<p>Neural networks are mathematical formulations that can be "trained" to perform certain functions. One particular application of these networks of interest in this thesis is to "model" a physical system using only input-output information. The physical system and the neural network are subjected to the same inputs. The neural network is then trained to produce an output which is the same as the physical system for any input. This neural network model so created is essentially a "blackbox" representation of the physical system. This approach has been used at the University of Saskatchewan to model a load sensing pump (a component which is used to create a constant flow rate independent of variations in pressure downstream of the pump). These studies have shown the versatility of neural networks for modeling dynamic and non-linear systems; however, these studies also indicated challenges associated with the morphology of neural networks and the algorithms to train them. These challenges were the motivation for this particular research.</p> <p>Within the Fluid Power Research group at the University of Saskatchewan, a "global" objective of research in the area of load sensing pumps has been to apply dynamic neural networks (DNN) in the modeling of loads sensing systems.. To fulfill the global objective, recurrent generalized neural network (RGNN) morphology along with a non-gradient based training approach called the complex algorithm (CA) were chosen to train a load sensing pump neural network model. However, preliminary studies indicated that the combination of recurrent generalized neural networks and complex training proved ineffective for even second order single-input single-output (SISO) systems when the initial synaptic weights of the neural network were chosen at random.</p> <p>Because of initial findings the focus of this research and its objectives shifted towards understanding the capabilities and limitations of recurrent generalized neural networks and non-gradient training (specifically the complex algorithm). To do so a second-order transfer function was considered from which an approximate recurrent generalized neural network representation was obtained. The network was tested under a variety of initial weight intervals and the number of weights being optimized. A definite trend was noted in that as the initial values of the synaptic weights were set closer to the "exact" values calculated for the system, the robustness of the network and the chance of finding an acceptable solution increased. Two types of training signals were used in the study; step response and frequency based training. It was found that when step response and frequency based training were compared, step response training was shown to produce a more generalized network.</p> <p>Another objective of this study was to compare the use of the CA to a proven non-gradient training method; the method chosen was genetic algorithm (GA) training. For the purposes of the studies conducted two modifications were done to the GA found in the literature. The most significant change was the assurance that the error would never increase during the training of RGNNs using the GA. This led to a collapse of the population around a specific point and limited its ability to obtain an accurate RGNN.</p> <p>The results of the research performed produced four conclusions. First, the robustness of training RGNNs using the CA is dependent upon the initial population of weights. Second, when using GAs a specific algorithm must be chosen which will allow the calculation of new population weights to move freely but at the same time ensure a stable output from the RGNN. Third, when the GA used was compared to the CA, the CA produced more generalized RGNNs. And the fourth is based upon the results of training RGNNs using the CA and GA when step response and frequency based training data sets were used, networks trained using step response are more generalized in the majority of cases.</p>

<p>Neural networks are mathematical formulations that can be "trained" to perform certain functions. One particular application of these networks of interest in this thesis is to "model" a physical system using only input-output information. The physical system and the neural network are subjected to the same inputs. The neural network is then trained to produce an output which is the same as the physical system for any input. This neural network model so created is essentially a "blackbox" representation of the physical system. This approach has been used at the University of Saskatchewan to model a load sensing pump (a component which is used to create a constant flow rate independent of variations in pressure downstream of the pump). These studies have shown the versatility of neural networks for modeling dynamic and non-linear systems; however, these studies also indicated challenges associated with the morphology of neural networks and the algorithms to train them. These challenges were the motivation for this particular research.</p> <p>Within the Fluid Power Research group at the University of Saskatchewan, a "global" objective of research in the area of load sensing pumps has been to apply dynamic neural networks (DNN) in the modeling of loads sensing systems.. To fulfill the global objective, recurrent generalized neural network (RGNN) morphology along with a non-gradient based training approach called the complex algorithm (CA) were chosen to train a load sensing pump neural network model. However, preliminary studies indicated that the combination of recurrent generalized neural networks and complex training proved ineffective for even second order single-input single-output (SISO) systems when the initial synaptic weights of the neural network were chosen at random.</p> <p>Because of initial findings the focus of this research and its objectives shifted towards understanding the capabilities and limitations of recurrent generalized neural networks and non-gradient training (specifically the complex algorithm). To do so a second-order transfer function was considered from which an approximate recurrent generalized neural network representation was obtained. The network was tested under a variety of initial weight intervals and the number of weights being optimized. A definite trend was noted in that as the initial values of the synaptic weights were set closer to the "exact" values calculated for the system, the robustness of the network and the chance of finding an acceptable solution increased. Two types of training signals were used in the study; step response and frequency based training. It was found that when step response and frequency based training were compared, step response training was shown to produce a more generalized network.</p> <p>Another objective of this study was to compare the use of the CA to a proven non-gradient training method; the method chosen was genetic algorithm (GA) training. For the purposes of the studies conducted two modifications were done to the GA found in the literature. The most significant change was the assurance that the error would never increase during the training of RGNNs using the GA. This led to a collapse of the population around a specific point and limited its ability to obtain an accurate RGNN.</p> <p>The results of the research performed produced four conclusions. First, the robustness of training RGNNs using the CA is dependent upon the initial population of weights. Second, when using GAs a specific algorithm must be chosen which will allow the calculation of new population weights to move freely but at the same time ensure a stable output from the RGNN. Third, when the GA used was compared to the CA, the CA produced more generalized RGNNs. And the fourth is based upon the results of training RGNNs using the CA and GA when step response and frequency based training data sets were used, networks trained using step response are more generalized in the majority of cases.</p>

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