Integrated Engine Prognostics and Health Management (IEPHM)

1
Integrated Engine Prognostics and Health
Management (IEPHM)
Demonstrate an Integrated Set of PHM Technologies
for Gas Path Health Determination
2
Kalman Filter Theory

• The current optimizer algorithm used in the
  tracking filter is a modified Kalman filter,
  based on feedback control. At each time step the
  sensor residuals are multiplied by the average
  gains matrix to adjust the QLTYs.
• The Kalman filter is a recursive filter it
  estimates a process by using a form of feedback
  control. In theory, the Kalman filter can be
  optimal. The Kalman filter applied to the F414 is
  a linear approximation. For each iteration, it
  cycles through 2 sets of equations time update
  and measurement update.

3
Kalman Filter Algorithm Equations
Time Update Equations Measurement Update
Equations
4
Kalman Filter Applied to F414 Engine

• X represents the QLTY estimates vector (8x1).
• Notation notes the carrot over the X symbolizes
  that it is an estimate. The super minus
  represents the a priori estimate, while the X
  calculated in the measurement update equations
  represents the measurement corrected estimate.
• Z is the sensor measurements vector (9x1). H is
  the average gains matrix (9x8) it remains
  constant.
• P is the estimate error covariance (8x8) matrix.
• K represents the Kalman gain (8x9) matrix.

5
Results

• Certain assumptions were made to simply the
  Kalman filter for easier implementation on the
  F414.
• For the linear stochastic difference equation
  (equation 1 of the time update equations)
• A is an identity matrix. i.e. QLTYs arent
  dynamic.
• There is no control input, so u is zero
• Process noise, w, is white
• Note In the real world, both w and u would be
  non-zero. However, because input data is coming
  from CLM_ENG into CLM_MOD, w is treated to be
  zero.
• For the error covariance matrices
• R (9x9), measurement error covariance and
• Q (8x8), process error covariance, are constant
  diagonal matrices

6
Results

• QLTY values were initially set to .001.
• A nominal run at 17.5K ft and M.625 for 1080
  seconds was made.
• The following figure compare the performance of
  the Kalman filter to the current tracking filter.
  The tracking filter out-performs the Kalman
  filter, obtaining a value as low as 10-5,
  while the Kalman filters minimum value was 10-4.

BLACK TF GREEN KALMAN