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Adaptive lọc và phát hiện thay đổi P11

Consider a batch of data over a sliding window, collected in a measurement vector Y and input vector U. As in Chapter 6, the idea of a consistency test is to apply a linear transformation to a batch of data, AiY + BiU + ci. The matrices Ai, Bi and vector G are chosen so that the norm of the linear transformation is small when there is no change/fault according to hypothesis Hi, and large when fault Hi has appeared. | Adaptive Filtering and Change Detection Fredrik Gustafsson Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-49287-6 Hardback 0-470-84161-3 Electronic 11 Change detection based on algebraical consistency tests 11.1. Basics.403 11.2. Parity space change detection.407 11.2.1. Algorithm derivation.407 11.2.2. Some rank results .409 11.2.3. Sensitivity and robustness.411 11.2.4. Uncontrollable fault states.412 11.2.5. Open problems.413 11.3. An observer approach.413 11.4. An input-output approach.414 11.5. Applications .415 11.5.1. Simulated DC motor.415 11.5.2. DC motor.417 11.5.3. Vertical aircraft dynamics.419 11.1. Basics Consider a batch of data over a sliding window collected in a measurement vector Y and input vector U. As in Chapter 6 the idea of a consistency test is to apply a linear transformation to a batch of data AiY BiU Cj. The matrices Ai Bi and vector Cj are chosen so that the norm of the linear transformation is small when there is no change fault according to hypothesis Hi and large when fault Hi has appeared. The approach in this chapter measures the size of AiY BiU a as a distance function in a algebraic meaning in contrast to the statistical meaning in Chapter 6 . The distance measure becomes exactly zero in the non-faulty case and any deviation from zero is explained by modeling errors and unmodeled disturbances rather than noise. 404 Change detection based on algebraical consistency tests That is we will study a noise free state space model xt i AfXt Budut Bdjdt Bfjft 11-1 yt CtXt DU tut Ddjdt Dfjft. 11.2 The differences to for example the state space model 9.1 are the following The measurement noise is removed. The state noise is replaced by a deterministic disturbance dt which may have a direct term to yt. The state change may have a dynamic profile ft. This is more general than the step change in 9.1 which is a special case with ft ot-k - There is an ambiguity over how to split the influence from one fault between Bf Df and ft- The convention .