TABLE OF CONTENTS - The Professional Green Building Council

Theme B: Creating a livable, healthy and environmentally viable citiesThe airflow mode [9] in Fig 5 was excluded from the simplified mathematicalmodel because it requires complex modeling and detailed information. Based onthe descriptions given above, the mathematical model was expressed with acontinuous state-space equation as shown in Eq. (9).x& = A( u, t) x+b( u,t)(9)where x : State variable vector, A : State matrix, u : Input vector, b: Load vector4. PARAMETER ESTIMATIONThe mathematical model introduced in the earlier section contains unknownparameters including the convective thermal transfer coefficients ( outhca,3,ca,4h , inh , hca,1, hca,2,h ) in Fig 4, the form loss factor in Eq. (1), and the flow coefficientand the flow exponent in Eqs. (3), (7) and (8). The parameter estimation techniqueis to find unknown parameters which minimize the difference between actualmeasurement and simulation prediction. The parameter estimation technique canbe express as minimizing the objective function(S) as in Eq. (10).min S=T∑[ Y −ψ ( ξk k i)] [ Y −ψ k k( ξi)]k = 1st ..: lb≤ξ≤ ubz(10)where, Y k: observation vector, ψ k: discrete state vector in discrete state space, z :number of observations, ξ : vector of unknown parameters, lb : upper bounds of theunknown parameters, ub : lower bounds of the unknown parametersThe function ‘LSQNONLIN' in the MATLAB optimization toolbox was used tosolve for Eq. (10). The function ‘LSQNONLIN' is specially designed to solve forthis kind of constrained nonlinear optimization problems. The unknown parameterswere expressed as equations in Eq.(10) as follows.503