28 Review of a Pilot Internet System Dynamics Course 277 The most current mathematical formulation of the UMPA Model is: n Pi D0 Œ˛i fXkC1gD m Pj D0 ˇj ffkC1g Time Domain n Pi D0 .Sk/ i Œ˛i fX.Sk/gD m Pj D0 .Sk/ j ˇj fF .Sk/g Generalized Frequency Domain Where Œ˛i is the i Coefficient Matrix of the response vector ˇj is the j Coefficient Matrix of input vector fxkCi g is the response vector time domain ˚fkCj is the input vector time domain fX.sk/g is the response vector frequency domain fF.sk/g is the input vector frequency domain k is the equation index I is the response index J is the input index s is the generalize frequency variable Using the UMPA procedure, it is possible to write a very small MATLAB script that will emulate nearly all of the current commercial time-domain algorithms. This is why the students are able to develop an emulation program in the 3–5 week period allocated in the SDA II course. In the SDA II course, the students are required to use the time domain UMPA model to emulate the Complex Exponential Algorithm (CAE), Ibrahim Time Domain (ITD), Polyreference Time Domain (PTD), and the Eigenvalues Realization Algorithm (ERA). All of these algorithms can be emulated using the ERA algorithm, so the students are required to write a MATLAB ERA script and then use this script to emulate the other algorithms. They are then required to process one analytical data set (a 15 DOF system) and the two C-Plate data sets measured in the SDA I class into modal parameters (eigenvalues, eigenvectors and modal scale factor). This basic process is demonstrated to the SDA class by emulating a single measurement using the ERA algorithm. This is one extreme of the emulation process since the ERA was developed to process MIMO data sets. A classroomdemonstration of this process is shown in a short document which is available for download. This document includes a boiler plate MATLAB program which demonstrates a number of ways of generating the data matrices for the UMPA ERA algorithm which is used, in turn, to emulate the CEA algorithm. The document also contains a second MATLAB script of the standard formulation of the CEA algorithm. Furthermore the document also includes several other small MATLAB scripts which are standard display and data manipulation scripts useful in developing MATLAB scripts. 28.10 SDA II Project The student groups are required to develop MATLAB software to extract modal parameters from analytical and measurement data sets of a component or systems’ measured FRFs, free decays, power spectrums, etc. The analytical data sets are a 15DOF system, and two FRF measurements sets are taken on the C-Plate structures described in the previous section. In the following section, a brief review of results of this project will be shown. However, a much more detailed review will be shown in results extracted from some typical student reports. This includes several MATLAB scripts, for processing the data sets, and a more extensive review of the data taken in SDA I as well as the results generated in the SDA II course. OverviewofSDAIandSDAIIResults: This hyperlink is a more detailed write-up of the theory, and a look at typical student results. 28.11 SDA III The main theme of the SDA III course is building dynamic system models directly from experimentally measured data. These models can be used to predict the influence of modifications to these systems and to validate or to update analytical
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