Sensitivity analysis of airport noise using computer simulation

This paper presents the method to analyze the sensitivity of airport noise using computer simulation with the aid of Integrated Noise Model 7.0. The technique serves to support the selection of alternatives to better control aircraft noise, since it helps identify which areas of the noise curves experienced greater variation from changes in aircraft movements at a particular airport.


LIST OF SYMBOLS
ANAC: National Civil Aviation Agency Sc xi : Sensitivity cofficient of the movement variable Sc xi' : Sensitivity coefficient of the movement variable without 10% of the aircrafts dB: Decibel dB(A): Decibel, according to the A ponderation curve DNL: Day-night average noise level ΔΦ: Variation in the area of the noise curve FAA: Federal Aviation Administration Φ: Area of the noise curve INM: Integrated Noise Model L Aeq : Equivalent sound pressure level L AeqD : Day equivalent sound pressure level L AeqN : Night equivalent sound pressure level RBAC: Brazilian Regulation for Civil Aviation SEL: Sound exposure level S xi : Sensitivity to a movement x i SBRF: Guararapes International Airport (Recife/PE -Brazil) Movement Variable for a group of aircrafts

InTrOducTIOn
With the global growth of aerial navigation, airport authorities have become more concerned about issues related to aircraft noise.For Infraero (2010), to navigate means to safely conduct a watercraft or an aircraft from one point to another, which is a complex guidance process that enables long journeys with the goal to reach a specific place safely.The safety aspect should also include issues related to sound emission, once they can cause not only discomfort, but also damage to those who are continuously exposed to this type of noise.It is possible to say that the study of airport noise is really relevant worldwide, especially regarding issues related to aircraft noise.As to this aspect, the study concerning the sensitivity analysis is significantly helpful, since it allows identifying which areas of the noise curves have varied more from the changes in the aircraft movements at a specific airport.
Airport noise is usually a result of discreet events, such as landings and take-offs.There are different noise sources in airports, coming from land operations involving aircraft fueling, movements and maintenance, however, landing and take-off operations are considered as the main noise sources of an airport.According to Morais, Slama and Mansur (2008), airport noise is a result of a sound field with intermittent temporal characteristics.The noise coming from the aircraft movements is directly related to the procedures of the aircrafts on the ground, be it before take-off or after landing.The study concerning airport noise embraces different fields of knowledge, from physics to mechanical engineering, especially focusing on the acoustic phenomenon and issues concerning the environment.
The sensitivity analysis of airport noise is a method that uses acoustics software to simulate scenarios, with the objective to help control airport noise.

Equivalent sound pressure level -L aeq
Noise levels can usually vary during a definite period of time.For Gerges (2000), the damaging effects of noise depend not only on its level, but also on how long it lasts.It is possible to say that L aeq is a constant sound pressure level that is equal to the variable noise levels during the measuring period, in terms of acoustic energy.As a consequence, L aeq represents the average sound level resulting from the integration throughout a period of time that can be defined with the logarithmic sum of all sound levels.L aeq can be divided between day and night.L aeqD is the day equivalent sound pressure level and represents the average sound energy calculated during daytime, from 7 to 22h, with a total of 15 hours.L aeqD is determined by Eq. 1.
L AeqN is the night equivalent sound pressure level, and represents the average sound energy calculated during the night, from 22h to 7h, with a total of 9 hours.L aeqN is determined by Eq. 2.
Sound exposure level -SEL SEL represents the total noise energy produced from an event.It is possible to say that SEL represents a logarithmic expression of the acoustic energy of the event, once it exceeds a specific type of noise, as if it had happened within a second.Thus, SEL is obtained by the sum of all sound pressure levels in one unit of time, inside the analyzed interval.Since SEL is a logarithmic expression regarding sound exposure in time, it can be used to compare the noise energy of events that last for different periods.The mathematical formulation to express the definition of SEL is demonstrated in Eq. 3:

day-night Average Sound Level -dnL
DNL is commonly used to define the level of exposure to airport noise, and it also corresponds to the average sound energy caused by all airport events in a period of 24 hours.Ten dB (A) are added to the noise level for sound levels that occur during the night, from 22h to 7h of the next day, due to the higher sensitivity and disturbances caused by noise at night.According to the Code of Federal Regulations 14 CFR 150 (2004), DNL combines the sound energy of all aircraft operations from events that occur during daytime at an average noise exposure for that day.It is possible to say that the calculation of DNL is similar to L aeq , except that DNL adds 10 dB (A) to the night sound and is calculated in a period of 24 hours.According to Bistafa (2006) 2004) also emphasizes that DNL has a penalty for night events since they cause more discomfort.We can say that DNL will identify the events that cause higher noise levels.

METHOdS And dATA
With the use of INM 7.0, the variations of the area of the noise curve (Δφ) will be studied with DNL, as established by RBAC 161 (2011), in relation with variations of airport movements.The values of sensitivity coefficients are calculated after the elaboration of noise curves with INM, over the individual variation of each parameter, with other fixed parameters.Thus, it is possible to say that = (x 1 , x 2 ,..., x n ) , in which the variable x n corresponds to the aircraft movements, during the daytime or the night.Considering the φ variation when x 1 , x 2 ,..., x n varies to x 1 + ∆x 1 , x 2 + ∆x 2 ,…, x n + ∆x n , as demonstrated in Eq. 5: Thus, Δφ can be described as demonstrated in Eq. 6: Therefore, it is possible to obtain the relative variation, which is equivalent to Eq. 7: x 1 ,x 2 ,...,x n x 1 x 1 ,x 2 ,...,x n x 1 ,x 2 ,...,x n x n x n x n x n x 1 ,x 2 ,...,x n (7) The x i motion sensitivity can be defined by Eq. 8: x 1 x i S xi = x 1 ,x 2 ,...,x n (8) Replacing Eq. 8 in Eq. 7, we come to Eq. 9: The values of sensitivity coefficients are defined from the determination of areas of noise curve using INM for the variation of each x i movement.Thus, φ values were determined for x 1 , x 2 , x 3, (…), x n in the initial situation and after the parameter variation for x 1 + Δx 1, x 2 + Δx 2, x 3 + Δx 3, (…), x n + Δx n .Therefore, the sensitivity coefficient for x i will be demonstrated in Eq. 10: The sensitivity coefficients can be expressed for x 1 movements (group A, daytime), x 2 (group A, night), x 3 (group B, daytime), and x 4 (group B, night).Equation 11represents the sensitivity coefficient for a determinate x i movement: Considering a logarithmic relation, it is possible to relate the logarithm of the area of the noise curve and the logarithm in relation to the movements multiplied by their respective sensitivity coefficients, which will result in Eq. 12: log e x 1 x 2 ,...,x n CS x1 log e x 1 + CS x2 log e x 2 + ...

+ CS xn log e x n + cte
(12) The sensitivity analysis was conducted with computational numerical analysis in Guararapes International Airport -Recife/PE, Brazil (SBRF).Information concerning the flights was gathered via online airline schedule provided by the National Civil Aviation Agency (ANAC), from Brazil (2011).Table 1 presents aircraft movements by period.

rESuLTS
The areas of noise curves were calculated for all the aircrafts.Afterwards, the areas of noise curves in groups A and B were calculated both for daytime (D) and night (N)   Sensitivity variations are more noticeable for bigger changes in noise curve areas, which were calculated and are demonstrated in Tables 2 and 3.
From the analysis conducted after obtaining the sensitivity coefficients, it is possible to imply there will be a higher variation in the noise curve areas for the movement variables x 3, x 4 (Table 2) and x 3', x 4' (Table 3).
The higher the variation of the area of noise curves, the bigger the reduction of the noise, since the area of the noise curve will decrease.For movements x 1, x 2, x 1', x 2', especially x 2, x 2', lower values of sensitivity coefficients were calculated in almost all the curves, which shows a lower variation as to noise curves for the respective movements and the maintenance of higher noise levels, close to the initial condition.

cOncLuSIOnS
Using the sensitivity analysis by computational numerical simulation enables to identify the variations in the most significant areas of noise curves that should be carefully analyzed by airport authorities.Since the subject of airport noise is really relevant in the international context and due to the expectations as to the growth of the aerial modal, the study of sensitivity analysis can be seen as a tool to help noise control, especially since it enables identifying which areas of noise curve vary the most.Thus, its use makes measurements to control airport noise more effective.

AcKnOWLEdGEMEnTS
To Instituto alberto Luiz coimbra, of post-graduation and Research in Engineering of Universidade Federal do Rio de Janeiro and to the study group in Airport Noise, which allowed the performance of this study.
, the relation between them is obtained with L aeq of every hour of each day.The average energy sum of the day and night, with extra 10 dB (A), results in the DNL.Eq. 4 mathematically defines DNL.

Table 1 .
Aircraft movements by period.

Table 2 .
Values of noise curve areas with all the aircrafts.

Table 3 .
Values of noise curve areas after 10% of the aircrafts were removed.

Table 4 .
Values of sensitivity coefficients for different noise curves before and after the aircrafts were removed.movements.Table2presents the values of areas of noise curves calculated for the respective groups of aircrafts.Calculation was conducted with DNL, as recommended by RBAC 161 (2011), for different noise curves, and the object of analysis was Guararapes International Airport -Recife/PE, Brazil (SBRF).

Table 3
Table 4 presents the sensitivity coefficient values before (Sc xi ) and after (cS xi' ) 10% of the aircrafts were removed.