Electrical Machines , Drives and Measurements, Wroclaw University of Technology , Wroclaw, Poland The paper deals with the implementation of optimized neural networks (NNs) for state variable estimation of the drive system with an elastic joint. The signals estimated by NNs are used in the control structure with a state-space controller and additional feedbacks from the shaft torque and the load speed. High estimation quality is very important for the correct operation of a closed-loop system. The precision of state variables estimation depends on the generalization properties of NNs. A short review of optimization methods of the NN is presented. Two techniques typical for regularization and pruning methods are described and tested in detail: the Bayesian regularization and the Optimal Brain Damage methods. Simulation results show good precision of both optimized neural estimators for a wide range of changes of the load speed and the load torque, not only for nominal but also changed parameters of the drive system. The simulation results are verified in a laboratory setup. In most electrical drives, the elasticity of the shaft between a driving motor and a load machine must be taken into - account. In order to obtain drive response to a reference signal with high dynamics, and to minimize torsional vibrations, different control methods of the drive system with elastic joint, based on control theory, like PI/PID methods, state controller-based methods, sliding-mode, and adaptive or predictive control methods [16] are used. All these control methods require feedbacks from different mechanical state variables of the system (load side speed, torsional torque, load torque). These mechanical variables can be measured, but only in laboratory environments. In the real drive systems, in industry, torsional or load torque can not be measured, as the torque transducer is never mounted between the driven motor and the loading machine because lack of space and generation of additional (high) cost. Similarly, the load side speed is hardly measured because lack of place for additional speed transducer and additional cabling, which is troublesome. In such a case, only estimation of those state variables is the solution for the industry conditions. This is the reason why we have to estimate the torsional torque and the load side speed of a two-mass system. In many applications connected with electrical drives, algorithmic methods are applied for the non-measurable state variables estimation, for example, the Kalman filters [4, 5] and the Luenberger observers [6]. However, the algorithmic estimators require the mathematical model and parameter knowledge of the system, which could change during the system operationso to obtain the good estimation quality the parameters of the state estimators must be tuned on-line (by on-line plant parameters identification or estimation). Alternative ways of solving this problem are estimators based on neural networks (NNs). Such estimators do not need a mathematical model and parameters of the system, only the training data are required [79] for the estimator design. Moreover, the generalization ability causes that neural estimators are less sensitive to parameters or measurement signals uncertainties. However, in the case of NN applications in state variable estimation, the determination of NN structure for a specific task is one of the most important problems. This structure should be carefully chosen to obtain good estimation quality also in the case of NN input data different than those used in the training procedure. It means that a suitable generalization ability is required. Data generalization is one of the main advantages of the NN and consists in the possibility of solving a given task by a trained network in case the elements of the input vector are not taken into account in the NNs training process. In the technical literature, many methods for the improvement of the NN generalization properties are presented. It is possible to distinguish three main trends [7]: impact on the length of the learning process (early stopping) [10], application of regularisation method [11], modification of neural networks topology (growing or pruning) [12, 13]. Many methods for NN structure optimization are presented in the literature. Most of them require the initial choice of NN structure, and then, selected neural connections are eliminated. One of the simplest ways to choose a specific inter-node connection for elimination is the analysis of absolute values of NNs weights. Another method consists in checking the influence of each connection on the generalization error. In this case, the generalization errors before and after the elimination each weight factor are compared [7, 14]. Very good results are obtained with the sensitivity methods. These algorithms are base (...truncated)


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Teresa Orlowska-Kowalska, Marcin Kaminski. Influence of the optimization methods on neural state estimation quality of the drive system with elasticity, Neural Computing and Applications, 2014, pp. 1327-1340, Volume 24, Issue 6, DOI: 10.1007/s00521-013-1348-4