Sensitivity analysis and parameter estimation in a model of anaerobic waste water treatment processes with substrate inhibition

Abstract

Anaerobic waste water treatment processes are commonly presented by the ®fth order Hill and Barth nonlinear model, describing three main stages of anaerobic digestion. The model investigated in the present work is a modi®ed version of the Hill and Barth model, which includes substrate inhibition of growth of methanogenic bacteria. Parameter estimation of this model is a dif®cult problem because of the high number of parameters to be estimated and the rather restricted information concerning the variables.The aim of the present work is to use sensitivity theory to ®nd a method for selecting the most signi®cant parameters. In particular, we develop a sensitivity model for anaerobic digestion using relative sensitivity functions. Simulation results from the sensitivity model show that the number of parameters to be estimated can be reduced from 12 to 4. We suggest a 2-step procedure for parameter estimation, which is also based on sensitivity analysis. This procedure gives results, which allow for off-line determination of parameter values if the experimental data for biogas production rate are known.

Quantitative analyses of anaerobic wastewater treatment processes: Identifiability and parameter estimation

“…To ®nd useful identi®able parameter combinations, we also used the results from sensitivity analysis (Noykova and Gyllenberg, 2000). Depending on their in¯uence on the output variable Q, we divided all parameters into three groups: (1) kinetic parameters included in the equation for l 1 , b, and decay coecient k 1 ;…”

“…The terms oQ op 2 are the sensitivity functions of the parameters p 2 with respect to the output measurable variable Q. The sensitivity analysis is a central task in the practical identi®ability study (Holmberg, 1982;Noykova and Gyllenberg, 2000;Vanrolleghem and Dochain, 1998;Yordanova and Noykova, 1996). Here we use the relative sensitivity functions, logarithmic sensitivity functions, because they are nondimensional and allow us to compare the results for dierent parameters and variables.…”

Assessment and parameter identification of simplified models to describe the kinetics of semi-continuous biomethane production from anaerobic digestion of green and food waste

“…For AD systems, the sensitivity analysis is local in nature and it is usually presented as the variation in the output signal with respect to the parameters [ 24 ]. In fact the analysis performed by Bernard et al [ 5 ] showed that the kinetic parameters ( k s and µ max ) stoichiometric yield coefficients ( k 1 , k 2 , k 3 , k 6 ), and the Inhibition constant ( k i ) were the most important parameters in terms of methane production sensitivity.…”

“…In this case, the cost function is given by Eq. ( 23 ), this is simply the sum of the square between the model and the experimental data points, and it is commonly used for parameter estimation studies in this field [ 13 , 23 , 24 ]. Nevertheless, to measure the extent of the deviation of the model results from observed value obtained from experimental investigations, the relative root mean square error (rRMSE) is implemented since this allows comparison of the data obtained from different experiments and it is expressed as a percentage of the time-based mean of the measured methane flow rate ( σ qm,exp ).…”

In-Storage-Psychrophilic-Anaerobic-Digestion (ISPAD) process. Part I: Model Development and Calibration

“…Local and global sensitivity analysis (Bernard, HadjSadok, Dochain, Genovesi, & Steyer, 2001;Noykova & Gyllenberg, 2000;Tartakovsky et al, 2008;V. Vavilin, Rytov, Pavlostathis, Jokela, & Rintala, 2003) evaluate respectively: linear perturbations for the output for a specific set of parameters, and; the sensitivity for a broader spectrum of input parameters in nonlinear models.…”