A linear ASM1 based multi-model for activated sludge systems

Abstract

In the search for a reliable but simple model for the biodegradation processes of an activated sludge wastewater treatment plant, this paper presents a multi-model which is valid for the global operating region of a standard carbon and nitrogen removing facility. In a first step, locally valid linear models are derived. Two linearization procedures are compared. The first procedure is the classical Taylor series expansion, while the second is a newly developed linearization procedure based on weighted linear combinations. In a second step, the locally valid models are combined to obtain one globally valid multi-model. Previous work has focused on the most basic configuration of one anoxic and one aerated tank followed by a point settler [Smets, I.Y., Haegebaert, ]. Refinements to the methodology are however needed (and presented here) once the influent flow rate range is increased and the benchmark configuration, proposed by the COST 682 working group no. 2, is taken as the simulation protocol. The main advantage of the obtained linear model (structure) remains the alliance of high predictive power with low complexity, rendering the multi-model fit for on-line optimization and control schemes.

A Simplified Model Structure for an Activated Sludge System

“…As the values of the premise parameters are fixed, the overall output can be expressed as linear combinations of consequent parameters. (10) which is linear in the consequent parameters 1 1 1 2 2 , , , , p q r p q and 2 r . In the backward pass, the error signal propagates backward and the set of premise parameters are updated by gradient descent method.…”

“…The linearized model significantly tracks much closely the ASM1 responses. The proposal by [10] uses linearization around one or more operating point to obtain a multi-model, the global model is realized by combining the valid local multi-model. Another linearized model based on Taylor's series linearization principle was proposed [11], the approach significantly reduced the computational time.…”

Model structure simplification of a biological reactor

“…The MM structure is then used here to reduce the complexity of a simplified ASM1 model (Activate Sludge Model no.1) (Olsson and Newell [1999]) which describes a biological degradation process of an activate sludge reactor. Different linearization techniques were proposed, like a linearization around one or several operating points (Smets et al [2006]) in order to obtain a multiple model. The loss of information constitutes the first drawback of this technique.…”

Linearization of the full activated sludge model No 1 for interaction analysis

“…A linear approximation of the ASM1 model is classically obtained by a Taylor series expansion around a given operating point or process trajectory. Zero and first-order terms are retained [13]. In some works, ad hoc procedures are adopted [7,12].…”

“…In [6] the growth and decay of autotrophic and heterotrophic population processes and the states X COD , S NH , S NO , X BH and X BA are retained in the simplified model. The approach proposed by [12,13] conserves the main features of the original ASM1 model. Assuming pH control, weak interactions between S O and the other process dynamics, and no growth limitation by low dissolved oxygen set point, the mass balance equations for S I , X I , S ALK and S O are excluded from the model.…”