The Best Regime Recognition Algorithm for HUMS

Eric Bechhoefer Goodrich Sensors and Integrated Systems

Vergennes, VT 05491

Abstract1 Usage monitoring for Health and Usage Monitoring Systems (HUMS) equipped aircraft entails determining the actual usage of a component over time. This allows the actually usage/damage from a flight to be assigning to that component instead of the more conservative, worst case usage. By measuring the actually usage on the aircraft, the life of components can be extended, resulting in reduced maintenance cost. Alternatively, for aggressively flown aircraft, safety is maintained in that a component usage may be “consumed” to a greater extent than expected by the original flight spectrum data.

Usage Monitoring requires an accurate representation of regime (e.g. Regime Recognition (RR)), where regime is the flight profile of the aircraft at each instant of flight time. For each regime, there is a usage assigned for each component that is life limited (e.g. accumulated damage over time). For example, the damage accumulated for a component would be higher if the aircraft is undergoing a high G maneuver vs. straight and level flight.

In the past, RR algorithms have used logical tests (Goodrich IVHMU or that presented in Ref [1]) or neural networks (VMEP, Ref [2]). Logical tests can be prone to errors due to inherently noisy parameter used. Neural networks in general are difficult to certify and could require a large amount of training data. Other methods, such as Markov Models (Ref [3]) show promise, but could be computationally expensive. Presented here is a noise tolerant algorithm that does not present the problems associated with: logical test (dealing with noise), certification of neural networks, or computational complexities.

Notation The equations that are described within this document use BOLD upper case letters (A, etc) to represent a matrix of n rows by m columns, and bold lower case letters (x, etc.) to represent a column vector. The basic arithmetic operations performed on a matrix are performed as per Ref[5].

Introduction While HUMS equipped aircraft are showing improved operational readiness and a corresponding reduction in maintenance cost (Ref [4]), many of the HUMS

1 Presented at the American Helicopter Society Specialist’s Meeting on Condition Based Maintenance, 2008. Copyright @ 2008 by the American Helicopter Society International, Inc. All rights reserved.

functionalities are still immature. Mechanical Diagnostics/Prognostics and Regime Recognition are two functions that have not been fully exploited. Once validated, RR could extend the service life of life-limited components, reducing maintenance cost and improving operational readiness. While the RR functionality in the IVHMU is enabled, the lack of investment in this functionality by the customer has allowed RR to lag other HUMS capabilities. Essentially, the use of RR for the purpose of gaining maintenance credit is in its infancy.

The goal of this paper is to present an algorithms which is quantitatively, the best. The “best” is a rather subjective statement, but here in the contest of HUMS, best is:

• Based on mathematically rigorous methodology which is optimal (in that sense that for a given probability of false alarm, it maximizes the probability of correct classification)

• Computationally simple to implement and configure

• Scaleable: easily expanded to encompass new regimes.

• For a known regime class, calculated performance characteristics: e.g. the Receiver Operating Characteristics (ROC). From a certification perspective, this is essential.

In the method presented, a maximum likelihood estimator (MLE) methodology is derived. MLEs assume that input parameters are noisy, and weights the validity of a parameter by the information the parameter conveys (the inverse of variance is information). The output of the algorithm is the regime that is most likely, as a function of the a priori parameter mean value and variance. This a priori information constitutes configuration data.

The MLE takes the current set of measurements and calculates a normalized distance between the measurements and a notional set of regimes. The regime that is closest statistically to the measurement is most likely. In this implementation, the MLE is a multiple dimension hypothesis test, in which the aircraft parameters are used to test the hypothesis that the aircraft is in a given regime.

Hypothesis Test Using the Bayes Classifier Let us define P(Hi|z) as the probability that Hi was the true regime given a measured observation, z. The correct hypothesis is the one corresponding to the largest probability of the m possible regimes. The decision rule will be to choose Ho if:

P(Ho|z) > P(H1|z), P(H2|z),… P(Hm|z).

else choose the greatest P(Hi|z). The null hypothesis P(Ho|z) will represent the aircraft turning on the deck, or some other default case.

For illustration, consider the binary case, where the rule becomes:

P H1 | z( )P H0 | z( )

H1

><

H0

1

This is the maximum a posteriori probability criterion, wherein the chosen hypothesis corresponds to the maximum of two posterior probabilities. Using Bayes’ rules to write the criterion gives:

P Hi | z( )=p z | Hi( )P Hi( )

p z( ), i = 0,1

where P(Hi) is the probability of Hi in the observation space, such that:

P H1 | z( )P H0 | z( )

=p z | H1( )P H1( )p z | H0( )P H0( )

This allows the test to become:

p z | H1( )p z | H0( )

H1

><

H0

P H0( )P H1( )

Let us further define the ratio l(z) = p(z|H1)/p(z|H0) as the likelihood ratio. If the likelihood ratio is assumed to be well behaved and everywhere continuous and differentiable, then without loss of generality, the natural logarithm of both sides can be taken. The logarithm is a monotonically increasing function so that the inequality holds. The log-likelihood ratio become:

ln l z( )

H1

><

H0

lnP H0( )P H1( )

It is desirable to take the log of the likelihood ratio because the probability function P(Hi) is usually some exponential function, such as Rayleigh, Gaussian, etc. Taking the log linearizes the function, simplifying the problem.

In making a decision in a binary hypothesis-testing problem (e.g. Regime 0 vs Regime 1), there are four possible outcomes:

Say Ho, and it is true that the AC is in regime 0; Say H1, and it is true that the AC is in regime 1; Say H1, but the AC is in regime 0; and Say Ho, but the AC is in regime 1.

An error occurs when either the third or four conditions are chosen. The third condition is a type I error and the forth

condition is a type II error. It will be shown that the Bayes Classifier, for a given probability of error, maximizes the probability of correct detection.

The Bayes Classifier for the Normal Distribution Under many circumstances, the Normal distribution is a valid model of the distribution of the data. Besides being attractive from a mathematical sense (e.g. there are well established tools and procedures to address Gaussian data), it is the case that many natural phenomena can be described with a Gaussian probability function. Without loss of generality, the Gaussian model is assumed for a generalized n dimension decision space. This decision space describes the parameters associated with the RR algorithms.

As noted, the default case is the hypothesis H0, defined as the mean of the parameter vector space, m0, representing the parameters for regime 0. The probability distribution function of the parameter vector, z, given H0 is defined by the Gaussian distribution (centered on m0)

H0 : m0 = E z0[ ]p z | H0( )=

1 2π( )n 2 Σ0−1 2 exp −1 2 z − m0( )T Σ0

−1 z − m0( )[ ]

An alternative hypothesis is;

H1 : m1 = E z1[ ]p z | H1( )=

1 2π( )n 2 Σ1−1 2 exp −1 2 z − m1( )T Σ1

−1 z − m1( )[ ]

where Σi is the covariance of the regime parameters. The normalized distance squared between the measured parameters z and any m:

d2 = z − m( )T Σ−1 z − m( ) Eq 1.

Substituting the distance function into the log likelihood ratio test give:

1 2 d02 − d1

2[ ]+1 2ln Σ0 Σ1( )

H1

><

H0

ln P0 P1( ) Eq 2.

where |Σ| is the determinant of the covariance. This states that if the normalized distance squared between z and m0 (plus a threshold offset which represents the log ratio of test case probabilities. It is assumed that P0 is equally likely with P1, such that the offset is ln(1) = 0) is greater than the normalized distance between z and m1, then accept the alternate hypothesis, H1. In this specific aircraft regime case where there are 90 regimes, we conduct 89 tests against the null hypothesis. If after completing the 89 test, where each test is negative, one cannot reject the null hypothesis (e.g.

aircraft in regime 0). If there are positive test values, select the maximum test value: this accepts the alternative hypothesis and represents the maximum likely regime the aircraft is in.

Transformation for Optimality The normalized distance squared between z and m, defined above, represents a shift in space that can be defined by a new function: x = z – m, giving d2(x) = xTΣ-1x. We wish to find an x that maximizes this distance function, subject to the side constraint xTx = I (which enforces orthogonality). This maximizes both the separation of the mean vector (for a given hypothesis) from the general observation vector, and the separation between the components of the observation space (i.e. regime parameters). Using the standard Lagrange multiplier to find the local extrema (i.e. the maximum) gives:

∂∂x{xT Σ−1x − µ(xT x − I)} = 2Σ−1x − 2µx

Setting to zero to find the extrema (thereby maximizing the separation) and solving for x results in:

Σ-1x = µx or Σx = λx Where λ = 1/ µ.

The solution to λ must satisfy the determinant: |Σ-λI| =0: the solution is defined as the eigenvalues of Σ (ref 5). Because Σ is a symmetric n x n matrix (e.g. a covariance matrix), there are n real eigenvalues (λ1…λn) and n real eigenvectors φ1...φn. The characteristic equation can then be written as:

ΣΦ = ΦΛ

where Φ is an n x n matrix consisting of n eigenvectors and Λ is a diagonal matrix of eigenvalues. Note that the eigenvectors corresponding to two different eigenvalues are orthonormal

ΦΤΦ=Ι,

The solution of the Eigenvalue problem implies that Φ can be used as a transformation matrix,

y = ΦΤx, It follows that the variance in the transformed space, y, is independent, because:

Σy = ΦΤΣΦ = Λ, which is diagonal (no cross correlation). Note that the eigenvalues are the variance of the respective components of the transformed variable (yi).

Furthermore, this result can be expanded to find a transformation that generates unit covariance (i.e. identity matrix). Selecting ΦΛ−1/2 as the new transformation matrix A:

y = Λ−1/2ΦΤx = (ΦΛ−1/2)Tx,

it follows that the y space covariance is given by:

Σ y = Λ−1/2ΦΤΣzΦΛ−1/2 = Λ−1/2ΛΛ−1/2 = I

This is the whitening process, and has the property that the transformation is not orthonormal:

(ΦΛ−1/2)ΤΦΛ−1/2 = Λ−1/2ΦΤΦΛ−1/2 = Λ−1

i.e. ATA≠I, as was the case when the eigenvector matrix was selected as transformation matrix, illustrating that Euclidean distances are not preserved (e.g. maximizes the distance).

In the cases where the respective covariance Σ0, Σ1 of the two distributions are not equal, it is necessary to simultaneously diagonalize the covariance (as per the Lagrangian) to maximize the distance between the distributions. The process requires whitening Σ0. However, applying the transformation to Σ1 results in:

Λ−1/2ΦΤΣ1ΦΛ−1/2 = K. The resulting covariance, K, of the transformed coordinates (y) in the decision space H1 is not diagonal. K can be diagonlized by an appropriate orthnormal transformation:

w = ΨTy,

where Ψ is the eigenvector matrix of K such that ΨΤΚΨ is diagonal. Combining these processes yields the overall transformation matrix A = ΦΛ−1/2Ψ The Optimal Decision Rule

Using the developed transformation matrix A, we can now apply this to the Bayes classifier to maximize the separation between the decision spaces. This transformation is optimal in that no other transformation will provide a higher probability of correct classification (recall that the transformation A is based on the Eigenmatrix solution to the characteristic function). Given Eq 1. and Eq 2, the following change of variables are made:

Y = AT z − m0( )Π = AT Σ1A

Λ = AT Σ0−1 − Σ1

−1( )−1A

L = AT m1 − m0( )V = −Π−1L

c = − 12 LTV − 1

2 lnΠ

Substitution yields (ref 6):

h(y) = 12Y T Λ-1Y - VT Y +c Eq. 3

Note that many of the substituted variables can be pre-computed and reside as configuration data, such as: Λ, V, and c.

The Regime Data

While parametric data for RR is collected with every operation, there are few opportunities to evaluate the performance of the flight data. There simply is few flight where the ground truth is know for the flight. Ground truth is obtained by flying an event where a test pilot flies a “flight card.” This flight card is a script on which a series of maneuvers have been designed to fly the aircraft for a given set of flight regimes. For each regime, the entry and exit times are recorded, as well as specific flight parameters (e.g. 60 degree angle of bank, 90 knots airspeed, 1000 ft).

The data set consisted of three flight card events and the accompanying data files, covering 50 out of 90 possible regimes (see appendix for list. The regimes where defined by the OEM). The regime data consists of 15 parameters sampled at 10 Hz (Table 1).

Table 1. Monitored parameters in IVHMU Parameter

No. Parameter

Name Parameter Description

1 AOB Angle of Bank 2 Alt/dt Altitude Rate 3

CrNz Corrected Normal Acceleration

4 Lat/dt2 Lateral Acceleration 5 Nr Main Rotor RPM 6 Ptch At Pitch Attitude 7 Rad Alt Radar Altimeter 8 Roll At Roll Attitude 9

Torque Total Engine Torque

10 TGT

Turbine Gas Temperature

11 Vert/dt2

Vertical Acceleration

12 Vh

Airspeed Vh Fraction

13 YawDt Yaw Rate 14 WOW Weight on Wheels 15

Time Time in ms of from start of operation

Implementation Issues

There are two issues that must be addressed for successful implementation: regime statistics data and computational order of operations. Regime statistics involves estimating the mean and covariance for each regime. Computational order of operations means that we are interested in a computationally efficient design that requires as few floating-point operations as possible to achieve a result.

Estimation of the regime statistics requires a set of parameters for a known regime. As noted, there is a limited data set of flight cards where parameters can be mapped to a know regime. In fact, this study is based on a sample of one, which realistically, is too small. Ideally, one would prefer 20+ flight cards from a variety of aircraft/pilots: the mean and covariance should be representative of the aircraft/pilot

population as a whole, performing a given maneuver/regime. 20 flight cards for all 90 regimes might represent 60 flight hours of test pilot time from a squadron of aircraft. This is an expensive proposition.

Additionally, there are some regimes that are damaging (or even dangerous) to fly. Given the limited flight card data, and the fact that for some regimes based line data does not exits, what can be done? The pragmatic engineer makes the best of it and:

• Partitions the available flight card data for know regimes into training and test data.

• Uses engineering judgment and estimate what the mean and covariance would be for regimes without know data.

Estimating mean and covariance for the regimes that are missing is not as daunting a task as might be presumed. For example, in a logic based decision tree, which is currently used on IVHMU, rules are given such as in table 2:

Table 2: Logical Test Regime Example Regime Takeoff Power

Climb Parameter Operator Threshold

WOW = False Roll Attitude >= -10 Roll Attitude <= 10 Altitude Rate > 600

Lateral Acceleration >= -0.01 Lateral Acceleration <= 0.15

Yaw Rate >= -5 Yaw Rate <= 5

Corrected NZ <= 1.2 Corrected NZ >= 0.8 Derived TGT >= 850 VH Fraction <= 1.05 VH Fraction > .3

Converting this to a mean and variance, the statistics are as per table 3:

Table 3: Estimated Regime Statistics Parameter Mean Standard

Deviation WOW 0 0.001

Roll Attitude 0 6.079 Altitude Rate 1000 243.18

Lateral Acceleration -.1+(.15-.01)/2=.06 0.0426 Yaw Rate 0 3.04

Corrected NZ 1 0.1216 Derived TGT 975 75.99 VH Fraction .675 0.228

Essentially, the mean is taken from the bounds of a parameter (Table 2), and the standard deviation is calculated such that the probability of being greater or less than the given bounds is less that 95%. For example, the mean of the bounds of Nz is 1 ( (0.8+1.2)/2 = 1), and the standard deviation is that values from which the inverse of the normal cumulative distribution is the threshold. In this case, the

standard deviation for p = .95, such that x = (1-.8) = .2. In this case, the standard deviation is 0.12.

In cases where there is no bounded limited, the mean is derived by taking the lower bound, and the maximum possible value. For example, TGT, which is may be lower bounded at 850. The max TGT may be 1100, then the mean is 850+(1100-850)/2 = 975. The standard deviation is the value such that p = .95, exceeds (1100-850)/2 = 125, or 75.99.

Admittedly this is a crude estimation of the “real” mean and variance for this regime, but with the limited information available, it is one method to derive these statistics. Note that when implementing HUMS on a new fleet/type of aircraft it may be that not flight card data exits. In this case, the aforementioned methodology provides at least a starting point for RR development.

In terms of order of operations, it is desirable to have RR run on the limited computational resources of an embedded system. From Eq. 3, it is seen that the characteristic requires one n x n matrix operation, and two vector produces of size n, where n is the number of parameters. This is n2+2n operation. To find the maximum likely regime, it requires m-1 calls to the characteristic function. The order of operation is then O((m-1)(n2+2n)), or for this example, O(19936*c) floating point operations. Relative to NN or a series of logical test, it is admittedly slow.

Conversely, one can take advantage of the regime structure and reduce the number of calls to the characteristic function. Consider that WOW is a Boolean – when WOW is true, the aircraft is on he ground – thus, one can construct a series of hypothesis test for ground regimes that have been organized into a tree structure (figure 1)

Figure 1 Ground Regime Tree Structure

Here one tests the hypothesis (e.g. call the characteristic function) for Rotors Not Turning vs. Rotors Turning. If the Rotors are Turning (e.g. now the new null hypothesis) test the alternative hypothesis that the aircraft is Taxiing, Taking off or Landed. If Taxing (promoted to the current null hypothesis) one testing the alternative hypothesis that that aircraft is in a left turn or a right turn. In this simple

example, instead of 8 hypothesis testing, at most one would call the characteristic function 5 times).

For flight regimes a structure similar to figure 2 is implemented. Here the initial test determines if the aircraft is in a Hover, Reward or Forward flight. If the maximum likely regime is hover, further test are conduct until the null hypothesis cannot be rejects. If the current null hypothesis is forward flight, a structure similar to figure 3 is traversed.

Figure 2 Initial Flight Regime Structure

Figure 3 Forward Flight Regime Structure

If each node (e.g. current null hypothesis) has on average 3 sub nodes, then for 90 regimes, the tree structure would have a depth log390 = 4. This would give, on average 3 *4 = 12 calls the characteristic function. Using this structure, the order for operation is now O(2340*c).

Performance of the Results

For the 50 regimes flown, where each regime was on average 20 seconds long or 200 tests per regime (given the 10 Hz sample rate,). For 23 regimes, the probability of being correct was 1. For the remaining 27 regimes, the following confusion matrix identifies the regime, the probability of being correct (Pc), and the regimes that where miss identified (table 4). The minimum probability of correct identification was for regime 24 (Pc = .86). The mean Pc for all regimes was .9765.

Table 4: Confusion Matrix Results

Regime Pc Incorrect Regimes and Pe

3 5 2 0.993 0.004 0.002

3 5 0.965 0.035

5 8 7 0.877 0.012 0.111

7 8 0.996 0.004

10 9 0.945 0.055

12 11 0.982 0.018

11 13 12 0.936 0.014 0.050

16 15 0.968 0.032

15 17 16 0.986 0.007 0.007

31 19 0.918 0.082

31 20 0.896 0.104

30 31 21 0.963 0.002 0.035

31 22 0.994 0.006

31 23 0.970 0.030

30 31 24 0.859 0.003 0.138

30 31 88 25 0.943 0.007 0.046 0.004

27 28 26 0.953 0.034 0.014

26 28 27 0.862 0.009 0.128

27 28 0.911 0.089

31 42 0.996 0.004

46 43 0.989 0.011

43 45 46 0.984 0.010 0.006

49 48 0.983 0.017

30 31 56 55 0.979 0.000 0.019 0.001

55 76 56 0.983 0.005 0.012

59 60 0.999 0.001

31 63 0.996 0.004

Discussion

The greatest source of error in the RR algorithm was a result of poor mean and variance statistics for the missing regimes. The confusion matrix show that most of the errors where a result of misidentifying a given regime as regime 30 and 31. Both of these regimes mean and standard deviation where

generated using engineering judgment (e.g. a guess) and obviously incorrect. It is felt that with some “tweaking” the maximum error could be reduced to less that 1%.

However, it must additionally be noted that this algorithm has not been tested on a larger aircraft data set. While it is impractical to assume that 20 flight test cards from as many aircraft would be generated, it is hoped that flight cards from 10 different flight cards could be made available for RR development. The worry is that with small populations to sample from, the regimes configuration will be “over trained”.

Additionally, for the calculation of damage, not only regime but gross weight (GW) is needed. The tools available to automate the estimation of GW are limited. Inferred GW is another area where research is still in its infancy.

Is this the best RR algorithm? From a mathematical perspective, this statement is defensible. This algorithm is also very scalable: simply add a new mean and variance for each new regime, without retraining the existing regime data. Because it is based on Gaussian statistical procedures, for a set of regimes and measurements, an ROC could be constructed. Thus, we are able to explicitly describe performance (helpful when wishing to certify). Finally, the algorithm is polynomial time, but the order of operation is probably higher than a logic test tree or a NN. Again, “best” is rather a subjective term: at the least it is hoped that this algorithm will spur other researchers to consider this as a viable technique for RR.

References [1] Barndt, Gene; Miller, Charles; Sarkar, Subhasis, “Maneuver Regime Recognition Development and Verification for H-60 Structural Monitoring”, American Helicopter Society 63rd Annual Forum, Virginia Bearch, VA, May 1 – 3, 2007.

[2] Berry, J., Vaughan, R., Keller, J., Jacobs, J., Grabill, P., and Johnson, T., “Automatic Regime Recognition using Neural Networks”, American Helicopter Society 62nd Annual Forum, Phoenix, AZ, May 9 – 11, 2006.

[3] He, D., Wu, S., and Bechhoefer, E., “Development of Regime Recognition Tools for Usage Monitoring”, IEEE Aerospace Conference, Big Sky, MT, March 3 – 10, 2007.

[4] Bonino, R., et al., “HUMS/MMIS as an Aviation Combat Mulitplier” American Helicopter Society 63rd Annual Forum, Virginia Bearch, VA, May 1 – 3, 2007.

[5] Strang, Gilbert. Linear Algebra and its Applications. San Diego, Harcourt Brace Jovanovich, 1988.

[6] Fukunaga, Keinosuke. Introduction to Statistical Pattern Recognition. Academic Press, San Diego, 1990, page 91 – 93.

Appendix: Regime Names 1 Power On Aircraft, Rotors Not Turning 2 Power On Aircraft, Rotors Turning, Taxi or Stationary 3 Left Taxi Turn

4 Right Taxi Turn Take Off Landing IGE Hover less than 80 feet 0GE Hover greater than 80 feet Fwd Flight to 0.3 Vh Right Sideward Flight Left Sideward Flight Rearward Flight Left Hover Turn Right Hover Turn Rudder Reversal in Hover Longitudinal Reversal in Hover Lateral Reversal in Hover Level Flight up to 0.3 Vh Level Flight up between 0.3 and 0.4 Vh Level Flight up between 0.4 and 0.5 Vh Level Flight up between 0.5 and 0.6 Vh Level Flight up between 0.6 and 0.7 Vh Level Flight up between 0.7 and 0.8 Vh Level Flight up between 0.8 and 0.9 Vh Level Flight up between 0.9 and 1.0 Vh Rudder Reversal in Level Flight to 1.0 Vh Lateral Reversal in Level Flight to 1.0 Vh Longitudinal Reversal in Level Flight to 1.0 Vh Left Sideslip in Level Flight Right Sideslip in Level Flight Best Rate of Climb Intermediate Power Climb Takeoff Power Climb Left Sideslip in Climb Right Sideslip in Climb Left Climbing Turn Right Climbing Turn Approach Rough Approach Autorotation Autorotation with Left Sideslip Autorotation with Right Sideslip Rudder Reversal in Autorotation Longitudinal Reversal in Autorotation Lateral Reversal in Autorotation Collective Reversal in Autorotation Partial Power Descent Rudder Reversal in Partial Power Descent Longitudinal Reversal in Partial Power Descent Lateral Reversal in Partial Power Descent Dive Rubber Reversal in Dive Longitudinal Reversal in Dive Lateral Reversal in Dive Level Left Turn: 30 d AOB Level Left Turn: 45 d AOB Level Left Turn: 60 d AOB Level Left Turn: > 60 d AOB Level Right Turn: 30 d AOB Level Right Turn: 45 d AOB Level Right Turn: 60 d AOB Level Right Turn: > 60 d AOB Descending Left Turn: 30 d AOB Descending Left Turn: 45 d AOB Descending Left Turn: 60 d AOB Descending Left Turn: > 60 d AOB Descending Right Turn: 30 d AOB Descending Right Turn: 45 d AOB Descending Right Turn: 60 d AOB

Descending Right Turn: > 60 d AOB Autorotation Left Turns Autorotation Right Turns Symmetrical Pullouts: 1.8 Gs Symmetrical Pullouts: 3.0 Gs Symmetrical Pullouts: 4.0 Gs Left Rolling Pullout: 1.8 Gs Left Rolling Pullout: 3.0 Gs Left Rolling Pullout: 4.0 Gs Right Rolling Pullout: 1.8 Gs Right Rolling Pullout: 3.0 Gs Right Rolling Pullout: 4.0 Gs Pushover: 0.8 Gs Pushover: 0.3 Gs Pushover to 0 Gs Dynamic Yaw Other Maneuver 1, Left Climb Turn Exc AOB Other Maneuver 2, Right Climb Turn Exc AOB Other Maneuver 3, Lvl Flight Exd 1.0 Vh Other Maneuver 4, Dive Excd 1.2 Vh Other Maneuver 5, Symmetrical Pullout 1.2 Vh