Towards Conditional Parameter Estimation for Automatic Model Structure Identification: Using Mixed-Integer Calibration for Model Development

2020 ◽  
Author(s):  
Diana Spieler ◽  
Juliane Mai ◽  
Bryan Tolson ◽  
James Craig ◽  
Niels Schütze
Keyword(s):  
Parameter Estimation ◽  
Mixed Integer ◽  
Structure Identification ◽  
Model Parameters ◽  
Suitable Model ◽  
Model Structure ◽  
Hydrologic Modelling ◽  
Vast Number ◽  
Calibration Process ◽  
Decision Variables

<p>A recently introduced framework for Automatic Model Structure Identification (AMSI) allows to simultaneously optimize model structure choices (integer decision variables) and parameter values (continuous decision variables) in hydrologic modelling. By combining the mixed-integer optimization algorithm DDS and the flexible hydrologic modelling framework RAVEN, AMSI is able to test a vast number of model structure and parameter combinations in order to identify the most suitable model structure for representing the rainfall runoff behavior of a catchment. The model structure and all potentially active model parameters are calibrated simultaneously. This causes a certain degree of inefficiency during the calibration process, as variables might be perturbed that are not currently relevant for the tested model structure. In order to avoid this, we propose an adaption of the current DDS algorithm allowing for conditional parameter estimation. Parameters will only be perturbed during the calibration process if they are relevant for the model structure that is currently tested. The conditional parameter estimation setup will be compared to the standard DDS algorithm for multiple AMSI test cases. We will show if and how conditional parameter estimation increases the efficiency of AMSI.</p>

How good does Automatic Model Structure Identification work? A Benchmark Study with 6915 Model Structures.

2021 ◽  
Author(s):  
Diana Spieler ◽  
Niels Schütze
Keyword(s):  
Optimization Algorithms ◽  
Calibration Procedure ◽  
Mixed Integer ◽  
Structure Identification ◽  
Model Parameters ◽  
Model Structure ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Standard Calibration ◽  
Model Structures

<p>Recent investigations have shown it is possible to simultaneously calibrate model structures and model parameters to identify appropriate models for a given task (Spieler et al., 2020). However, this is computationally challenging, as different model structures may use a different number of parameters. While some parameters may be shared between model structures, others might be relevant for only a few structures, which theoretically requires the calibration of conditionally active parameters. Additionally, shared model parameters might cause different effects in different model structures, causing their optimal values to differ across structures. In this study, we tested how two current “of the shelf” mixed-integer optimization algorithms perform when having to handle these peculiarities during the automatic model structure identification (AMSI) process recently introduced by Spieler et al. (2020).</p><p>To validate the current performance of the AMSI approach, we conduct a benchmark experiment with a model space consisting of 6912 different model structures.  First, all model structures are independently calibrated and validated for three hydro-climatically differing catchments using the CMA-ES algorithm and KGE as the objective function. This is referred to as standard calibration procedure. We identify the best performing model structure(s) based on validation performance and analyze the range of performance as well as the number of structures performing in a similar range. Secondly, we run AMSI on all three catchments to automatically identify the most feasible model structure based on the KGE performance. Two different mixed-integer optimization algorithms are used – namely DDS and CMA-ES. Afterwards, we compare the results to the best performing models of the standard calibration of all 6912 model structures.</p><p>Within this experimental setup, we analyze if the best performing model structure(s) AMSI identifies are identical to the best performing structures of the standard calibration and if there are differences in performance when using different optimization algorithms for AMSI. We also validate if AMSI can identify the best performing model structures for a catchment at a fraction of the computational cost than the standard calibration procedure requires by using “off the shelf” mixed-integer optimization algorithms.</p><p> </p><p> </p><p> </p><p>Spieler, D., Mai, J., Craig, J. R., Tolson, B. A., & Schütze, N. (2020). Automatic Model Structure Identification for Conceptual Hydrologic Models. Water Resources Research, 56(9). https://doi.org/10.1029/2019WR027009</p>

Model structure identification for wastewater treatment simulation based on computational fluid dynamics

2002 ◽  
Vol 45 (4-5) ◽  
pp. 325-334 ◽  
Author(s):  
J. Alex ◽  
G. Kolisch ◽  
K. Krause
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Wastewater Treatment ◽  
Dynamic Simulation ◽  
Cfd Simulation ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
Structure Identification ◽  
Suitable Model ◽  
Model Structure

The objective of this presented project is to use the results of an CFD simulation to automatically, systematically and reliably generate an appropriate model structure for simulation of the biological processes using CSTR activated sludge compartments. Models and dynamic simulation have become important tools for research but also increasingly for the design and optimisation of wastewater treatment plants. Besides the biological models several cases are reported about the application of computational fluid dynamics (CFD) to wastewater treatment plants. One aim of the presented method to derive model structures from CFD results is to exclude the influence of empirical structure selection to the result of dynamic simulations studies of WWTPs. The second application of the approach developed is the analysis of badly performing treatment plants where the suspicion arises that bad flow behaviour such as short cut flows is part of the problem. The method suggested requires as the first step the calculation of fluid dynamics of the biological treatment step at different loading situations by use of 3-dimensional CFD simulation. The result of this information is used to generate a suitable model structure for conventional dynamic simulation of the treatment plant by use of a number of CSTR modules with a pattern of exchange flows between the tanks automatically. The method is explained in detail and the application to the WWTP Wuppertal Buchenhofen is presented.

scholarly journals Identifying Sensitivities in Flood Frequency Analyses using a Stochastic Hydrologic Modeling System

2021 ◽  
Author(s):  
Andrew J. Newman ◽  
Amanda G. Stone ◽  
Manabendra Saharia ◽  
Kathleen D. Holman ◽  
Nans Addor ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Flood Frequency ◽  
Model Parameters ◽  
Model Structure ◽  
Structure Model ◽  
Return Periods ◽  
Hydrologic Modelling ◽  
Modelling Framework ◽  
Flood Generation ◽  
Model Structures

Abstract. This study assesses sources of variance in stochastic hydrologic modelling to support flood frequency analyses. The major components of the modelling chain, including model structure, model parameter estimation, initial conditions, and precipitation inputs were examined across return periods from 2 to 100,000 years at two watersheds representing different hydro-climates across the western United States. Ten hydrologic model structures were configured, calibrated and run within the Framework for Understanding Structural Errors (FUSE) modular modelling framework for each of the two watersheds. Model parameters and initial conditions were derived from long-term calibrated simulations using a 100-member historical meteorology ensemble. A stochastic event-based hydrologic modelling workflow was developed using the calibrated models; millions of flood event simulations were performed at each basin. The analysis of variance method was then used to quantify the relative contributions of model structure, model parameters, initial conditions, and precipitation inputs to flood magnitudes for different return periods. The attribution of the variance of flood frequencies to each component of a stochastic hydrological modelling framework, including several hydrological model structures, is a novel contribution to the flood modelling literature. Results demonstrate that different components of the modelling chain have different sensitivities for different return periods. Precipitation inputs contribute most to the variance of rare events, while initial conditions are most influential for the more frequent events. However, the hydrological model structure and structure-parameter interactions together play an equally important role in specific cases, depending on the basin characteristics and type of flood metric of interest. This study highlights the importance of critically assessing model underpinnings, understanding flood generation processes, and selecting appropriate hydrological models that are consistent with our understanding of flood generation processes.

scholarly journals Model Structure Optimization for Fuel Cell Polarization Curves

Computers ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 60 ◽  
Author(s):  
Markku Ohenoja ◽  
Aki Sorsa ◽  
Kauko Leiviskä
Keyword(s):  
Genetic Algorithms ◽  
Fuel Cell ◽  
Polarization Curve ◽  
Cell System ◽  
Cell Polarization ◽  
Operating Conditions ◽  
Model Complexity ◽  
Structure Identification ◽  
Model Parameters ◽  
Model Structure

The applications of evolutionary optimizers such as genetic algorithms, differential evolution, and various swarm optimizers to the parameter estimation of the fuel cell polarization curve models have increased. This study takes a novel approach on utilizing evolutionary optimization in fuel cell modeling. Model structure identification is performed with genetic algorithms in order to determine an optimized representation of a polarization curve model with linear model parameters. The optimization is repeated with a different set of input variables and varying model complexity. The resulted model can successfully be generalized for different fuel cells and varying operating conditions, and therefore be readily applicable to fuel cell system simulations.

scholarly journals Identification of support vector machines for runoff modelling

2004 ◽  
Vol 6 (4) ◽  
pp. 265-280 ◽  
Author(s):  
Michaela Bray ◽  
Dawei Han
Keyword(s):  
Learning Community ◽  
Response Curve ◽  
Factor Model ◽  
Model Identification ◽  
Kernel Functions ◽  
Unit Response ◽  
Support Vector ◽  
Model Parameters ◽  
Suitable Model ◽  
Model Structure

This paper describes an exploration in using SVM (Support Vector Machine) models, which were initially developed in the Machine Learning community, in flood forecasting, with the focus on the identification of a suitable model structure and its relevant parameters for rainfall runoff modelling. SVM has been applied in many fields and has a high success rate in classification tasks such as pattern recognition, OCR, etc. The applications of SVM in regression of time series are relatively new and they are more problematic in comparison with classifications. This study found that exhaustive search of an optimum model structure and its parameter space is prohibitive due to their sheer size and unknown characteristics. Some parameters are very sensitive and can increase the CPU load tremendously (and hence result in very long computation times). All these make it very difficult to efficiently identify SVM models, which has been carried out by manual operations in all study cases so far. The paper further explored the relationships among various model structures (ξ-SV or ν-SV regression), kernel functions (linear, polynomial, radial basis and sigmoid), scaling factor, model parameters (cost C, epsilon) and composition of input vectors. These relationships should be able to provide useful information for more effective model identification in the future. The unit response curve from SVM was compared with a transfer function model and it is found that a TF model outperforms SVM in short-range predictions. It is still unclear how the unit response curve could be utilised for model identification processes and future exploration in this area is needed.

Analysis and design of suitable model structures for activated sludge tanks with circulating flow

1999 ◽  
Vol 39 (4) ◽  
pp. 55-60 ◽  
Author(s):  
J. Alex ◽  
R. Tschepetzki ◽  
U. Jumar ◽  
F. Obenaus ◽  
K.-H. Rosenwinkel
Keyword(s):  
Activated Sludge ◽  
Large Scale ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
High Sensitivity ◽  
Suitable Model ◽  
Model Structure ◽  
Analysis And Design ◽  
Hydraulic Behaviour ◽  
Model Structures

Activated sludge models are widely used for planning and optimisation of wastewater treatment plants and on line applications are under development to support the operation of complex treatment plants. A proper model is crucial for all of these applications. The task of parameter calibration is focused in several papers and applications. An essential precondition for this task is an appropriately defined model structure, which is often given much less attention. Different model structures for a large scale treatment plant with circulation flow are discussed in this paper. A more systematic method to derive a suitable model structure is applied to this case. Results of a numerical hydraulic model are used for this purpose. The importance of these efforts are proven by a high sensitivity of the simulation results with respect to the selection of the model structure and the hydraulic conditions. Finally it is shown, that model calibration was possible only by adjusting to the hydraulic behaviour and without any changes of biological parameters.

scholarly journals Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 387
Author(s):  
Yiting Liang ◽  
Yuanhua Zhang ◽  
Yonggang Li
Keyword(s):  
Parameter Estimation ◽  
Kinetic Model ◽  
Model Parameters ◽  
Hydrogen Ions ◽  
Removal Process ◽  
Cobalt Removal ◽  
Estimation Scheme ◽  
Zinc Hydrometallurgy ◽  
The Impact ◽  
Parameter Estimation Scheme

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

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.

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