ceemdan {Rlibeemd}

CEEMDAN decomposition

Description

Decompose input data to Intrinsic Mode Functions (IMFs) with the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm [1], a variant of EEMD.

Usage

ceemdan(
  input,
  num_imfs = 0,
  ensemble_size = 250L,
  noise_strength = 0.2,
  S_number = 4L,
  num_siftings = 50L,
  rng_seed = 0L,
  threads = 0L
)

Arguments

input

Vector of length N. The input signal to decompose.

num_imfs

Number of Intrinsic Mode Functions (IMFs) to compute. If num_imfs is set to zero, a value of num_imfs = emd_num_imfs(N) will be used, which corresponds to a maximal number of IMFs. Note that the final residual is also counted as an IMF in this respect, so you most likely want at least num_imfs=2.

ensemble_size

Number of copies of the input signal to use as the ensemble.

noise_strength

Standard deviation of the Gaussian random numbers used as additional noise. This value is relative to the standard deviation of the input signal.

S_number

Integer. Use the S-number stopping criterion for the EMD procedure with the given values of $S$. That is, iterate until the number of extrema and zero crossings in the signal differ at most by one, and stay the same for S consecutive iterations. Typical values are in the range 3–8. If S_number is zero, this stopping criterion is ignored. Default is 4.

num_siftings

Use a maximum number of siftings as a stopping criterion. If num_siftings is zero, this stopping criterion is ignored. Default is 50.

rng_seed

A seed for the GSL's Mersenne twister random number generator. A value of zero (default) denotes an implementation-defined default value. For ceemdan this does not guarantee reproducible results if multiple threads are used.

threads

Non-negative integer defining the maximum number of parallel threads (via OpenMP's omp_set_num_threads. Default value 0 uses all available threads defined by OpenMP's omp_get_max_threads.

Details

The size of the ensemble and the relative magnitude of the added noise are given by parameters ensemble_size and noise_strength, respectively. The stopping criterion for the decomposition is given by either a S-number [2] or an absolute number of siftings. In the case that both are positive numbers, the sifting ends when either of the conditions is fulfilled.

Value

Time series object of class "mts" where series corresponds to IMFs of the input signal, with the last series being the final residual.

References

1. M. Torres et al, "A Complete Ensemble Empirical Mode Decomposition with Adaptive Noise" IEEE Int. Conf. on Acoust., Speech and Signal Proc. ICASSP-11, (2011) 4144–4147

2. N. E. Huang, Z. Shen and S. R. Long, "A new view of nonlinear water waves: The Hilbert spectrum", Annual Review of Fluid Mechanics, Vol. 31 (1999) 417–457

See Also

eemd

Examples

imfs <- ceemdan(UKgas, threads = 1)
# trend extraction
ts.plot(UKgas, imfs[, ncol(imfs)], col = 1:2, 
        main = "Quarterly UK gas consumption", ylab = "Million therms")

# CEEMDAN for logarithmic demand, note that increasing ensemble size 
# will produce smoother results
imfs <- ceemdan(log(UKgas), ensemble_size = 50, threads = 1)
plot(ts.union("log(obs)" = log(UKgas), Seasonal = imfs[, 1], 
     Irregular = rowSums(imfs[, 2:5]), Trend = imfs[, 6]), 
     main = "Quarterly UK gas consumption")