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Nonlinear identification using a B-spline neural network and chaotic immune approaches

机译：使用B样条神经网络和混沌免疫方法进行非线性识别

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摘要

One of the important applications of B-spline neural network (BSNN) is to approximate nonlinear functions defined on a compact subset of a Euclidean space in a highly parallel manner. Recently, BSNN, a type of basis function neural network, has received increasing attention and has been applied in the field of nonlinear identification. BSNNs have the potential to "learn" the process model from input-output data or "learn" fault knowledge from past experience. BSNN can be used as function approximators to construct the analytical model for residual generation too. However, BSNN is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of a modified artificial immune network inspired optimization method - the opt-aiNet -combined with sequences generate by Henon map to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods are useful for building good BSNN model for the nonlinear identification of two case studies: (i) the benchmark of Box and Jenkins gas furnace, and (ii) an experimental ball-and-tube system.
机译：B样条神经网络（BSNN）的重要应用之一是以高度并行的方式逼近在欧几里得空间的紧凑子集上定义的非线性函数。近来，BSNN，一种基函数神经网络，受到越来越多的关注，并已应用于非线性识别领域。 BSNN具有从输入输出数据“学习”过程模型或从过去的经验中“学习”故障知识的潜力。 BSNN也可以用作函数逼近器，以构造用于残差生成的分析模型。但是，BSNN是通过基于梯度的方法训练的，在学习过程中可能会陷入局部最小值。使用前馈BSNN时，近似质量取决于样条函数的控制点（结）位置。本文介绍了一种改进的人工免疫网络启发式优化方法的应用-opt-aiNet-结合Henon映射生成的序列，以提供随机搜索来调整BSNN的控制点。此处提供的数值结果表明，人工免疫网络优化方法对于建立良好的BSNN模型以非线性识别两个案例研究很有用：（i）Box和Jenkins煤气炉的基准，以及（ii）实验性的球和管系统。

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