What are the best tools and methods for nonlinear process identification and model validation?

1 Nonlinear process identification

Nonlinear process identification is the task of finding a suitable nonlinear model that describes the input-output behavior of a process, based on observed data. There are different types of nonlinear models, such as polynomial, neural network, fuzzy, or hybrid models, that can capture different aspects of the process nonlinearities. To select the best model, you need to consider several factors, such as the complexity, interpretability, accuracy, and generality of the model. You also need to use appropriate identification methods, such as least squares, maximum likelihood, or subspace methods, that can estimate the model parameters and structure from the data.

2 Model validation

Model validation is the process of checking whether the identified model is consistent with the actual process behavior, and whether it meets the desired specifications and objectives. Model validation involves several steps, such as data partitioning, residual analysis, model comparison, and performance evaluation. Data partitioning is the technique of dividing the available data into training, validation, and test sets, to avoid overfitting and ensure generalization. Residual analysis is the technique of examining the difference between the model output and the measured output, to detect any model errors or outliers. Model comparison is the technique of using statistical tests or criteria, such as F-test, AIC, or BIC, to compare different models and select the best one. Performance evaluation is the technique of using metrics or indicators, such as MSE, RMSE, R-squared, or NRMSE, to measure the quality and fit of the model.

3 Nonlinear model predictive control

Nonlinear model predictive control (NMPC) is one of the most advanced and powerful techniques for nonlinear control design. NMPC is based on the idea of using a nonlinear model to predict the future behavior of the process, and then optimizing a control input that minimizes a cost function, subject to constraints. NMPC can handle complex nonlinear dynamics, multiple inputs and outputs, and various constraints, such as input saturation, output limits, or state bounds. NMPC can also adapt to changes in the process parameters or disturbances, by updating the model and the control input at each sampling time.

4 Software tools for nonlinear process identification and model validation

There are many software tools that can help you with nonlinear process identification and model validation, depending on your needs and preferences. Some of the most popular and widely used tools are MATLAB, Simulink, and their toolboxes, such as System Identification Toolbox, Neural Network Toolbox, Fuzzy Logic Toolbox, and Model Predictive Control Toolbox. These tools offer a variety of functions, graphical interfaces, and examples that can help you create, fit, validate, and compare nonlinear models, and design and simulate NMPC controllers. Other tools that can be useful are Python, R, and their libraries, such as SciPy, NumPy, scikit-learn, TensorFlow, Keras, and Pyomo. These tools offer more flexibility and customization options, but may require more programming skills and experience.

5 Tips and best practices for nonlinear process identification and model validation

To achieve successful nonlinear process identification and model validation, there are some tips and best practices that can help enhance results and avoid common pitfalls. This includes collecting enough data that covers the relevant operating range and dynamics of the process, as well as preprocessing the data to remove noise, outliers, trends, or other disturbances. Additionally, it is important to choose a model that is suitable for your process characteristics and control objectives, and validate the model using independent data sets, residual analysis, model comparison, and performance evaluation methods. Furthermore, it is recommended to test the model using realistic scenarios and disturbances, and update the model periodically or adaptively to account for any changes in the process behavior or conditions.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?