## 4 Methods
### Connected and Automated Vehicles (CAVs) Data Characteristics and Anomaly Model
Similarly, Figure 14(a) indicates that the proposed method demonstrates a significant improvement by values of 0.7%, 5.3% and 1.1 compared with the performance of DWT- CNN, BDL and CNN respectively. Finally, results in Figure 14(b) also indicates that the propose approach provides significant improvement in performance by values of 2.1%, 0.4% and 2.6 over DWT- CNN, BDL and CNN, respectively. Figure 13: Detection performance and 95% CIs and CRIs across 15 to 20 different executions for all three methods, at anomaly rate \(\alpha=10\%\) an in the presence of all the types of anomalies. Discussion of the Mechanisms Under Multiple Anomaly

The purpose of this experiment is to establish a likely situation of multiple anomaly/attack which depicts real-time scenarios. The proposed approach demonstrates a reasonable detection performance as a result of the Bayesian prior probability to establish synergies/fusion between heterogeneous information and classification of out-of-distribution instances as unknown, for impressive detection of unknown attacks/anomalies in a system [40, 41]. ## 6 Conclusions

From CAVs framework standpoint, the proposed mechanism is developed by combining DWT and BDL. The DWT applies wavelet transform to decompose the sequence of measurements of the anomalous input vectors (BSMs sensor readings) and to denoise them before being fed into BDL for further analysis. The simulation results show the effectiveness of the proposed approach in real-time detection/identification of anomalous sensor values in CAVs setting. In particular, the experiment shows the ability of the proposed approach in adapting and capturing of anomalous behaviours in the unstable CAVs network states (density, duration and anomaly rate) and hence providing good

Figure 14: Performance Variation of the Various Methods trained on Instance Anomaly, on Gradual Drift Anomaly at \(\alpha=10\%\) and \(\alpha=10\%\). Figure 15: Performance Variation of the Various Methods trained on Bias Anomaly, on Gradual Drift Anomaly at \(\alpha=50\%\) and \(\alpha=50\%\). performance. More specifically, simulation results shows the ability of the proposed approach to detect and identify anomalous sensor values in real time with high precision, accuracy, F1-score and sensitivity by using BDL empowered by DWT on raw sensor data. Moreover, the simulation results show the performance gain of the proposed approach in comparison with the baseline mechanisms, with a significant difference. The anomalous values of sensors used in the experiments are simulated, along with previous literature researches, primarily because this form of data is not yet readily available. Additionally, the tests are limited to on-board sensors due to the lack of data on CAVs. As a conclusion, manufactures and policy-makers will benefit from the findings in this study on the importance of providing redundant information for a particular parameter such as curvature radius and speed of a vehicle. Consequently, more redundant sensors and systems for collecting information may be introduced and considered in CAVs to improve their resilience against anomalous sensor values. The proposed mechanisms presented in this paper are also intended to be extended to various sources of CAVs/M2M networks to improve their safety. [PERSON] conceived and designed the experiments as well as analyzing the data generated from the experiments. [PERSON], S.A., L.M.S.-J., A.P., and D.C.-D.-W. reviewed and discussed the manuscript. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Authors thank to the WiCIP Lab for providing all the equipment necessary to collect the information which is analyzed and discussed in this manuscript. The authors declare no conflicts of interest. ## References

* [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] Entropy-Based Recommendation Trust Model for Machine to Machine Communications. In _Ad Hoc Networks_; Springer: Berlin, Germany, 2017; pp. 297-305. * [PERSON] et al.