Mercurial > hg > ltpda

comparison m-toolbox/html_help/help/ug/sdomainfit_content.html @ 0:f0afece42f48

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
parents
children
comparison
equal deleted inserted replaced
-1:000000000000 0:f0afece42f48
1 <!-- $Id: sdomainfit_content.html,v 1.3 2009/08/27 11:38:58 luigi Exp $ -->
2
3 <!-- ================================================== -->
4 <!-- BEGIN CONTENT FILE -->
5 <!-- ================================================== -->
6 <!-- ===== link box: Begin ===== -->
7 <p>
8 <table border="1" width="80%">
9 <tr>
10 <td>
11 <table border="0" cellpadding="5" class="categorylist" width="100%">
12 <colgroup>
13 <col width="37%"/>
14 <col width="63%"/>
15 </colgroup>
16 <tbody>
17 <tr valign="top">
18 <td>
19 <a href="#description">Description</a>
20 </td>
21 <td>S-domain system identification in LTPDA.</td>
22 </tr>
23 <tr valign="top">
24 <td>
25 <a href="#algorithm">Algorithm</a>
26 </td>
27 <td>Fit Algorithm.</td>
28 </tr>
29 <tr valign="top">
30 <td>
31 <a href="#examples">Examples</a>
32 </td>
33 <td>Usage example of s-domain system identification tool.</td>
34 </tr>
35 <tr valign="top">
36 <td>
37 <a href="#references">References</a>
38 </td>
39 <td>Bibliographic references.</td>
40 </tr>
41 </tbody>
42 </table>
43 </td>
44 </tr>
45 </table>
46 </p>
47 <!-- ===== link box: End ====== -->
48
49 <h2><a name="description">S-domain system identification in LTPDA</a></h2>
50 <p>
51 System identification in s-domain is performed with the function
52 <a href="matlab:doc('ao/sDomainFit')">sDomainFit</a>.
53 It is based on a modeified version of the vector fitting algorithm.
54 Details on the core agorithm can be found in [1 - 2].
55 </p>
56
57
58
59 <h2><a name="algorithm">Fit Algorithm</a></h2>
60
61 <p>
62 The function performs a fitting loop to automatically identify model
63 order and parameters in s-domain. Output is a s-domain model expanded
64 in partial fractions:
65 </p>
66 <div class="fragment"><pre>
67 r1 rN
68 f(s) = ------- + ... + ------- + d
69 s - p1 s - pN
70 </pre></div>
71 <p>
72 Since the function can fit more than one input analysis object at a time
73 with a common set of poles, output
74 <a href="parfrac.html">parfrac</a> are embedded in a
75 <a href="class_desc_matrix.html">matrix</a> (note that this characteristic
76 will be probably changed becausse of the introduction of the
77 <a href="class_desc_collection.html">collection</a> class).
78 </p>
79 <p>
80 Identification loop stops when the stop condition is reached.
81 Stop criterion is based on three different approachs:
82 <ol>
83 <li> Mean Squared Error and variation <br>
84 Check if the normalized mean squared error is lower than the value specified in
85 <tt>FITTOL</tt> and if the relative variation of the mean squared error is lower
86 than the value specified in <tt>MSEVARTOL</tt>.
87 E.g. <tt>FITTOL = 1e-3</tt>, <tt>MSEVARTOL = 1e-2</tt> search for a fit with
88 normalized meam square error lower than <tt>1e-3</tt> and <tt>MSE</tt> relative
89 variation lower than <tt>1e-2</tt>.
90 </li>
91 <li> Log residuals difference and root mean squared error
92 <ul>
93 <li> Log Residuals difference </br>
94 Check if the minimum of the logarithmic difference between data and
95 residuals is larger than a specified value. ie. if the conditioning
96 value is <tt>2</tt>, the function ensures that the difference between data and
97 residuals is at lest two order of magnitude lower than data itsleves.
98 <li> Root Mean Squared Error </br>
99 Check that the variation of the root mean squared error is lower than
100 <tt>10^(-1*value)</tt>.
101 </ul>
102 </li>
103 <li> Residuals spectral flatness and root mean squared error
104 <ul>
105 <li> Residuals Spectral Flatness </br>
106 In case of a fit on noisy data, the residuals from a good fit are
107 expected to be as much as possible similar to a white noise. This
108 property can be used to test the accuracy of a fit procedure. In
109 particular it can be tested that the spectral flatness coefficient of
110 the residuals is larger than a certain qiantity sf such that <tt>0 < sf < 1</tt>.
111 <li> Root Mean Squared Error </br>
112 Check that the variation of the root mean squared error is lower than
113 <tt>10^(-1*value)</tt>.
114 </ul>
115 </li>
116 </ol>
117
118 </p>
119 <p>
120 The function can also perform a single loop without taking care of
121 the stop conditions. This happens when <span class="string">'AutoSearch'</span> parameter is
122 set to <span class="string">'off'</span>.
123 </p>
124
125
126 <h2><a name="examples">Usage example of s-domain system identification tool</a></h2>
127 <p>
128 In this example we fit a given frequency response to get a partial fraction model.
129 For the meaning of any parameter please refer to
130 <a href="matlab:doc('ao')">ao</a> and
131 <a href="matlab:doc('ao/sDomainFit')">sDomainFit</a>
132 documentation pages.
133 </p>
134
135 <div class="fragment"><pre>
136 pl = plist(...
137 <span class="string">'fsfcn'</span>, <span class="string">'(1e-3./(f).^2 + 1e3./(0.001+f) + 1e5.*f.^2).*1e-10'</span>,...
138 <span class="string">'f1'</span>, 1e-6,...
139 <span class="string">'f2'</span>, 5,...
140 <span class="string">'nf'</span>, 100);
141
142 a = ao(pl);
143 a.setName;
144
145 <span class="comment">% Fit parameter list</span>
146 pl_fit = plist(...
147 <span class="string">'AutoSearch'</span>,<span class="string">'on'</span>,...
148 <span class="string">'StartPolesOpt'</span>,<span class="string">'clog'</span>,...
149 <span class="string">'maxiter'</span>,50,...
150 <span class="string">'minorder'</span>,7,...
151 <span class="string">'maxorder'</span>,15,...
152 <span class="string">'weightparam'</span>,<span class="string">'abs'</span>,...
153 <span class="string">'CONDTYPE'</span>,<span class="string">'MSE'</span>,...
154 <span class="string">'FITTOL'</span>,1e-3,...
155 <span class="string">'MSEVARTOL'</span>,1e-2,...
156 <span class="string">'Plot'</span>,<span class="string">'on'</span>,...
157 <span class="string">'ForceStability'</span>,<span class="string">'off'</span>);
158
159 <span class="comment">% Do fit</span>
160 mod = sDomainFit(a, pl_fit);
161 </pre></div>
162
163 <p>
164 <tt>mod</tt> is a <tt>matrix</tt> object containing a <tt>parfrac</tt> object.
165 </p>
166
167 <div class="fragment"><pre>
168 >> mod
169 ---- matrix 1 ----
170 name: fit(a)
171 size: 1x1
172 01: parfrac | parfrac(fit(a))
173 description:
174 UUID: 2dc1ac28-4199-42d2-9b1a-b420252b3f8c
175 ------------------
176 </pre></div>
177
178 <div class="fragment"><pre>
179 >> mod.objs
180 ---- parfrac 1 ----
181 model: fit(a)
182 res: [1.69531090137847e-006;-1.69531095674486e-006;1.39082537801437e-007;-1.39094453401266e-007;3.9451875151135e-007;-3.94524993613367e-007;4.53671387948961e-007;-4.53664974359603e-007;1124.81020427899;0.000140057852149302-i*0.201412268649905;0.000140057852149302+i*0.201412268649905]
183 poles: [-1.18514026248382e-006;1.18514354570495e-006;-0.00457311582050939;0.0045734088943545;-0.0316764149343339;0.0316791653277322;-0.276256442292693;0.27627799022013;330754.550617933;-0.0199840558095427+i*118.439896186467;-0.0199840558095427-i*118.439896186467]
184 dir: 0
185 pmul: [1;1;1;1;1;1;1;1;1;1;1]
186 iunits: []
187 ounits: []
188 description:
189 UUID: 2afc4c82-7c2a-4fe3-8910-d8590884d58c
190 -------------------
191 </pre></div>
192
193
194 <h2><a name="references">References</a></h2>
195 <p>
196 <ol>
197 <li> B. Gustavsen and A. Semlyen, "Rational approximation of frequency
198 domain responses by Vector Fitting", IEEE Trans. Power Delivery
199 vol. 14, no. 3, pp. 1052-1061, July 1999.
200 <li> B. Gustavsen, "Improving the Pole Relocating Properties of Vector
201 Fitting", IEEE Trans. Power Delivery vol. 21, no. 3, pp.
202 1587-1592, July 2006.
203 </ol>
204 </p>