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<h1>Data Matching Component</h1>


<table>
	<th colspan=2>Data Matching - Two Springs</th>
	<tr>
		<td>Description:</td>
		<td>
			<p>The Data Matching component is often used to help solve optimization problems when there are physical systems that can be used for experimental testing. These physical systems can typically be correlated to computational codes that are created to model these systems. When you have both of these types of models, you can create both sets of data by either running the experiments on the physical model and by executing the computational model on the same input data points. The optimization consists of minimizing the difference between the output data set points of the two models.</p>
			<p>The Two Spring problem is a two degree of freedom model consisting of two masses in series (M1 and M2), each mass attached with a spring constant (k1 and k2) and a damping coefficient (c1 and c2), as shown in the figure below. This system is then driven by a forcing function (f) which has a periodic sinusoidal input, and this forcing function is applied to M2 as shown. These values of M1, M2, k1, k2, c1, c2, and f are the input parameters to the design problem.
			<img class="figure" src="images/figure1.png" alt="Figure 1" /></p>
			<p>A simulation code is written in Fortran that computes several output parameters based on the input parameter values. These outputs are the displacement, velocity, and acceleration of each mass over time. The drawing below shows what each of those values corresponds to on the physical model.
			<img class="figure" src="images/figure2.png" alt="Figure 2" /></p>
			<p>These outputs are computed by the simulation code and plotted over time to yield a lot that looks like the following.
			<img class="figure" src="images/figure3.png" alt="Figure 3" /></p>
			<p>For testing of this model, the forcing function (f) is varied at regular intervals and the values for the maximum displacement, velocity, and acceleration are computed for a range in input forcing function. The resulting plot looks something like the following.
			<img class="figure" src="images/figure4.png" alt="Figure 4" /></p>
			<p>The simulation code is also written to compute these maximum values over the range of values for the input forcing function. It is this computed data of maximum displacement over the range of input forcing function that we will try to match up with the measured data of the same values.</p>
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		<td>Model:</td>
		<td><a href="TwoSprings.zmf">TwoSprings.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Simcode, Data Matching</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None - all in model</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None - all in model</td>
	</tr>
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