## 3 System Model and Problem Description  
We consider a delivery urban air mobility infrastructure in a wireless network, where RF signals and their sensory observation autonomously control the delivery drones as shown in Figure 1. Jamming and spoofing are the most common attacks for commercial UAM. The attacker attacks to steal the UAV and corresponding delivery goods, while in some cases, the intention is to crash the UAV. We consider that \(d\subset\mathcal{D}\) is \(N\)-dimensional data that control the UAM attitude and a binary variable \(\hat{x}=\{0,1\}\), where \(\hat{x}=1\) denotes an attack; otherwise, it is \(0\). Using the observation of historical UAM operational data, we can train the AI model. Consider each historical observation \(d\subset\mathcal{D}\) labeled with a binary indicator \(x=\{0,1\}\). Then, we can define the AI model as a function of historical observation \(d\subset\mathcal{D}\), given the label \(x=\{0,1\}\). The learning model can defined as follows:  
\[f(\mathcal{D}|x)=\min\phi(\sum_{\forall d\in\mathcal{D}}|x-\hat{x}|), \tag{1}\]  
where \(\hat{x}=1\) denotes an attack; otherwise, it is \(0\). In this work, our goal is to develop an AI-enabled analytical framework to predict and protect UAVs from cyberattacks and crashes. Therefore, we consider the data \(\mathcal{D}\) that include the behavior of a UAV's attitude [6; 25] and their changes in Equation (1) so that we can proactively detect abnormal attitudes caused by jamming or spoofing attacks. Therefore, it is imperative to build an analytical model based on the outcome of Equation (1) to proactively manage a UAV under a cyber-physical threat. In this work, we consider the Pearson's correlation coefficient [15] to analyze an upcoming event \(\hat{x}\). The Pearson's correlation coefficient [15] model for current UAM observation \(\hat{d}\) is formalized as follows:  
\[g(A,B)=\frac{\mathrm{E}(AB)-\mathrm{E}(A)\mathrm{E}(B)}{\sqrt{\mathrm{E}(A^{2 })-\mathrm{E}(A)^{2}}\sqrt{\mathrm{E}(B^{2})-\mathrm{E}(B)^{2}}}, \tag{2}\]  
where \(A\) and \(B\) are two random variables of UAM observation \(\hat{d}\). Therefore, the correlation coefficient for \(N\)-dimensional UAM in the observation \(\hat{d}\) can be represented as follows:  
\[G(\hat{d}|\hat{x})=\sum_{n\in N}\frac{\mathrm{E}(A_{n}B_{n})-\mathrm{E}(A_{n} )\mathrm{E}(B_{n})}{\sqrt{\mathrm{E}(A_{n}^{2})-\mathrm{E}(A_{n})^{2}}\sqrt{ \mathrm{E}(B_{n}^{2})-\mathrm{E}(B_{n})^{2}}}. \tag{3}\]  
Figure 1: System model of urban air mobility cyber-physical system. Equation (3) can determine the effect of the decision of the variable \(\hat{x}=\{0,1\}\). In this system model, our goal is to predict the status of a cyberattack \(\hat{x}\) using the trained model in Equation (1) and analyze the effect of that result on a UAM control message, such as longitudinal and roll, transverse and pitch, and vertical and yaw motions for controlling UAM attitude. Furthermore, the Pearson's correlation coefficient-based analytical model can find the switching states and received signal strength indicator of switching states so that the UAV becomes protected from being stolen or lost. In other words, the proposed exploratory cyber-physical safety analyzer framework can proactively detect jamming and spoofing attacks on UAVs while also being capable of analyzing the changes in parameters' values which are caused by such attacks. The UAM hacker or hijacker may set a target to steal or crash a UAV, which ends up as a loss of a UAV for the owner. Based on the proactive detection and characterizing changes of the parameters, the UAM provider can take the necessary steps to protect UAM from theft or loss by updating the UAM controlling parameters. The proposed system model provides a generic framework, where an AI model \(f(\mathcal{D}|x)\) can be trained by using existing AI algorithms that include decision trees, random forests, logistic regression, KNN, and LSTM to detect jamming and spoofing attacks.