The insights from this work highlight the critical role of trajectory library size in ensuring the accuracy and reliability of data-driven models for complex systems. To develop more efficient data collection strategies, one can focus on several key aspects:
Targeted Data Collection: Instead of random sampling, data collection efforts can be strategically focused on regions of the state space that are known to exhibit significant dynamics or where the system behavior is less understood. This targeted approach can help ensure that the trajectory library captures the most relevant dynamics, thereby improving the quality of the data-driven model.
Adaptive Sampling: Implementing adaptive sampling techniques can enhance data collection efficiency. By continuously evaluating the performance of the data-driven model, one can identify areas where additional data is needed and prioritize data collection in those regions. This iterative process allows for the dynamic adjustment of the trajectory library based on the evolving understanding of the system.
Utilization of Simulations: In scenarios where real-world data collection is costly or time-consuming, simulations can be employed to generate synthetic data that complements the real data. By simulating a variety of operating conditions and disturbances, one can enrich the trajectory library and ensure that it encompasses a wide range of system behaviors.
Incorporating Domain Knowledge: Leveraging domain-specific knowledge can guide the selection of lifting functions and the design of experiments. By understanding the underlying physics or mechanics of the system, one can make informed decisions about which trajectories to prioritize, thus enhancing the efficiency of data collection.
Balancing Width and Depth: The findings emphasize the importance of both the width (number of trajectories) and depth (length of trajectories) of the trajectory library. Data collection strategies should aim to achieve a balance between these two aspects, ensuring that the library is sufficiently rich to meet the persistent excitation condition while also being manageable in terms of data acquisition and processing.
By implementing these strategies, researchers and practitioners can optimize their data collection efforts, leading to more accurate and robust data-driven models for complex nonlinear systems.