Quaranta et al 2018a - Revision history

Rimni: /* 4. Data completion */

2021-07-07T14:23:01Z

‎4. Data completion

Rimni at 14:21, 7 July 2021

2021-07-07T14:21:49Z

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Rimni at 14:09, 7 July 2021

2021-07-07T14:09:24Z

Rimni at 14:08, 7 July 2021

2021-07-07T14:08:36Z

Rimni at 12:55, 7 July 2021

2021-07-07T12:55:56Z

Rimni at 12:53, 7 July 2021

2021-07-07T12:53:03Z

Rimni at 12:35, 7 July 2021

2021-07-07T12:35:02Z

Rimni: /* 3. Damage location via Machine Learning techniques */

2021-07-07T12:33:51Z

‎3. Damage location via Machine Learning techniques

Rimni at 12:29, 7 July 2021

2021-07-07T12:29:11Z

Rimni: /* 3. Damage location via Machine Learning techniques */

2021-07-07T12:26:33Z

‎3. Damage location via Machine Learning techniques

@@ Line 402: / Line 402: @@
 |[[Image:review_Quaranta_et_al_2018a-problem_2d_subdomains.png|600px|''Domain division for the dictionary learning.'']]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 5'''. Domain division for the dictionary learning
+| colspan="1" style="padding:10px;"| '''Figure 5'''. Domain division for the dictionary learning
 |}
@@ Line 516: / Line 516: @@
 | style="text-align: center;font-size: 75%;"|(c)
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 6'''. Results when using data completion for the first three different positions of the damaged zone
+| colspan="2" style="padding:10px;"| '''Figure 6'''. Results when using data completion for the first three different positions of the damaged zone
 |}
@@ Line 537: / Line 537: @@
 | style="text-align: center;font-size: 75%;"|(d)
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 7'''. Results when using data completion for the last two different positions of the damaged zone
+| colspan="2" style="padding:10px;"| '''Figure 7'''. Results when using data completion for the last two different positions of the damaged zone
 |}

@@ Line 398: / Line 398: @@
 <div id='img-5'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 50%;"
 |-
 |[[Image:review_Quaranta_et_al_2018a-problem_2d_subdomains.png|600px|''Domain division for the dictionary learning.'']]

@@ Line 388: / Line 388: @@
 |[[Image:review_Quaranta_et_al_2018a-identified_pca_complete_5.png|270px|First three principal components of the absolute value of the residual field for case (b) of  Figure&nbsp;[[#img-2|2]]. Red points belong to the damaged zone.]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" style="padding:10px;"| '''Figure 4'''. First three principal components of the absolute value of the residual field for case (b) of  Figure&nbsp;[[#img-2|2]]. Red points belong to the damaged zone
+| colspan="2" style="padding:10px;"| '''Figure 4'''. First three principal components of the absolute value of the residual field for case (b) of  [[#img-2|Figure 2]]. Red points belong to the damaged zone
 |}

@@ Line 395: / Line 395: @@
 The main difficulty when considering the approach discussed above is that the displacement field is needed in as many locations as possible (e.g. the nodes considered in the finite element mesh). Having access to all this local information could become prohibitive in practical applications. Thus, in this section, we consider data acquisition in few locations, from which fields are completed before applying the rationale discussed previously.
-For this purpose  a dictionary of simulations is performed, that contains the displacements and residuals fields everywhere for the damage located in different zones and taking different sizes (both perfectly known). In what follows we consider a subdivision of the domain like the one depicted in Figure&nbsp;[[#img-5|5]].
+For this purpose  a dictionary of simulations is performed, that contains the displacements and residuals fields everywhere for the damage located in different zones and taking different sizes (both perfectly known). In what follows we consider a subdivision of the domain like the one depicted in [[#img-5|Figure 5]].
 <div id='img-5'></div>
@@ Line 402: / Line 402: @@
 |[[Image:review_Quaranta_et_al_2018a-problem_2d_subdomains.png|600px|''Domain division for the dictionary learning.'']]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 5:''' Domain division for the dictionary learning.
+| colspan="1" | '''Figure 5'''. Domain division for the dictionary learning
 |}
-We consider 102 scenarios to create our dictionary: the first 48 are given by choosing as damaged zone one of the 16 areas depicted in Figure [[#img-5|5]] and assigning to each area 3 different sizes of the damaged zone. The others 54 scenarios are given by choosing as damaged area the 9 intersections of the previous areas (the red points in Figure [[#img-5|5]]) and assigning to each point 6 possible different sizes of the damaged zone centered on it.
+We consider 102 scenarios to create our dictionary: the first 48 are given by choosing as damaged zone one of the 16 areas depicted in  [[#img-5|Figure 5]] and assigning to each area 3 different sizes of the damaged zone. The others 54 scenarios are given by choosing as damaged area the 9 intersections of the previous areas (the red points in  [[#img-5|Figure 5]]) and assigning to each point 6 possible different sizes of the damaged zone centered on it.
 Obviously the dictionary can be enriched with many other locations and sizes of the damaged zone, but the goal in this work is to show how the dictionary learning technique can be used to perform data completion and for this reason the scenarios previously described seem sufficient.
@@ Line 496: / Line 496: @@
 As in the previous section the k-means technique is then applied on the absolute value of the completed residual field <math display="inline">\mathbf{R}_{com}</math>. Again, in order to reduce the dimensionality of the problem, the PCA is applied on the absolute value of the completed residual field before performing clusterization.
-Results on the damaged zone detection by using the proposed methodology for the different positions of the damage considered in the previous section are presented in Figures [[#img-6|6]] and [[#img-7|7]]. We can notice that  results are in good agreement to the ones presented in the previous section, with a quite good identification of the damaged zone.
+Results on the damaged zone detection by using the proposed methodology for the different positions of the damage considered in the previous section are presented in  [[#img-6|Figures 6]] and [[#img-7|7]]. We can notice that  results are in good agreement to the ones presented in the previous section, with a quite good identification of the damaged zone.
 <div id='img-6a'></div>
@@ Line 502: / Line 502: @@
 <div id='img-6c'></div>
 <div id='img-6'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;"
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_3.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_3.png|270px|(a)]]
-| (a)
+| style="text-align: center;font-size: 75%;"|(a)
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_5.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_5.png|270px|(b)]]
-| (b)
+| style="text-align: center;font-size: 75%;"|(b)
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_6.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_6.png|270px|(c)]]
-| (c)
+| style="text-align: center;font-size: 75%;"|(c)
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 6:''' Results when using data completion for the first three different positions of the damaged zone.
+| colspan="2" | '''Figure 6'''. Results when using data completion for the first three different positions of the damaged zone
 |}
@@ Line 523: / Line 523: @@
 <div id='img-7b'></div>
 <div id='img-7'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;"
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_9.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_9.png|270px|(d)]]
 |-
-| (a)
+| style="text-align: center;font-size: 75%;"|(a)
-| (c)
+|  style="text-align: center;font-size: 75%;"|(c)
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_10.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_10.png|270px|(e)]]
 |-
-| (b)
+| style="text-align: center;font-size: 75%;"|(b)
-| (d)
+| style="text-align: center;font-size: 75%;"|(d)
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 7:''' Results when using data completion for the last two different positions of the damaged zone.
+| colspan="2" | '''Figure 7'''. Results when using data completion for the last two different positions of the damaged zone
 |}
 ==5. Conclusions==

@@ Line 347: / Line 347: @@
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_3.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_complete_3.png|270px|(a)]]
-| (a)
+| style="text-align: center;font-size: 75%;"|(a)
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_5.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_complete_5.png|270px|(b)]]
-| (b)
+|style="text-align: center;font-size: 75%;"|(b)
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_6.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_complete_6.png|270px|(c)]]
-| (c)
+| style="text-align: center;font-size: 75%;"|(c)
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" style="padding:10px;"| '''Figure 2'''. Prediction versus reference damage location for the first three different positions of the damaged zone
@@ Line 369: / Line 369: @@
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_complete_9.png|270px|(d)]]
 |-
-| (a)
+| style="text-align: center;font-size: 75%;"|(a)
-| (c)
+| style="text-align: center;font-size: 75%;"|(c)
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_10.png|270px|]]
 |[[Image:review_Quaranta_et_al_2018a-identified_damage_complete_10.png|270px|(e)]]
 |-
-| (b)
+| style="text-align: center;font-size: 75%;"|(b)
-| (d)
+| style="text-align: center;font-size: 75%;"|(d)
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" style="padding:10px;"| '''Figure 3'''. Prediction versus reference damage location for the last two different positions of the damaged zone

@@ Line 357: / Line 357: @@
 | (c)
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 2'''. Prediction versus reference damage location for the first three different positions of the damaged zone
+| colspan="2" style="padding:10px;"| '''Figure 2'''. Prediction versus reference damage location for the first three different positions of the damaged zone
 |}
 <div id='img-3a'></div>
@@ Line 377: / Line 378: @@
 | (d)
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 3'''. Prediction versus reference damage location for the last two different positions of the damaged zone
+| colspan="2" style="padding:10px;"| '''Figure 3'''. Prediction versus reference damage location for the last two different positions of the damaged zone
 |}
 <div id='img-4'></div>
@@ Line 386: / Line 388: @@
 |[[Image:review_Quaranta_et_al_2018a-identified_pca_complete_5.png|270px|First three principal components of the absolute value of the residual field for case (b) of  Figure&nbsp;[[#img-2|2]]. Red points belong to the damaged zone.]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 4'''. First three principal components of the absolute value of the residual field for case (b) of  Figure&nbsp;[[#img-2|2]]. Red points belong to the damaged zone
+| colspan="2" style="padding:10px;"| '''Figure 4'''. First three principal components of the absolute value of the residual field for case (b) of  Figure&nbsp;[[#img-2|2]]. Red points belong to the damaged zone
 |}

@@ Line 343: / Line 343: @@
 <div id='img-2c'></div>
 <div id='img-2'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 800%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 80%;"
 |-
 |[[Image:review_Quaranta_et_al_2018a-correct_damage_3.png|270px|]]

@@ Line 192: / Line 192: @@
 Principal Components Analysis can be viewed as an information extractor from a data set that attempts to find a linear subspace of lower dimensionality than the original space. If the data has more complicated structures which cannot be well represented in a linear subspace, standard PCA fails for performing dimensionality reduction. In that case its nonlinear counterparts (kernel-based PCA or local-PCA) could be valuable alternatives for defining reduced bases.
-When projecting into this reduced basis the measured field, undamaged regions are expected being better approximated that the ones in which damage occurs. Thus, data-mining strategies could be then used to differentiate both regions (undamaged and damaged depicted in Figure [[#img-1|1]]).
+When projecting into this reduced basis the measured field, undamaged regions are expected being better approximated that the ones in which damage occurs. Thus, data-mining strategies could be then used to differentiate both regions (undamaged and damaged depicted in  [[#img-1|Figure 1]]).
 For that purpose, problem ([[#eq-7|7]]) is solved with the same geometrical and mechanical properties defined in  [[#table-1|Table 1]] but without any damaged zone.