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      A Novel Protocol for Model Calibration in Biological Wastewater Treatment

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          Abstract

          Activated sludge models (ASMs) have been widely used for process design, operation and optimization in wastewater treatment plants. However, it is still a challenge to achieve an efficient calibration for reliable application by using the conventional approaches. Hereby, we propose a novel calibration protocol, i.e. Numerical Optimal Approaching Procedure (NOAP), for the systematic calibration of ASMs. The NOAP consists of three key steps in an iterative scheme flow: i) global factors sensitivity analysis for factors fixing; ii) pseudo-global parameter correlation analysis for non-identifiable factors detection; and iii) formation of a parameter subset through an estimation by using genetic algorithm. The validity and applicability are confirmed using experimental data obtained from two independent wastewater treatment systems, including a sequencing batch reactor and a continuous stirred-tank reactor. The results indicate that the NOAP can effectively determine the optimal parameter subset and successfully perform model calibration and validation for these two different systems. The proposed NOAP is expected to use for automatic calibration of ASMs and be applied potentially to other ordinary differential equations models.

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          Parameter estimation in biochemical pathways: a comparison of global optimization methods.

          Here we address the problem of parameter estimation (inverse problem) of nonlinear dynamic biochemical pathways. This problem is stated as a nonlinear programming (NLP) problem subject to nonlinear differential-algebraic constraints. These problems are known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based) local optimization methods fail to arrive at satisfactory solutions. To surmount this limitation, the use of several state-of-the-art deterministic and stochastic global optimization methods is explored. A case study considering the estimation of 36 parameters of a nonlinear biochemical dynamic model is taken as a benchmark. Only a certain type of stochastic algorithm, evolution strategies (ES), is able to solve this problem successfully. Although these stochastic methods cannot guarantee global optimality with certainty, their robustness, plus the fact that in inverse problems they have a known lower bound for the cost function, make them the best available candidates.
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            Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods

            Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided.
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              Recent developments in parameter estimation and structure identification of biochemical and genomic systems.

              The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.
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                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                16 February 2015
                2015
                : 5
                : 8493
                Affiliations
                [1 ]Key Laboratory of Beijing for Water Quality Science and Water Environmental Recovery Engineering, Engineering Research Center of Beijing, Beijing University of Technology , Beijing 100124, PR China
                [2 ]Advanced Water Management Centre (AWMC), The University of Queensland , St Lucia, Brisbane, QLD 4072, Australia
                [3 ]Tsinghua Holding Human Settlements Environment Institute , Beijing 100083, PR China
                Author notes
                Article
                srep08493
                10.1038/srep08493
                4329560
                25682959
                87454b9b-b448-4cf7-aff6-c71a11d5c31c
                Copyright © 2015, Macmillan Publishers Limited. All rights reserved

                This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                History
                : 19 November 2014
                : 20 January 2015
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