Learning Algorithms of Process Neural Networks Based on Orthogonal Function Basis Expansion

Both the input and link weights of process neural network can be all time-various functions, an aggregation operator on time is added to the process neuron, which provides the neural network with the capability of handling simultaneously two dimension information of time and space. In consideration of the complexity of the aggregation operation of time in process neural networks, a new learning algorithm based on function orthogonal basis expansion is proposed. Firstly a group of proper function orthogonal bases in the input function space of the neural network is selected, and then the input functions and the network weight functions are represented as expansion of the same orthogonal basis. With orthogonality of basis functions, the aggregation operation of process neurons to time is simplified. The application shows that the algorithms simplify the computing complexity of process neural networks, and raise the efficiency of the network learning and the adaptability to real problem resolving. The effectiveness of the algorithm has been proved in the rotation machinery fault diagnosis and the simulation in oil field development process.