Document Type



This work uses the adjoint sensitivity model of the counter-flow cooling tower derived in the accompanying PART I to obtain the expressions and relative numerical rankings of the sensitivities, to all model parameters, of the following model responses: (i) outlet air temperature; (ii) outlet water temperature; (iii) outlet water mass flow rate; and (iv) air outlet relative humidity. These sensitivities are subsequently used within the “predictive modeling for coupled multi-physics systems” (PM_CMPS) methodology to obtain explicit formulas for the predicted optimal nominal values for the model responses and parameters, along with reduced predicted standard deviations for the predicted model parameters and responses. These explicit formulas embody the assimilation of experimental data and the “calibration” of the model’s parameters. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.


© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (

Fang, R., Cacuci, D. G., & Badea, M. (2016). Predictive modeling of a paradigm mechanical cooling tower model: Ii. Optimal best-estimate results with reduced predicted uncertainties. Energies, 9(9), 747 doi:10.3390/en9090747