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...@@ -76,18 +76,18 @@ To improve the initial guess of the forces provided to the optimizer, the forces ...@@ -76,18 +76,18 @@ To improve the initial guess of the forces provided to the optimizer, the forces
> >
> The next iteration of optimization will be done on particles number 5 and 7 as they both have a solved contact from the neighbors (particles 3 and 4). All possible combinations for particle number 5 are illustrated in Fig.6. note that the contact force value with particles 3 and 4 are the same for all combinations. After this step of iteration, the particle 5 is solved but not the 7 (Fig.7). > The next iteration of optimization will be done on particles number 5 and 7 as they both have a solved contact from the neighbors (particles 3 and 4). All possible combinations for particle number 5 are illustrated in Fig.6. note that the contact force value with particles 3 and 4 are the same for all combinations. After this step of iteration, the particle 5 is solved but not the 7 (Fig.7).
> >
> <img src="uploads/c67491baa350db50f7252e0499c9b7b4/second_it.svg" width="800"> > ![img](uploads/c67491baa350db50f7252e0499c9b7b4/second_it.svg){width=800}
> >
> The next iteration of optimization will only be carried out on particles 6 and 7. The only unknowns are the contact forces with the walls. This step allows us to retrieve the photoelastic response of Fig.3. > The next iteration of optimization will only be carried out on particles 6 and 7. The only unknowns are the contact forces with the walls. This step allows us to retrieve the photoelastic response of Fig.3.
> >
> The following pictures show the same algorithm on a more complex example. The first picture is the experimental photoelastic response. The next pictures illustrate the iterations 1 to 5, after that the algorithm does not reach the specified SSIM value on any new particle and the optimization process ends. > The following pictures show the same algorithm on a more complex example. The first picture is the experimental photoelastic response. The next pictures illustrate the iterations 1 to 5, after that the algorithm does not reach the specified SSIM value on any new particle and the optimization process ends.
> >
> <img src="uploads/cadedc89a2659bbcb5d0d927d5767e85/Picture.png" width="250"> > ![img](uploads/cadedc89a2659bbcb5d0d927d5767e85/Picture.png){width=250}
> <img src="uploads/093ba577f1853595e148c32d324fb0da/synthetic0.png" width="250"> > ![img](uploads/093ba577f1853595e148c32d324fb0da/synthetic0.png){width=250}
> <img src="uploads/7ec3e96162cda9ad086b560426877142/synthetic1.png" width="250"> > ![img](uploads/7ec3e96162cda9ad086b560426877142/synthetic1.png){width=250}
> <img src="uploads/5cf649d69e2a1180a8a59511b339ceb9/synthetic2.png" width="250"> > ![img](uploads/5cf649d69e2a1180a8a59511b339ceb9/synthetic2.png){width=250}
> <img src="uploads/7e5f9fa31da2d739f34f372157221460/synthetic3.png" width="250"> > ![img](uploads/7e5f9fa31da2d739f34f372157221460/synthetic3.png){width=250}
> <img src="/ploads/a0ea651b60494eb790cef8ef30a2dac9/synthetic4.png" width="250"> > ![img](uploads/a0ea651b60494eb790cef8ef30a2dac9/synthetic4.png){width=250}
## 3. Examples ## 3. Examples
...@@ -95,16 +95,16 @@ To improve the initial guess of the forces provided to the optimizer, the forces ...@@ -95,16 +95,16 @@ To improve the initial guess of the forces provided to the optimizer, the forces
### Force propagation ### Force propagation
The following pictures show the picture of an experiment (left) and the corresponding photoelastic signal (right). In this experiment, the frame is vertically vibrated while the blender (stadium black shape at the center) oscillates by rotating around its upper extremity (that does not move vertically). In this experiment a circular bright-field polariscope is used, this is why the background is white. The following pictures show the picture of an experiment (left) and the corresponding photoelastic signal (right). In this experiment, the frame is vertically vibrated while the blender (stadium black shape at the center) oscillates by rotating around its upper extremity (that does not move vertically). In this experiment a circular bright-field polariscope is used, this is why the background is white.
<img src="uploads/6cb8360723ac75a52b43600e86d74bde/Wiki_Global.png" width="250"> ![img](uploads/6cb8360723ac75a52b43600e86d74bde/Wiki_Global.png){width=250}
<img src="uploads/31712778bfe2de3263c13d30a0b615cc/PhotoElast.png" width="250"> ![img](uploads/31712778bfe2de3263c13d30a0b615cc/PhotoElast.png){width=250}
The quality of the picture only allows us to correctly identify good enough initial forces to converge the photoelastic signal on disks with simple force distribution (top left figure). The force propagation procedure allows to reach convergence on more disks with more complex loading. The quality of the picture only allows us to correctly identify good enough initial forces to converge the photoelastic signal on disks with simple force distribution (top left figure). The force propagation procedure allows to reach convergence on more disks with more complex loading.
<img src="uploads/d5fa3d72a01cb149cfafe889ed594540/synthetic0.png" width="250"> ![img](uploads/d5fa3d72a01cb149cfafe889ed594540/synthetic0.png){width=250}
<img src="uploads/ffb7930bcf8f1ab5fc19bebfb92726ad/synthetic1.png" width="250"> ![img](uploads/ffb7930bcf8f1ab5fc19bebfb92726ad/synthetic1.png){width=250}
<img src="uploads/381567fa79c5355828309dfb539bbcae/synthetic3.png" width="250"> ![img](uploads/381567fa79c5355828309dfb539bbcae/synthetic3.png){width=250}
<img src="uploads/1f5ec507b8fef180cf598736c1f02c26/synthetic6.png" width="250"> ![img](uploads/1f5ec507b8fef180cf598736c1f02c26/synthetic6.png){width=250}
Eventually, the procedure did not succeed to reach convergences on all disks (bottom right figure) for reasons related to picture quality as well as assumption violation: Eventually, the procedure did not succeed to reach convergences on all disks (bottom right figure) for reasons related to picture quality as well as assumption violation:
* Some disks show so close fringes that the picture of the signal is just gray, leading to completely wrong forces estimation; * Some disks show so close fringes that the picture of the signal is just gray, leading to completely wrong forces estimation;
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