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Article Type:
Research Article

Wind Tunnel Results for a Distributed Flush Airdata System

Roger J. Laurence III Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado

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Brian M. Argrow Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado

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Eric W. Frew Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado

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Print Publication:
01 Jul 2017
DOI:
https://doi.org/10.1175/JTECH-D-16-0242.1
Page(s):
1519–1528
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Abstract

The multihole probe (MHP) is an effective instrument for relative wind measurements from small unmanned aircraft systems (sUAS). Two common drawbacks for the integration of commercial MHP systems into low-cost sUAS are that 1) the MHP airdata system cost can be several times that of the sUAS airframe; and 2) when extended from the airframe, the pressure-measuring probe is often exposed to damage during normal operations. A flush airdata system (FADS) with static pressure sensing ports mounted flush with the airframe skin provides an alternative to the MHP system. This project implements a FADS with multiple static pressure sensors located at selected locations on the airframe. Computational fluid dynamics simulations are used to determine the airframe locations with the highest pressure change sensitivity to changes in the airframe angle of attack and sideslip angle. Wind tunnel test results are reported with nonlinear least squares and neural networks regression methods applied to the pressure measurements to estimate the instantaneous angle of attack and sideslip. Both methods achieved mean errors of less than . A direct comparison of the regression methods show that the neural network method provides a more accurate relative wind angle estimate than the nonlinear least squares method.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Roger Laurence, roger.laurenceiii@colorado.edu

Abstract

The multihole probe (MHP) is an effective instrument for relative wind measurements from small unmanned aircraft systems (sUAS). Two common drawbacks for the integration of commercial MHP systems into low-cost sUAS are that 1) the MHP airdata system cost can be several times that of the sUAS airframe; and 2) when extended from the airframe, the pressure-measuring probe is often exposed to damage during normal operations. A flush airdata system (FADS) with static pressure sensing ports mounted flush with the airframe skin provides an alternative to the MHP system. This project implements a FADS with multiple static pressure sensors located at selected locations on the airframe. Computational fluid dynamics simulations are used to determine the airframe locations with the highest pressure change sensitivity to changes in the airframe angle of attack and sideslip angle. Wind tunnel test results are reported with nonlinear least squares and neural networks regression methods applied to the pressure measurements to estimate the instantaneous angle of attack and sideslip. Both methods achieved mean errors of less than . A direct comparison of the regression methods show that the neural network method provides a more accurate relative wind angle estimate than the nonlinear least squares method.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Roger Laurence, roger.laurenceiii@colorado.edu
Keywords: Aircraft observations; In situ atmospheric observations; Neural networks

1. Introduction

Small unmanned aircraft systems (sUAS) have proven effective at making in situ meteorological measurements within the atmospheric boundary layer (e.g., Houston et al. 2012; Balsley et al. 2013; Reuder et al. 2012), including operations in, and near, supercell thunderstorms (Elston et al. 2011; Roadman et al. 2012). This demonstrated ability to operate in both quiescent and dynamic environments uniquely qualifies sUAS for in situ wind measurements. Size, weight, and power requirements preclude the integration of some proximal wind measurement tools used on manned aircraft, such as lidar, into an sUAS. Many other approaches have been explored, such as one that uses only the inertial sensors already in use for control of the aircraft (Mayer and Hattenberger 2012), a strip of pressure sensors on the wing (Callegari et al. 2006), and multihole probes (MHP), which are a modification of the classic pitot-static probe to enable three-dimensional wind measurements (Telionis et al. 2009; Johansen et al. 2001).

The multihole probe has been used effectively for wind measurements from sUAS (Houston et al. 2016; Kocer et al. 2011; van den Kroonenberg et al. 2008). They are highly accurate for relative wind measurements (errors less than 1 m airspeed and angle of attack and sideslip), and miniaturized commercial versions that can be integrated into sUAS are now available (Aeroprobe 2016). By combining the aircraft state with the relative wind measurement (from an MHP or some other relative wind instrument), it is possible to estimate the inertial winds (e.g., in the north-east-down frame). The aircraft state is generally estimated with an onboard inertial measurement unit (IMU) that provides an estimate of the instantaneous orientation and rotation rates coupled with a GPS receiver that provides the inertial position and velocity of the aircraft. A description of this process is presented in Nichols et al. (2017).

As the Aeroprobe MHP is a commercial off-the-shelf (COTS) system, it is effectively “plug and play,” where the user is responsible for installing the probe in a suitable location on the aircraft but is not required to modify the software. However, this simplicity means that an MHP with an accompanying airdata computer can cost several times that of the sUAS airframe on which it is being flown. Additionally, the MHP must be mounted such that it has access to the freestream (typically sticking out from the nose), which can make it vulnerable to damage, especially on sUAS without landing gear (real-world examples include clipping a wing in tall grass or skipping on a rock upon landing, both of which can lead the aircraft to impact the ground nose first). One configuration that has been used previously is shown in Fig. 1.

Fig. 1.
Fig. 1.

Aeroprobe MHP mounted on the X-8 Skywalker UAS.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

Flush airdata systems (FADS) are an alternative to the MHP that rely on the same principles. FADS effectively turn part of the airframe into an MHP. They have been implemented on a range of aircraft, from a space shuttle (Larson and Siemers 1980), to an F-18 (Whitmore 1991), to other manned aircraft (Tjernstrom and Friehe 1991; Kalogiros and Wang 2002a,b), and even on an sUAS (Quindlen and Langelaan 2013). All of these FADS have been located on the nose of the aircraft, which is not always a viable option for sUAS due to the wide variety of shapes (Elston et al. 2015). While a FADS also requires significantly more user input than a COTS MHP, it does remove the need for an exposed probe.

This paper presents a modification to the “conventional” FADS configuration: rather than restrict the pressure ports on the nose cone, the ports are allowed to be distributed across the aircraft. A method is developed to determine suitable locations for an arbitrarily shaped fixed-wing aircraft. With the use of small microelectromechanical systems (MEMS)-style COTS pressure sensors,1 this method also reduces the hardware cost by an order of magnitude over the MHP. While the selection of sensor locations is not the focus of this paper, section 2 will provide a short background on how the locations were chosen. Section 3 will detail the wind tunnel model and how it was calibrated. Finally, section 4 will present the results2 and highlight how nonlinear least squares and neural networks were used to produce estimates of the angle of attack and sideslip from the pressure measurements. Section 5 closes the paper with a comparison of the accuracy of the two estimation methods.

2. Sensor location selection

Both Whitmore (1991) and Quindlen and Langelaan (2013) show how potential flow can be used to determine the layout of the pressure ports on a nose cone. However, not all sUAS have nose cones (one such example is shown in Figs. 2 and 3), and of the ones that do, the nose cone could be rendered unusable if the aircraft has a propeller installed on the nose. Additionally, without an a priori analysis, there is no guarantee that the nose cone is the optimal location for a FADS, particularly for unconventional airframe designs. Because of the variety of sUAS shapes, there is a need for a robust method of sensor location selection. A brief background on how computational fluid dynamics (CFD) can be used is provided here; Laurence et al. (2015) provides a more detailed discussion.

Fig. 2.
Fig. 2.

Plots showing the values of the two cost functions used for the selection of pressure port locations. Locations for the (a) cost function (to be minimized) and (b) cost function (to be maximized). Arrows show approximate locations of sensors that are hidden by the current view.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

Fig. 3.
Fig. 3.

Completed wind tunnel model. (a) Tubing installation. (b) Finished version of (a) in the wind tunnel.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

The Eagle Owl sUAS (Figs. 2 and 3) is used here because of its unconventional, but simple, geometry. STAR-CCM+3 was used to predict how the pressure on the surface changes with varying angle of attack (α; defined as pitching up relative to the oncoming airflow) and sideslip (β; defined as rotating right in the horizontal plane of the aircraft). This enables identification of the locations with the highest sensitivity to changes in the wind angles. Steady-state simulations were run with α ranging from to (in increments), β ranging from to (in increments), and the airspeed fixed at 15 m . The reference pressure for the simulations was set to 830 hPa (roughly the pressure at ground level in Boulder, Colorado, which was the location of the wind tunnel experiments) and the temperature was set to 293.15 K. An ideal gas was assumed, and the k–ϵ model [a description of which can be found in Mohammadi and Pironneau (1994, 51–62)] was used to simulate turbulence. The simulation model contained approximately 185 000 grid points on the surface of the Eagle Owl, with the largest dimension of the cells being in the 1–4-mm range.

High priority was placed on aircraft locations that had a large range in pressure (the sensor noise/bias would therefore have less of an effect on the estimate of α and β), as well as locations that experienced a smooth/predictable pressure response to variations in α and β. To prioritize these two aspects, a simple cost function was implemented:
e1
where RMSE is the root-mean-square error of the fit between pressure, α, and β; and is the difference of the maximum and minimum pressure experienced over all 126 simulations (for a specified grid point). The value of this cost function can be seen for all the grid points in Fig. 2a. A lower value implies either a more predictable response or a greater pressure range. The leading edges of the top airfoil are where is lowest, followed by the leading edges of the bottom airfoil. These locations are insensitive to changes in β (compared to changes in α), which makes them poorly suited for the determination of sideslip (this behavior was apparent in the wind tunnel results as well). A second cost function was then produced, with a greater emphasis on sensitivity to β:
e2
where is the average range of pressure across the sideslips (averaged over all β for a given α); and are the minimum and maximum average sideslip ranges, respectively; and and are the lower and upper limits of acceptable RMSE values, respectively. The lower limit was set to 0.0609, as that was the lowest value achieved, while was set to 1.0 as an upper limit. The cost function has larger values for locations that are better suited for determining sideslip (Fig. 2b). The leading edges of the side plates are best suited for measuring sideslip. Using both of these cost functions, and excluding certain areas (such as the underside of the aircraft and the extreme forward portions of the leading edges), 10 locations were chosen and are superimposed on the cost functions in Fig. 2. Since locations 1–4 were chosen with , it is predicted that these locations will have the greatest influence on the measurement of α, with locations 5–10 being the most important to determining β.

3. Wind tunnel tests

a. Wind tunnel model

To investigate the feasibility of a distributed FADS for obtaining wind measurements, a two-thirds-scale model was fabricated and used in the low-speed wind tunnel at the National Center for Atmospheric Research (NCAR) in Boulder. The model has a wingspan of 0.6 m and a height of 0.2 m. It is constructed from expanded polystyrene (EPS) foam, basswood, and epoxy. The nearly completed model can be seen in Fig. 3a, while the finished model can be seen mounted in the wind tunnel in Fig. 3b. For these experiments, the pressure was recorded with TE Connectivity MS5611-01BA pressure sensors, with the technical specifications reported in Table 1. These sensors were chosen for their low cost, high resolution, and availability.

Table 1.

Technical specifications of the MS5611-01BA pressure sensor.

Table 1.

For simplicity, the pressure sensors were housed off the aircraft and outside the wind tunnel. Future work involves mounting the sensors in the aircraft, thus allowing this method of wind sensing to be performed in flight. Holes were drilled to allow 3.175-mm outer-diameter Tygon tubing to run from the underside/interior face of the wings/side plates to the locations chosen through CFD. Slots were cut into the undersides/interior face to route the tubing while maintaining a smooth surface to minimize flow disturbance. A wooden spar was installed along the centerline of the lower wing; this connected to a carbon fiber rod that extended the model in front of the vertical support in the wind tunnel. The final step involved running the tubing cleanly off the model and out of the wind tunnel.

b. Calibration

The first phase of the experiment involved collecting data for calibration. As mentioned previously, only α and β were varied in the tunnel. Future work will incorporate varying airspeed and density (through altitude changes) during in-flight calibration. The range of (α, β) orientations is shown in Fig. 4, with the blue dots representing orientations used for calibration and red dots for validation. For each orientation, 300 samples were taken, where a “sample” refers to a pressure measurement taken simultaneously from all 10 sensors.

Fig. 4.
Fig. 4.

Aircraft orientations used for wind tunnel calibration and validation tests.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

It is assumed that the airflow through the tunnel is parallel to the walls through the test section. Therefore, all α measurements are relative to the floor of the test section. For clarity, α is defined as the angle between the wingtip chord line of the top wing and the flow through the tunnel, with the positive direction being nose up. An AccuMaster 7434 digital inclinometer was used to measure the angle between the model and tunnel floor. It features an accuracy of and a resolution of . The definition of β is the angle between the centerline of the model and the airflow. A positive sideslip is a rotation to the right from the incoming freestream wind vector. Rotating the vertical support changes β and was measured on an analog vernier scale to about accuracy.

Before and after each fixed α, the room pressure was measured. The average of the before and after measurements was calculated and represents the freestream pressure. This average is then subtracted from each individual sensor, yielding P. All the results presented will be in terms of P, and the relation between α, β, and P can be seen in Fig. 5 for several locations. For example, at location 3, increasing α reduces the pressure compared to the freestream pressure. As will be explained in the next section, the surface fits shown in Fig. 5 will be used for the nonlinear least squares method, but they are not needed for the neural networks.

Fig. 5.
Fig. 5.

Measurement models used with NLS. Surface fits are second-order polynomials in both directions.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

4. Results

a. Nonlinear least squares

The first method investigated for estimating α and β from pressure measurements was nonlinear least squares (NLS). This approach, as outlined in Crassidis and Junkins (2011, 25–29), attempts to minimize the residuals, which are the difference between the true pressure measurements and the predicted pressure measurements, by minimizing the cost function:
e3
where the residual vector is represented by and the weighting matrix by . This weighting matrix assigns a weight to each sensor based on the noise in the measurements; that is, a sensor with less noise will be trusted more than a sensor with greater noise and therefore contribute more to the final solution. The P measurements from all 10 sensors are represented by . The estimate of α and β is the vector . The nonlinear relationship between α, β, and P for sensor i is , where can be written as a second-order polynomial:
e4
with the individual coefficients determined with the MATLAB fit function. All 10 relationships are stored in the term, with , , , and visually represented in Fig. 5. Additionally, the Gauss–Newton method was used for finding the minimum of J, and all estimates are produced with an initial guess of .

b. Neural networks

The independent variables are α and β, while pressure (or more specifically, P) is the dependent variable. The first step in the least squares method is to determine how the dependent variable is related to the independent variables for each sensor ( P), then it is possible to work in reverse so that by measuring only the dependent variable, the independent variables can be estimated (P ). Neural networks, on the other hand, can directly relate the measured dependent variable to the independent variables to be estimated in one step. The networks are trained with the data from the calibration phase, resulting in a simple function that accepts P and calculates α and β.

The layout of a network used for this project is shown in Fig. 6. The output of layer i is given by
e5
where for the ith layer is the weight matrix, is the bias vector, is the input, and is the transfer function. The P measurements are the inputs for the hidden layer, which uses the MATLAB tansig transfer function with Eq. (5). These values are then the inputs into the output layer, which uses the purelin transfer function to output the values of α and β.
Fig. 6.
Fig. 6.

Schematic showing the layout of a single neural network.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

The neural networks were trained using the MATLAB Neural Network Toolbox [the foundation of which is provided by Hagan et al. (2014)]. Two ways the user can affect the accuracy of the results are by choosing the training method and the number of hidden-layer neurons. Three of the training methods used for regression in the toolbox are Levenberg–Marquardt (Hagan and Menhaj 1994; Marquardt 1963), Bayesian regularization (Foresee and Hagan 1997; MacKay 1992) and scaled conjugate gradient (Moller 1993; Charalambous 1992). Among these methods, Bayesian regularization is the only one specifically designed to generalize well. Since the orientations used to collect the training data were different from the orientations used for validation, being able to generalize outside of the training points was of high priority, hence the reason why Bayesian regularization is the chosen training method.

In addition to choosing the training method, the number of neurons in the hidden layer must also be specified. Too few neurons and the network cannot handle the complexity of the relationship between P, α, and β (underfitting the data); too many neurons and it will not generalize well outside of the training points (overfitting the data). The optimal number of hidden-layer neurons to use can be seen in Fig. 7. Using four neurons leads to the smallest mean-square error for α and β simultaneously. The number of neurons in the output layer is determined by the number of outputs, and as such are not user changeable.

Fig. 7.
Fig. 7.

MSE using different numbers of neurons in the hidden layer.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

Neural networks are initialized with random weights and biases. Even if the network is retrained using the same data, it is possible to produce different results. Therefore, it is possible to use an ensemble of networks and get a range of outputs. The number of networks to use in the ensemble is shown in Fig. 8. Convergence starts around 30–40 networks. The only penalty incurred for using more networks is a larger amount of time training them. For all the results presented in this paper, an ensemble size of 30 networks was used.

Fig. 8.
Fig. 8.

Convergence of the MSE as a function of the ensemble size.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

c. Results

While 300 samples were taken at each validation orientation, only a single sample was used at a time to produce an estimate. This led to 300 estimates for each orientation. The case where the true orientation was is shown in Figs. 9a and 9b (for NLS and the neural networks, respectively). The black diamond shows the true orientation, and each blue dot is an estimate produced by using one of the pressure samples. It is immediately clear that for this particular orientation, NLS has a significantly stronger bias in the estimates than the neural networks. In addition, the neural network estimates are grouped tighter than the NLS estimates. The estimates produced for all 20 test orientations are shown in Figs. 9c and 9d. For the lower α values, there is a clear bias in NLS, although as α increases the bias decreases.

Fig. 9.
Fig. 9.

Scatterplots showing the estimates produced by NLS and the ensemble of neural networks. Estimates from (a) NLS and (b) the neural networks are shown for the case where the true orientation is (, ). Estimates for all the validation orientations for (c) NLS and (d) neural networks.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

With the true orientation expressed as , the error for an estimate is calculated with
e6
Each test orientation therefore has 300 errors associated with the estimates. The statistics of those errors are shown in Fig. 10. The mean error and two standard deviation (σ) bounds for α are shown in Figs. 10a and 10b for NLS and the neural networks, respectively. For example, when the true orientation is , NLS has a mean error of almost , while the neural networks have a mean error of only about . It is also easier to see the trend mentioned earlier for NLS, where it is less biased for higher angles of attack. It should also be noted that both methods almost always overestimate the angle of attack.
Fig. 10.
Fig. 10.

Comparison of mean errors and 2σ bounds. Errors in α for (a) NLS and (b) neural networks, and errors in β for (c) NLS and (d) neural networks.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

The mean errors and bounds for β are shown in Figs. 10c and 10d. Again, it is immediately apparent that the neural networks produce significantly smaller mean errors than NLS. For NLS, the mean errors tend to be biased in the same direction as the true β, and they scale with the true β as well. The most positive sideslip tested generally has the most positive bias to the estimates, while the most negative sideslip tested almost always has the most negative bias. This trend is significantly weaker when using neural networks, but it still appears for some of the validation orientations.

While all the sensors worked the entire time, it is possible that a sensor might fail at some point. To investigate the effects of a failed sensor, estimates were produced ignoring the measurements from a single sensor at a time. The resulting mean-square errors (MSE) are shown in Fig. 11 for neural networks. The case of NLS with failed sensors was not considered. Note that the dashed lines represent the baseline MSE with all 10 sensors being used for estimates of the orientation. It will also be useful to refer back to Fig. 5 to see why some sensors have a larger effect on α or β.

Fig. 11.
Fig. 11.

MSE for the removal of an individual sensor.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

When sensors 2–4 are ignored, there is relatively little effect on the β errors. This makes sense, as the pressure at these locations is nearly independent of β (sensors 2 and 4 have nearly identical surfaces to sensor 3). However, the pressure at location 1 is independent of β at low α, but as α is increased, the pressure does become dependent on β, which is why MSEβ jumps when sensor 1 is removed. It is unsurprising that MSEβ increases after removing sensors 5–10, as these locations were chosen specifically because they are more sensitive to changes in β. Locations 1–4 were chosen for their sensitivity to α; it is therefore surprising that removing sensor 1 or 4 has minimal impact on MSEα. Perhaps the most surprising result is when sensor 9 is removed. This location was chosen for its sensitivity to β, yet this sensor has the largest effect on MSEα.

Finally, it is also interesting to look at how the errors for both methods are distributed. Histograms of the errors for all the validation orientations are shown in Fig. 12. The errors from neural networks are well represented by a Gaussian distribution, although only the β errors have zero mean. All of the estimates of α were within of the truth, while only 2 out of the 6000 total estimates for β were greater than from the truth. For NLS, the β errors are close to a zero-mean Gaussian, but the α errors are clearly not representative of a Gaussian distribution. Additionally, 93.1% of the α errors and 98.0% of the β errors are within of the truth.

Fig. 12.
Fig. 12.

Histogram of all the errors from (a),(c) NLS and (b),(d) neural networks.

Citation: Journal of Atmospheric and Oceanic Technology 34, 7; 10.1175/JTECH-D-16-0242.1

5. Conclusions

The wind tunnel results presented show that a distributed flush airdata system is indeed a viable method of wind sensing from small UAS. Different locations contribute to the final estimate in varying amounts, so it is important to choose suitable locations. It was also quite clear that using an ensemble of neural networks leads to better results than the nonlinear least squares approach. While neural networks performed better, both methods achieved mean errors that were less than , which is the maximum error specified by commercial multihole probe systems (specifically, the Aeroprobe five-hole probe). Last, for the neural networks, 100% of the errors in the angle of attack α and 99.97% of the errors in sideslip β were less than .

While this paper presented wind tunnel results, the method is currently being adapted for wind sensing in flight. The distributed flush airdata system can be expanded to provide estimates of the airspeed as well. However, a different calibration procedure must be developed, since even for a small UAS it is usually not practical to perform wind tunnel calibration due to size constraints of the typical wind tunnel test section. Ongoing work involves testing the feasibility of using the multihole probes to perform in-flight calibration as opposed to wind tunnel calibration (with the probes then removed upon completion of the calibration flights).

Acknowledgments

The authors thank Steven Semmer of the National Center for Atmospheric Research for his help with access to, and operation of, the wind tunnel; James Mack and Will Finamore for their help during the assembly of the model; and Nick Campbell for helping to collect the data. The authors are also grateful to Dr. Jack Elston for his early contributions to this project. Finally, the authors also acknowledge the support of the U.S. Air Force Office of Scientific Research (AFOSR; Award FA9550-12-1-0412), the National Science Foundation (NSF; Award AGS-1231096), and the National Robotics Initiative (NRI; Award IIS-1527919).

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  • Larson, T. J., and P. M. Siemers III, 1980: Use of nose cap and fuselage pressure orifices for determination of air data for space shuttle orbiter below supersonic speeds. NASA Tech. Rep. 1643, 129 pp.

  • Laurence, R. J., J. S. Elston, and B. M. Argrow, 2015: A low-cost system for wind field estimation through sensor networks and aircraft design. Proc. AIAA Infotech @ Aerospace, Kissimmee, FL, AIAA SciTech, AIAA 2015-1425, doi:10.2514/6.2015-1425.

    • Crossref
    • Export Citation

  • Laurence, R. J., B. M. Argrow, and E. W. Frew, 2016: Development of wind sensing from small UAS with distributed pressure sensors. Proc. Eighth AIAA Atmospheric and Space Environments Conf., Washington, DC, AIAA Aviation, AIAA 2016-4199, doi:10.2514/6.2016-4199.

    • Crossref
    • Export Citation

  • MacKay, D. J. C., 1992: Bayesian interpolation. Neural Comput., 4, 415–447, doi:10.1162/neco.1992.4.3.415.

  • Marquardt, D. W., 1963: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 11, 431–441, doi:10.1137/0111030.

  • Mayer, S., and G. Hattenberger, 2012: A ‘no-flow-sensor’ wind estimation algorithm for unmanned aerial systems. J. J. Micro Air Veh., 4, 15–29, doi:10.1260/1756-8293.4.1.15.

    • Search Google Scholar
    • Export Citation

  • Mohammadi, B., and O. Pironneau, 1994: Analysis of the K-Epsilon Turbulence Model. Wiley-Masson Series Research in Applied Mathematics, Vol. 2, Wiley, 51–62.

  • Moller, M. F., 1993: A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks, 6, 525–533, doi:10.1016/S0893-6080(05)80056-5.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Nichols, T., B. Argrow, and D. Kingston, 2017: Error sensitivity analysis of small UAS wind-sensing systems. Proc. AIAA Information Systems–AIAA Infotech @ Aerospace, Grapevine, TX, AIAA SciTech Forum, AIAA 2017-0647, doi:10.2514/6.2017-0647.

    • Crossref
    • Export Citation

  • Quindlen, J. F., and J. W. Langelaan, 2013: Flush air data sensing for soaring-capable UAVs. Proc. 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, AIAA, AIAA 2013-1153, doi:10.2514/6.2013-1153.

    • Crossref
    • Export Citation

  • Reuder, J., M. O. Jonassen, and H. Ólafsson, 2012: The Small Unmanned Meteorological Observer SUMO: Recent developments and applications of a micro-UAS for atmospheric boundary layer research. Acta Geophys., 60, 1454–1473, doi:10.2478/s11600-012-0042-8.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Roadman, J., J. Elston, B. Argrow, and E. Frew, 2012: Mission performance of the Tempest unmanned aircraft system in supercell storms. J. Aircr., 49, 1821–1830, doi:10.2514/1.C031655.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Siemens, 2017: STAR-CCM+. Accessed 31 March 2017. [Available online at http://mdx.plm.automation.siemens.com/star-ccm-plus.]

  • Telionis, D., Y. Yang, and O. Rediniotis, 2009: Recent developments in multi-hole probe (MHP) technology. Proc. 20th Int. Congress of Mechanical Engineering, Gramado, RS, Brazil, ABCM, 29 pp. [Available online at http://abcm.org.br/anais/cobem/2009/pdf/COB09-3415.pdf.]

  • TE Sensor Solutions, 2015: MS5611-01BA03 barometric pressure sensor, with stainless steel cap. Measurement Specialties Inc. Datasheet, 22 pp. [Available online at http://www.te.com/commerce/DocumentDelivery/DDEController?Action=srchrtrv&DocNm=MS5611-01BA03&DocType=Data+Sheet&DocLang=English.]

  • Tjernstrom, M., and C. Friehe, 1991: Analysis of a radome air-motion system on a twin-jet aircraft for boundary-layer research. J. Atmos. Oceanic Technol., 8, 19–40, doi:10.1175/1520-0426(1991)008<0019:AOARAM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • van den Kroonenberg, A., T. Martin, M. Buschmann, J. Bange, and P. Vorsmann, 2008: Measuring the wind vector using the autonomous mini aerial vehicle M2AV. J. Atmos. Oceanic Technol., 25, 1969–1982, doi:10.1175/2008JTECHA1114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Whitmore, S. A., 1991: Development of a pneumatic high-angle-of-attack flush airdata sensing (HI-FADS) system. NASA Tech. Memo. NASA TM-104241, 28 pp.

    • Crossref
    • Export Citation
1

In the case of the MS5611-01BA, a piezoresistive sensor for pressure (TE Sensor Solutions 2015).

2

The results presented in this paper are a more thorough update to the results presented in Laurence et al. (2016).

3

CFD simulation software (Siemens 2017).

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Cover Journal of Atmospheric and Oceanic Technology
Journal of Atmospheric and Oceanic Technology

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  • Houston, A. L., R. Laurence, T. Nichols, S. Waugh, B. Argrow, and C. Ziegler, 2016: Intercomparison of unmanned aircraftborne and mobile mesonet atmospheric sensors. J. Atmos. Oceanic Technol., 33, 1569–1582, doi:10.1175/JTECH-D-15-0178.1.

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  • Larson, T. J., and P. M. Siemers III, 1980: Use of nose cap and fuselage pressure orifices for determination of air data for space shuttle orbiter below supersonic speeds. NASA Tech. Rep. 1643, 129 pp.

  • Laurence, R. J., J. S. Elston, and B. M. Argrow, 2015: A low-cost system for wind field estimation through sensor networks and aircraft design. Proc. AIAA Infotech @ Aerospace, Kissimmee, FL, AIAA SciTech, AIAA 2015-1425, doi:10.2514/6.2015-1425.

    • Crossref
    • Export Citation

  • Laurence, R. J., B. M. Argrow, and E. W. Frew, 2016: Development of wind sensing from small UAS with distributed pressure sensors. Proc. Eighth AIAA Atmospheric and Space Environments Conf., Washington, DC, AIAA Aviation, AIAA 2016-4199, doi:10.2514/6.2016-4199.

    • Crossref
    • Export Citation

  • MacKay, D. J. C., 1992: Bayesian interpolation. Neural Comput., 4, 415–447, doi:10.1162/neco.1992.4.3.415.

  • Marquardt, D. W., 1963: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 11, 431–441, doi:10.1137/0111030.

  • Mayer, S., and G. Hattenberger, 2012: A ‘no-flow-sensor’ wind estimation algorithm for unmanned aerial systems. J. J. Micro Air Veh., 4, 15–29, doi:10.1260/1756-8293.4.1.15.

    • Search Google Scholar
    • Export Citation

  • Mohammadi, B., and O. Pironneau, 1994: Analysis of the K-Epsilon Turbulence Model. Wiley-Masson Series Research in Applied Mathematics, Vol. 2, Wiley, 51–62.

  • Moller, M. F., 1993: A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks, 6, 525–533, doi:10.1016/S0893-6080(05)80056-5.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Nichols, T., B. Argrow, and D. Kingston, 2017: Error sensitivity analysis of small UAS wind-sensing systems. Proc. AIAA Information Systems–AIAA Infotech @ Aerospace, Grapevine, TX, AIAA SciTech Forum, AIAA 2017-0647, doi:10.2514/6.2017-0647.

    • Crossref
    • Export Citation

  • Quindlen, J. F., and J. W. Langelaan, 2013: Flush air data sensing for soaring-capable UAVs. Proc. 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, AIAA, AIAA 2013-1153, doi:10.2514/6.2013-1153.

    • Crossref
    • Export Citation

  • Reuder, J., M. O. Jonassen, and H. Ólafsson, 2012: The Small Unmanned Meteorological Observer SUMO: Recent developments and applications of a micro-UAS for atmospheric boundary layer research. Acta Geophys., 60, 1454–1473, doi:10.2478/s11600-012-0042-8.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Roadman, J., J. Elston, B. Argrow, and E. Frew, 2012: Mission performance of the Tempest unmanned aircraft system in supercell storms. J. Aircr., 49, 1821–1830, doi:10.2514/1.C031655.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Siemens, 2017: STAR-CCM+. Accessed 31 March 2017. [Available online at http://mdx.plm.automation.siemens.com/star-ccm-plus.]

  • Telionis, D., Y. Yang, and O. Rediniotis, 2009: Recent developments in multi-hole probe (MHP) technology. Proc. 20th Int. Congress of Mechanical Engineering, Gramado, RS, Brazil, ABCM, 29 pp. [Available online at http://abcm.org.br/anais/cobem/2009/pdf/COB09-3415.pdf.]

  • TE Sensor Solutions, 2015: MS5611-01BA03 barometric pressure sensor, with stainless steel cap. Measurement Specialties Inc. Datasheet, 22 pp. [Available online at http://www.te.com/commerce/DocumentDelivery/DDEController?Action=srchrtrv&DocNm=MS5611-01BA03&DocType=Data+Sheet&DocLang=English.]

  • Tjernstrom, M., and C. Friehe, 1991: Analysis of a radome air-motion system on a twin-jet aircraft for boundary-layer research. J. Atmos. Oceanic Technol., 8, 19–40, doi:10.1175/1520-0426(1991)008<0019:AOARAM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • van den Kroonenberg, A., T. Martin, M. Buschmann, J. Bange, and P. Vorsmann, 2008: Measuring the wind vector using the autonomous mini aerial vehicle M2AV. J. Atmos. Oceanic Technol., 25, 1969–1982, doi:10.1175/2008JTECHA1114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Whitmore, S. A., 1991: Development of a pneumatic high-angle-of-attack flush airdata sensing (HI-FADS) system. NASA Tech. Memo. NASA TM-104241, 28 pp.

    • Crossref
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Aeroprobe MHP mounted on the X-8 Skywalker UAS.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Plots showing the values of the two cost functions used for the selection of pressure port locations. Locations for the (a) cost function (to be minimized) and (b) cost function (to be maximized). Arrows show approximate locations of sensors that are hidden by the current view.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Completed wind tunnel model. (a) Tubing installation. (b) Finished version of (a) in the wind tunnel.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Aircraft orientations used for wind tunnel calibration and validation tests.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Measurement models used with NLS. Surface fits are second-order polynomials in both directions.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Schematic showing the layout of a single neural network.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    MSE using different numbers of neurons in the hidden layer.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Convergence of the MSE as a function of the ensemble size.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Scatterplots showing the estimates produced by NLS and the ensemble of neural networks. Estimates from (a) NLS and (b) the neural networks are shown for the case where the true orientation is (, ). Estimates for all the validation orientations for (c) NLS and (d) neural networks.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Comparison of mean errors and 2σ bounds. Errors in α for (a) NLS and (b) neural networks, and errors in β for (c) NLS and (d) neural networks.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    MSE for the removal of an individual sensor.

  • <sc>Fig</sc>. 12.
    View in gallery
    Fig. 12.

    Histogram of all the errors from (a),(c) NLS and (b),(d) neural networks.

Fig. 1.

Aeroprobe MHP mounted on the X-8 Skywalker UAS.
Fig. 2.

Plots showing the values of the two cost functions used for the selection of pressure port locations. Locations for the (a) cost function (to be minimized) and (b) cost function (to be maximized). Arrows show approximate locations of sensors that are hidden by the current view.
Fig. 3.

Completed wind tunnel model. (a) Tubing installation. (b) Finished version of (a) in the wind tunnel.
Fig. 4.

Aircraft orientations used for wind tunnel calibration and validation tests.
Fig. 5.

Measurement models used with NLS. Surface fits are second-order polynomials in both directions.
Fig. 6.

Schematic showing the layout of a single neural network.
Fig. 7.

MSE using different numbers of neurons in the hidden layer.
Fig. 8.

Convergence of the MSE as a function of the ensemble size.
Fig. 9.

Scatterplots showing the estimates produced by NLS and the ensemble of neural networks. Estimates from (a) NLS and (b) the neural networks are shown for the case where the true orientation is (, ). Estimates for all the validation orientations for (c) NLS and (d) neural networks.
Fig. 10.

Comparison of mean errors and 2σ bounds. Errors in α for (a) NLS and (b) neural networks, and errors in β for (c) NLS and (d) neural networks.
Fig. 11.

MSE for the removal of an individual sensor.
Fig. 12.

Histogram of all the errors from (a),(c) NLS and (b),(d) neural networks.
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