Distributed parameter systems (DPSs) are commonly used to characterize various industrial processes, but the coupling of spatiotemporal data and time-delay effects poses challenges for their fault detection. This article proposes a fault detection method for a class of nonlinear parabolic DPSs with limited sensors. A time/space separation method is first applied to decouple the spatiotemporal data to obtain time coefficients that are available for data-driven modeling. Then, the obtained dominant time coefficients are modeled by a dynamic partial least-squares (D-PLSs) method. Finally, the residual space is utilized to establish two monitoring statistics and a reference boundary is established with the aid of the mirrored data kernel density estimation (KDE). This method exploits the separable characteristics of parabolic DPSs and is a data-driven method that is independent of an explicit mathematical model of the system processes. The proposed method is validated on a curing oven experimental platform, and comparative results with other methods show that it achieves satisfactory performance in fault detection accuracy and first-time detection timeliness.

中文翻译：

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非线性分布参数系统基于动态偏最小二乘的故障检测

分布式参数系统（DPS）通常用于表征各种工业过程，但时空数据和时滞效应的耦合给故障检测带来了挑战。本文提出了一种传感器有限的非线性抛物线 DPS 故障检测方法。首先应用时间/空间分离方法对时空数据进行解耦，以获得可用于数据驱动建模的时间系数。然后，通过动态偏最小二乘（D-PLS）方法对获得的主导时间系数进行建模。最后，利用残差空间建立两个监测统计量，并借助镜像数据核密度估计（KDE）建立参考边界。该方法利用抛物线 DPS 的可分离特性，是一种数据驱动的方法，独立于系统过程的显式数学模型。所提方法在固化炉实验平台上进行了验证，与其他方法的对比结果表明，该方法在故障检测精度和首次检测及时性方面均取得了令人满意的表现。