Parameter Identification in Time Domain and Frequency Domain for Dynamic Systems

Time domain and frequency domain parameter identification methods in system identification represent two crucial technical approaches for analyzing dynamic systems. Time domain identification utilizes temporal signal characteristics such as step responses and impulse responses, employing algorithms like least squares method or maximum likelihood estimation to fit differential equation parameters. This approach is particularly suitable for systems with pronounced transient processes, where implementation often involves solving optimization problems through iterative algorithms like gradient descent or Gauss-Newton methods. Frequency domain identification employs sine sweep or noise excitation to obtain Frequency Response Functions (FRF), identifying transfer function parameters through Bode plots or Nyquist diagrams. This method demonstrates superior performance in noise suppression and resonance peak detection, typically involving Fast Fourier Transform (FFT) processing and complex curve fitting techniques. The two methods are frequently combined in practice: time domain data reflects dynamic characteristics while frequency domain data reveals steady-state harmonic properties. Complementary validation through both domains significantly enhances model accuracy, where cross-validation can be implemented using correlation analysis or residual checking algorithms. In practical engineering applications, selection between methods depends on signal types, sampling conditions, and system nonlinearity degrees, often requiring preliminary analysis using statistical tests or model order selection criteria before final implementation.