Verifying hyperparameter sensitivities of optimal filter design methods for fault signature enhancement

Recent advances in vibrations, noise, and their use for machine monitoring

Open Access

Table 2

The three optimisation problems and selected algorithms are considered in this work. The objective function ξ is either the objective $ξ (h) = ψ (h)$ or the natural logarithm of the objective $ξ (h) = \ln ψ (h)$ .

#	Label	Optimisation problem	Selected algorithm
1	CG	Unconstrained:	Conjugate Gradient (CG) [44]
		$min_{h} - ξ (\frac{h}{\| \| h \| \|_{2}}; x)$

2	SLSQP	Constrained - Variant 1:	Sequential Least Squares Programming (SLSQP) [44]
		$min_{h} - ξ (h; x), s.t. h^{T} h = 1$

3	IED	Constrained - Variant 2: $max_{h} h^{T} A (h) h, s.t. h^{T} B (h) h = 1$	Iterative Eigenvalue Decomposition (IED). Refer to the discussion in Appendix C.
		where
		$ψ (h; x) = \frac{h^{T} A (h) h}{h^{T} B (h) h}$

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