Linear Programming-Based Optimization for Robust Data Modeling in a Distributed Sensing Platform

Abstract

Creating accurate data models describing the dynamics of physical phenomena in time and space is important in optimized control and decision making. Models highlight various trends and patterns. However, producing accurate models is challenging as different errors are introduced by sampling platforms with limited resources, e.g., insufficient sampling rates, data loss due to buffer overwriting, reduced communication bandwidth, and long communication delays. Furthermore, the dynamics of the environment, like mobile energy sources and sinks, might further increase errors as resources must be shared between the sampling and communication activities. This paper presents a procedure to systematically construct robust data models using samples acquired through a grid network of embedded sensing devices with limited resources, like bandwidth and buffer memory. Models are in the form of ordinary differential equations. The procedure constructs local data models by lumping state variables. Local models are then collected centrally to produce global models. The proposed modeling scheme uses a linear programming formulation to compute the lumping level at each node, and the parameters of the networked sensing platform, i.e., best data communication paths and bandwidths. Two algorithms are described to predict the trajectories of mobile energy sources/sinks as predictions can further reduce data loss and delays during communication. The computed parameters and trajectory predictions are used to configure the local decision making routines of the networked sampling nodes. Even though the procedure can be used to model a broader set of phenomena, experiments discuss the effectiveness of the method for thermal modeling of ULTRASPARC Niagara T1 architecture. Experiments show that the presented method reduces the overall error between 58.29% and 76.91% with an average of 68.87%, and communication delay between −11.49% and 57.62% with an average of 21.85%.

Survey of Scientific Programming Techniques for the Management of Data-Intensive Engineering Environments

“…Gradient descent search [144] Integer linear programming Linear algebra/solvers [141] Linear programming [142] Matrix calculation [143] Nonlinear programming Numerical methods…”