Table 3 Parameters of denoising algorithms.

ICEEMDAN–RPE–AITD

ICEEMDAN noise amplitude is 0.2, number of realizations is 100, maximum number of iterations is 1000

RFE embedding dimension is 5

RFE delay time is 1

RFE thresholds Lth and Hth are 0.4 and 0.48, respectively

β is 0.719, ρ is 2.01, C is 0.7, α is 5

ICEEMDAN–CMSE–AITD

ICEEMDAN noise amplitude is 0.2, signal averaging count is 100, maximum number of iterations is 1000

β is 0.719, ρ is 2.01, C is 0.7, α is 5

ICEEMDAN–FE–AITD

ICEEMDAN noise amplitude is 0.2, signal averaging count is 100, maximum number of iterations is 1000

FE embedding dimension is 5

FE delay time is 1

FE threshold is 0.1

β is 0.719, ρ is 2.01, C is 0.7, α is 5

ICEEMDAN–PE–WTD

ICEEMDAN noise amplitude is 0.2, signal averaging count is 100, maximum number of iterations is 1000

PE embedding dimension is 5

PE delay time is 1

PE threshold is 0.35

Wavelet basis is “sym7”

Decomposition level is 7

Threshold is “sqtwolog”

Threshold function is hard threshold function

AFD

Maximum steps of the decomposition is 50

Tolerance is 1e-3

OWSWATD

Wavelet basis set is “db2 ~ 10”, “sym2 ~ s10”, and “coif1 ~ 5”³⁷

Decomposition level set is \(1,2, \cdots ,\left\lfloor {\log_{2} \left( N \right)} \right\rfloor\)

Improved thresholds³⁹: \(\lambda_{j} = \frac{{\sigma_{j} \sqrt {2\log N} }}{{\log \left( {j^{2} + 1} \right)}}\), \(\sigma_{j} = \frac{{{\text{median}}\left( {\left| {w_{j,k}^{D} } \right|} \right)}}{0.6745}\), where \(\lambda_{j}\) is the threshold of the jth level, \(\sigma_{j}\) is the standard deviation of the detail coefficients of the jth level, \(w_{j,k}^{D}\) is the detail coefficients of the jth level

Improved threshold function²⁰: \(\hat{w}_{j,k} = \left\{ {\begin{array}{*{20}c} {{\text{sgn}} \left( {w_{j,k} } \right)\left[ {\left| {w_{j,k} } \right| - \frac{{2\lambda_{j} }}{{1 + e^{{\left( {\left| {w_{j,k} } \right| - \lambda_{j} } \right)}} }}} \right],} & {\left| {w_{j,k} } \right| \ge \lambda_{j} } \\ {0,} & {\left| {w_{j,k} } \right| < \lambda_{j} } \\ \end{array} } \right.\), where \({\text{sgn}} \left( \cdot \right)\) is sign function