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Modeling foundations for executable model-based testing of self-healing cyber-physical systems

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Abstract

Self-healing cyber-physical systems (SH-CPSs) detect and recover from faults by themselves at runtime. Testing such systems is challenging due to the complex implementation of self-healing behaviors and their interaction with the physical environment, both of which are uncertain. To this end, we propose an executable model-based approach to test self-healing behaviors under environmental uncertainties. The approach consists of a Modeling Framework of SH-CPSs (MoSH) and an accompanying Test Model Executor (TM-Executor). MoSH provides a set of modeling constructs and a methodology to specify executable test models, which capture expected system behaviors and environmental uncertainties. TM-Executor executes the test models together with the systems under test, to dynamically test their self-healing behaviors under uncertainties. We demonstrated the successful application of MoSH to specify 11 self-healing behaviors and 17 uncertainties for three SH-CPSs. The time spent by TM-Executor to perform testing activities was in the order of milliseconds, though the time spent was strongly correlated with the complexity of test models.

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Notes

  1. The term of self-healing originates from the IBM’s vision of autonomic computing [3], and self-healing is one of the so-called self-* properties. Self-healing is tightly related to “fault-tolerant,” but not all fault-tolerant mechanisms can be seen as self-healing behaviors.

  2. The reason to select RAMA as the running example is that RAMA is an example of SH-CPS and contains a set of self-healing behaviors that are affected by uncertainties.

  3. \( M_{\text{Low}} (10) = 1/\left( {1 + e^{{0.1 \cdot \left( {\left| {10} \right| - 10} \right)}} } \right) = 0.5 \).

  4. In case a system behaves differently from a test model that is derived from an incomplete requirement, it only indicates that a potential fault has been detected. Developers or designers who have more knowledge of the requirement can determine whether it is indeed an implementation fault.

  5. Include Gauss, generalized bell, triangular, difference between two sigmoid, pi-shaped, sigmoid functions.

  6. Include Poisson, Bernoulli, categorical, logarithmic, discrete uniform, exponential, gamma, normal, triangular, and trapezoidal distributions.

  7. If the value of an uncertain feature depends on the values of some other uncertain features, OCL constraints can be used to specify the dependency.

  8. Though there are several other co-simulation standards, such as HLA (coming from military applications) and SMP (in the space domain), FMI gained the most attention from both research and industry. Thus, it is used in our work.

  9. There are four kinds of standard interfaces defined in FMI: init, which initializes the execution time of a FMU; set, which assigns a given value to a variable in a FMU; get, which queries the value of a variable in a FMU; and doStep, which performs an execution step on a FMU, using a given step size Δt.

  10. We could not use PeMS and VSS to answer RQ3 as we didn’t have access to their implementations.

  11. One example of the product specifications can be downloaded from:

    https://www.invensense.com/wp-content/uploads/2015/02/MPU-6000-Datasheet1.pdf.

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Acknowledgements

This work was supported by the MBT4CPS (Project# 240013) project funded by the Research Council of Norway (RCN). Tao Yue and Shaukat are also supported by the Zen-Configurator project (Project# 240024) of RCN.

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  1. Simula Research Laboratory, Oslo, Norway

    Tao Ma, Shaukat Ali & Tao Yue

  2. University of Oslo, Oslo, Norway

    Tao Ma & Tao Yue

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Correspondence to Tao Yue.

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Communicated by Dr Juergen Dingel.

Appendices

Appendix A: Execution process of an executable test model

This appendix presents an activity diagram to illustrate the execution process of an executable test model (Fig. 15).

Fig. 15
figure 15

Execution process of an executable test model

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Appendix B: Extensions to fUML and PSSM

To facilitate executable model-based testing, we made several extensions to fUML and PSSM, and they are given in Table 13.

Table 13 Summary of the extensions to fUML and PSSM
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Ma, T., Ali, S. & Yue, T. Modeling foundations for executable model-based testing of self-healing cyber-physical systems. Softw Syst Model 18, 2843–2873 (2019). https://doi.org/10.1007/s10270-018-00703-y

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