Nonlinearity in Structural Dynamics —— Detection, Identification and Modelling

----- 结构动力学中的非线性

ISBN: 9780750303569 出版年：2019 页码：680 Worden, K CRC Press

Summary chapter and guidelines on nonlinear procedures: Flow diagrams. Why not dynamical systems theory. Summary of linear system theory: Continuous-time. Discrete-time. Dynamic testing of linear and nonlinear structures: Simple procedures for detecting nonlinearity in dynamic testing. Sine, Chirp, Random, Impulse etc. Linearisation. Correlations-coherence. FRFs of linear and nonlinear systems: Harmonic balance. Averaging methods. Nyquist plots. Carpet plots. MDOF systems. Hilbert transform - a practical approach: Definition in terms of odd/even functions. Time-frequency domain definitions. Computation - fast method. Correction terms. Principal component analysis. Corehence. Damping estimation (Khalid's work). Linearisation from random testing. Spectral moments. Hilbert transform - a complex analytical approach: Contour integrals. Titchmarsh's theorem. Artificial noncausality. Correction for asymptotic behaviour. Viscous v. Hysteretic damping - exponential integrals. Pole-zero decomposition - estimation without truncation. Restoring force surfaces and direct parameter estimation: Masri/Caughey theory. Link models/Khalids approach. Application requirements - integration/differentiation of data. Least-squares estimation: Normal equations. Orthogonal estimator. SVD. Recursive LS. - forgetting factors. Discrete-time methods: NARMAX. AVD. Model validity. Functional series: Volterra series. Existence, uniqueness, convergence. Connection with Green's functions - calculation - symmetries. Fliess/Lamnabhi power series approach. Wiener series - high-dimensional correlations - Volterra limit. Higher order FRFs/Transfer functions: Harmonic probing. Interpretaton. SDOF/MDOF systems. Hypercurve fitting (S. Gifford). Convergence revisited (Dr Lee). Neural networks: Multi-layer perceptrons. Radial basis functions. Modelling nonlinear systems. Dynamics neurons. Networks as nonlinear dynamical systems. Classification of nonlinear systems: Pattern recognition/feature extraction. Wigner-Ville distribution. Wavelet transform. Neural networks. FRFs for classification SDOF/MDOF. Nonlinear least-squares: Piecewise-linear systems. Hysteretic systems. Yar/Hammond - GA parameter estimation. Gradient descent - shock absorber model.