Question

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6. Loftv Estimation Goals [+5 Points Extra Credit] Biogen Aeronautic Defence and Space Systems makes Biofuel-powered jet airplanes For their new model, the Bein' Green-17, they placed a greener jet forward of the wing: but, as its nacelle (or inlet cowl) generates lift at high angles of attack (such as those during take-off), it is necessary to compensate tor the positive teedback mode this causes in the plane's pitch. Note, this is particularly the case when the air is a little thinner, such as at "hot or high" airports. Also, other design changes (a new inlet, larger landing gear, etc.) would be less fuel efficient and more costly.] In response, a control program is added to automatically pitch the nose down just before a stall (i.e. a condition in which ift is lost due to airflow separation at large angles of attack). This, in turn, requires an estimate of the airplane's angle of attack. Four engineers are debating what strategy to take to observe this value . Engineer W suggests that median value from three of the same sensors is taken Engineer X suggests that only two of the most accurate and robust sensors are needed Engineer X recommends a sensor that has an MTBF (mean time between failures) of 20,000 hours (2.2 years continuous operation) and to take the maximum value of the two sensors . Engineer Y suggests state estimation of the value from different two different types of sensors (of which, at least one of each is needed, though more is nice). Engineer Y's initial suggestion is an Extended Kalman Filter, to get the average value (u) and its variance (o) . Engineer Z suggests an integrated Bayesian estimation and control strategy that considers the o value,its likelihood, and the next controlled action, States would be conditioned on the sequence of flight motions, state of the overall flight (e.g., taxi, take-off, etc.), etc. Engineer Z adds that this approach is more robust and even allows for active-sensing (e.g. self-diagnosis and calibrating the sensor when on (presumably level) ground, etc.) Who (if any, some, or all) is right? Please discuss

Answer 1

In my point of view:

Engineer W: W uses the median method ,which can't be used for the further algebraic treatment. Median is not rigidly defined, If one more sensor is added or removed out of 3 sensors the it is difficult to find median. moreover the interpolation formula applied in the continuous series is based on the unrealistic assumption that the frequency of the median class is evenly spread over the magnitude. More cost is needed as 3 sensors are used.

Engineer X: According to X , MTBF is how reliable a hardware product is. He uses the sensor that has a MTBF of 20000 hours.Usually, the failure rate is inversely proportional to the MTBF. failure rate =1/MTBF=R/T.

R=Rate of failure.

T=total time

But the probability of any hardware that can survive to its calculated MTBF is 36%(nearly).As it takes the maximum value of 2 sensors if any one fails. The maximum value would be the other sensor value only.

Engineer Y: According to Y, he uses the 2 sensors from these values mean and variance is calculated by using extended Kalman Filter. EKF (Extended Kalman Filter) is the extension of the kalman filter, EKT is used for the nonlinear systems with a linear model. But it fails to perform well during some cases. In those cases estimator designers have to add some noise to guarantee numerical stability. It doesn't work if perfect value(noise) is given.

According to me Engineer Z suggestion is good under these conditions

Engineer Z: According to Z, Bayesian estimation uses the probability to model the uncertain things, Pitching the noise down is uncertain so this model better to estimate these conditions. this model has better average accuracy. The control strategy is based on its likelihood values. point estimation is made for the parameters obtained to maximize the likelihood. We have the data (D)and the parameters(Q) and need to find particular set of parameters(Q*) to make a prediction about the future values.

In Bayesian estimation P(Q/D)={P(D/Q)P(Q)}/P(D)

Where P(Q)=prior. in order to make the prediction about the future events we need to integrate it over the distribution of Q.