F UGITIVE M ETHANE D ETECTION AND L OCALIZATION W ITH S MALL U NMANNED A ERIAL S YSTEMS :C HALLENGES AND O PPORTUNITIES D EREK H OLLENBECK ,Y ANG Q UAN C HEN Department of Mechanical Engineering, University of California, Merced. Contact: {dhollenbeck,ychen53}@ucmerced.edu Acknowledgements: NSF NRT Fellowship (http://www.nrt-ias.org) R EFERENCES [1] Matheou et al. Environ Fluid Mech., 2016. [2] Li et al. Int. Conf. on Rob. and Biomim., 2009. [3] Smith et al. ICUAS Miami., 2017. [4] Farrell et al. Env. Fluid Mech., 2002. [5] Nurzaman et al. PLos ONE, 2011. I NTRODUCTION Natural gas is one of our main methods to gener- ate power today. Utility companies that provide this gas are tasked with maintaining and survey- ing leaks. These leaks are referred to as fugitive methane emissions and detecting these fugitive gases can be pivotal to preventing incidents such as the San Bruno explosion, killing 8 and injur- ing dozens due to a gas leak going undetected. Recently, using NASA technology onboard low cost vertical takeoff and landing (VTOL) small unmanned aerial systems (sUAS) we can detect fugitive methane at 1 ppb (parts per billion) lev- els. C HALLENGES IN D ETECTION General challenges include: FAA regulations (no flights over people), battery life, and complex dy- namic plume behavior. Factors that impact de- tection can be: propeller wash, sensor placement, wind, and mechanical/electrical noises. Even distance to source and flight altitudes can change the probability of detection (Sigmoid like) scal- ing with topology and atmospheric stability. Lo- calization by CFD approaches are costly making real-time estimations and visualizations difficult. Q UASI -S TEADY I NVERSION Following the work by Matthes et al (2005), Carslaw (1959), and Roberts (1923) the solution to a single point source advection diffusion equa- tion (ADE) can be solved for a dynamic system approximately by making a quasi-steady state as- sumption if the variance and transient behavior of the wind small. W 0 is the Lambert function. ∂C ∂t - D ∂ 2 C ∂x 2 i + v ∂C ∂x i =2q 0 δ (t - t 0 )δ (x i - x i0 ) ¯ C (¯ x i ,x 0 ,q o ) i = q 0 exp( ¯ v (¯ x i -x 0 ) 2D ) π 2 3 Dd d i (C i ,x 0 ,q 0 ) ≈ 2D ¯ v W 0 ( ¯ vq 0 4πD 2 C i exp( v 2D (¯ x i -x 0 ))) min q 0 ,x 0 : m X i,j =1 (y 0,i (x 0 ,q 0 ) - y 0,j (x 0 ,q 0 )) 2 A DAPTIVE S EARCH M ODEL In the foraging literature the Levy walk has been shown to be effective at searching sparse environ- ments. However, Brownian motion is more effi- cient in dense areas. This adaptive search model [5] can switch dynamically from Levy to Brown- ian based on finding targets using tumble proba- bility P (x(t)), x(t) is governed by the stochastic differential equation (SDE) below P (x(t)) = e -x(t) , 0 ≤ x ≤ 5 ˙ x = - ∂U ∂x A+, U =(x - h) 2 , : ( H = 1 2 , N(0,σ ) H 6= 1 2 , fGn A = max(A min ,α(t)) α k = C α α k-1 + k t F ( F =1, found target F =0, otherwise. we extend [5] by adding, fGn, defined as Y j = B H (j + 1) - B H (j ) and fraction Brownian motion is given below. A DAPTIVE S EARCH AND L OCALIZATION The adaptive search model has shown to adjust from Brownian motion to Levy walks in a 2D ran- dom search. By reducing the problem to a 1D path problem (i.e. survey route) adding decision trees and modeling fugitive gas with a small time scale filament model [4] we have the opportunity to optimize random search for application. Gather enough information to form a sample(s) to use in the inversion method for a Zeroth order approxi- mation of source localization (x 0 ,y 0 ) and quantifi- cation (q 0 ). B H (x) ≈ X φ(x - y )B (Δy ) φ(x)= Γ(H +1 - d/2+ ||x||) Γ(||x|| + 1)Γ(H +1 - d/2) ≈ ||x|| H -d/2 Γ(H +1 - d/2) E XPERIMENTAL R ESULTS Using the quasi-steady inversion method on ex- perimental data we can see the results from just two samples (blue) in the presence of two sources (red). Only taking a small section of raw data from each longitudinal pass we can approximate the source (green) from our measurement with the OPLS [3]. F UTURE R ESEARCH This work hopes to optimize this adaptive search strategy efficiency η = N/L (N is the number of targets found and L is the total distance trav- eled) through transition parameters (C α , A min , and k t ) the potential (h), and the choice of noise (i.e. Gaussian or fGn) by means of evolution- ary algorithms. Furthermore, we want to answer how the level of noise σ and how the Hurst pa- rameter H , stochastically shift the tumble prob- ability through x(t). Once we have an optimal model we look to compare with current methods (i.e. Zig-Zag, spiral surge [2]), and other gradi- ent or flux based approaches (stochastic gradient descent, fluxotaxis, infotaxis etc.).
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FUGITIVE METHANE DETECTION AND LOCALIZATION WITH SMALL UNMANNED AERIALSYSTEMS: CHALLENGES AND OPPORTUNITIES
DEREK HOLLENBECK, YANGQUAN CHENDepartment of Mechanical Engineering, University of California, Merced.
Contact: {dhollenbeck,ychen53}@ucmerced.edu Acknowledgements: NSF NRT Fellowship (http://www.nrt-ias.org)
REFERENCES
[1] Matheou et al. Environ Fluid Mech., 2016.
[2] Li et al. Int. Conf. on Rob. and Biomim., 2009.
[3] Smith et al. ICUAS Miami., 2017.
[4] Farrell et al. Env. Fluid Mech., 2002.
[5] Nurzaman et al. PLos ONE, 2011.
INTRODUCTIONNatural gas is one of our main methods to gener-ate power today. Utility companies that providethis gas are tasked with maintaining and survey-ing leaks. These leaks are referred to as fugitivemethane emissions and detecting these fugitivegases can be pivotal to preventing incidents suchas the San Bruno explosion, killing 8 and injur-ing dozens due to a gas leak going undetected.Recently, using NASA technology onboard lowcost vertical takeoff and landing (VTOL) smallunmanned aerial systems (sUAS) we can detectfugitive methane at 1 ppb (parts per billion) lev-els.
CHALLENGES IN DETECTIONGeneral challenges include: FAA regulations (noflights over people), battery life, and complex dy-namic plume behavior. Factors that impact de-tection can be: propeller wash, sensor placement,wind, and mechanical/electrical noises. Evendistance to source and flight altitudes can changethe probability of detection (Sigmoid like) scal-ing with topology and atmospheric stability. Lo-calization by CFD approaches are costly makingreal-time estimations and visualizations difficult.
QUASI-STEADY INVERSIONFollowing the work by Matthes et al (2005),Carslaw (1959), and Roberts (1923) the solutionto a single point source advection diffusion equa-tion (ADE) can be solved for a dynamic systemapproximately by making a quasi-steady state as-sumption if the variance and transient behaviorof the wind small. W0 is the Lambert function.
∂C
∂t−D∂
2C
∂x2i
+ v∂C
∂xi= 2q0δ(t− t0)δ(xi − xi0)
C(xi, x0, qo)i =q0 exp( v(xi−x0)
2D )
π23Dd
di(Ci, x0, q0) ≈ 2D
vW0(
vq0
4πD2Ciexp(
v
2D(xi−x0)))
minq0,x0
:m∑
i,j=1
(y0,i(x0, q0)− y0,j(x0, q0))2
ADAPTIVE SEARCH MODELIn the foraging literature the Levy walk has beenshown to be effective at searching sparse environ-ments. However, Brownian motion is more effi-cient in dense areas. This adaptive search model[5] can switch dynamically from Levy to Brown-ian based on finding targets using tumble proba-bility P (x(t)), x(t) is governed by the stochasticdifferential equation (SDE) below
P (x(t)) = e−x(t), 0 ≤ x ≤ 5
x = −∂U∂x
A+ε,
U = (x− h)2, ε :
{H = 1
2 ,N(0, σ)
H 6= 12 , fGn
A = max(Amin, α(t))
αk = Cααk−1 + ktF
{F = 1, found target
F = 0, otherwise.
we extend [5] by adding, fGn, defined as Yj =BH(j+ 1)−BH(j) and fraction Brownian motionis given below.
ADAPTIVE SEARCH AND LOCALIZATION
The adaptive search model has shown to adjustfrom Brownian motion to Levy walks in a 2D ran-dom search. By reducing the problem to a 1Dpath problem (i.e. survey route) adding decisiontrees and modeling fugitive gas with a small timescale filament model [4] we have the opportunityto optimize random search for application. Gatherenough information to form a sample(s) to use inthe inversion method for a Zeroth order approxi-mation of source localization (x0,y0) and quantifi-cation (q0).
BH(x) ≈∑
φ(x− y)B(∆y) φ(x) =Γ(H + 1− d/2 + ||x||)
Γ(||x||+ 1)Γ(H + 1− d/2)≈ ||x||H−d/2
Γ(H + 1− d/2)
EXPERIMENTAL RESULTS
Using the quasi-steady inversion method on ex-perimental data we can see the results from justtwo samples (blue) in the presence of two sources(red). Only taking a small section of raw datafrom each longitudinal pass we can approximatethe source (green) from our measurement withthe OPLS [3].
FUTURE RESEARCHThis work hopes to optimize this adaptive searchstrategy efficiency η = N/L (N is the numberof targets found and L is the total distance trav-eled) through transition parameters (Cα, Amin,and kt) the potential (h), and the choice of noise(i.e. Gaussian or fGn) by means of evolution-ary algorithms. Furthermore, we want to answerhow the level of noise σ and how the Hurst pa-rameter H , stochastically shift the tumble prob-ability through x(t). Once we have an optimalmodel we look to compare with current methods(i.e. Zig-Zag, spiral surge [2]), and other gradi-ent or flux based approaches (stochastic gradientdescent, fluxotaxis, infotaxis etc.).
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