This paper presents a new approach for identifying interval fuzzy models, which enables estimating fuzzy model structures, parameters, and upper and lower bounds simultaneously and online. It is based on a filtered recursive least squares method combined with an incrementally evolving Gaussian clustering. The proposed method generates interval fuzzy models online, on the fly, and in an evolving manner. This means that the algorithm starts with no a priori information, evolves the structure of the model, adjusts the model parameters simultaneously, and computes the upper and lower intervals simultaneously. The fuzzy partitioning of the input-output data space is based on the eGauss+ method; the parameters of the local linear models, which together form the fuzzy model, are determined using a recursive least squares method. The interval fuzzy model, used in a predictive manner as a single or multi-level predictor, can be successfully applied in on-line monitoring, fault detection, and the control of dynamic systems. The proposed identification procedure was used to identify the fuzzy interval model of two different processes: a simplified Hammerstein-type nonlinear dynamic process and a realistic industrial continuously stirred tank reactor. The main contribution and advantage of the proposed new method is the identification of an interval fuzzy model in an online manner, which means that the structural and parametric identification of nonlinear systems is done simultaneously and from the data stream. The structural and parametric uncertainties are modeled and integrated into the upper and lower fuzzy models, which form the fuzzy interval in which the measured data samples of the process output are located with a certain probability. The approach is limited to processes that have Wiener-Hammerstein structures.

本文提出了一种识别区间模糊模型的新方法，该方法能够同时在线估计模糊模型结构、参数和上下界。它基于过滤递归最小二乘法与增量演化的高斯聚类相结合。所提出的方法在线、动态地和以不断发展的方式生成区间模糊模型。这意味着算法从没有先验信息开始，演化模型结构，同时调整模型参数，同时计算上下区间。输入输出数据空间的模糊划分基于eGauss+方法；使用递归最小二乘法确定共同构成模糊模型的局部线性模型的参数。区间模糊模型，以预测方式用作单级或多级预测器，可成功应用于在线监测、故障检测和动态系统的控制。提出的识别程序用于识别两个不同过程的模糊区间模型：简化的 Hammerstein 型非线性动态过程和现实的工业连续搅拌釜反应器。所提出的新方法的主要贡献和优势是以在线方式识别区间模糊模型，这意味着非线性系统的结构和参数识别是从数据流中同时进行的。将结构和参数不确定性建模并集成到上下模糊模型中，形成过程输出的测量数据样本以一定概率位于其中的模糊区间。该方法仅限于具有 Wiener-Hammerstein 结构的过程。