Compute loss functions for single-output ARX models
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Syntax
V = arxstruc(dataest,dataval,NN)
V = arxstruc(___,Name,Value)
Description
example
V = arxstruc(dataest,dataval,NN) estimates the loss function V for the estimation and validation data in dataest and dataval, respectively. dataest and dataval can be in the form of a timetable, a comma-separated pair of numeric matrices, or an iddata object. It can also be an idfrd object defining frequency-response data.
If dataest and dataval are timetables, you can select specific input and output channels to use for estimation by specifying the channel names in the InputName and OutputName name-value arguments. Otherwise, the software assumes that the last timetable variable channel is the single output channel and the remaining variables are all input channels.
V contains both the loss functions and the corresponding orders and delays. You can analyze V with selstruc, which evaluates V and allows you to select a suitable model structure.
Use arxstruc only for single-output ARX models. arxstruc supports both single-input and multiple-input systems.
V = arxstruc(___,Name,Value) uses additional options specified by one or more name-value arguments.
Examples
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Generate Model-Order Combinations and Estimate Single-Input ARX Model
Open Live Script
Create an ARX model for generating data.
A = [1 -1.5 0.7];B = [0 1 0.5];m0 = idpoly(A,B);
Generate random input and additive noise signals.
u = idinput(400,'rbs');e = 0.1*randn(400,1);Simulate the model output using the defined input and error signals.
y = sim(m0,[u e]);
Generate model-order combinations for estimation. Specify a delay of 1 for all models, and a model order range between 1 and 5 for na and nb.
Estimate ARX models and compute the loss function for each model order combination. The input data is split into estimation and validation data sets.
V = arxstruc(u(1:200),y(1:200),u(201:400),y(201:400),NN);
Select the model order with the best fit to the validation data.
order = selstruc(V,0)
order = 1×3 2 2 1Estimate an ARX model of selected order.
M = arx(u,y,order)
M =Discrete-time ARX model: A(z)y(t) = B(z)u(t) + e(t) A(z) = 1 - 1.498 z^-1 + 0.6971 z^-2 B(z) = 1.004 z^-1 + 0.5028 z^-2 Sample time: 1 seconds Parameterization: Polynomial orders: na=2 nb=2 nk=1 Number of free coefficients: 4 Use "polydata", "getpvec", "getcov" for parameters and their uncertainties.Status: Estimated using ARX on time domain data "u". Fit to estimation data: 97.75% (prediction focus)FPE: 0.009874, MSE: 0.009582
Generate Model-Order Combinations and Estimate Multi-Input ARX Model
Open Live Script
Load estimation and validation data sets and view the variable names.
load co2datatt tte ttvhead(tte,3)
Time u1 u2 y1 _______ ___ __ _______ 0.5 sec 170 50 -44.302 1 sec 170 50 -44.675 1.5 sec 170 50 -45.29
Generate model-order combinations for:
na=2:4nb=2:5for the first input, and1or4for the second input.nk=1:4for the first input, and0for the second input.
NN = struc(2:4,2:5,[1 4],1:4,0);
Estimate an ARX model for each model order combination.
V = arxstruc(tte,ttv,NN);
Select the model order with the best fit to the validation data.
order = selstruc(V,0)
Estimate an ARX model of selected order.
M = arx(tte,order)
M =Discrete-time ARX model: A(z)y(t) = B(z)u(t) + e(t) A(z) = 1 - 1.252 z^-1 + 0.302 z^-2 B1(z) = -0.3182 z^-2 - 0.1292 z^-3 + 0.2883 z^-4 + 0.001051 z^-5 B2(z) = -0.02705 + 0.01948 z^-1 + 0.1695 z^-2 + 0.3278 z^-3 Sample time: 0.5 seconds Parameterization: Polynomial orders: na=2 nb=[4 4] nk=[2 0] Number of free coefficients: 10 Use "polydata", "getpvec", "getcov" for parameters and their uncertainties.Status: Estimated using ARX on time domain data "tte". Fit to estimation data: 88.59% (prediction focus)FPE: 3.993, MSE: 3.938
Input Arguments
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dataest — Estimation data
timetable | numeric matrix pair | iddata object | idfrd object
Estimation data, specified as a timetable, a comma-separated pair of numeric matrices, an iddata object, or an idfrd object.
The specification for dataest depends on the data type.
Timetable
Specify dataest as a timetable that uses a regularly spaced time vector containing variables that represent input and output channels. Use the InputName and OutputName name-value arguments to select specific channels for estimation.
Comma-Separated Matrix Pair
Specify dataest as a comma-separated pair of matrices that contain the input and output time-domain signal values u,y.
Data Object
Specify dataest as an iddata object or an idfrd that contains the input and output data.
For more information about working with estimation data types, see Data Domains and Data Types in System Identification Toolbox.
dataval — Validation data
timetable | numeric matrix pair | iddata object | idfrd object
Estimation data, specified in the same format and input/output channel order as dataest. dataval can be the same data as dataest.
NN — Number of model structures
integer matrix
Number of ARX model structures to evaluate, specified as an Nn-by-3 matrix, where Nn is the number of model structures.
Each row of NN has the form nn = [na nb nk].
Name-Value Arguments
Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose Name in quotes.
Example: V = arxstruc(dataest,dataval,NN,'InputName',"u2") selects the timetable variable u2 as the single input channel.
InputName — Input channel names
string | character vector | string array | cell array of character vectors
Input channel names, specified as a string, character vector, string array, or cell array of character vectors.
If you are using a timetable for the data source, the names in InputName must be a subset of the timetable variables.
Example: V = arxstruc(tt,__,'InputName',["u1" "u2"]) selects the variables u1 and u2 as the input channels from the timetable tt to use for the estimation.
OutputName — Output channel name
string | character vector | string array | cell array of character vectors
Output channel name, specified as a string or character vector.
If you are using a timetable for the data source, the name in OutputName must be a subset of the timetable variables.
Example: V = arxstruc(___,'OutputName',"y3") selects the variable y3 as the output channel from the timetable tt to use for the estimation.
Output Arguments
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V — Loss function
numeric matrix
Loss function, specified as an 4-by-(Nn+1) matrix.
The first row of V contains the loss functions. The remaining rows of V contain the transpose of NN, so that the orders and delays are given just below the corresponding loss functions. The last column of V contains the number of data points in dataest.
Version History
Introduced before R2006a
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R2023a: Time-domain estimation data is accepted in the form of timetables and matrices
Most estimation, validation, analysis, and utility functions now accept time-domain input/output data in the form of a single timetable that contains both input and output data or a pair of matrices that contain the input and output data separately. These functions continue to accept iddata objects as a data source as well, for both time-domain and frequency-domain data.
See Also
arx | idpoly | ivstruc | selstruc | struc
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