# Data Fusion-Based Structural Damage Identification Approach Integrating Fractal and RCPN
## 4 Damage Identification of ASCE Benchmark Structure [41]
### Damage Detection Results of Single RCPN Classifier  
The Benchmark problem data generation program Datagen was used to simulate various structural damage conditions and generate time-history response data of each damage condition. Based on the measured response data obtained by the Y-direction sensor, the correlation dimension values of each sensor under various damage modes were calculated according to Equation (13) in Section 3.2, which was taken as the damage characteristic parameters and as the input vectors of the RPN network model. Considering the inevitability of noise in actual signal measurement, three noise levels of 30%, 50%, and 70% are generated in the simulation. \[y_{i}=y_{i}^{a}(1+\varepsilon R) \tag{17}\]  
Here, y\({}_{i}\) is the acceleration signal after noise pollution; \(y_{i}^{a}\) is the measured acceleration signal; \(R\) is a normally distributed random number with a mean of 0 and a deviation of 1; \(\varepsilon\) is the noise degree index, and here, \(\varepsilon\) is set as 0%, 50% and 70% respectively. Each damage condition at each noise level generates 1200 samples randomly; that is, each damage mode at each noise level can obtain 1200 correlation dimensions through calculation. These can be divided equally into two groups, namely, the first 6 \(\times\) 100 data were used as training samples, and the last 6 \(\times\) 100 data were used as test samples, which were divided into three groups (where each group has two columns, and each column has 100 correlation dimensions), represented by _NC1_, _NC2_ and _NC3_ (where each group has two columns). The RCPN structure of each noise level was the same. RCPN classifier 1 was taken as an example to illustrate the establishment process of the network model. Firstly, if the input vector is _NC1_, the number of neurons in the input layer is equal to the number of characteristic parameters of the sample, namely, the number \begin{table}
\begin{tabular}{c c} \hline
**Damage Pattern** & **Damage Simulation** \\ \hline
1 & Remove all support from the first layer \\
2 & Remove all supports from Layers 1 and 3 \\
3 & Remove 1 brachce from 1 st layer \\
4 & Remove 1 brachce each from the 1 st and 3 rd layers \\ \hline \end{tabular}
\end{table} 
Table 1: Structural damage simulation scenarios. Figure 3: ASCE benchmark structural model [41]. (**a**) Experimental model of steel frame. (**b**) Analysis model. of neurons in the input layer is 2. Secondly, the number of neurons in the output layer is equal to the number of damage modes; there are four damage modes in this paper, so the number of output neurons is four. Finally, the number of neurons in the competition layer is equal to the number of input samples. Since there are 400 samples, the number of neurons in the competition layer is 400, and the structure of the established RCPN model is 2-400-4. The identification accuracy of all training samples is 100%, and the RCPN network training is completed. Here, \(\alpha\) and \(\beta\) are both set as 0.1. There is a test sample \(A\) of network input, that is, the input layer provided by \(a_{i}\) to the network. The winning neuron \(g\) of the neurons in the competition layer can be obtained as follows:  
\[\mathrm{b}_{g}=\max_{i=1,2,\ldots,Q}(\sum_{i=1}^{N}w_{ji}a_{i}) \tag{18}\]  
Set \(b_{g}=1\), and the rest of the output equals 0, according to the equation \(c_{j}=v_{jg}b_{g}\), the output of each neuron in the output layer can be obtained. Thus, an output mode \(C=(c_{1},c_{2},\ldots,c_{M})\) is generated, and the corresponding classification result of the output is the classification result of input A. Damage identification accuracy (IA) is defined here as the ratio of the total number of correctly identified samples to the total number of tested samples.