In modern engineered systems, cyber and physical components have been increasingly integrated for the purpose of monitoring and control. Advances in sensor hardware and networks have been critical to this development, as sensors form the key linkage between the cyber and physical domains. In this way, sensors are often the key source for real-time disaster risk information and can detect functional degradation when disasters occur.
These advances have greatly increased the number of potential data streams available for users to analyze. They have been accompanied by the rise of increasingly advanced analytical methods such as artificial intelligence, machine learning, and digital twins. As the capacity to draw insights from more complex and heterogeneous data sources has improved, advanced sensor networks have become nearly ubiquitous in applications across diverse domains, from intruder detection to power and water system monitoring.
However, with this increased cross-domain integration also come new and poorly understood threats that may cascade and propagate in unexpected ways. Sensors, in particular, are vulnerable to attacks in both the cyber (e.g., cyberattacks) and physical domains (e.g., targeted attacks, natural hazards, and disasters). The vulnerability at the data source can have downstream impacts on disaster response and recovery.
At the same time, the design of sensor networks tends to focus on how to make a given system operate more efficiently under normal conditions. In this stable environment, efficiency is the primary concern, typically in terms of maximizing coverage with minimal sensors. But in such highly optimized sensor networks, a disruption to even a single sensor can lead to missing information and failure to detect anomalies.
Resilience in Sensor Networks
Thus, while sensors are crucial for disaster detection and response, they are also vulnerable to these same events. Applications of advanced sensor networks should accept that disruptions to the network will occur. Instead of working to minimize or eliminate all risks, developers must plan for resilience, designing sensor networks to absorb and quickly recover from disruption.
The idea of resilient engineering, including sensing design, has rapidly evolved from theoretical concepts to practical applications and engineering designs. Resilience thinking accepts that disruptions and disasters will inevitably occur and, instead of shielding the system from threat or hardening to reduce vulnerabilities, focuses on the ability to maintain or quickly recover critical systemic functionality.
This can be accomplished by designing systems either to be resilient (i.e., resilience by design) or to bring external resources to recover critical functionality through resilience by intervention.
Measuring Resilience in Sensor Networks
The National Academies defines resilience as the ability to plan for, absorb, recover from, or more successfully adapt to actual or potential adverse events. In this article, the focus is on the first two aspects of resilience: to plan for and absorb.
The objective is to determine sensor locations that would preserve wireless sensor network (WSN) functionality if some sensors were disabled, hence absorb the disruption. This can be thought of at the system level, where the primary focus is the persistent delivery of a system’s critical function, as opposed to the hardening of a specific asset to resist failure.
Linkov et al. (2013) proposed a resilience matrix framework that divides resilience into the four temporal domains defined by the National Academies (plan, absorb, recover, adapt) as well as into the four components of network-centric operations: physical, information, cognitive, and social. Within an integrated cyber-physical system, sensors are key for ensuring access to the information domain through all stages of a disaster. Furthermore, sensors can be impacted by threats in the physical domain, while threats to cyber operations can impact the cognitive ability of decision-makers to process and understand data collected from sensors. In this way, sensor networks have cross-cutting impacts on and relationships with the different components of resilience, requiring further research on methods for the resilient design of sensor networks.
Existing Research on Sensor Resilience
Generally, research on the resilience of sensors and sensor networks is fairly limited, with most studies focusing on only one aspect of resilience. Security is the most common risk-minimization strategy for sensors, with many methods such as key assignment applied to secure sensor networks from threats. While strengthening security is an important part of the planning phase for the sake of mitigating risk, it cannot be assumed to protect against all forms of risk.
Other studies address the fault-tolerance of sensors, such as the introduction of a clustering method for energy-efficient routing of data through a wireless sensor network. Similarly, some work addresses the reliability of sensors under disruption. While both concepts are related to mitigating risks and absorbing disruptions, resilience focuses on critical functionality more holistically and should also consider the ability to recover lost critical function of the network.
The literature on sensor resilience was reviewed in this context to identify the resilience phase of past work, as shown in Table 1. Because of the broad role wireless sensor networks play across network-centric operations, it is necessary to consider their resilience at all levels of the system, largely divided into subsystems of the sensor domain, sensor hardware, processing, communication, and power supply.
Balancing Resilience and Efficiency in Sensor Networks
In the context of sensor network resilience, the bulk of research has focused on resilient communication networks. This manifests in several studies, such as improving path-routing algorithms or designing the network structure to maintain functionality during disruption. However, more emphasis in future work must address the additional need to quickly recover a failed network to an acceptable level of service when faults do occur.
Furthermore, this definition is applied only to the computing network itself, but sensors have a physical hardware component often ignored in network-based studies. In sensor research, the optimal placement of sensor hardware is an important design criterion, typically based on efficiency only. Research on the resilience of sensors, however, focuses primarily on the communication network and not on the physical arrangement of sensors.
One study examined the optimization of sensor placement within a water quality sensor network for resilience by measuring how overall relative performance changes with disrupted sensors. Further developments are needed to extend these methods to assess the recovery of sensors. Moreover, more research is necessary on the physical placement of sensors within a network in order to ensure resilience of WSNs at a system level.
To incorporate the concept of resilience by design into sensor networks, this article advances a methodology for optimizing the placement of sensors by taking resilience as well as efficiency into account. Conventionally, the sensor placement problem centers on minimizing a desired objective, such as the number of sensors to achieve a specified level of coverage. However, in this most efficient case, disabling any single sensor leads to loss of coverage in a certain area and, therefore, potentially a degradation in the critical functionality of the entire network.
Incorporating additional sensors can introduce redundancy to the system, such that if one sensor fails, particularly in a high-interest area, another sensor will still be in place to collect data. These additional sensors come with additional resource costs, making it cost-prohibitive to have a fully redundant or resilient network. Balancing the trade-offs between these two objectives in a user-controlled way is the goal of the method proposed here.
Optimizing Sensor Placement for Resilience
The most common approaches to the optimal sensor placement problem are based on combinatorial optimization, random placement, cheap sensors open large areas, or heuristic placement strategies. An extensive overview of these approaches is provided in prior work related to sensor placement.
The core approach in this article is based on the algorithm described in Vecherin et al. (2011, 2017), which is a fast algorithm providing an approximate solution to the binary linear programming problem formulated for sensor performance in the probabilistic framework. However, the details of its application to the considered task and analysis of the solutions with and without resilience constraints were not explored previously.
The performance of any sensor is characterized in terms of the probability of detection (P_d) and the probability of false alarm (P_fa). Along with information about noise energy probability density functions, P_fa determines the value of the threshold of signal detection by a sensor, which, along with the signal energy probability density function, allows for the calculation of the probability of signal detection P_d at a location r by a sensor at location r_s.
Another parameter that needs to be specified for each location where coverage is required is a desired minimal probability of detection P_pr. This leads to the following condition for each point r:
log(1 – P_d(r, r_1, …, r_M)) ≤ log(1 – P_pr(r))
Where P_d(r, r_1, …, r_M) is the probability of signal detection at r by at least one sensor. Taking the logarithm on both sides of the inequality, one can convert the product into a summation and yield the following condition for each point r:
A_Q×K * p_K×1 ≥ b_Q×1
Where A_Q×K is the coverage matrix, p_K×1 is a binary vector indicating sensor placement, and b_Q×1 is a preference vector.
The problem of optimal sensor placement can now be formulated as the following binary linear programming problem:
min c_K×1 * p_K×1
s.t. A_Q×K * p_K×1 ≥ b_Q×1
p_K×1 ∈ {0, 1}^K
Where c_K×1 is a cost column-vector representing factors such as monetary value, power consumption, or sensor installation time.
Incorporating Resilience into Sensor Placement
To incorporate resilience by design into the sensor network, the objective is to determine sensor locations that would preserve WSN functionality if some sensors were disabled, hence absorb the disruption. This can be achieved by introducing the concept of depth of resilience (D), which indicates how many sensors in a network can be disabled without loss of coverage.
For a depth of resilience D, all resilience points need to be covered by at least R=D+1 sensors to allow any D of them to be disabled without loss of coverage. This requirement can be incorporated into the existing binary linear programming framework by modifying the corresponding rows of the coverage matrix A and the preference vector b:
A_Q×K * p_K×1 ≥ R * b_Q×1
The approximate solution to this resilient sensor placement problem is presented in the context of monitoring human presence at a workplace in a large building using commercial infrared sensors.
2D Sensor Placement
For the 2D problem, the candidate sensor locations are set along the walls inside the coverage area, assuming each sensor has an omnidirectional 2D field of view. Figure 3 shows the optimal sensor placement when only efficiency is required, with a limited sensor supply of 17 sensors.
In this case, the algorithm places sensors at the corners of the walls, the only locations providing maximum coverage at the intersections of the corridors. However, in more complex scenarios with obstacles, sensor placement in prohibited areas, and so on, an optimal placement may not be inferred intuitively.
When a requirement for resilience with depth D=1 is introduced, the total number of available sensors is increased to 36. Figure 4 shows the optimal sensor placement, with sensors placed on adjacent corners or opposite walls to provide the needed redundancy and ensure necessary coverage even when one sensor is disabled.
3D Sensor Placement
For the 3D problem, the candidate sensor locations are not limited to walls, and the sensors have a finite field of view in 3D, resulting in an omnidirectional field of view in the 2D horizontal plane. Additionally, the cubicle walls are short, allowing sensors on the ceiling to see the interior of the cubicles.
Figure 5 shows the optimal location of 25 sensors without resilience, with the sensors placed at intersections and corners to provide maximum coverage on the floor. Figure 6 depicts the optimal placement of 45 sensors with a depth of resilience D=1, with the sensors located almost uniformly over the possible candidate location area on the office ceiling to maximize coverage area while providing the required redundancy.
Conclusion and Future Research Directions
To be able to face the threats of the future, sensor hardware and networks must be designed with resilience in mind. This resilience will require a compromise with the goals of efficiency, given the potential for additional resource costs incurred by adding sensors. By balancing both efficiency and resilience optimization, the framework proposed here seeks to address the challenges of this delicate trade-off.
The results show the value of this algorithm that can optimize for resilience while reducing the cost of adding too many sensors. Further research is required in several areas to advance resilience applications for sensor networks:
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Adaptivity and Recovery: The described methodology is focused on the absorption of disruptions. Future research efforts could tackle the adaptivity and recovery aspects of resilience in WSNs.
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Cyber-Physical System Resilience: This research should center on ensuring the resilience of cyber-physical systems as a whole, where sensors may not just deliver information to end-users but could inform an automated response by the system to recover from a threat.
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Edge Computing and AI/Digital Twins: Technologies such as edge computing and advanced analytical tools have the potential to further strengthen system resilience through redundancy and fast optimization solutions, particularly when a decision-maker response is required during a disruption.
By incorporating resilience into all levels of cyber-physical monitoring and control systems, users can be better prepared to maintain or recover functionality in the face of disasters. This shift from traditional efficiency-focused design to a resilience-oriented approach is crucial for the continued advancement of sensor networks and their critical applications.
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