ARIMA Forecasting of Industrial Robot Motor Temperature for Predictive Maintenance from Synthetic Time Series

Project info

• Field of studyRobotics and Mechatronics
• LevelDoctoral dissertation (S3)
• Method typeCommunications and Forecasting
• Estimated build time± 7 working days
• Toolsarima, estimate, forecast, infer, aicbic (Econometrics Toolbox)
• PriceUS$31 - US$206

Research goal

Analyse the motor temperature using an ARIMA model and examine its sensitivity to the autoregressive order and the moving average order.

Variables

Example result

• 4.416Holdout RMSE
• 2.292Holdout MAPE (%)
• 0.348AR coefficient
• 0.524MA coefficient
• 446.106AIC
• 1.016Residual std

The ARIMA(1,1,1) model forecasts Motor temperature 14 steps ahead with a holdout RMSE of 4.416 and MAPE of 2.29%; the AR coefficient is 0.348 and MA 0.524, and near-uncorrelated residuals make the 95% band trustworthy.

Computed from illustrative synthetic data, not from a real study.

About Forecasting with ARIMA

ARIMA models a time series with autoregressive, differencing, and moving-average components to forecast future values. It suits economic, energy, or sales time series whose autocorrelation pattern must be modelled explicitly.

Steps

1. 1Plot the series and check stationarity (trend, seasonality)
2. 2Determine the differencing order d with a unit-root test or ACF plot
3. 3Compare several orders p and q with AIC and BIC
4. 4Estimate the best model with estimate
5. 5Check residuals (autocorrelation, normality)
6. 6Forecast with forecast and plot with intervals

Assumptions to check

• The series is stationary after differencing
• Residuals are white noise
• The model structure does not change in the forecast period

Reading and reporting the results

Report the chosen order with AIC/BIC rationale, estimated parameters, residual tests, and forecast error (RMSE or MAPE) on test data. Include forecast intervals and explain the rising uncertainty at long horizons.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(8);
trueMdl = arima('Constant', 0.5, 'AR', {0.6}, 'MA', {0.3}, 'Variance', 1);
motor_temperature = simulate(trueMdl, 300);
autoregressive_order = (1:300)';
ytr = motor_temperature(1:276);  yte = motor_temperature(277:end);

best = inf;
for p = 0:2
    for q = 0:2
        [est, ~, logL] = estimate(arima(p, 0, q), ytr, 'Display', 'off');
        aic = aicbic(logL, p + q + 2, numel(ytr));
        fprintf('ARIMA(%d,0,%d)  AIC = %.2f\n', p, q, aic);
        if aic < best, best = aic; bestMdl = est; bp = p; bq = q; end
    end
end
fprintf('Chosen order: p = %d, q = %d\n', bp, bq);

res = infer(bestMdl, ytr);
[~, pLB] = lbqtest(res / std(res), 'Lags', 10);
fprintf('Ljung-Box p (residuals) = %.3f\n', pLB);

[yF, yMSE] = forecast(bestMdl, numel(yte), 'Y0', ytr);
ci = [yF - 1.96*sqrt(yMSE), yF + 1.96*sqrt(yMSE)];
fprintf('Forecast RMSE = %.3f\n', sqrt(mean((yte - yF).^2)));

figure;
plot(autoregressive_order(251:end), motor_temperature(251:end), 'k'); hold on;
plot(autoregressive_order(277:end), yF, 'r', 'LineWidth', 1.5);
plot(autoregressive_order(277:end), ci, 'r--');
legend('Data', 'Forecast', '95% interval'); xlabel('Time');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions