The linear inverse problem in energy beam processing with an application to abrasive waterjet machining

The linear inverse problem for energy beam processing, in which a desired etched profile is known and a trajectory of the beam that will create it must be found, is studied in this paper. As an example, abrasive waterjet machining (AWJM) is considered here supported by extensive experimental investigations. The behaviour of this process can be described using a linear model when the angle between the jet and the surface is approximately constant during the process, as occurs for shallow etched profiles. The inverse problem is usually solved by simply controlling dwell time in proportion to the required depth of milling, without considering whether the target surface can actually be etched. To address this, a Fourier analysis Is used to show that high frequency components in the target surface cannot be etched due to the geometry of the jet and the dynamics of the machine. In this paper, this frequency domain analysis is used to improve the choice of the target profile in such a way that it can be etched. The dynamics of the machine also have a large influence on the actual movement of the jet. It is very difficult to describe this effect because the controller of the machine is usually unknown. A simple approximation is used for the choice of the slope of a step profile. The tracking error between the desired trajectory and the real one is reduced and the etched profile is improved. Several experimental tests are presented to show the usefulness of this approach. Finally, the limitations of the linear model are studied

A two-level decision making approach for optimal integrated urban water and energy management

A spatial-temporal model is proposed for optimal integrated water and energy resource management in urban areas, considering daily surplus output from residential grid-connected rooftop photovoltaics as an energy source for sustainable supply. The model addresses optimal investment and operational decisions of a desalination-based water supply system driven by surplus photovoltaic output and grid electricity. The two-level mixed integer linear programming model considers demands, systems configuration, resources capacity and electricity tariffs and gives the solution such that the highest compatibility with available renewable energy is achieved. The model is then applied to Perth, Australia and solved for three operational scenarios. The results show, for a given year, hourly (flexible) basis scenario leads to $9 521 425 and$18 673 545 economic benefits over seasonal (semi-flexible) and yearly (fixed) basis scenarios, respectively. They also indicate 19.9% better economic performance in terms of annualised unit cost of water production over existing Southern seawater desalination plant in Perth. Additionally, it is shown that the seasonal change on the optimal solutions mainly corresponds to the share of each energy resource to meet water-related energy demand. Finally, the results indicate higher sensitivity to the variation of the photovoltaic installation density compared to financial rate