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Published on: February 4, 2018
Statistical analysis of nonlinear parameter estimation for Monod biodegradation kinetics using bivariate data
1Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Biotechnology and Bioengineering
|June 22, 2000
Summary
A new nonlinear regression technique enhances Monod parameter estimation for biodegradation kinetics. This method, using maximum likelihood, improves accuracy and confidence in results compared to traditional least squares regression.
Area of Science:
- Environmental microbiology
- Biochemical engineering
- Statistical modeling
Background:
- Estimating Monod parameters (q(max), K(S), Y) is crucial for modeling biodegradation kinetics.
- Traditional least squares regression struggles with bivariate data possessing different error structures.
- Aerobic biodegradation of polycyclic aromatic hydrocarbons (PAHs) like naphthalene and 2-methylnaphthalene serves as a relevant case study.
Purpose of the Study:
- To present and analyze a nonlinear regression technique for estimating Monod parameters.
- To address challenges in parameter estimation when dealing with bivariate data and complex error structures.
- To compare the efficacy of a bivariate maximum likelihood method against a univariate least squares approach.
Main Methods:
- Developed a maximum likelihood optimization function assuming a nondiagonal covariance matrix for measured variables.
- Applied log transformation to substrate concentration data due to observed log-normal error distribution.
- Analyzed residual errors and covariance between substrate and biomass concentrations.
Main Results:
- The bivariate maximum likelihood method provided unique estimates for Monod parameters for naphthalene.
- For 2-methylnaphthalene, while q(max) and K(S) were not uniquely estimated, the ratio q(max)/K(S) was determined.
- The bivariate approach yielded higher confidence in parameter estimates and offered better insights into model fit compared to univariate methods.
Conclusions:
- The developed maximum likelihood technique is superior to simple nonlinear least squares regression for estimating Monod parameters.
- Including biomass concentration data, even with some imprecision, significantly enhances the reliability and information content of parameter estimates.
- The method effectively handles log-normally distributed errors in substrate data and nonzero covariance between variables.
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