CSR: Small: Provably Correct Design of Observation for Fault Diagnosis and State Estimation under Privacy and Network Constraints

(NSF Project CNS-1816369)


During the operation of complex cyber-physical systems, operation planning and control need to be performed using limited available information. There are two reasons for this limitation. First, privacy issues may limit what information can be shared. Second, in a complex cyber-physical systems, not all state information can be measured, and the communication between subsystems may be limited.

These limitations give rise to a number of fundamental research questions as follows. Question 1: Can the right inference be made using the available state information, for the purposes of fault diagnosis and state estimation? Question 2: What state measurement or observation can be made available to facilitate the answer to Question 1 without violating privacy constraints? Question 3: When the information is transmitted through a non-ideal communication network, resulting in transmission delay or limited bandwidth, how does it affect Questions 1 and 2 above?

In this project we develop a framework that provides us with provably correct answers to all of the questions above. Our framework is a model-based approach to obtain provably correct methods for designing state measurement/observation that meets the need for fault diagnosis and state estimation while meeting privacy and network constraints. This is a hard problem especially for complex systems that are marked by hybrid behavior (i.e. involving both discrete and continuous dynamics), high dimensional state space, and nonlinear dynamics.

Our approach is based on approximating the behavior of the system, i.e. the set of all possible execution trajectories, with a behavior with finitely many trajectories that are obtained from numerical simulations. This approximation can be done with controllable precision, resulting in a trade-off between the complexity of generating the approximation and its precision. In this framework, state measurement/observation are performed by online monitors that implement dense time temporal logic formulae. The formulae are defined over measured variables (provided by sensors) and logical predicates over these variables (provided by software-defined sensors). We also develop a framework with which state observers will be designed on top of the online monitors.

In case the computation for creating the finite approximate behavior is prohibitively costly, we will also explore the use of randomized algorithms. We propose to develop a method to speed-up known randomized algorithms by exploiting the local properties of the generated samples.

Publications (only published peer-reviewed ones)

[1] Z. Xu, S. Saha, A. A. Julius, Provably Correct Design of Observations for Fault Detection with Privacy Preservation. In Proc. IEEE Int. Conf. Decision and Control, Melbourne, Australia, 2017.

[2] M. H. Jahnes, D. J. Glowny, T. A. Spafford, J. L. Clough, E. S. Herkenham, W. Wu, A. A. Julius. Generating Enthusiasm for Mathematics Through Robotics. In Proc. ASEE Annual Conference and Expositions, Columbus, Ohio, 2017.


Application in privacy and fault detection in smart buildings. Recently, we applied our framework on a model of the HVAC control in a smart building. The model is in the form of a switched dynamical systems consisting of differential equations that govern the evolution of the temperature and humidity in a room as affected by their environmental counterparts and the room occupancy.  The four states of the room are empty-normal, occupied-normal, empty-faulty, and occupied-faulty as shown in Fig. 1. Fault is represented as an open window that increases the thermal and humidity loads to the HVAC system. Similarly, room occupancy results in increasing thermal and humidity loads. To make the problem more interesting, we choose the model parameters such that the steady-state temperatures of the occupied-normal and empty-faulty modes are the same. We analyze the model and found that we can use the room temperature signal to detect the fault and to infer about the room occupancy. However, we are interested in figuring out if we can construct an observation that can be used to detect the fault but oblivious to the change in occupancy, because of privacy concern. Such observation can be constructed as an online monitor that implements a temporal logic formula that is constructed based on the the simulated trajectories of the model. The formula (not unique) that we computed reads: “(Between 160 and 180 s the temperature is always above 290.75) OR (between 0 and 20 s the temperature is sometime below 290.516 AND between 39 and 65 s the temperature is sometime above 290.525 AND between 122 and 161 s the temperature is sometime below 290.625)”

Figure 1
Fig. 1. Four modes of operation of the HVAC control system in a smart building.

Educational Outreach. This project supported Engineering Ambassadors, who created and presented STEM modules to K-12 students in the Capital Region of NY State. This year, we wrote and presented a paper at the 2017 ASEE Annual Conference in Columbus, OH. The paper presents data collected from our outreach activities at Berlin Junior/Senior High School in Berlin, NY and Lansingburgh High School in Troy, NY. The outreach activity was focused on generating enthusiasm for mathematics through robotics. Participants of these programs were asked to fill out a questionnaire before and after they take part in the program. The questionnaire consists of seven questions:
1. I enjoy doing activities within the area of robotics.
2. I enjoy doing activities within the subject of engineering.
3. I enjoy the subject of mathematics.
4. I enjoy the subject of science.
5. I enjoy doing activities like coding or computer science.
6. Mathematics is important when learning robotics.
7. The Engineering Design Process is an important tool for solving challenges.
The responses to the questionnaires are summarized in Fig. 2. To summarize, there is a statistically significant (p<0.05 in a paired t-test) increase in the participants' responses to the questions is all cases, except in the cases of Questions 3 and 4 in Lansingburgh High School. For these cases, however, we still observe a slight increase in the responses (p=0.06 and p=0.22, respectively).
Figure 2
Fig. 2. Survey results from our educational outreach activities showing statistically significant positive impacts on the participants.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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