Time-series clustering for sensor fault detection in large-scale Cyber-Physical Systems

Large-scale Cyber-Physical Systems (CPSs) are information systems that involve a vast network of sensor nodes and other devices that stream observations in real-time and typically are deployed in uncontrolled, broad geographical terrains. Sensor node failures are inevitable and unpredictable events in large-scale CPSs, which compromise the integrity of the sensors measurements and potentially reduce the quality of CPSs services and raise serious concerns related to CPSs safety, reliability, performance, and security. While many studies were conducted to tackle the challenge of sensor nodes failure detection using domain-specific solutions, this paper proposes a novel sensor nodes failure detection approach and empirically evaluates its validity using a real-world case study. This paper investigates time-series clustering techniques as a feasible solution to identify sensor nodes malfunctions by detecting long-segmental outliers in their observations' time series. Three different time-series clustering techniques have been investigated using real-world observations collected from two various sensor node networks, one of which consists of 275 temperature sensors distributed around London. This study demonstrates that time-series clustering effectively detects sensor node's continuous (halting/repeating) and incipient faults. It also showed that the feature-based time series clustering technique is a more efficient long-segmental outliers detection mechanism compared to shape-based time-series clustering techniques such as DTW and K-Shape, mainly when applied to shorter time-series windows

Large scale stochastic inventory routing problems with split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC