This section revisits the research question and associated research issues presented in Chapter 1 (Section 1.3) and describes how each was resolved in terms of a set of “main findings”. The section is organised by considering each of the identified research issues in turn as follows.
1. Training Set Generation. The challenge of how best to generate the required train- ing data was resolved by first converting the input clouds into a grid representation which allowed for comparison of two surfaces. By comparing the two surfaces, and using normal calculations, it was possible to determine the springback values as- sociated with individual grid squares. This then provided for a generic format in which to present training data. In total eight different raw data sets were used.
An issue was the optimum value for d the size of the grid representation, to be used. The conducted experimental analysis established that there was no best overall value for d, but that each technique had a specific best value associated with it: d= 10 mm was found to be the best grid size for the LGM techniques, (ii) d = 2.5 mm was was found to be the best grid size for the LDM technique and (iii) d= 5 mm was was found to be the best grid size for the PS techniques. By using different values for d, a large collection of training data were produced, and successfully utilised with respect to the evaluation of the different surface representations. As noted above, the advantage offered by the grid representation was its generic nature and its compatibility with “higher level” representations. It is difficult to conceive of alternative formats for the training data that offer the same advantages and thus it is suggested here that the grid representation is the most appropriate format for training set generation (more details can be found in Chapter 3).
2. 3D Surface Representation. The main challenge for this thesis was to determine the most appropriate 3D surface representation in order to capture the most im- portant local geometrical features (in the context of sheet metal forming) and consequently facilitate the operation of the classification process. This was ad- dressed through presenting three different surface representation techniques based on three different concepts: (i) the LGM technique was founded on representing the geometrical information in terms of the local surrounding neighbourhood, (ii) the LDM technique was founded on representing a 3D surface in terms of its “crit- ical” features and (iii) the PS technique was founded on the idea of representing a 3D surface in terms of “curves”. The three techniques were presented in Chap- ters 4, 5 and 6 respectively. An extensive evaluation of the proposed techniques
was conducted. Two types of classifier performance experiments were conducted: (i) classifiers trained and tested on the same data and (ii) classifiers trained and tested on different data. The evaluation of the proposed techniques indicated that the PS techniques produced the best overall classification performances in that it outperformed the other techniques in terms of accuracy and AUC. In order to significantly differentiate between the operation of the proposed techniques, a statistical evaluation based on the Friedman and Nemenyi statistical tests was performed. This also confirm the superiority of the PS techniques with respect to the other techniques considered (more details can be found in Chapter 7).
3. Best Classification Technique. The challenge of identifying the most suitable clas- sification techniques with respect to each proposed representation technique was resolved by selecting a number of popular classification techniques: (i) C4.5, (ii) Bayes, (iii) JRIP, (iv) PART, (v) Neural Network and (iv) k-Nearest Neighbour (k-NN). The generated classifiers were then incorporated into the IPM concept to predict the errors (springback) and generate corrected clouds. The obtained results indicated that there were no significant difference between the different supervised classification technique considered, but the C4.5 technique was selected to be the most suitable when using the LGM and LDM techniques due to its simplicity and powerful interpretation capabilities, especially for non experts from other fields. The last technique (k-NN) was found to be the most suitable classification tech- nique with respect to the PS technique. Despite the advantages offered by the labelling concept, label size was an issue. The uneven distribution of the spring- back phenomena over shapes was the main reasons behind this issue. However, to eliminate the effect of springback distribution, equal frequency discretising was adopted.
4. Corrected Input Generation. The challenge of how the predicted errors can best be translated into an acceptable format for the manufacturing process was resolved by applying the predicted errors in the reverse direction to generate a “corrected cloud”. Practically, the corrected cloud was successfully applied in a real manu- facturing environment and the effect of the springback in the produced parts was minimised (more details can be found in Chapter 8). However, the challenge to obtain the most “optimal” corrected cloud was resolved by the proposed iterative IPM process where the corrected cloud was repeatedly generated until an optimal cloud was obtained (more details can be found in Chapter 9).
Returning to the main research question “How best can 3D surfaces be represented to reflect local geometrical information according to certain feature(s) of interest so that classification techniques can be applied effectively?”. The techniques presented in Chap- ters 4, 5 and 6 respectively, clearly indicated that local geometrical information can be represented effectively using any of these techniques. However, the PS technique was found to outperform the other techniques. The statistical evaluation confirmed that
the PS technique was the “best” techniques. However, all the proposed representations could easily and effectively be used to generate a classifier that served to predict the feature of interest (springback value in our case). It was also demonstrated that the springback predictions could be successfully utilized to manufacture better parts.
The main contributions of the work described in this thesis may be summarised as follows:
1. A grid representation which provides for the comparison of 3D surfaces.
2. A springback calculation mechanism to identify the springback values between the desired and the actual formed shape (given appropriate before and after data).
3. The RASP framework to support the classifier generation process.
4. The LGM surface representation technique that was used to describe 3D surfaces in terms of local neighbourhoods.
5. The LDM surface representation technique that was used to represent 3D surfaces in terms of proximity to the nearest corner or edge.
6. The PS surface representation technique that was used to describe 3D surfaces in terms of point series curves.
7. A statistical comparison to identify the significant difference between the proposed techniques.
8. A mechanism to generate corrected clouds based on the predicted values.
9. The concept of an Intelligent Process Model that combines the proposed techniques with the corrected cloud generation mechanism into a single process with respect to sheet metal forming.