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Nonlinear Process Modeling Using a Dynamically Recurrent Neural Network
Copyright © IFAC Artificial Intelligence in Real-Time Control, Arizona, USA, 1998
NONLINEAR PROCESS MODELING USING A DYNAMICALL Y RECURRENT NEURAL NETWORK Shi-Rong Liu and * Jin-Shou Yu Research Institute of Automation East China University of Science & Technology 130 Meilong Road Shanghai 200237, China Email: [email protected] Fax: 0086-021-64253078
Extended Abstract A dynamically recurrent neural network, also called a feedback neural network, is one in which self-loops and backward connections between nodes are allowed. One of the consequences of these connections is that dynamical behaviors not possible with strictly feedforward networks, such as limit cycles and chaos, can be produced with dynamically recurrent networks. Dynamically recurrent networks with symmetric weight connections always converge to stable state in the well-known Hopfield networks. But the dynamically recurrent networks without the symmetry constraint have more complex dynamical behaviors than dynamically symmetric recurrent networks. The diversity of dynamical behaviors suggests that recurrent networks may be well suited to the time series prediction. Another possible benefit of recurrent networks is that smaller networks may provide the functionality of much larger number of nodes. This will ease complexity analysis with traditionally assumes a large number of nodes. Partially recurrent networks are a class of simple recurrent networks with asymmetric connections. In partially recurrent networks, the weight on the feedback links are fixed, and so the standard back-propagation learning rule may be easily used for training. Such networks are also referred to as sequential networks , and the nodes receiving feedback signals are called context units. At time t, the context units have signals coming from part of the network state at time (t-1). Thus the state of the whole network at a particular time depends on an aggregate of previous states as well as on the current input. The Elan network (Elan 1990) is a type of partially recurrent network. There have much research interests in this network and it has been applied to dynamical system identification. Elan network only have an output-layer, a hidden-layer and an input-layer, and the inputlayer includes context nodes and input nodes. Pham and Liu pointed out that the basic Elan network trained by the standard back-propagation algorithm was able to model only firstorder dynamical systems. A modified Elan network has proposed by Pham and Liu (1992). In the modified Elan network, self-feedback linkes with fixed gains are introduced to the context units to enable the Elan network to represent higher-order systems. And the selection of self-feedback link gains is difficult, no general methods, which affects the network behaviors. In this paper, we discuss how to select the gains and give some illustrative examples. Simulation results have shown that the modified Elan network has sufficient approximate capability to non linear dynamic systems, and the structure of the modified Elan network is simpler than one of multi-layer feed forward networks for solving the same problem. Finally, the paper reports on the application of the modified Elan network to model a continuous stirred-tank reactor(CSTR) with a irreversible reaction.
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NONLINEAR PROCESS MODELING USING A DYNAMICALL Y RECURRENT NEURAL NETWORK Shi-Rong Liu and * Jin-Shou Yu Research Institute of Automation East China University of Science & Technology 130 Meilong Road Shanghai 200237, China Email: [email protected] Fax: 0086-021-64253078
Extended Abstract A dynamically recurrent neural network, also called a feedback neural network, is one in which self-loops and backward connections between nodes are allowed. One of the consequences of these connections is that dynamical behaviors not possible with strictly feedforward networks, such as limit cycles and chaos, can be produced with dynamically recurrent networks. Dynamically recurrent networks with symmetric weight connections always converge to stable state in the well-known Hopfield networks. But the dynamically recurrent networks without the symmetry constraint have more complex dynamical behaviors than dynamically symmetric recurrent networks. The diversity of dynamical behaviors suggests that recurrent networks may be well suited to the time series prediction. Another possible benefit of recurrent networks is that smaller networks may provide the functionality of much larger number of nodes. This will ease complexity analysis with traditionally assumes a large number of nodes. Partially recurrent networks are a class of simple recurrent networks with asymmetric connections. In partially recurrent networks, the weight on the feedback links are fixed, and so the standard back-propagation learning rule may be easily used for training. Such networks are also referred to as sequential networks , and the nodes receiving feedback signals are called context units. At time t, the context units have signals coming from part of the network state at time (t-1). Thus the state of the whole network at a particular time depends on an aggregate of previous states as well as on the current input. The Elan network (Elan 1990) is a type of partially recurrent network. There have much research interests in this network and it has been applied to dynamical system identification. Elan network only have an output-layer, a hidden-layer and an input-layer, and the inputlayer includes context nodes and input nodes. Pham and Liu pointed out that the basic Elan network trained by the standard back-propagation algorithm was able to model only firstorder dynamical systems. A modified Elan network has proposed by Pham and Liu (1992). In the modified Elan network, self-feedback linkes with fixed gains are introduced to the context units to enable the Elan network to represent higher-order systems. And the selection of self-feedback link gains is difficult, no general methods, which affects the network behaviors. In this paper, we discuss how to select the gains and give some illustrative examples. Simulation results have shown that the modified Elan network has sufficient approximate capability to non linear dynamic systems, and the structure of the modified Elan network is simpler than one of multi-layer feed forward networks for solving the same problem. Finally, the paper reports on the application of the modified Elan network to model a continuous stirred-tank reactor(CSTR) with a irreversible reaction.
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