Parameter estimation for the first-order BOD equation using nonlinear techniques

1977 ◽  
Vol 4 (4) ◽  
pp. 462-470 ◽  
Author(s):  
Thomas W. Constable ◽  
Edward A. McBean
Keyword(s):  
Parameter Estimation ◽  
Pollution Control ◽  
Control Plant ◽  
Estimation Methods ◽  
First Order ◽  
Expected Values ◽  
Parameter Estimation Methods ◽  
Parameter Estimation Techniques ◽  
Study Application

Two nonlinear parameter estimation techniques are used to obtain expected values, variances, and covariance estimates for L and k in the first-order BOD equation. The techniques are compared with a number of other BOD parameter estimation methods with respect to both estimated values of L and k and necessary assumptions about the measurement error structure of BOD analyses. The techniques that historically have been used to estimate the parameters in the first-order BOD equation are shown to often give erroneous answers because of their use of an incorrect error structure.A case study application of the methodology to the raw influent and primary effluent of the Waterloo Pollution Control Plant is included.

Bayesian model discrimination for BOD analyses

1977 ◽  
Vol 4 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Thomas W. Constable ◽  
Edward A. McBean
Keyword(s):  
Pollution Control ◽  
Bayesian Model ◽  
Control Plant ◽  
Model Discrimination ◽  
First Order ◽  
Point Estimates ◽  
Probability Estimates ◽  
Two Parameter ◽  
Study Application

The Hsiang–Reilly method, a discrete Bayesian model discrimination technique, is used to select the best model of several alternative models to describe data relating observed BOD exertion as a function of time. Use of this approach avoids the need for linearization of equations and results in distributed probability estimates of the parameter magnitudes rather than simply point estimates. A case study application to the raw influent and primary effluent of the Waterloo Pollution Control Plant is included. The results indicate that although a three-parameter model often gives a better fit to observed BOD data than the two-parameter first-order model, differences between the BOD-progression curves for the models are often so small as to be insignificant. In view of these small differences, and considering that none of the proposed models could adequately describe observed deviations from the exponential BOD curves, the use of the first-order equation to describe BOD-progression relationships for the Waterloo Pollution Control Plant appears to be justified.

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