An Optimal Control Approach to Helicopter Noise and Emissions Abatement Terminal Procedures

Abstract

Civil aviation plays an irreplaceable role in the current global civilization. Even though the 2008 economic crisis has limited growth in the western world, it can only be expected that due to continuing development in the Far East, South America and Africa this role will increase further over the years to come. Also in the field of helicopter operations continuous growth is predicted, mainly attributed to the growth of the private and corporate transport sectors. To reduce and control the negative impacts of aviation – mainly noise nuisance and pollutant emissions – both in Europe and the United States major research efforts have been initiated with the main objective to provide step changes in the development of environmentally friendly or green aircraft. Although the larger part of the research effort has been focused on the development of new air vehicles, also the development of green operations is being researched, especially with a focus on noise abatement. Researchers have mainly focused on the development of noise abatement departure and arrival procedures for fixed-wing aircraft in an effort to reduce the noise impact in near-airport communities, with promising results. With the current fleet of helicopters the total noise nuisance caused by helicopter operations is significantly smaller than that of fixed-wing aircraft. However, due to their specific types of operations – often flying in close proximity to densely populated areas – individual operations can lead to unacceptable levels of nuisance, which require a specific approach in the development of noise abatement procedures. Therefore, in this research the European Clean Helicopter Optimization (ECHO) software suite has been developed which provides an efficient and sufficiently accurate means to numerically optimize site-specific helicopter approach trajectories, focusing specifically (but not exclusively) on noise mitigation in the surrounding communities. To provide a step change in helicopter optimization frameworks, the ECHO suite has been developed with a strong emphasis on computational efficiency. For this purpose, an advanced optimization methodology based on optimal control theory has been selected. In this method, the infinite-dimensional optimal control problem is discretized, and the time, state and control variables at the discretization point are treated as the variables of a large-scale Non-Linear Programming (NLP) problem. The method – more specifically a direct solution method based on pseudospectral collocation using Radau quadrature – has been chosen as it offers the best trade-off between accuracy and computational efficiency for three main reasons. Firstly, the use of a direct solution method to solve the optimal control problem requires significantly less complex problem setups, and as such results in a more flexible and versatile optimization suite. In addition, the selected methodology allows for a relatively easy imposition of constraints on both the state and control variables, and the use of collocation based on Gaussian quadrature reduces the overall problem size for a given level of accuracy. Finally, the specific use of Radau quadrature has been shown to provide good convergence behavior, specifically in open ended trajectory optimization problems such as considered in this study. To model the free motion of a helicopter an eight Degrees-of-Freedom (DoF) helicopter flight dynamics model with quasi-steady inflow angles for both the main and tail rotor has been integrated in ECHO. The model ensures that the motion of the helicopter is simulated sufficiently accurate, and ensures that the required input parameters to determine the helicopter source noise are directly available. The model has been adapted to simulate operations in non-standard atmospheric conditions including stationary wind fields. In addition, a fuel and gaseous emissions model has been integrated in the flight dynamics model to determine the total fuel burn and total emission of nitrogen oxides based on the required engine power. This allows for the optimization of trajectories with respect to fuel and NOx emissions. Although the model is a generic flight dynamics model, to test the capabilities of the suite a set of parameters representing a Messerschmitt-Bölkow-Blohm (MBB) Bo-105 has been used. These include a set of generic limits and constraints related to passenger comfort and the helicopter's flight envelope. To allow assessment of and hence optimization with respect to the noise impact on the ground, the ECHO suite contains a helicopter noise model consisting of three main components. The first component determines the source noise levels emitted by the helicopter. To model this, a database of source noise levels for different frequencies and different flight conditions is available, projected on a hemisphere centered around the helicopter's main rotor hub. The database has been derived aeroacoustically based on the disc-tilt angles and the advance ratio following from the flight dynamics model. Source noise levels corresponding to the actual flight conditions encountered in the optimization process are found through interpolation between the hemispheres. The second step in determining the noise exposure on the ground is the assessment of the propagation loss between source and receiver. An efficient model to determine the propagation loss was developed specifically for integration in the ECHO suite to comply with the continuity requirements following from the selected optimization methodology and to maintain relatively short execution times. The propagation model uses a geometrical approach to ray-tracing to determine the path of sound rays traveling from the source to the receiver. This approach allows for a significantly lower number of integration steps – and hence shorter runtimes – with sufficient accuracy for the atmospheric conditions considered in this research. The propagation model integrated in ECHO accounts for spreading loss, ground effect and atmospheric absorption, and includes a model to approximate the noise penetrating the shadow zone to ensure continuity in all observer locations and hence in the objective function. The final component of the helicopter noise model determines the total noise impact on the ground in order to allow for the optimization of noise abatement trajectories. A number of generic and site-specific noise impact assessment criteria is available in ECHO to quantify the total noise impact in the area surrounding the trajectory. To exemplify the capabilities of the ECHO suite a number of case studies with increasing complexity and different optimization criteria is presented. The first scenario, a relatively simple two-dimensional approach, shows that in order to minimize the noise Sound Exposure Level (SEL) footprint areas in general flight at low altitude and high airspeeds are preferred. Apart from the relatively low source noise levels at high airspeeds, also the total exposure time is reduced, reducing the SEL values. Furthermore, the presence of shadow zones and the dissipation of sound energy by the ground surface results in lower noise levels astride the helicopter's trajectory when flying at low altitudes. Consequently, SEL contours remain relatively narrow, and hence the generic noise footprint becomes smaller. In the second case study a more complex three-dimensional trajectory is optimized in a densely populated area. In addition, for this scenario the site-specific awakenings criterion was used in the objective function, and different atmospheric and ground surface conditions were assessed. Similar to the conclusions drawn from the first scenario, again low altitude flight at high airspeeds reduce the SEL values on which the awakenings criterion is partly dependent. In addition, the use of a site-specific noise criterion and a three-dimensional flight path allows the helicopter not only to reduce the noise levels astride or below the trajectory, but also to avoid densely populated areas. In the cases where wind from different directions and different strengths were considered, it was found that even though the effect of wind on the total number of awakenings was significant, the effect on the relative improvements to be gained through optimization was small when compared to optimization in standard atmospheric conditions. The effect on the total number of awakenings can be attributed mainly to changes in ground speed on the one hand, and the positioning of the helicopter such that significant parts of the population are inside the shadow zone on the other. In cold atmospheric conditions the atmospheric absorption loss increases, resulting in a generally higher flight profile in order to increase the slant range between source and receiver. The opposite is true in case softer ground surfaces (such as e.g. snow) are modeled. The soft ground surface leads to an increased dissipation of sound energy on the ground, and hence to a larger lateral attenuation leading to a stronger preference for low altitude flight. Finally, the third case study was set up to assess the effect of different site-specific noise optimization criteria on a complex three-dimensional arrival trajectory. The third scenario further supported the findings with respect to noise abatement found in the first two case studies, and additionally showed that the different site-specific criteria do not lead to significant changes in the helicopter trajectory when minimizing the total noise impact. In addition to the main conclusions from the case studies regarding noise abatement, with respect to the efficiency of the ECHO suite – one of the main objectives of the software, the case studies have shown that the suite is capable of optimizing helicopter trajectories with a complex set of constraints imposed with relatively short runtimes, depending highly on the overall problem size and problem complexity. From the development and the analysis of the capabilities of the ECHO suite it can be concluded that the objective of providing an efficient means to optimize helicopter trajectories with respect to different environmental and economic criteria has been met. Although the objectives with respect to total problem runtimes were not met in all cases, further development of the suite has seen a further step change in the overall efficiency, showing the potential to indeed meet the challenging requirements. Although the case studies have shown the potential of the suite, and ECHO meets the accuracy requirements to indeed prove to be a step change with respect to state of the art research, further improvements were identified. Especially the source noise model requires an expansion of the database to allow modeling of flight conditions other than steady forward level or descending flight at different airspeeds. This, in combination with the modeling of noise other than the main rotor would allow for a more accurate assessment of the noise impact for a wider range of flight conditions. Furthermore, the capabilities of the ECHO suite should be assessed for different helicopter classes, and in more realistic case studies, better accounting for all operational constraints encountered in real-world operations. Finally, although the ECHO suite has been developed specifically for the optimization of conventional helicopter trajectories, the flight dynamics, noise modeling and model integration in general could easily be adapted for the optimization of novel helicopter concepts or fixed-wing aircraft trajectories, further extending the research scope of the suite.