Time series modelling and analysis

In class activities

Author

Ranjeet Utikar

Published

August 20, 2023

Activities

  1. Estimating Transfer Function Models for a Heat Exchanger

    In this example we estimate the transfer function for a heat exchanger. The heat exchanger consists of a coolant temperature, product temperature, and disturbance ambient temperature. We will estimate the coolant to product temperature transfer function.

    The measured data is stored in an excel file heat_exchanger.xlsx and includes measurements of changes in coolant temperature around a nominal and changes in product temperature around a nominal. Estimate a transfer function for the heat exchanger.

    1. From the physics of the problem we know that the heat exchanger can be described by a first order system with delay. Use the tfest command specifying one pole, no zeroes, and an unknown input/output delay to estimate a transfer function.

    2. The compare and resid commands allow us to investigate how well the estimated model matches the measured data.

    Detailed instructions are given here.

  2. AR model: Australia COVID-19 Infection

    The cumulative daily data for COVID-19 infections is given in Australia_covid_cases.xlsx. Fit an autoregression model to the data.

  3. For the transfer function below, develop an ARX model for the above system, with 1 unit step change in input and sampling time Ts = 1 unit.

    \[ G_p = \frac{ 2 exp (-s)}{(10s + 1)} \tag{1}\]

  4. Iron ore prices: The price history for iron ore spot prices is given in iron_ore.xlsx.

    Use the following Matlab functions

    1. arima(p,d,q) => to build ARIMA model
    2. estimate(Mdl,X) => to estimate the ARMA model parameters
    3. simulate(EstMdl,t) => to simulate the ARMA model
    4. plot(tx,X,tx,y) = > to compare the data and model estimation

  5. Follow the Building and Estimating Process Models Using System Identification Toolbox example from Matlab documentation.

Citation

BibTeX citation:
@online{utikar2023,
  author = {Utikar, Ranjeet},
  title = {Time Series Modelling and Analysis},
  date = {2023-08-20},
  url = {https://amc.smilelab.dev//content/notes/05-time_series_modelling_and_analysis/in-class-activities.html},
  langid = {en}
}
For attribution, please cite this work as:
Utikar, Ranjeet. 2023. “Time Series Modelling and Analysis.” August 20, 2023. https://amc.smilelab.dev//content/notes/05-time_series_modelling_and_analysis/in-class-activities.html.