The random pilot response model, the random aircraft weight model, and the stochastic wind variation model are incorporated with the fast-time aircraft simulator to form a Monte Carlo simulation tool.
Arrival procedures can be executed hundreds of times with different aircraft types and configurations under different wind conditions. Separation and throughput analysis can then be applied on simulated trajectories8. The Monte Carlo engine and the separation analysis methodology to be presented are collectively referred to as the Tool for the Analysis of Separation And Throughput (TASAT) as illustrated in Fig. 3-10.
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
A small slice of traffic at separation s
A small slice of traffic at separation s
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
A small slice of traffic at separation s
A small slice of traffic at separation s
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
A small slice of traffic at separation s
A small slice of traffic at separation s
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
Intermediate Metering Point Runway Threshold
Time of Trailing AC Initial Position
of Leading AC
A small slice of traffic at separation s
A small slice of traffic at separation s
Figure 3-10 Tool for the Analysis of Separation And Throughput (TASAT).
During each simulation run, for a given aircraft type, a unique aircraft landing weight will be generated by the random landing weight model. The wind profile will also be different for each simulation run. Pilot response time will be randomly generated for each control action. Procedure definition, FMS descent forecast winds (zero if not provided), and aircraft flap/gear schedule (as given to the pilots for real world operations) are provided to the simulator as deterministic inputs. It is assumed that there are no direct interactions between consecutive flights performing the same procedure. Thus, when multiple aircraft types are involved in performing a procedure, each aircraft can be simulated separately.
The application of the wind model needs special attention. To make best use of the inter-flight wind variation model, flights are identified as leading flights and trailing flights. For a given nominal wind condition, this can be done as following. For each aircraft type, an ensemble of flights can be simulated with the fixed nominal wind condition while retaining variations in other factors such as the pilot response and the aircraft weight. Another ensemble of flights can be simulated with nominal wind condition plus a stochastic inter-flight wind variation profile in addition to other random factors. A simulated trajectory from the leading ensemble and a simulated trajectory from the trailing ensemble can be selected to form a random flight pair. By enumerating flights from each ensemble, a large number of flight pairs can be constructed. Separation analysis (discussed in a separate chapter later) can then be applied on those flight pairs accordingly.
3.5 SUMMARY
A Monte Carlo simulation tool built around a fast-time aircraft simulator was developed to simulate variations in flight trajectories for noise abatement approach and arrival procedures. The fast-time aircraft simulator was developed with a careful trade-off between simplicity, fast execution, accuracy, and the capability to simulate 3D aircraft trajectories. Focus is given to macro level aircraft trajectories rather than micro dynamic behavior. Because wind is the most important single factor affecting aircraft trajectory variations, non-steady state equations of motion were used in the aircraft dynamics model. This would allow aircraft behavior under various wind conditions to be accurately simulated. Major aircraft navigation and control systems such as the FMS and the autopilot models were included in the simulator.
A pilot model was also included in the simulator to control the extension of flaps, landing gear, and speedbrakes during simulation runs. A previously developed probability distribution pilot response delay model, a newly developed probability distribution aircraft landing weight model, and a newly developed stochastic process wind variation model were incorporated with the fast-time aircraft simulator to form the Monte Carlo simulation tool. The tool enables approach and arrival procedures to be simulated hundreds of times for each aircraft type under various external conditions with a short amount of time and at very low cost. The large pool of aircraft trajectories obtained through these simulation runs can then be used to analyze variations in aircraft trajectories for the specific procedure design and operating environment.
Future enhancements of the Monte Carlo simulation tool could include incorporating performance variations due to differences in wearing, weathering, and adjusting between individual aircraft units within the same aircraft type. A probability distribution model of aircraft CG position could also be developed. The model of aircraft drag polars in the fast-time aircraft simulator could be revised to enable the effect of aircraft CG position being accurately simulated. Limitations to these future enhancements mostly rely on data available to support the modeling efforts.
REFERENCES
1 Ho, N. T. and Clarke, J.-P. B., “Mitigating Operational Aircraft Noise Impact by Leveraging on Automation Capability,” AIAA-2001-5239, 1st AIAA Aircraft Technology, Implementation, and Operations Forum, AIAA, Los Angeles, California, 2001.
2 Ren, L., Ho, N. T., and Clarke, J.-P. B., “Workstation Based Fast-Time Aircraft Simulator for Noise Abatement Approach Procedure Study,” AIAA-2004-6503, AIAA 4th Aviation Technology, Integration and Operations (ATIO) Forum, Chicago, Illinois, 20-22 Sep. 2004.
3 Clarke, J.-P. B., “A System Analysis Methodology for Developing Single Events Noise Abatement Procedures,” Sc.D. Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 1997.
4 Clarke, J.-P. B., “Systems Analysis of Noise Abatement Procedures Enabled by Advanced Flight Guidance Technology,” AIAA 97-0490, Journal of Aircraft, Vol. 37, No.2, Mar.-Apr. 2000, pp.266-273.
5 Ren, L., Clarke, J.-P. B., and Ho, N. T., “Achieving Low Approach Noise without Sacrificing Capacity,” Proceedings: the 22nd Digital Avionics Systems Conference (22nd DASC), Indianapolis, Indiana, 12-16 Oct. 2003, pp. 1.E.3-1.1-9 vol.1
6 UPS B757/767 Aircraft Operating Manual, Document: UPS33075, UPS Flight Publications, Louisville, Kentucky, 2003.
7 Evans, M., Hastings, N., and Peacock, B. Statistical Distributions, 3rd ed., John Willey & Sons, Inc., New York, 2000, pp. 34-42.
8 Ren, L., and Clarke, J.-P. B., “Development and Application of Separation Analysis Methodology for Noise Abatement Approach Procedures,” AIAA-2005-7397, AIAA 5th Aviation Technology, Integration and Operations (ATIO) Forum, Arlington, Virginia, 26-28 Sep. 2005.
CHAPTER 4
MODELING AND SIMULATING WIND VARIATIONS BETWEEN FLIGHTS
NOMENCLATURE
ai = the coefficients of an AR model a^i = estimated coefficients of an AR model
a^Ei = estimated coefficients of the AR model of east wind variation
a^HEi = estimated coefficients of the AR model of higher frequency signal of east wind variation a^HNi = estimated coefficients of the AR model of higher frequency signal of north wind variation a^LEi = estimated coefficients of the AR model of lower frequency signal of east wind variation a^LNi = estimated coefficients of the AR model of lower frequency signal of north wind variation a^Ni = estimated coefficients of the AR model of north wind variation
bi = the coefficients of an FIR filter E( ) = expectation, mean operator H(z) = filter
hn = ACARS wind profile re-sampling altitude n = discrete sequence index
K^(T) = estimated power spectra density function N = number of measurements in a finite sequence m = discrete sequence index
p = the order of an AR model q = the order of an FIR filter
wDCj,E = DC signal of east wind variation observed by flight j wDCj,N = DC signal of north wind variation observed by flight j wfj,E(hn) = filtered east wind variation observed by flight j at altitude hn
wfj,N(hn) = filtered north wind variation observed by flight j at altitude hn
wHE[n] = simulated higher frequency signal of east wind variation
wHj,E(hn) = higher frequency signal of east wind variation observed by flight j at altitude hn
wHj,N(hn) = higher frequency signal of north wind variation observed by flight j at altitude hn
wHN[n] = simulated higher frequency signal of north wind variation Wj(hn) = re-sampled wind profile from flight j at altitude hn
Wj,D(hn) = wind direction of re-sampled wind profile from flight j at altitude hn
Wj,E(hn) = east wind component of re-sampled wind profile from flight j at altitude hn
Wj,N(hn) = north wind component of re-sampled wind profile from flight j at altitude hn
Wj,V(hn) = wind speed of re-sampled wind profile from flight j at altitude hn
wLE[n] = simulated lower frequency signal of east wind variation
wLj,E(hn) = lower frequency signal of east wind variation observed by flight j at altitude hn wLj,N(hn) = lower frequency signal of north wind variation observed by flight j at altitude hn wLN[n] = simulated lower frequency signal of north wind variation
x[n] = generic sequence
'WE[n] = simulated east wind variation component
'Wj,D(hn)= wind variation in direction observed by flight j at altitude hn 'Wj,E(hn)= east wind variation component observed by flight j at altitude hn 'Wj,N(hn)= north wind variation component observed by flight j at altitude hn 'Wj,V(hn)= wind variation in speed observed by flight j at altitude hn
'WN[n] = simulated north wind variation component JQ = innovation variance
J^Q = estimated innovation variance
Nx[m] = covariance sequence of generic sequence x N^x[m] = covariance sequence of generic sequence x Q[n] = white sequence
QE[n] = white noise sequence for simulating the east wind variation
QHE[n] = white noise sequence for simulating the higher frequency signal of east wind variation QHN[n] = white noise sequence for simulating the higher frequency signal of north wind variation QLE[n] = white noise sequence for simulating the lower frequency signal of east wind variation QLN[n] = white noise sequence for simulating the lower frequency signal of north wind variation QN[n] = white noise sequence for simulating the north wind variation
4.1 INTRODUCTION
Wind is arguably the most significant single factor that influences aircraft trajectory. Separation analysis requires an accurate model of wind variations in speed and direction between consecutive flights conducting the same approach or arrival procedure. Such a model requires large amount of data. One source of this data is the Aircraft Communications Addressing and Reporting System (ACARS) automated weather reports. ACARS is an air-ground communication system managed by Aeronautical Radio Inc. (ARINC). Airlines use this system to transmit digital messages between the aircraft and ground. Weather reports are automatically transmitted by the aircraft to ground at certain intervals1. Using ACARS metrological reports, it is possible to create a large set of inter-flight wind variation profiles from which the model is derived. The wind variation model may then be used in the Monte Carlo simulation tool described in the previous chapter to simulate aircraft trajectory variations with high accuracy.
A modeling approach was developed to model wind variations between consecutive flights. In this modeling approach, wind variation profiles are viewed as stochastic processes along the altitude. Because these processes deems non-stationary, a unique mode decomposition approach is used to separate each wind variation component profile – the east wind or the north wind profile – into a zero mean higher frequency signal, a zero mean lower frequency signal, and a static (DC) signal. Each separated signal is then viewed as a stationary process. The decomposed wind variation signals are then approximated as autoregressive (AR) signals. The final AR model for each decomposed signal is built based on the average of estimated covariances of data samples of the corresponding component signal.
As mentioned in the previous chapter, the winds experienced by a pair of consecutive flights are assumed the sum of a nominal wind profile that is common to both the leading and trailing flights, and a wind variation profile that is only applied to the trailing flight. This is a simplified scenario in that the nominal wind profile and the wind variation profile can be modeled separately. The selection of the nominal wind profile is site dependent. The nominal wind profile could be either selected to signify the most common wind conditions or any wind conditions with a special concern at the airport.
The rest of this chapter is organized as follows. Details of the ACARS wind data, as compared with other data sources available in the US, are explained in Section 4.2. The modeling approach is introduced in the section to lay the ground for more detailed discussions that follow. The process for the mode-decomposition of raw ACARS wind variation profiles, and the process for modeling the decomposed signals as autoregressive signals are discussed in Sections 4.3 and 4.4 respectively. Finally, the process whereby the wind variation model is used in simulating trajectories of aircraft performing noise abatement approach and arrival procedures is explained in Section 4.5. Examples are also presented to demonstrate the accuracy and the effectiveness of the modeling technique. The summary of this chapter is provided in the last section.