bj {sysid} | R Documentation |
Estimate Box-Jenkins Models
Description
Fit a box-jenkins model of the specified order from input-output data
Usage
bj(z, order = c(1, 1, 1, 1, 0), init_sys = NULL, options = optimOptions())
Arguments
z |
an |
order |
Specification of the orders: the five integer components (nb,nc,nd,nf,nk) are order of polynomial B + 1, order of the polynomial C, order of the polynomial D, order of the polynomial F, and the input-output delay respectively |
init_sys |
Linear polynomial model that configures the initial parameterization.
Must be a BJ model. Overrules the |
options |
Estimation Options, setup using
|
Details
SISO BJ models are of the form
y[k] = \frac{B(q^{-1})}{F(q^{-1})}u[k-nk] +
\frac{C(q^{-1})}{D(q^{-1})} e[k]
The orders of Box-Jenkins model are defined as follows:
B(q^{-1}) = b_1 + b_2q^{-1} + \ldots + b_{nb} q^{-nb+1}
C(q^{-1}) = 1 + c_1q^{-1} + \ldots + c_{nc} q^{-nc}
D(q^{-1}) = 1 + d_1q^{-1} + \ldots + d_{nd} q^{-nd}
F(q^{-1}) = 1 + f_1q^{-1} + \ldots + f_{nf} q^{-nf}
The function estimates the coefficients using non-linear least squares
(Levenberg-Marquardt Algorithm)
The data is expected to have no offsets or trends. They can be removed
using the detrend
function.
Value
An object of class estpoly
containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
options |
Option set used for estimation. If no custom options were configured, this is a set of default options |
termination |
Termination conditions for the iterative
search used for prediction error minimization:
|
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 14.4.1, 17.5.2, 21.6.3
Examples
data(bjsim)
z <- dataSlice(bjsim,end=1500) # training set
mod_bj <- bj(z,c(2,1,1,1,2))
mod_bj
residplot(mod_bj) # residual plots