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Online nonlinear sequential Bayesian estimation of a biological wastewater treatment process

机译：在线非线性顺序贝叶斯估计的生物废水处理过程

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摘要

Online estimation of unknown state variables is a key component in the accurate modelling of biological wastewater treatment processes due to a lack of reliable online measurement systems. The extended Kalman filter (EKF) algorithm has been widely applied for wastewater treatment processes. However, the series approximations in the EKF algorithm are not valid, because biological wastewater treatment processes are highly nonlinear with a time-varying characteristic. This work proposes an alternative online estimation approach using the sequential Monte Carlo (SMC) methods for recursive online state estimation of a biological sequencing batch reactor for wastewater treatment. SMC is an algorithm that makes it possible to recursively construct the posterior probability density of the state variables, with respect to all available measurements, through a random exploration of the states by entities called 'particle'. In this work, the simplified and modified Activated Sludge Model No. 3 with nonlinear biological kinetic models is used as a process model and formulated in a dynamic state-space model applied to the SMC method. The performance of the SMC method for online state estimation applied to a biological sequencing batch reactor with online and offline measured data is encouraging. The results indicate that the SMC method could emerge as a powerful tool for solving online state and parameter estimation problems without any model linearization or restrictive assumptions pertaining to the type of nonlinear models for biological wastewater treatment processes.
机译：由于缺乏可靠的在线测量系统，在线估计未知状态变量是生物废水处理过程精确建模的关键组成部分。扩展卡尔曼滤波器（EKF）算法已广泛应用于废水处理过程。但是，EKF算法中的序列近似无效，因为生物废水处理过程是高度非线性的，具有时变特性。这项工作提出了一种使用顺序蒙特卡罗（SMC）方法的在线估算方法的替代方案，用于递归在线估算废水处理生物排序批处理反应器。 SMC是一种算法，通过对称为“粒子”的实体进行状态的随机探索，可以相对于所有可用度量来递归构造状态变量的后验概率密度。在这项工作中，使用经过简化和修改的具有非线性生物动力学模型的3号活性污泥模型作为过程模型，并在应用于SMC方法的动态状态空间模型中进行了表述。 SMC方法用于在线状态估计的在线和离线测量数据应用于生物测序间歇反应器的性能令人鼓舞。结果表明，SMC方法可以成为解决在线状态和参数估计问题的有力工具，而无需任何模型线性化或涉及生物废水处理过程非线性模型类型的限制性假设。

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