Final Report Summary - DIESIS (Distributed Estimation In Sensor Networks)
Several contemporary applications involve processing of information residing in a large number of decentralised nodes, e. g., wireless sensor networks, electrical power grids, computer networks, gene regulatory networks. DIESIS is targeting decentralised methods for estimation, detection, and tracking on large-scale networks, adhering to the limitations imposed by the specific application of interest.
Considering first sensor network applications, two characteristics should be identified: (c1) the underlying physical model is typically nonlinear; and (c2) sensors are prone to failure. These two limitations have been at the focus during the first phase of DIESIS.
Regarding (c1), the diffusion model describing the concentration of a physical, chemical, or biological compound is a nonlinear function of the sensor's locations. Aiming to estimating such a diffusion field, we resorted to the Volterra series expansion, a model with well-documented merits. Given that nature itself is parsimonious, we looked for sparse Volterra models, i. e., polynomial models having many parameters equal to zero. This requirement has high interpretative value, but unfortunately cannot be met by standard least-squares or machine learning methods. The recent advances in compressed sensing (CS) assert that under mild conditions a sparse system can in general be recovered using a number of linear observations smaller than the number of unknowns. Extending such a premise in the Volterra setup was one of DIESIS's research achievements. Note that such a generalisation is non-trivial due to the complex input dependencies. We showed analytically that when such models are sparse, they can be recovered by far fewer measurements. Efficient batch and adaptive algorithms were developed for the recovery of sparse polynomial models. Apart from wireless sensor networks, sparse polynomial models have a wide gamut of applications ranging from hearing aid technology, wireless and satellite communications, to unveiling high-order gene interactions in phenotype expressions.
Concerning (c2), extracting information from a multitude of distinct, but unreliable sensors is one of the key challenges in sensor as well as other networks. Failures in sensing devices, low battery, physical obstruction, and (un) intentional interference, all can lead to unreliable sensors and severely degrade the consistency of the network-wide task. DIESIS's second research thrust was to efficiently accomplish this robust sensing task. The latter was formulated as that of finding the maximum number of feasible subsystems of linear equations, and unfortunately, proved to be an NP-hard (i. e., hard to solve) problem. To practically tackle it, we first established useful links with CS. Yet interestingly, the signals here are not sparse, but give rise to sparse residuals: reliable sensors give small or close to zero residual error. Capitalising on this form of residual sparsity, sensing schemes of complementary strengths were developed. The first scheme is a convex relaxation of the original problem was proposed. It was also shown that under certain conditions, the latter solves the original NP-hard problem with overwhelming probability. Under a noisy sensor data setup, a more general convex problem was proposed and efficient optimisation algorithms were derived.
During DIESIS's second phase, the focus shifted towards power networks. It should be appreciated that the power grid has been recognised as probably the most important engineering achievement. Further, the challenges and opportunities towards a smart grid make research on this field timely and influential to the society. Under DIESIS, three were the grid-related problems considered: (p1) phasor measurement unit (PMU) placement; (p2) power system state estimation (PSSE); and (p3) generalised PSSE.
With regard to (p1), PMUs are contemporary metering devices that can be installed at the grid nodes and record precisely electrical quantities of interest. Instrumenting power networks with PMUs facilitates grid optimisation and monitoring, and enables situational awareness. The installation and networking cost of PMUs currently prohibits their deployment on every bus, which in turn motivates their strategic placement across the grid; cf. PMU placement was optimised here adopting a Bayesian state estimation framework and posed as an optimal experimental design task. To bypass the combinatorial search involved, a convex relaxation was developed to obtain solutions with numerical optimality guarantees. Targeting large networks, an efficient algorithm was also derived. The results indicate that independent system operators and power utilities could benefit by such a careful placement of their available units.
Targeting (p2), PSSE, that is the task of finding the grid node voltages given some meter readings, is a key component in modern grid operation. Currently, deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for PSSE at a continent-wide level. Implementing such a centralised estimator though is practically infeasible due to the complexity scale, the communication bottleneck, and regional disclosure policies. In this context, decentralised methods were considered under a unified and systematic framework. Given the power grid hierarchy where nodes are naturally grouped into different control areas, a novel algorithm was developed. The algorithmic framework respects privacy, exhibits low communication load, and is bad-data resilient. Numerical results showed that the attainable accuracy can be reached within a few inter-area exchanges;
The above decentralised approach was further extended to the task of generalised PSSE [cf. (p3) ], where PSSE additionally identifies which of the switches are open/closed. Most of the switch status information is forwarded to the control center, but oftentimes it is erroneous and hence degrades the estimator. The decentralised generalised PSSE developed exploits the power grid hierarchy, scales favourably with the network size, and can identify topological errors.
To conclude, DIESIS results are of highly interdisciplinary value. Estimating sparse polynomial models upon exploiting the exciting CS results goes beyond the WSN context. Furthermore, being able to perform information processing (estimation, detection, clustering), while simultaneously rejecting outliers is a universal task re-occurring in disguise: erroneous readings in environmental monitoring, bad data in electric power grids. Finally, the optimised instrumentation of power networks and the decentralised framework for robust (generalised) PSSE developed under DIESIS, contribute towards implementing a more efficient, reliable, and greener smart grid
Considering first sensor network applications, two characteristics should be identified: (c1) the underlying physical model is typically nonlinear; and (c2) sensors are prone to failure. These two limitations have been at the focus during the first phase of DIESIS.
Regarding (c1), the diffusion model describing the concentration of a physical, chemical, or biological compound is a nonlinear function of the sensor's locations. Aiming to estimating such a diffusion field, we resorted to the Volterra series expansion, a model with well-documented merits. Given that nature itself is parsimonious, we looked for sparse Volterra models, i. e., polynomial models having many parameters equal to zero. This requirement has high interpretative value, but unfortunately cannot be met by standard least-squares or machine learning methods. The recent advances in compressed sensing (CS) assert that under mild conditions a sparse system can in general be recovered using a number of linear observations smaller than the number of unknowns. Extending such a premise in the Volterra setup was one of DIESIS's research achievements. Note that such a generalisation is non-trivial due to the complex input dependencies. We showed analytically that when such models are sparse, they can be recovered by far fewer measurements. Efficient batch and adaptive algorithms were developed for the recovery of sparse polynomial models. Apart from wireless sensor networks, sparse polynomial models have a wide gamut of applications ranging from hearing aid technology, wireless and satellite communications, to unveiling high-order gene interactions in phenotype expressions.
Concerning (c2), extracting information from a multitude of distinct, but unreliable sensors is one of the key challenges in sensor as well as other networks. Failures in sensing devices, low battery, physical obstruction, and (un) intentional interference, all can lead to unreliable sensors and severely degrade the consistency of the network-wide task. DIESIS's second research thrust was to efficiently accomplish this robust sensing task. The latter was formulated as that of finding the maximum number of feasible subsystems of linear equations, and unfortunately, proved to be an NP-hard (i. e., hard to solve) problem. To practically tackle it, we first established useful links with CS. Yet interestingly, the signals here are not sparse, but give rise to sparse residuals: reliable sensors give small or close to zero residual error. Capitalising on this form of residual sparsity, sensing schemes of complementary strengths were developed. The first scheme is a convex relaxation of the original problem was proposed. It was also shown that under certain conditions, the latter solves the original NP-hard problem with overwhelming probability. Under a noisy sensor data setup, a more general convex problem was proposed and efficient optimisation algorithms were derived.
During DIESIS's second phase, the focus shifted towards power networks. It should be appreciated that the power grid has been recognised as probably the most important engineering achievement. Further, the challenges and opportunities towards a smart grid make research on this field timely and influential to the society. Under DIESIS, three were the grid-related problems considered: (p1) phasor measurement unit (PMU) placement; (p2) power system state estimation (PSSE); and (p3) generalised PSSE.
With regard to (p1), PMUs are contemporary metering devices that can be installed at the grid nodes and record precisely electrical quantities of interest. Instrumenting power networks with PMUs facilitates grid optimisation and monitoring, and enables situational awareness. The installation and networking cost of PMUs currently prohibits their deployment on every bus, which in turn motivates their strategic placement across the grid; cf. PMU placement was optimised here adopting a Bayesian state estimation framework and posed as an optimal experimental design task. To bypass the combinatorial search involved, a convex relaxation was developed to obtain solutions with numerical optimality guarantees. Targeting large networks, an efficient algorithm was also derived. The results indicate that independent system operators and power utilities could benefit by such a careful placement of their available units.
Targeting (p2), PSSE, that is the task of finding the grid node voltages given some meter readings, is a key component in modern grid operation. Currently, deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for PSSE at a continent-wide level. Implementing such a centralised estimator though is practically infeasible due to the complexity scale, the communication bottleneck, and regional disclosure policies. In this context, decentralised methods were considered under a unified and systematic framework. Given the power grid hierarchy where nodes are naturally grouped into different control areas, a novel algorithm was developed. The algorithmic framework respects privacy, exhibits low communication load, and is bad-data resilient. Numerical results showed that the attainable accuracy can be reached within a few inter-area exchanges;
The above decentralised approach was further extended to the task of generalised PSSE [cf. (p3) ], where PSSE additionally identifies which of the switches are open/closed. Most of the switch status information is forwarded to the control center, but oftentimes it is erroneous and hence degrades the estimator. The decentralised generalised PSSE developed exploits the power grid hierarchy, scales favourably with the network size, and can identify topological errors.
To conclude, DIESIS results are of highly interdisciplinary value. Estimating sparse polynomial models upon exploiting the exciting CS results goes beyond the WSN context. Furthermore, being able to perform information processing (estimation, detection, clustering), while simultaneously rejecting outliers is a universal task re-occurring in disguise: erroneous readings in environmental monitoring, bad data in electric power grids. Finally, the optimised instrumentation of power networks and the decentralised framework for robust (generalised) PSSE developed under DIESIS, contribute towards implementing a more efficient, reliable, and greener smart grid