## 5 Simulation Results
### Validating the Multi-Layer Based Proposed Security Approach  
This section is dedicated to illustrating and validating the efficiency of the multi-layer security approach against cyber-attacks. To this end, we try to use the probability computing approach to reveal the probability of successful attacks. In addition, validating this method is represented by comparing to the other methods such as single-layer security based on machine learning and blockchain concepts. As it was said in previous sections, the blockchain technology in this approach is utilized to secure and cover over the network as the public defense in the first place. On the other hand, the machine-learning-based private defense as the second layer is obliged to only safe the vulnerable and sensitive points of the grid to prevent the unauthorized access of hackers. Keeping this brief description in mind, it is needed to first provide how the blockchain system can secure the network. In this paper, we focus on an attack of FDI type in order to calculate the probability and assess the functionality of the blockchain. It is significant to say that such attacks do not interrupt the network but they will lead to misgiving. Hence, the attacker tries to penetrate the network for an FDI attack. This work can be carried out everywhere in the network. When making a cyber-penetration within the network, it is needed to compute the probability of an attack launched by hackers. Hence, the successful probability of attacks for carrying out destruction can be achieved in the following:  
\[\lambda=h(X_{d}+c)-h(X_{d}) \tag{45}\]  
\[P_{a}=\frac{1}{3}\left(\prod_{k=1}^{n}\lambda_{k}\right) \tag{46}\]  
where, \(0\leq\lambda_{k}\leq 1\), \(k=1,\ 2,\ \ldots,\ n,\ \ldots,\ N\). In the above equation, \(\lambda\) is the attack vector, \(c\) is a factor that defines the alternation of data due to the attack \(X_{d}\) defines the data of the system. As \(h(0)\) shows the function of the measurement device based on the relevant data can be different for each device. The success probability of attack (\(P_{a}\)) can be computed by Equation (46) in which \(n\) is the number of attacks and \(\lambda\) indicates the occurring probability of attack in iteration \(k\) for the system. In addition, the attack needs to update its data to delude the system's devices. According to the argument aforementioned, the Sabotage probability in the network is dependent on the type of cyber-security scheme considered for preventing attacks. Firstly, we implement three cases based on the security approach including, case1: the single-layer security schemes based on the machine learning method, case 2: the block-chain-based single-layer security case 3: the multi-layer based proposed security method. Moreover, we try to prove the proposed security framework (case 3) in order to prevent the attack in vulnerable areas of the network structure compared to the other cases. In the first step, we as an FDI attack apply the incorrect data to the measurement devices based on (45) in order to monitor these data for the network operator. This process continues for iteration number 100 under launching three cases based on the security scheme (second step). As the last step, we compute the successful probability of attack for three schemes considering Equation (46). For instance, regarding the reinforcement learning method (case 1), the occurring probability of attack will be \(1\) if not detected by the RL method. This description can be expanded for other cases in order to calculate the attack probability in system. In this regard, by launching a FDI attack in the network, the successful probabilities of this attack for three cases are calculated and represented in Figure 15. It can be seen in this figure, by increasing the percentage of iteration, the successful probability of attack in the proposed method is more downtrend than case 1 and case 2 for the various iterations.