Parameter estimation of nonlinear dynamical Hammerstein processes is a renowned stiff optimization problem with extensive applications in the design, robustness and stability analysis. Introduction of the fractional calculus theories and concepts further escalates the competency of accurate modelling of Hammerstein system but at the cost of increase in the stiffness of parameter estimation and complexity. This study deals with a presentation of new design of fractional-order nonlinear Hammerstein control auto-regressive (FO-NHCAR) model for heat exchanger system by introducing fractional derivative of polynomial based transformation operator in linear dynamic block. The system identification problem of FO-NHCAR heat exchanger system is constructed by exploiting approximation theory in mean squared error sense taken between the actual and estimated responses. Exhaustive simulations are conducted via well-known global search efficacy of the fuzzy-evolutionary computing paradigm i.e., fuzzy-genetic algorithms (GAs), for FO-NHCAR heat exchanger model by variation in signal to noise ratios, model's degrees of freedom, fractional orders, and Hammerstein kernels. The parameter vectors of FO-NHCAR models are identified consistently with the fuzzy-GAs for various noisy environments with negligible proximity error. Results comparison on rigorous statistical analysis further endorse the efficient, accurate, robust and stable performance of fuzzy- GAs for estimation of FO-NHCAR heat exchanger system parameters.

中文翻译：

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用于换热器系统辨识的分数阶 Hammerstein 控制自回归模型的设计：模糊进化计算论文


非线性动态 Hammerstein 过程的参数估计是著名的刚性优化问题，在设计、鲁棒性和稳定性分析中具有广泛的应用。分数阶微积分理论和概念的引入进一步提升了Hammerstein系统精确建模的能力，但代价是参数估计的刚性和复杂性的增加。本研究通过在线性动态块中引入基于多项式的变换算子的分数阶导数，介绍换热器系统分数阶非线性 Hammerstein 控制自回归 (FO-NHCAR) 模型的新设计。 FO-NHCAR 换热器系统的系统识别问题是通过利用实际响应和估计响应之间的均方误差意义上的近似理论来构建的。通过模糊进化计算范式（即模糊遗传算法 (GA)）众所周知的全局搜索功效，通过信噪比、模型自由度、分数阶的变化，对 FO-NHCAR 热交换器模型进行详尽的模拟和 Hammerstein 内核。对于各种噪声环境，FO-NHCAR 模型的参数向量与模糊遗传算法一致，邻近误差可以忽略不计。严格统计分析的结果比较进一步证实了模糊遗传算法用于估计 FO-NHCAR 换热器系统参数的高效、准确、鲁棒和稳定的性能。