On the equivalence between the unbiased minimum-variance estimation and the infinity augmented Kalman filter

Ding, Bo; Zhang, Tianping; Fang, Huajing

doi:10.1080/00207179.2019.1574984

Cited by 7 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is assumed that the parameters k s and µ of the introduced model ( 17) are unknown. The contact force can be estimated by estimating the state η k and the parameters k s and µ of (17). By applying the contact force model (7), the estimations of the contact force are achieved.…”

Section: State and Contact Force Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Stator-Rotor Contact Force Estimation of Rotating Machine

Spiller¹,

Söffker²

2021

Automation

View full text Add to dashboard Cite

In turbomachines, dry friction resulting from stator–rotor contacts is a severe problem that may degrade lifetime of the machine or even lead to complete failure. Knowledge about the system states and contact forces is beneficial for system monitoring or to prevent contacts through, e.g., active magnetic bearings. In this paper, a nonlinear model is derived that describes the lateral rotor vibrations in the case of contact and no contact. The elastic behavior of the shaft is modeled based on the finite-element method. The contact is described by a dry friction model. An augmented system description is formulated that allows estimation of rotor displacements and contact forces by means of nonlinear filtering approaches like an extended Kalman filter. A simulation study was conducted that explicitly considered the hazardous backward whirl. The suggested approach shows suitable estimation performance related to both state and contact force estimation.

show abstract

Section: State and Contact Force Estimationmentioning

confidence: 99%

“…It is a design parameter that is typically tuned by trial and error. In [17], it was recently shown that a direct connection between the MVU and ASKF approaches exists. If the considered noise variance related to the augmented state is selected as infinity, then the ASKF algorithm equals the Gillijns-De-Moore filter.…”

Section: Introductionmentioning

confidence: 99%

Stator-Rotor Contact Force Estimation of Rotating Machine

Spiller¹,

Söffker²

2021

Automation

View full text Add to dashboard Cite

show abstract

“…Definition 1 ([19], Definition 3.2) Let

falsefalse{P_{n} falsefalse} \in R^{q \times q}

be a matrix sequence. If

det false(P false)

and each diagonal elements of

falsefalse{P_{n} falsefalse}

approach to infinity, i.e.…”

Section: Equivalence Between Iakf and Rtsfmentioning

confidence: 99%

“…Some important properties about the matrix limit are given in the following lemma. Lemma 4 ([19], Lemma 3.4) Let

P \in R^{q \times q}

R \in R^{m \times m}

H \in R^{m \times q}

P ≻ 0

R ≻ 0

rk false(H false) = q

and

m ⩾ q

. If

P false\to normal∞

, then

P - P H^{⊤} false(R + H P H^{⊤} false)^{- 1} H P false\to false(H^{⊤} R^{- 1} H false)^{- 1}

false(R + H P H^{⊤} false)^{- 1} false\to R^{- 1} - R^{- 1} H false(H^{⊤} R^{- 1} H false)^{- 1} H^{⊤} R^{- 1}

P H^{⊤} false(R + H P H^{⊤} false)^{- 1} false\to false(H^{⊤} R^{- 1} H false)^{- 1} H^{⊤} R^{- 1}

…”

Section: Equivalence Between Iakf and Rtsfunclassified

“…Intuitively, when

Q_{k}^{d}

tends to be infinity, the result of AKF will be equal to that of the RTSF method. More recently, the equivalence between AKF in the infinity condition and MVU filter has been proved, respectively, in [19, 20] for the system that unknown input only affects the state. However, in the direct feedthrough systems, whether or not the result of corresponding AKF in the infinity condition will be equal to that of RTSF is still unknown.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation