Evaluation and Analysis of F-16XL Wind Tunnel Data from Dynamic Tests

EVALUATION AND ANALYSIS OF F-16XL WIND TUNNEL

DATA FROM DYNAMIC TESTS

† * Sungwan Kim and Patrick C. Murphy NASA Langley Research Center Hampton, Virginia 23681 ‡ Vladislav Klein The George Washington University NASA Langley Research Center Hampton, Virginia 23681 Abstract A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes.

Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this paper, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.

measured outputs and accuracy of parameter estimates Introduction are presented. Application of the tools to both repeated A concern in any scientific experiment is the issue of and ensemble-averaged experimental data is obtaining sufficient measurement accuracy. In particular, demonstrated. In this analysis, a linear aerodynamic it is a concern when investigating nonlinear dynamic model appropriate for conventional forced-oscillation systems since these systems can exhibit behaviors that experiments is assumed although more general may substantially complicate responses and model aerodynamic models can also be used with the tools identification. For these experiments the amount of care presented.

taken in both experiment design and measurement In an effort to obtain a more general formulation of procedures will be reflected in the final measurement the aerodynamic model for aircraft, a series of wind accuracy. Two approaches can be used to estimate tunnel tests were conducted in the NASA Langley measurement accuracy. One approach is to use repeated Research Center (LaRC) 12-Foot Low-Speed Tunnel measurements that allow a statistical estimate of the using a 10% scale model of the F-16XL. Two of measurement variance to be made. This approach can be tunnel tests, conducted in 1996 and 2000, provided costly and time consuming in some cases; however, it static and dynamic data for nonlinear modeling has the advantage of directly reflecting measurement research. Initial studies identifying unsteady uncertainty. Another approach, based on system aerodynamic models from these data were reported in identification theory, is to utilize the difference between Refs. [1]-[3]. During both the 1996 and 2000 measured responses and that predicted by an adequate experiments, for certain test conditions and signals, model. The advantage in this case is that repeated forced oscillation measurements did not reflect the measurements are not required, although the presence of expected harmonic motion related to the input signal.

any modeling error will increase the residual error. Both Single-run time histories and ensemble-averaged time approaches are presented and compared in this paper.

histories were used to determine the final experimental For the latter approach, a method is presented for results, namely, non-dimensional static forces, static harmonic analysis utilizing the least squares principle. In moments, and stability derivatives. Combinations of this approach, tools for assessing both accuracy of stability derivatives were estimated in the * conventional form of in-phase and out-of-phase Research Engineer, Associate Fellow AIAA † components. No evaluation of the measurement data Senior Research Engineer, Associate Fellow AIAA ‡ (before averaging) was done to test repeatability of the Professor Emeritus, Associate Fellow AIAA 1996 data. During the 2000 experiment, to reduce American Institute of Aeronautics and Astronautics

The tests were conducted at a dynamic pressure of ensemble average errors and to enhance measurement 192 Pa (= 4 psf) producing an equivalent wind speed accuracy analysis, each test was repeated 10 times. As of V =17.52 m/sec and a Reynolds number of 10 part of a review process for these experiments, an initial based on the mean aerodynamic chord. During evaluation of measurement accuracy for the 2000 dynamic tests, pitch angle readings were made with a experiment has been done and is presented in this paper.

Linear Variable Differential Transformer (LVDT), Many problems that occur in testing can be quickly six-component force and moment data were obtained removed through careful monitoring by test engineers.

from a strain-gauge balance, and wind tunnel dynamic However, in modern test facilities there is always a pressure measurements were obtained from pressure desire to automate systems to achieve greater production transducer. with fewer errors. This may tend to remove the test engineer from close observation of the experiment. Also, For the 2000 experiment, data from single- some measurement error may not be immediately frequency forced oscillation in pitch were obtained at observable without analysis. In any case, data with 5 different frequencies (0.5, 0.9, 1.1, 1.5, and 2.0 Hz) greater error than desired may be produced even when and 13 different values of the initial angle of attack experimentalists exercise significant care. In this paper, ( α = 2, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and examples of problem data that can occur during testing 60 degrees) with amplitude of ± 5 ° . Repeated runs are provided and then procedures to reduce these were made at the same test conditions and ensemble problems, in an automated testing environment, are averages over the repeated runs were computed.

suggested.

The uncertainty of an experimental measurement is a Theoretical Tools combination of bias error and precision error. The Analysis and evaluation methods, metrics to assess squared sum of these terms is often used although other measurement accuracy, and procedures that may help formulations are sometimes used . In order to eliminate to identify and reduce measurement error are offered systematic errors or bias errors, careful calibration and in this paper as a means of improving final attention to environmental variables are required. Bias experimental results. In this section, the main tools for errors can be difficult and in some cases impossible to analysis and evaluation are presented. First, a method estimate and remove from the data after the experiment for harmonic analysis that facilitates computation of is performed. Therefore in this paper only precision of higher harmonics and parameter error bounds is the output measurements and estimated parameters will presented. This method effectively provides a test to be evaluated. Also, no attempt is made to separate detect nonlinear responses when nonzero high-order contributions to uncertainty from other factors such as harmonics exist. Second, a conventional linear scale effects or wind-tunnel turbulence. Since rigid body aerodynamic model representing a single degree of dynamics are assumed for this work and the dynamic rig freedom forced-oscillation experiment is presented.

is assumed to be rigid, aeroelastic or structural responses Third, key metrics for assessing measurement of the scale model and dynamic rig are not investigated.

accuracy are provided.

In this paper, measured data are presented that have Measurement error, e , is generally assumed to be a been obtained from single frequency forced-oscillation zero mean, normally distributed, stochastic process tests in the LaRC 12-Foot Tunnel. Analysis is limited to 2 with variance, σ . Measurement, z , true value, y , and small amplitude dynamic data in order to limit nonlinear error, e are related as responses contained in the measurements. The approach e y z + = . (1) for harmonic analysis described in this paper facilitates 2 2 In this case, E [ z ] = y and E [ (z-y) ] = σ . Since the testing this assumption as part of the analysis.

true value, y , is unknown and unknowable, a model is usually identified that provides estimates of the Model and Tests ˆ responses as . Using the model estimates of y A three-dimensional view of the 10% scale F-16XL response, the measurement equation becomes model is shown in Fig. 1. Dynamic tests were conducted ˆ in the LaRC 12-Foot Low-Speed Tunnel. For these tests, ε + = y z .

2 2 the model was mounted on a dynamic test rig through a In this case, E [ ε ] does not equal σ since the model six-component strain-gauge balance. The dynamic test ˆ estimate may contain error contributions from y rig is a computer controlled hydraulically actuated several sources. In addition to measurement error, the system that was sting-mounted on a C-strut support model may be inadequate to predict the responses. For system. The mounting arrangement rotated the model example, if the inputs produce nonlinear responses a about the reference center of gravity location of 0.558 c .

linear model will be inadequate and predict responses Further description of the dynamic test rig may be found with additional errors. The analysis method suggested in Ref. [5].

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in this paper offers an approach that can detect this From (6) and (7), the estimates of parameter problem. variance are s 2 s 2 2 , ˆ (9) ˆ a s ) ˆ ( = b s a s ) ( ) ( = = 0 k k Harmonic Analysis N N It is assumed that a periodic function

( ) ) 2 ( π + = t f t f

for all k .

with the period 2 π is specified by a time series of measured The model adequacy can be assessed by the Multiple Correlation Coefficient defined as π 2 data points

( ) ( ) ( ) ( ) i t N z N z z z at z(0) = , 1 ... , 1 , 0 = −

i

[ ] ) ( ˆ ) ( − i y i z

N

∑

, (10) 2 i 0 1 < < R for . Further, the postulated model for 1 − = R

) 1 ( ,..., − N i 1 , 0 = ( ) i y

[ ] ) ( − z i z

∑

is assumed in the form i m m (2) where z is the mean value of z .

+ + = i k b i k a a i y ) sin( ) cos( ) ( ω ω

∑ ∑ k k 0 0 0

= = k k 1 1 Conventional Forced Oscillation Analysis π 2 where and for N i ,..., 2 , 1 = ω = During conventional forced-oscillation tests the N model is assumed to undergo periodic motion. In this m ,..., 2 , . k 1 = study only small amplitude motions are considered so The parameters and b are the Fourier , , a a linear responses are expected. For analysis of this 0 k k conventional oscillatory data it is assumed that the coefficients obtained from the measured data by aerodynamic coefficients are linear functions of angle applying the least squares principle of attack, pitching velocity and their rates. Then the N . (3)

[ − i y i z Min ) ( ) ( ]

increment in the lift coefficient with respect to its

∑

= i 1 mean value can be formulated as The resulting estimates of the parameters are the 2 l l l   (11) solution to the equation q C q C C C C & & + + + ∆ = ∆ α α   L L L L L q q & & α α V V V   1 − ˆ (4) g M = θ where for the harmonic motion where t ω α α sin = ∆ A T ˆ ˆ ˆ ˆ ˆ ... …

[ ˆ ˆ ˆ a a a = θ ˆ b b b a ]

b (12) 2 1 0 3 2 1 m m & t q ω ωα α cos = = A  … = ) cos( ) ( ) ( i i z i z g ω ) cos( ) ( i m i z ω

& & & ∑ ∑ 0 ∑ 0

t q ω α ω α sin − = =  A  i i i T Substitution of (12) into (11) yields  … ) sin( ) ( i i z ω i z ( i m ) sin( ω )

0 ∑ ∑ 0 ( ) ( ) t C C k t C k C C ω α ω α cos sin + + − = ∆

 L L A L L A L q q α α & & i (13) i 

( ) t C k t C ω ω α cos sin + =

 N L L A  N N …. .

q α = N diag M   2 2   where Then the parameter estimates are obtained as (14) V k / l ω = and = i z a ) ( ˆ

∑ 0

N i (15)

( ) C k C C − = α α

L L A L A q & α α (5) ˆ = i kw i z a ) cos( ) (

∑ k 0 (16)

( ) C C k C k + = α α

L L A L A N q q α & i represent the Fourier coefficients. The in-phase and ˆ = i kw i z b ) sin( ) (

∑ k 0

out-of-phase components of and can C ( C C ) N L L L i α q If the measurement errors form a e ) ( ) ( ) ( i y i z i − = be obtained by integrating the time histories of ∆ C L zero mean random sequence with the variance σ , then over cycles as n c the parameter covariance matrix is T n c 1 2 − ∆ = dt t t C sin ) ( ω C ˆ L L . (6)

∫ α Cov ) ( = M σ θ

T n α (17) o c A The estimation for the variance σ can be found as T n c ∆ = dt t t C C cos ) ( ω 2 2 (7) L L

∫

q ˆ [ ) ( ) ( i y i z s − = ]

T kn α ∑

o c A N i where . Using the results from harmonic T = 2 π ω where analysis, the integrals in (17) represent continuous- . (8) ˆ ˆ ˆ ˆ + + = i k b i k a a i y ) sin( ) cos( ) ( ω ω

∑ ∑ k k 0 0 0

k k American Institute of Aeronautics and Astronautics

time versions of (5). Therefore, the in-phase and out-of- accuracy. In this paper, the methodology has been phase components can be also expressed as applied as part of a data post-processing procedure; however, some calculations may be done during the ˆ a ˆ b 1 , (18) = C = C L experiment for a faster on-line assessment. This L q α α k α A A section demonstrates application of the analysis and their variance as methods to sample data from the 2000 experiment.

2 s 2 s 2 2 , . (19) ) ( C = s ) ( C s = L L 2 2 α q Timing Signal N α ) ( k N α A A The first data check for dynamic tests should be to determine the accuracy of the time stamp and then the Evaluation Metrics and Outlier Rejection Rules sample time fidelity. Accuracy of the time stamp may The Multiple Correlation Coefficient ( R ), expressed be an important issue when a large number of signals in (10), may be computed as part of the parameter are measured. Time stamp accuracy was not an issue estimation process. This metric varies between 0 and 1 for this study. Checking fidelity of the sample time and provides a measure of model adequacy. As the during each duty cycle is a key test for dynamic output signal fails to be represented by the model, the R experiments, especially when the analysis involves term will be reduced from 1.

mathematical transforms. Commonly used transform Mean square error ( s ) defined in (7) characterizes algorithms require the sample time to be in equal time the fit error of the model. A check to determine how well intervals. If a personal computer (PC) or workstation this metric reflects measurement accuracy can be made if is used to run the real-time experiment, it is not repeated measurements are available. Calculation of the uncommon for the operating system to introduce variance from repeated measurements provides a direct delays (from multitasking) in the duty cycle and thus estimate of measurement accuracy. The variance can be produce uneven sample time intervals. If this type of computed from repeated measurements at each point in error exists, it may require the data to be re-sampled or time as the experiment re-run depending on the degree of N r 2 1 error. Re-sampling the data assumes that in spite of the (20) ( ( )) [ ( )] ( ) s C t C t C t = −

( )

i a i a i r a i

∑

1 N − r duty cycle error, the measurements and the associated 1 r = time stamp are still correct. If large delays or variable where N is the number of repeated runs, C (t ) is a r a i delays exist between the time stamp and measurement, measured value of an aerodynamic coefficient at time t , i then clearly no analysis would be possible. Fidelity of and is the mean value of C for the repeated runs.

C a a the sample time and accuracy of the time stamp must From these results an equivalent fit error, comparable to be ensured before any analysis is done.

(7), can be computed as A simple test metric to assess the degree of this 2 2 . (21) s s = problem is to compute the time difference, δ t ,

i ∑

a N i between samples n and n+1 . δ t is defined as a Comparison of s , computed from harmonic analysis (7), a a (22) t t t δ = − 1 a n + n with the variance computed from repeated measurements where “ a ” indicates actual sample times. For 100 Hz (20)-(21) provides an indication of the level of sample rate, a graph of δ t vs. sample number index a measurement accuracy and an indication of good model should always equal 0.01 seconds for perfect sample adequacy if the two metrics are close in value.

timing. Another helpful sample-time metric is defined During execution of an experiment, occasionally data as the time difference between actual measured time points are obtained that appear to be outliers. If the and expected clock time or simulated time, both at experimentalist can determine verifiable problems with sample n . δ t is defined as s those points, then clearly these points should be a s (23) t t t δ = − removed. However, in some cases the results are not s n n clearly wrong and no obvious problem can be found.

where “ s ” indicates expected clock time or simulated Points outside the 2 σ bound might be good candidates time. This metric reflects the cumulative delay that should be checked for problems. Statistical methods experienced during the run. Consequently, as delays to check results can be easily automated so these tests occur this metric will grow in magnitude and indicate can be used frequently. Among the various statistical the total delay for the whole run at the last index methods, Chauvenet’s Criterion is used in this paper.

value.

These two metrics (22) and (23) could be easily added to testing software to ensure high-fidelity Data Evaluation and Analysis sample times.

Evaluation and analysis methods proposed in this study are suggested as a method to assess measurement American Institute of Aeronautics and Astronautics

An example highlights some of the issues associated Mean Standard Error with checking sample time fidelity. Analysis of the 2000 C N α 2.7273 0.0200 data revealed some cases where sampling was not C N q 4.5606 0.0582 occurring at 100 Hz as expected. As desktop computers and workstations have become very fast it has become Using a single run from the ensemble of runs, popular to use these machines to run experiments and fictitious data were created with varying time delay.

real-time simulations. Although the operating system Results shown in the table below provide mean values was required to give the highest priority to the for a varying number of sample delays. The first experimental task, duty cycle slips likely occurred due to column shows the mean value for the case without any multi-user, multi-tasking, or system level service. Fig. 2 (a) depicts the proper timing signal and duty cycle and delay.

No. of Slips 0 5 10 20 30 Fig. 2 (b) depicts the timing problem when a duty cycle Delay (sec) 0.00 0.05 0.10 0.20 0.30 slip or frame overrun occurs. Fig. 2 (b) also shows C N α 2.7349 2.7314 2.7252 2.7347 2.7441 another anomaly, unique to this experiment, i.e., C sampling could be done faster than 100 Hz to N q 4.5087 4.4944 4.4862 4.4391 4.0176 compensate for any delay caused by duty cycle slips.

This occurred because the data acquisition logic required Based on these results, estimated coefficients were the number of samples to be consistent with the desired within ±2 σ of their correct mean values when delays sample rate and length of run where no sampling delays were less than 10 samples. Since 90% of all test runs occur. Also the timing logic comparing actual time with contained delays less than 0.05 seconds or 5 cycle desired time was not a controlling factor after a duty slips, it is likely both in-phase and out-of phase cycle slip.

coefficients for the 2000 experiment are computed Data, typical of 75% of all cases in this study, are within an error bound less than ±2 σ . This is consistent shown in Fig. 3 (s726: 1.5 Hz and α =10 ° ). In the with the intended purpose of the 2000 experiment but figure, the pitch angle position measurement in the wind may not be satisfactory for investigations where tunnel (equivalent to angle of attack) is analyzed and nonlinear dynamics play a significant role.

found to have numerous cases where the sample time is not stepping in increments of 0.01 seconds as expected.

Input Measurements In this example, the δ t error is occasionally in the 20% a Input tests involve calculation of test metric values to 30% range or 0.002 to 0.003 seconds. Note that no that should bring attention to faulty input signals and visible error appears in the angle of attack time history.

errors that may not be immediately visible in a graphic Fig. 3 also shows another timing metric, δ t . In this s representation or in a large data set generated in an particular experiment, the timing logic requiring a faster automated fashion. Graphical tests are always sample rate to make up missed samples and logic included, however, to catch relatively large or obvious requiring the system to “catch up” has the effect of errors. The numerical values of the test metrics are canceling any delays that occur. Consequently only for generally very large for cases where the errors become this particular experiment does this metric return to zero visible in a graph.

after a delay period.

The primary input signal for this study was angle Fig. 4 shows a test case (s768: 1.5 Hz and α =35 ° ) of attack and it is the only input signal tested in this with timing slips greater than 6 samples. The angle-of- paper. Secondary inputs are temperature and tunnel attack time history reflects this delay and shows dynamic pressure that had very slow variation and are significant distortion from the expected sinusoidal shape.

assumed to be constant for these dynamic tests.

10% of all test runs contained timing delay greater than Three issues associated with the primary input 0.05 seconds (5 cycle slips). In this case, the abnormality measurement are addressed and then harmonic is clearly visible and easily detected and removed with analysis is applied to check the impact of those only visual inspection.

anomalies in input measurement.

To investigate the impact of duty cycle slip on Time delay, discussed in Effect of Timing Signal experimental results a fictitious time delay followed by a the earlier section, impacts the angle of attack time catch-up sequence was added to good data. This created history by causing a deviation from a single-frequency a second data set for comparison of in-phase and out-of pure sinusoidal waveform (see Fig. 4). Harmonic phase coefficients. The test case used 1.5 Hz forced analysis of the input is done to further investigate the oscillation data at α =10 ° . Using ensemble-averaged timing issue.

data, estimates of mean values and standard deviations Along with the two cases in Figs. 3 and 4, two for this case are given in the below table.

other test cases used for this analysis were individual American Institute of Aeronautics and Astronautics runs s738 and s815. One duty cycle slip was found in commanded and measured input values should be the s738 while timing slips greater than 9 samples occurred same.

more than 10 times in s815.

A model with the first harmonic is estimated and 2 2 used to compute R and s from (10) and (7). Computed values are shown in the below table.

2 2 Test Case R s s726 0.9986 0.0043 A test case is considered using 1.0 Hz forced s738 0.9978 0.0143 oscillation data at α =70 ° . The top graph in Fig. 5 s768 0.9954 0.0454 shows an example of commanded and measured angle s815 0.9615 0.4478 of attack versus sample number index. The second 2 plot shows the difference or residuals between these With bigger delays in time, R value is decreasing 2 two graphs. Besides relatively large residual values, a and s value is increasing. Though the trend makes bias error of 4.7 ° exists and the amplitudes are sense, it is much less sensitive than expected for this different between the top and bottom of the oscillation analysis. This result brought attention to the difference (6.2459 ° vs. 6.5102 ° ). This is shown in the bottom in using actual measured time vs. a timing index for two graphs by subtracting out the mean angle of attack analysis. The timing index (sampling point number) can from the top two graphs. This also removes the bias only be used with the assumption that test data are between the two plots. These new large residuals equally spaced in time. When timing delay is present, a brought attention to a calibration technique used for legitimate option might be re-sampling to obtain data this experiment. In this case, instead of an exact point- that is equally spaced in time. Computed values with re- to-point table look up to convert degree to voltage and sampled data are shown in the below table.

rd visa-versa, a 3 order polynomial approximation was 2 2 Test Case R s used. This approach was intended to save test time but s726 0.9986 0.0043 the cost was some distortion in the harmonic input s738 0.9973 0.0203 signal. Deviation from a pure sinusoid introduced s768 0.9850 0.1729 additional harmonics and biases into the experiment.

s815 0.1160 13.6544 With the same test data, harmonic analysis with the 2 2 first harmonic is used to compute R and s from (10) Due to a significant distortion in test case s815, R is and (7). Computed values are presented in the below far less than 1 with a large error ( s ) and implies that the table.

model with the first harmonic is inadequate. For the 2 2 2 2 Mean( α ) Amplitude( α ) R s other test cases, the values of R and s indicate much 0.9959 0.0023 74.7230 ° 6.3626 ° more adequate models have been estimated, although sensitivity to the timing errors are not as large as With the proper consideration of bias error expected. Each individual run contained 10 oscillation (74.7230-70) and amplitude scaling error (6.3626/5), cycles. By using 10 cycles for analysis the effect of the the test data presents reasonably linear dynamics. An timing error was minimized and caused a lack of adequate linear model was obtained with R almost 1 sensitivity to small time delays. Analysis with one cycle and very small model variance.

could show the sensitivity in R value but the analysis Mechanical Issues The next test considers the with one cycle is not recommended for this study. So, mechanical system, Test Rig, in the above figure. A except few extreme cases, analysis indicates the large “jump” distortion was found in several runs. As estimated models were adequate to explain the data ( R ~ an example, Fig. 6 (s789: α = 45 ° and f = 1.5 Hz) 1, s << 1) and that the test data is reasonably well 0 shows the α signal plotted against time in the top represented by linear models since a single-frequency harmonic was the dominant feature. graph and then the same plot with a zoomed view of the distortion in the lower graph. In cases where this Calibration A second test is a comparison of the commanded and measured input signals without the problem occurred the large jump in α was always followed by a large timing error. Jump errors were hardware in the loop, i.e., without including the test rig dynamics. sometimes large enough to observe visually during the A simplified block diagram of test setup is shown test. This seems likely to be caused by a mechanical below and the output of the first conversion (from system anomaly.

degree to voltage) is directly fed to the input of the Another input anomaly that may be caused by the second conversion (from voltage to degree) as depicted mechanical system is input saturation. Since input with a dashed line. With a proper conversion, saturation can defeat the planned input spectrum used American Institute of Aeronautics and Astronautics

to excite a dynamic system, it can be an issue for the test components is investigated using the variance expressions given by (19) and (21).

engineer. Fig. 7 (s217: 0.5 Hz and α = 5 ° ) shows this issue for the single-frequency forced oscillation Aerodynamic Force and Moment Coefficients experiment. The effect of saturation is shown in the plots For the total force and moment outputs, mean and standard deviation of total aerodynamic loads are of α , C , and C . From other test cases, saturation is L N computed from the 10 repeated single runs. The observed in the low frequency experiments and does not variance at each time instant is used to compute appear to be affected by offset angle variation. This may overall variance. Then, harmonic analysis is applied imply a mechanical limitation of the test rig, however, to ensemble average run to estimate aerodynamic the exact source of this error has not been identified.

force coefficients with the parameter covariance To investigate the impact of mechanical issues on matrix for the estimated coefficients.

inputs, the same test data, shown in Fig. 6, is used for A co-plot of 10 repeated runs is shown in Fig. 8.

harmonic analysis. With only the first harmonic, 2 2 computed values of R and s from (10) and (7) are This case is for oscillations about α = 20 ° and at a frequency of 1.1 Hz. C measurement shows a good shown in the below table. Since the jump anomaly was N repeatability, while a degraded repeatability is followed by a time delay, computed values with re- sampled data are also presented. depicted in C measurement. This degradation is m 2 2 addressed in Ref. [1] and the cause is still unknown.

Test Case Note R s A significant anomaly is found in C measurement. It A 0.9926 0.0873 with measured data s789 shows a large inconsistency over 10 repeated runs and 0.9484 0.6949 with re-sampled data the measurement was dominated by noise.

As a first test case, the first cycle of C is used. A N For the analysis of input saturation, computed values 2 2 co-plot of 10 single runs and the corresponding plot of of R and s from (10) and (7) for a test case s217 (Fig.

computed mean values with 2 σ bounds at each time 7) are shown in the below table. Similar to the last case, instant are depicted in Fig. 9. Overall variance from the model appears to be adequate.

2 2 (20)-(21) is Mean( α ) Amplitude( α ) R s 0.9974 0.0110 4 - 2 2 5.3657 ° 5.3591 ° .

× = = s 10 0.9939 s

∑

i E N i After using only the first harmonic for harmonic In this section, three issues were addressed and analysis in (2) to compute an estimate of C , a co-plot harmonic analysis has been applied to assess the impact N of measured C and estimated C are also shown in by those issues. In general, the contribution from a large N N Fig. 9 (bottom plot). This figure illustrates the model number of repeated cycles in each test case allows with the first harmonic explains the measured data production of test data that is reasonably acceptable.

fairly well. Computed values of the parameter However, these kinds of issues would need to be resolved for investigations into nonlinear regimes. covariance from (7) for the estimated coefficients is 4 - 2 .

ˆ

[ ]

10 0.4224 ) ( ) ( × = − = i C i C s

∑ N N M

N Output Measurements i After conversion to non-dimensional engineering In order to investigate other cases, the first cycle of units, aerodynamic total force and moment coefficients C from the same test case is used to compute the m are direct output measurements. Substantial efforts have corresponding variances. Then, a different test case been made to develop methodology for ensuring data (1.1 Hz and α = 60 ° ) is used to compute variances for accuracy using various statistical measures. For this C and C . Computed variances with the N m paper, analysis is done with the assumption that the test corresponding standard errors are presented in the facility has followed recommended procedure and below table.

worked to obtain the accurate data. Even with this 1.1 Hz and α = 20 ° 1.1 Hz and α =60 ° deg 0 0 assumption, it is prudent for the investigator to evaluate C C C C N m N m experimental results. Fairly simple calculations can often 2 -4 -4 -3 -4 s E 0.9939X10 0.2462X10 0.5859X10 0.7201X10 be used to prevent a variety of errors and minimize data s 0.0100 0.0050 0.0242 0.0085 E uncertainty.

-4 -5 -3 -4 s In this section, a conventional linear aerodynamic M 0.4224X10 0.4487X10 0.1376X10 0.1628X10 model is assumed and harmonic analysis is performed on s 0.0065 0.0021 0.0117 0.0040 M angle of attack and force and moment measurements to estimate the in-phase and out-of-phase model s is a computed variance from repeated runs and E coefficients. Analysis of repeatability or dispersion of s is a computed one from model. Theoretically, the M the time histories and the in-phase and out-of-phase two variances are the same if there were no errors in American Institute of Aeronautics and Astronautics

modeling with the first harmonic and if accurate data dynamic data and assessing measurement accuracy with good repeatability were acquired during have been presented. A linear aerodynamic model is experiments. In these test cases, with s greater than assumed that is appropriate for conventional forced- E s , a larger error in test repeatability is implied relative oscillation experiments, although more general models M to modeling error. can be used with these tools. Application of the tools In-phase and out-of-phase components to experimental data is demonstrated and results Ensemble Average Runs The conventional procedure indicate the levels of uncertainty in output to obtain a model in forced-oscillation testing is to form measurements that can arise from experimental setup, an ensemble average of repeated runs. Harmonic calibration procedures, mechanical limitations, and analysis is then used to obtain the parameters in model input errors. During the evaluation, several issues equation (13). From (18) and (19), in-phase and out-of- have been highlighted: 1) duty-cycle slips in real-time phase components with the corresponding standard experiments, 2) signal-to-noise ratio (SNR), 3) errors are computed. Results for normal force calibration, and 4) input design. Suggestions that coefficient, C , are presented in Tables 1 and plotted could address these issues have been proposed for N against the angle of attack in Fig. 10. ensuring high measurement accuracy of future Ten Repeated Single Runs Harmonic analysis is also experiments.

applied to individual runs. For f =1.5 Hz, Fig. 11 shows Extension of this work may support in-phase and out-of-phase components of normal force implementation of closed-loop automated testing where feedback measurements are analyzed, in real- coefficient, with the 2 σ bounds, for each of the 10 runs time, with the appropriate metrics to produce the against angle of attack . This figure provides repeatability highest data quality possible during dynamic testing.

and error bound information. Fairly larger deviations are This would provide efficient experimental systems shown in Fig. 11 while a good repeatability is observed that can reduce experimental time and increase for most test cases. In this case, a test engineer can quickly assess progress of the experiment and the measurement accuracy.

presence of any outlier results.

Outlier Rejection Rules From Ref. [4], when the

Acknowledgements

number of repeats ( N ) is 10, the ratio of maximum Wind tunnel tests were carried out with the acceptable deviation to precision index is 1.96 with a assistance of NASA researcher Jay M. Brandon and corresponding probability of 0.95. Applying George Washington University student Leslie Gould.

Chauvenet’s criterion to the test case shown in Fig. 11 ( f = 1.5 Hz and α = 55 ° ), the outlier screening metric

References

(1.96* σ ) requires the single run, s815, to be rejected by 1. Vladislav Klein, Patrick C. Murphy, Timothy J. Curry this criterion. As described earlier, s815 has a significant and Jay M. Brandon, “Analysis of Wind Tunnel timing delay. In-phase and out-of phase coefficients Longitudinal Static and Oscillatory Data of the F-16XL both for all 10 runs and for selected runs (9 runs in this Aircraft,” NASA/TM-97-206276, December 1997.

2. Vladislav Klein and Patrick C. Murphy, “Estimation of case) are computed and shown in the table below. From Aircraft Nonlinear Unsteady Parameters From Wind the table, Chauvenet’s criterion successfully removed Tunnel Data,” NASA/TM-1998-208969, December the questionable test data and improved data consistency 1998.

by reducing standard deviations.

3. Patrick C. Murphy and Vladislav Klein, “Estimation of All 10 Runs Selected Runs Aircraft Unsteady Aerodynamic Parameters From Dynamic Wind Tunnel Testing,” AIAA Atmospheric Mean σ Mean σ Flight Mechanics Conference, Aug. 2001.

C N 1.2603 0.0830 1.2406 0.0582 α 4. H. W. Coleman and W. Glenn Steele, Jr.: C N q 4.8351 0.5424 4.9933 0.2224 Experimentation and Uncertainty Analysis For Engineers, 1989.

5. Brandon, J. M.: Dynamic Stall Effects and Application

Concluding Remarks

to High Performance Aircraft. Special Course on NASA LaRC has been conducting a series of wind Aircraft Dynamics at High Angles of Attack: tunnel tests to develop and test mathematical models and Experiment and Modeling. AGARD Report No. 776, system identification methodology for aircraft rigid- April 1991, pp. 2-1 to 2-15.

body aerodynamics in nonlinear unsteady flight regimes.

6. Michael J. Hemsch, “Development and Status of Data Analysis of measurement accuracy, especially for Quality Assurance Program at NASA Langley Research Center – Toward National Standards,” AIAA nonlinear dynamic systems that may exhibit complicated Advanced Measurement and Ground Testing behaviors, is an essential component of this ongoing Technology Conference, June 1996.

effort. In this paper, tools for harmonic analysis of American Institute of Aeronautics and Astronautics Figure 2. Proposed timing signal vs. signal with the timing issue.

Table 1. In-phase and out-of-phase components of C coefficient.

N Figure 1. Three-dimensional view of 10% F-16 XL model.

Figure 3. Typical timing signal of dynamic test data.

American Institute of Aeronautics and Astronautics Figure 6. Jump in Angle of Attack Time History.

Figure 4. Dynamic test data with the slippage of duty cycles.

Figure 7. Saturated Input Command and Corresponding C and C Time Histories.

Figure 5. Measured and Commanded Angles of Attack.

L N American Institute of Aeronautics and Astronautics Figure 10. Variation of in-phase and out-of-phase components of C .

N Figure 8. Typical dynamic test data: Ten repeated measurements.

Figure 11. Co-plot of 10 single-runs with 2 σ bounds of in-phase Figure 9. Co-plot of 10 Runs, Mean Values with 2 σ bound, and out-of-phase components of C for f =1.5 Hz.

N and Co-plot of Measured C and Estimated C .

N N American Institute of Aeronautics and Astronautics