Automated screw insertion monitoring using neural networks: A computational intelligence approach to assembly in manufacturing

How to efficiently solve eigen-problems of matrices is always a significant issue in engineering. Neural networks run in an asynchronous manner, and thus applying neural networks to address these problems can attain high performance. In this chapter, several recurrent neural network models are proposed to handle eigen-problems of matrices. Each model is expressed as an individual differential equation, with its analytic solution being derived. Subsequently, the convergence properties of the neural network models are fully discussed based on the solutions to these differential equations. Finally, the computation steps are designed toward solving the eigen-problems, with numerical simulations being provided to evaluate the effectiveness of each model. This chapter consists of three major parts, with each approach in these three parts being in the form of neural networks. Section 7.1 presents how to solve the eigen-problems of real symmetric matrices; Sections 7.2 and 7.3 are devoted to addressing the eigen-problems of anti-symmetric matrices; Section 7.4 aims at solving eigen-problems of general matrices, which are neither symmetric nor anti-symmetric. Finally, conclusions are made in Section 7.5 to summarize the whole chapter.