Patent ID: 8554712

Claim:
A non-compartmental method of predicting a time-dependent response of a component of a system to an input into the system, the method comprising: identifying the system, the component, the input, and the time-dependent response; wherein, the input includes a set of actual inputs and a test input, and the time-dependent response includes a set of time-dependent actual responses and a test response; obtaining the set of time-dependent actual responses of the component to the set of actual inputs; using the set of actual inputs and the set of time-dependent actual responses to provide a model for predicting the test response to the test input, the model comprising the formula C ⁡ ( t ) = [ M 0 0 + M 0 1 ⁡ ( kernel ) ] + [ M 1 0 + M 1 1 ⁡ ( kernel ) ] ⁢ { 1 - ⅇ - [ N 1 0 + N 1 1 ⁡ ( kernel ) ] ⁢ t 1 + ( ⅇ K - 2 ) ⁢ ⅇ - [ N 1 0 + N 1 1 ⁡ ( kernel ) ] ⁢ t } + … + [ M n 0 + M n 1 ⁡ ( kernel ) ] ⁢ { 1 - ⅇ - [ N n 0 + N 1 1 ⁡ ( kernel ) ] ⁢ t 1 + ( ⅇ K - 2 ) ⁢ ⅇ - [ N n 0 + N n 1 ⁡ ( kernel ) ] ⁢ t } ( 9 ) wherein, M 0 0 , . . . , M 0 n and M 1 0 , . . . , M 1 n are overall scaling parameters; N 0 1 , . . . , N 0 n and N 1 1 , . . . , N 1 n are exponential scaling parameters; n ranges from 1 to 4; K is an overall shifting parameter; and, C(t) is the time-dependent response to the test input at time t; and, kernel ≡ 1 - ⅇ - α p ⁢ C 0 1 + ( ⅇ K p - 2 ) ⁢ ⅇ - α p ⁢ C 0 ; wherein, C 0 is the initial amount of the test input; K p is a shifting parameter related to C 0 ; and, α p is shifting and scaling parameter related to C 0 ; and, using the model to obtain the time-dependent test response to the test input.