## 3 Laboratory Experiment
### Damage Detection
In Figure 6b, it can be seen that some anomalies are precisely recognized, while the others are not, so the problem was more carefully studied, and the results (for the ANN architecture 6-35-4) are shown in Figure 7. In this figure, the value that equals 0 corresponds to the correct tightening of  
\begin{table}
\begin{tabular}{|c|c|c|c|} \hline Input & Target & Output & Success Ratio \\ \(\mathbf{x}\) & \(\mathbf{t}\) & \(\mathbf{y}\) & \(SR\) \\ \hline \multicolumn{4}{|c|}{ANN TYPE 1} \\ \hline \multicolumn{4}{|c|}{\(\mathbf{x}=\{a,b,c,d,e,f\}\)} & \(\mathbf{t}=\{C\}\) & \(\mathbf{y}=\{C\}\) & \(87\%\) \\ affine transformation parameters & \(C\) - integer parameter & \(C\) - continuous value & \\  & describing the class & from the range & \\  & of anomaly & & \\  & \(C\in\{0,1,2,3,4,5,6,7,8\}\) & \(C\in<0,8>\) & \\ \hline \multicolumn{4}{|c|}{ANN TYPE 2} \\ \hline \multicolumn{4}{|c|}{\(\mathbf{x}=\{a,b,c,d,e,f\}\)} & \(\mathbf{t}=\{R1,R2,R3,R4\}\) & \(\mathbf{y}=\{R1,R2,R3,R4\}\) & \(94\%\) \\ affine transformation parameters & \(R1,R2,R3,R4\in\{0,1\}\) & \(R1,R2,R3,R4\in<0,1>\) & \\ \multicolumn{4}{|c|}{\(R_{r}\) - parameter} \\ \(\mathbf{x}=\{\Delta x_{1},\Delta x_{2},\Delta x_{3},\Delta y_{1},\Delta y_{2}, \Delta y_{3}\}\) & describing the condition & \\  & of \(r\)-th row of bolts & \\  & of every triangle vertex & \\ \(\mathbf{x}=\{\Delta x_{1},\ldots,\Delta x_{4},\Delta y_{1},\ldots,\Delta y_{4},\}\) & \\  & differences in location of every & \\  & vertex of the quadrangle & \\ \hline \multicolumn{4}{|c|}{ANN TYPE 3 - two-step procedure} \\ \hline \multicolumn{4}{|c|}{\(\mathbf{x}=\{a,b,c,d,e,f\}\)} & \(\mathbf{t}=\{D\}\) & \(\mathbf{y}=\{D\}\) & \(100\%\) \\ affine transformation parameters & \(D\in\{0,1\}\) & \(D\in<0,1>\) & appearance \\ \multicolumn{4}{|c|}{or} \\ \(\mathbf{x}=\{\Delta x_{1},\Delta x_{2},\Delta x_{3},\Delta y_{1},\Delta y_{2}, \Delta y_{3}\}\) & \(D\) - parameter & \\  & differences in location & describing occurrence & 95\% \\  & of every triangle vertex & of anomaly in the selected type & size \\ \hline \multicolumn{4}{|c|}{\(\mathbf{x}=\{D^{500},D^{533},D^{522},D^{523},D^{544},\)} & \(\mathbf{t}=\{C\}\) & \(\mathbf{y}=\{C\}\) & \\ \(D^{534},D^{514},D^{511},D^{512}\}\) & \(C\in\{0,1,2,3,4,5,6,7,8\}\) & \(C\in<0,8>\) & \\  & \(D^{534},D^{514},D^{511},D^{512}\}\) & in task & 92\% \\  & of location determination & & location \\  & or & \(C\in\{0,the fasteners (no defect identified); when it equals 1, the bolts in the considered row are loosened (a defect is found). A careful analysis of the charts shows that some different anomalies provide the same output vectors; e.g., Class S11 (damage only in the first row, \(\mathbf{t}^{i}=\{1,0,0,0\}\), see Table 1, in many cases gives \(\dot{\mathbf{y}}^{i}=\{1,0,0,1\}\)) is similar to Class S14 (damage in the first and fourth row, \(\mathbf{t}^{i}=\{1,0,0,1\}\), but in some cases \(\dot{\mathbf{y}}^{i}=\{1,0,0,0\}\)). The efficiency of the precise determination of the type of anomaly by the networks of this architecture remained at the same level regardless of the adopted input parameters (parameters of affine transformation or the difference in the position of the triangle or quadrangle vertexes). Considering the fact that some of the anomalies produce very similar effects, a different approach was considered. The two-step procedure, called \"ANN Type 3\", in which ANN Type 1 was combined, was implemented. Firstly, nine ANN Type 1 procedures were adopted, each trained to recognize only one type of anomaly (\(\mathbf{y}=D\)). Each time, the number of neurons in the hidden layer was optimized in an analogous manner, as described previously. The results of damage detection in nine analyzed cases are presented in Figure 8. It is also clearly visible in this case that some of the anomalies are precisely detectable when others are not. Therefore, the combination of all nine outputs should be the base for  
Figure 4: (a,b) One- and (c) two-step procedure for anomaly detection using ANNs.