Abstract
Safety-Critical Cyber-Physical System (SCCPS) refers to the system that if the system fails or its key functions fail, it will cause casualties, property damage, environmental damage, and other catastrophic consequences. Therefore, it is vital to verify the safety of safety critical systems. In the community, the SCCPS safety verification mainly relies on the statistical model checking methodology, but for SCCPS with extremely high safety requirements, the statistical model checking method is difficult/infeasible to sample the extremely small probability event since the probability of the system violating the safety is very low (rare property). In response to this problem, we propose a new method of statistical model checking for high-safety SCCPS. Firstly, with the CTMC-approximated SCCPS path probability space model, it leverages the maximum likelihood estimation method to learn the parameters of CTMC. Then, the embedded DTMC can be derived from CTMC, and a cross-entropy optimization model based on DTMC can be constructed. Finally, we propose an algorithm of iteratively learning the optimal importance sampling distribution on the discrete path space and an algorithm to check the statistical model of verifying the rare attribute. Eventually, experimental results show that the method proposed in this paper can effectively verify the rare attributes of SCCPS. Under the same sample size, comparing with the heuristic importance sampling methods, the estimated value of this method can be better distributed around the mean value, and the related standard deviation and relative error are reduced by more than an order of magnitude.
Highlights
Safety-Critical Cyber-Physical System (SCCPS) is characterized with high safety and high reliability and are widely used in fields closely related to the national economy and people’s livelihoods, such as aerospace, nuclear industry, public transportation, finance, and medical care
To evaluate the effectiveness and performance of the CrossEntropy Safety Verification Algorithm (CESVA) method proposed in this paper, we apply CESVA to a fault-tolerant controller for an aircraft elevator system (FTC4AE), that is, a Stateflow/Simulink hybrid system modeling case from MATLAB
E method proposed in this paper starts from the SCCPS path probability space, constructs a cross-entropy optimization model, and uses an iterative learning method to obtain an optimal importance sampling distribution from the parameterized distribution clusters of the path space
Summary
Safety-Critical Cyber-Physical System (SCCPS) is characterized with high safety and high reliability and are widely used in fields closely related to the national economy and people’s livelihoods, such as aerospace, nuclear industry, public transportation, finance, and medical care. Clarke and Zuliani [24] proposed the cross-entropy minimization importance sampling-based SMC method to verify the safety properties of the Stateflow/Simulink model system. By increasing the failure rate of the system parameters, several paths that satisfy the rare attributes are extracted at one time to calculate the optimal parameters for the exponential distribution to obtain an importance sampling distribution [25]. Jegourel et al [26] leveraged the cross-entropy minimum optimization method in the random model of a random guardian command system, which can approximate the path distribution of the system by increasing the number of commands (number of parameters), to obtain an importance sampling distribution in the random model. We propose a method with the SCCPS path space to construct a cross-entropy optimization model and use an iterative learning method to obtain an optimal importance sampling distribution from the parameterized distribution cluster of the path space. As evaluated in our experiments, the accuracy and efficiency of the rare attribute verification are significantly improved
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