SVMD (version 0.1.0)

sVMD: Spearman Variational Mode Decomposition

Description

Optimal number of modes of Variational Mode Decomposition (VMD) using Spearman's rank correlation coefficient

Usage

sVMD(
  series,
  alpha = 2000,
  tau = 0,
  DC = FALSE,
  init = 1,
  tol = 1e-07,
  threshold = 0.997,
  max_modes = 10,
  verbose = FALSE
)

Value

Returns a list containing the optimal number of modes, reconstructed signal, and additional outputs from the VMD process:

• optimal_K: The optimal number of modes.

• reconstructed_signal: The reconstructed signal from the selected modes.

• imfs: Intrinsic Mode Functions (IMFs) obtained from SVMD.

• u_hat: Estimated envelopes of the modes.

• omega: Frequencies of the modes.

Arguments

series

The input time series signal to be decomposed.

alpha

The balancing parameter of the data-fidelity constraint. Default is 2000.

tau

Time-step of the dual ascent (pick 0 for noise-slack). Default is 0.

DC

If TRUE, the first mode is put and kept at DC (0 frequency). Default is FALSE.

init

Mode initialization (1 = all omegas start at 0). Default is 1.

tol

Convergence tolerance criterion. Default is 1e-7.

threshold

The correlation coefficient threshold to determine the optimal number of modes. Default is 0.997.

max_modes

The maximum number of modes to consider. Default is 10.

verbose

Logical, if TRUE, prints detailed messages about the decomposition process.

References

Yang, H., Cheng, Y., and Li, G. (2021). A denoising method for ship radiated noise based on Spearman variational mode decomposition, spatial-dependence recurrence sample entropy, improved wavelet threshold denoising, and Savitzky-Golay filter. Alexandria Engineering Journal, 60(3), 3379-3400

Examples

{
# Example data generation:
# Set the number of observations
N <- 300
# Set a random seed for reproducibility
set.seed(123)
# Generate random uniform values
rand_unif <- runif(n = N, min = 0, max = 1.0)
# Create the components of the time series
sig1 <- 6 * rand_unif
sig2 <- sin(8 * pi * rand_unif)  # Using sine function
sig3 <- 0.5 * sin(40 * pi * rand_unif)  # Using sine function
# Combine the components to form the final signal
signal <- sig1 + sig2 + sig3
# Apply the sVMD function to the signal
result <- sVMD(signal)
}