Structural System Identification (KAIST, Summer 2017) Lecture Coverage: Lecture 1: System Theory-Based Structural Identification Lecture 2: System Elements and Identification Process Lecture 3: Time and Frequency-Domain Models Lecture4: Measurement Data and Impulse Response Functions Lecture 5: System Realization of Structural Models Lecture6: Extraction of Structural Parameters from Realization Lecture 7: Tutorials on System Identification Research Software Lecture 8: Recent Developments
Lecture 1: Systems Theory-Based Structural Identification What is system identification? For a given model characterized as ẋ(t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t), (1.1) utilizing the measured records of the input u(t) and the output y(t), the task of system identification is to determine the system model parameters, (A, B, C, D).
What is then dynamic response analysis? For a given model characterized as ẋ(t) = Ax(t) + Bu(t) y(t) = Cx(t) + Du(t), (1.2) assuming that the system model parameters, (A, B, C, D) and the excitation u(t) are known, the task of dynamic response analysis is to obtain x(t).
Develop an analytical model System identification process Establish the anticipated levels of responses Identify instrumentation needs, viz., actuators and sensors, their placement, etc. Carry out experiments (often many repeats for noisy systems) Employ system identification techniques to extract system parameters Construct an experimentally determined model Update the analytical model, and if necessary, repeat the process.
Major thrusts of this course Modal parameter identification or modal testing is a well-established discipline; System analysis and system identification for control problems are also a wellestablished discipline; However, model construction for each intended application is still wanting. For example, models for active control is normally different from models for passive vibration attenuation design purposes.
Major thrusts of this course - cont d Hence, experimental model determination for active control provides a basis for a wider class of application models. In addition, system theory-based realization methods offer the engineers to directly access modern noise filtering techniques, and new data processing tools such as wavelets and other filtering tools.
Emphasis of this course: Basic Theory Learn system theory-based realization fundamentals that yield minimum and unique order of identified models for noise-free data; Learn to utilize both FFT and Wavelet bases for data processing; Employ singular value decomposition as an indirect way of filtering noises and data-smoothing; Learn how to apply Kalmann filter and other filter theories Utilize the theory of observers for the improved identification of clustered frequencies and mode shapes.
Emphasis of this course: Applications Model development for control and design optimization Structural damage detection Non-structural inverse identification Application of various filtering theories and other de-noising techniques
Engineering analysis and system identification
System identification elements
1. Disturbances (input, u) and sensor output (y) Input signals must contain as large a number of frequency contents as possible. Input location(s) must be chosen to excite all the relevant dynamic responses for adequate identification synthesis (to be discussed more in detail later in the lecture) When only ambient excitations (e.g., bridges subjected to passing vehicles) are available, appropriate equivalent excitations need to derived. The same is true when only boundary displacements (velocities, accelerations) can be measured.
2. Signal conditioning Not only the input signal power but also the output signal sensitivity must be tuned to avoid saturations; Often the output signals need to be shaped, filtered and reconditioned to minimize noises. The suitability of each sensor type, e.g., strain gauge, displacement sensor, accelerometers, should be assessed and employed so that target measurement characteristics are adequately retained in the output signals (displacement sensor vs. fiber optics sensors, or even laser optics signals)
3. FRFs and IRFs This is, perhaps, the heart of the system identification process. The more accurate Frequency Response Functions (FRFs) and/or Impulse Response Functions (IRFs) one obtains from the measured (filtered) input and output data, the more accurate realization (i.e., obtain system matrices A, B, C, D ) is obtained. Ensembling can alleviate some levels of noises and inaccuracies in FRFs and/or IRFs, but not as effective as accurate FRFs and IRFs to begin with. In fact, a great deal of trade secrets are embedded in commercial system identification packages to advertise how cleaner FRFs or IRFs each package yields. In the context of the present lecture, signal processing and denoising techniques do bear their merits on how to obtain clean FRFs and/or IRFs.
4. Realization Input and output measured data consist of vectorial data. Realization process is to obtain system matrices (A, B, C, D) from the vectorial data. Here lies challenge. From the viewpoint of dat analysis, most realization can be viewed to exploit signal correlation matrices. The more diagonally dominated the corresponding correlation matrices, the more high-fidelity data subsequent realization can exploit.
5. Physical System Modeling From realized system matrices (A, B, C, D) Extract structural model matrices (M, D, K) While the singular values of A is the same, (A, B, C, D) are not unique. Hence, a series of transformations are necessary to arrive at (M, D, K) from the system identified matrices (A, B, C, D).
6. FEM/Active Control Models It is important to update FEM models for subsequent analysis and design optimization that yield the same static and dynamic properties as the identified models. Note that for control synthesis purposes, FEM models need to be further reduced as high-order models continue to challenge control synthesis procedures. Observe that models for structural analysis and optimization and those for control do not necessarily have to the same.
Analytical solution of impulse response functions
Analytical solution of impulse response functions
Analytical solution of impulse response functions
Matlab routines called
3 Degrees of freedom example
Analytical frequency response functions (FRFs)
Time histories of impulse response functions(irfs)
Random excitations for 3 DOF example problem
Computed impulse response functions excited by random input
Recap of system realization problem
Extraction of Physical Models from Realization