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In this chapter, the application of a DLRNN is demonstrated to simulate rainfall-runoff processes and recognize the transition of UHs in hydrology. Although most neural networks are black-box models that lack physical meanings of weights, the DLRNN developed in this chapter connects its weights with UHs that reveal the physical concepts from the network based on the special structure of RNNs. Without trial and error method, the structure and the weights of DLRNN can be quickly determined through a modified form of system identification that combines indirect system identification with the subspace algorithm. Then, the DLRNN learning algorithm based on the interchange of the roles of the network state variables and the weight matrix is derived for on-line training. In this chapter, the DLRNN introduced can not only simulate rainfall-runoff processes, but also recognize the transition of UHs. Owing to the feedback connections, DLRNN performs rainfall-runoff simulations as dynamic systems, and the advantage of DLRNN's dynamic feature has been proven after the comparison between DLRNN and FNN. The investigation of the connections between weights and physical meanings is an extension of neural networks applied in hydrological field due to the linearization of the RNN. Based on the linearization, weights of DLRNN are treated as Markov parameters to realize the transition of UHs. Through on-line learning, DLRNN modifies the weights to capture the relation between rainfall and runoff every time step, and the transition of rainfall-runoff processes can be emerged based on the changes of UHs. Furthermore, a modified system identification that combines indirect system identification with subspace algorithm is described to calibrate the DLRNN. This method determines the quantity of neurons in hidden layer and the weights of the network. It overcomes the drawback of costing time by traditional trial and error search for optimum structure of DLRNN. Additionally, the different forms of DLRNN have also been discussed herein. The results show that the performances of DLRNNs in different forms are close. Hence, the transformation of canonical form can be ignored in the flowchart of simulation via DLRNN. Finally, four criteria have been applied to evaluate the performance of rainfall-runoff simulation via DLRNN. The results show that the performance is satisfactory and DLRNN is competent to simulate dynamic systems, like rainfall-runoff processes. |
