APFC: Adaptive Particle Filter for Change Point Detection of Profile Data in Manufacturing Systems

Sun, 01 Jan 2023 00:00:00 +0000

Challenges

Nonlinear & non-stationary signals
Lateral oscillations (return difference)
Varying signal lengths

Goal

Develop a generic change point detection method for the pipe-casing tightening process by considering the mechanics in torque signals.

Two-Phase State Space Model

Measurement model

$$ y_k = \begin{cases} a_t + b_k t_k + \epsilon_k & t_k < c \\ a_0 + b_0 c + b_k (t_k - c) + \epsilon_k & t_k \geq c \end{cases} \quad \left( \begin{array}{c} a_0 \\ b_0 \end{array} \right) \sim \mathcal{N}(\mu, \Sigma) $$

$$ c \sim \text{Beta}(\alpha, \beta) $$ $$ \epsilon_k \sim \mathcal{N}(0, \sigma_k^2) $$

$t_k$: turns, $c$: change point position, $t_k$ and $y_k$ are observations, $k$: time
Prediction model

$$ a_k = \begin{cases} a_{k-1} & \text{with probability } 1 - p \\ a_0 + b_0 c & \text{with probability } p \end{cases} $$

$$ b_k = \begin{cases} b_{k-1} & \text{with probability } 1 - p \\ b_{k-1} + \delta & \text{with probability } p \end{cases} $$

$$ \delta \sim \text{truncateN}( \text{range}, \sigma^2 ) $$

Online Detection |

APFC: Adaptive Particle Filter for Change Point Detection of Profile Data in Manufacturing Systems

Challenges

Goal

Two-Phase State Space Model