Hi Afif,
System identification using Nonlinear Autoregressive models with Exogenous inputs (NARX) can be challenging, especially when determining the optimal number of lags for your model. Here are some steps and tips to help you find suitable lags and improve the accuracy of your model using MATLAB:
Step 1: Understand Your System
1. Data Collection: Ensure you have high-quality data that accurately represents the dynamics of your linear actuator system. The data should include both input (e.g., control signals) and output (e.g., actuator position) time series.
2. Initial Analysis: Perform an initial analysis of your data to understand its characteristics. Plot the time series data to visually inspect for patterns, delays, and noise.
Step 2: Preprocess Your Data
1. Normalize Data: Normalize or standardize your data to ensure it is on a similar scale, which can improve the performance of neural networks.
2. Remove Noise: Apply filtering techniques to remove noise from your data, if necessary.
Step 3: Choose Initial Lags
1. Initial Guess: Start with a reasonable guess for the number of input and output lags based on your understanding of the system dynamics. A common approach is to start with small lags (e.g., 1-5) and incrementally increase them.
2. Partial Autocorrelation: Use the Partial Autocorrelation Function (PACF) to help identify significant lags. This can give insights into how many past values are relevant for predicting the future values.
Step 4: Model Training and Validation
1. Train NARX Model: Use MATLAB’s Neural Network Toolbox to create and train your NARX model. You can use the `narxnet` function to create a NARX neural network.
% Example of creating a NARX network
inputDelays = 1:5; % Initial guess for input delays
feedbackDelays = 1:5; % Initial guess for feedback delays
hiddenLayerSize = 10; % Number of neurons in the hidden layer
net = narxnet(inputDelays, feedbackDelays, hiddenLayerSize);
2. Split Data: Divide your data into training, validation, and test sets to evaluate the model's performance effectively.
3. Iterative Tuning: Iteratively adjust the input and feedback delays and retrain the model to find the combination that yields the best fit. Use grid search or manual tuning to explore different configurations.
4. Performance Metrics: Evaluate the model using performance metrics such as Mean Squared Error (MSE) or R-squared to assess the accuracy.
Step 5: Optimize Model
1. Cross-Validation: Implement cross-validation to ensure the model generalizes well to unseen data.
2. Regularization: Consider adding regularization to prevent overfitting, especially if the model complexity increases with more lags.
3. Hyperparameter Tuning: Besides lags, tune other hyperparameters like the number of hidden neurons, learning rate, and training epochs.
Step 6: Use MATLAB Tools
1. Neural Network Toolbox: Leverage MATLAB’s Neural Network Toolbox for automated hyperparameter optimization and model training.
2. System Identification Toolbox: Use the System Identification Toolbox for additional insights and validation of your model.
Conclusion
Finding the optimal lags for a NARX model involves a combination of initial analysis, iterative tuning, and validation. By systematically exploring different configurations and using MATLAB’s powerful tools, you can improve the accuracy of your model. Remember to validate your model thoroughly to ensure it performs well on new data.
Thank you.
