Numerical solutions of elliptic inverse problems via the equation error method

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Design of high fidelity building energy monitoring system

Building energy meter network, based on per-appliance monitoring system, willbe an important part of the Advanced Metering Infrastructure. Two key issues exist for designing such networks. One is the network structure to be used. The other is the implementation of the network structure on a large amount of small low power devices, and the maintenance of high quality communication when the devices have electric connection with high voltage AC line. The recent advancement of low-power wireless communication makes itself the right candidate for house and building energy network. Among all kinds of wireless solutions, the low speed but highly reliable 802.15.4 radio has been chosen in this design. While many network-layer solutions have been provided on top of 802.15.4, an IPv6 based method is used in this design. 6LOWPAN is the particular protocol which adapts IP on low power personal network radio. In order to extend the network into building area without, a specific network layer routing mechanism-RPL, is included in this design. The fundamental unit of the building energy monitoring system is a smart wall plug. It is consisted of an electricity energy meter, a RF communication module and a low power CPU. The real challenge for designing such a device is its network firmware. In this design, IPv6 is implemented through Contiki operation system. Customize hardware driver and meter application program have been developed on top of the Contiki OS. Some experiments have been done, in order to prove the network ability of this system.