Practical approach to parameter estimation for ASM3+bio-P module applied to five-stage step-feed EBPR process

2006 ◽  
Vol 53 (1) ◽  
pp. 139-148 ◽  
Author(s):  
S.H. Lee ◽  
J.H. Ko ◽  
K.M. Poo ◽  
T.H. Lee ◽  
H.J. Woo ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Kinetic Parameters ◽  
Parameter Optimization ◽  
Prediction Performance ◽  
Data Sources ◽  
Batch Experiments ◽  
Function Calculation ◽  
Characteristic Features ◽  
Parameter Values

Various parameter optimization approaches to a five-stage step-feed EBPR process modeled using the ASM3+bio-P module were examined. Five stoichiometric (YSTO,NO, YH,O2, YH,NO, YPAO,O2, YPO4) and seven kinetic parameters (kSTO, ηNO, bH, μmax,PAO, qPHA, qPP, μmax,A) were estimated. The optimization approaches could be classified based on the data sources (batch experiments or CSTR operation data) and the number of target variables used in calculating the objective function. Optimized parameter values obtained by each approach were validated with CSTR operation data that were not used for parameter optimization. The results showed that the parameter optimization only with batch experimental results could not be directly applied to CSTR operation data. ASM3+bio-P module parameters could be finely optimized only with CSTR operation data when sufficient target variables for objective function calculation were applied. When the number of target variables was increased, prediction performance was significantly improved. Once optimized, the model was able to predict the characteristic features of the five-stage step-feed process; namely, a high PAO yield, fast PAO growth, fast XPP storage, slow XSTO and XPHA storage.

Estimation of kinetic parameters of a model for deammonification in biofilms and evaluation of the model

2007 ◽  
Vol 55 (8-9) ◽  
pp. 291-299 ◽  
Author(s):  
D. Brockmann ◽  
K.-H. Rosenwinke ◽  
E. Morgenroth
Keyword(s):  
Parameter Estimation ◽  
Kinetic Parameters ◽  
Batch Experiment ◽  
Continuous Reactor ◽  
Affinity Constant ◽  
Experimental Conditions ◽  
Transfer Resistance ◽  
Identifiability Analysis ◽  
Model Predictions ◽  
Parameter Values

A systematic approach to estimate and evaluate parameters for deammonification in biofilms from available experimental data was evaluated. Parameter estimation was based on a regional steady state sensitivity analysis to select relevant parameters and design of experiments based on a local identifiability analysis. The calibrated model was evaluated under different experimental conditions. Nine of the 16 kinetic and stoichiometric parameters had a significant influence on model predictions. Of these nine parameters only six kinetic parameters were identifiable from batch experiments regardless of the experimental design. More parameters were not identifiable due to high correlations between growth rates and the corresponding affinity constant for oxygen. Data from a batch experiment at 2 mg/L dissolved oxygen (DO) were used to estimate inactivation rates and affinity constants for oxygen for ammonium oxidisers (AO), nitrite oxidisers (NO) and anaerobic ammonium oxidisers (AN). In addition, it was found that not only kinetic and stoichiometric parameters but also the external mass transfer resistance significantly affected model predictions. The resulting model was able to reproduce batch test and continuous reactor operation where DO concentrations were similar to those in the batch experiment used for parameter estimation. However, the model overestimated deammonification for a batch experiment at a much higher DO concentration (5 mg/L). Thus, parameter values that are identifiable and are estimated for given environmental conditions may not necessarily be valid for significantly different experimental conditions.

Heterotrophic Kinetic Parameter Estimation for Enhanced Biological Phosphorus Removal Processes Operated in Conventional and Membrane-Assisted Modes

2006 ◽  
Vol 41 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Zhe Zhang ◽  
Eric R. Hall
Keyword(s):  
Parameter Estimation ◽  
Phosphorus Removal ◽  
Growth Yield ◽  
Pilot Scale ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Nitrogen And Phosphorus ◽  
Parameter Values ◽  
The Impact ◽  
Biological Phosphorus

Abstract Parameter estimation and wastewater characterization are crucial for modelling of the membrane enhanced biological phosphorus removal (MEBPR) process. Prior to determining the values of a subset of kinetic and stoichiometric parameters used in ASM No. 2 (ASM2), the carbon, nitrogen and phosphorus fractions of influent wastewater at the University of British Columbia (UBC) pilot plant were characterized. It was found that the UBC wastewater contained fractions of volatile acids (SA), readily fermentable biodegradable COD (SF) and slowly biodegradable COD (XS) that fell within the ASM2 default value ranges. The contents of soluble inert COD (SI) and particulate inert COD (XI) were somewhat higher than ASM2 default values. Mixed liquor samples from pilot-scale MEBPR and conventional enhanced biological phosphorus removal (CEBPR) processes operated under parallel conditions, were then analyzed experimentally to assess the impact of operation in a membrane-assisted mode on the growth yield (YH), decay coefficient (bH) and maximum specific growth rate of heterotrophic biomass (µH). The resulting values for YH, bH and µH were slightly lower for the MEBPR train than for the CEBPR train, but the differences were not statistically significant. It is suggested that MEBPR simulation using ASM2 could be accomplished satisfactorily using parameter values determined for a conventional biological phosphorus removal process, if MEBPR parameter values are not available.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521＾

Spatial scale effects on model parameter estimation and predictive uncertainty in ungauged basins

2012 ◽  
Vol 44 (3) ◽  
pp. 441-453 ◽  
Author(s):  
Denis A. Hughes ◽  
Evison Kapangaziwiri ◽  
Jane Tanner
Keyword(s):  
Parameter Estimation ◽  
Spatial Scale ◽  
Scale Effects ◽  
Physical Property ◽  
Hydrological Modelling ◽  
Ungauged Basins ◽  
Estimation Equations ◽  
Property Data ◽  
Physical Property Data ◽  
Parameter Values

The most appropriate scale to use for hydrological modelling depends on the model structure, the purpose of the results and the resolution of available data used to quantify parameter values and provide the climatic forcing. There is little consensus amongst the community of model users on the appropriate model complexity and number of model parameters that are needed for satisfactory simulations. These issues are not independent of modelling scale, the methods used to quantify parameter values, nor the purpose of use of the simulations. This paper reports on an investigation of spatial scale effects on the application of an approach to quantify the parameter values (with uncertainty) of a rainfall-runoff model with a relatively large number of parameters. The quantification approach uses estimation equations based on physical property data and is applicable to gauged and ungauged basins. Within South Africa the physical property data are available at a finer spatial resolution than is typically used for hydrological modelling. The results suggest that reducing the model spatial scale offers some advantages. Potential disadvantages are related to the need for some subjective interpretation of the available physical property data, as well as inconsistencies in some of the parameter estimation equations.

scholarly journals Calibration of Conceptual Rainfall-Runoff Models Using Global Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Chao Zhang ◽  
Ru-bin Wang ◽  
Qing-xiang Meng
Keyword(s):  
Global Optimization ◽  
Parameter Optimization ◽  
Hydrological Model ◽  
Optimization Method ◽  
Difficult Problem ◽  
Rainfall Runoff ◽  
True Parameter ◽  
Shuffled Complex Evolution ◽  
Structure Lead ◽  
Parameter Values

Parameter optimization for the conceptual rainfall-runoff (CRR) model has always been the difficult problem in hydrology since watershed hydrological model is high-dimensional and nonlinear with multimodal and nonconvex response surface and its parameters are obviously related and complementary. In the research presented here, the shuffled complex evolution (SCE-UA) global optimization method was used to calibrate the Xinanjiang (XAJ) model. We defined the ideal data and applied the method to observed data. Our results show that, in the case of ideal data, the data length did not affect the parameter optimization for the hydrological model. If the objective function was selected appropriately, the proposed method found the true parameter values. In the case of observed data, we applied the technique to different lengths of data (1, 2, and 3 years) and compared the results with ideal data. We found that errors in the data and model structure lead to significant uncertainties in the parameter optimization.

scholarly journals Investigation of the Biological Treatability of Pistachio Processing Industry Wastewaters in a Batch-operated Aerobic Bioreactor

2021 ◽  
Author(s):  
Sevtap Tırınk ◽  
Alper Nuhoğlu ◽  
Sinan Kul
Keyword(s):  
Kinetic Parameters ◽  
Growth Rates ◽  
Specific Growth ◽  
Batch Reactor ◽  
The Other ◽  
Batch Experiments ◽  
Processing Industry ◽  
Specific Growth Rates ◽  
Biological Treatability ◽  
Best Fit

Abstract This study encompasses investigation of treatment of pistachio processing industry wastewaters in a batch reactor under aerobic conditions, calculation of kinetic parameters and comparison of different inhibition models. The mixed microorganism culture used in the study was adapted to pistachio processing industry wastewaters for nearly one month and then concentrations from 50-1000 mg L− 1 of pistachio processing industry wastewaters were added to the medium and treatment was investigated in batch experiments. The Andrews, Han-Levenspiel, Luong and Aiba biokinetic equations were chosen for the correlations between the concentration of pistachio processing industry wastewaters and specific growth rates, and the kinetic parameters in these biokinetic equations were calculated. The µmax, Ks and Ki parameters, included in the Aiba biokinetic equation providing best fit among the other equations, had values calculated as 0.25 h− 1, 19 mg L− 1, and 516 mg L− 1, respectively.

scholarly journals Parameter Selection in the Parameter Estimation of Grade Transitions in a Polyethylene Plant

2015 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Niklas Andersson ◽  
Per-Ola Larsson ◽  
Johan Åkesson ◽  
Niclas Carlsson ◽  
Staffan Skålén ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Steady State ◽  
State Parameter ◽  
Parameter Selection ◽  
Selection Algorithm ◽  
Parameter Estimations ◽  
Dynamic Case ◽  
Nominal Parameter ◽  
Best Parameter ◽  
Parameter Values

A polyethylene plant at Borealis AB is modelled in the Modelica language and considered for parameter estimations at grade transitions. Parameters have been estimated for both the steady-state and the dynamic case using the JModelica.org platform, which offers tools for steady-state parameter estimation and supports simulation with parameter sensitivies. The model contains 31 candidate parameters, giving a huge amount of possible parameter combinations. The best parameter sets have been chosen using a parameter-selection algorithm that identified parameter sets with poor numerical properties. The parameter-selection algorithm reduces the number of parameter sets that is necessary to explore. The steady-state differs from the dynamic case with respect to parameter selection. Validations of the parameter estimations in the dynamic case show a significant reduction in an objective value used to evaluate the quality of the solution from that of the nominal reference, where the nominal parameter values are used.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

scholarly journals Robust multi-objective calibration strategies – possibilities for improving flood forecasting

2012 ◽  
Vol 16 (10) ◽  
pp. 3579-3606 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Model Performance ◽  
Data Depth ◽  
Automatic Calibration ◽  
Multi Objective ◽  
Robust Model ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

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