spod_matlab-master
所属分类:matlab编程
开发工具:matlab
文件大小:83457KB
下载次数:36
上传日期:2019-03-04 20:33:46
上 传 者:
重生之门爽
说明: 本征正交分解(Proper Orthogonal Decomposition, POD)作为一种大批量处理数据的方法,在众多的领域中都涉及应用
(Proper Orthogonal Decomposition, POD)
文件列表:
LICENSE.txt (2190, 2018-06-22)
example_1.m (2686, 2018-06-22)
example_2.m (3412, 2018-06-22)
example_3.m (2764, 2018-06-22)
example_4.m (4636, 2018-06-22)
example_5.m (2859, 2018-06-22)
example_6.m (2652, 2018-06-22)
jet_data (0, 2018-06-22)
jet_data\jetLES.mat (85785283, 2018-06-22)
spod.m (17387, 2018-06-22)
utils (0, 2018-06-22)
utils\getjet.m (105, 2018-06-22)
utils\trapzWeightsPolar.m (679, 2018-06-22)
# Spectral Proper Orthogonal Decomposition in Matlab
SPOD() is a Matlab implementation of the frequency domain form of proper orthogonal decomposition (POD, also known as principle component analysis or Karhunen-Loeve decomposition) called spectral proper orthogonal decomposition (SPOD). SPOD is derived from a space-time POD problem for stationary flows [[1](https://arxiv.org/abs/1708.04393),2] and leads to modes that each oscillate at a single frequency. SPOD modes represent dynamic structures that optimally account for the statistical variability of stationary random processes.
The large-eddy simulation data provided along with this example is a subset of the database of a Mach 0.9 turbulent jet described in [3] and was calculated using the unstructured flow solver Charles developed at Cascade Technologies. If you are using the database in your research or teaching, please include explicit mention of Bres et al. [3]. The test database consists of 5000 snapshots of the symmetric component (m=0) of a round turbulent jet.
`spod.m` is a stand-alone Matlab function with no toolbox dependencies. All other Matlab files contained in this repository are related to the six examples that demonstrate the functionality of the code (see file descriptions below). A physical interpretation of the results obtained from the examples can be found in [[4](https://arxiv.org/abs/1711.06296)].
## Download
### Using your browser
Repository zip file with examples (81.5 MB): [https://github.com/SpectralPOD/spod_matlab/archive/master.zip](https://github.com/SpectralPOD/spod_matlab/archive/master.zip)
Matlab function only (15 KB): [https://raw.githubusercontent.com/SpectralPOD/spod_matlab/master/spod.m](https://raw.githubusercontent.com/SpectralPOD/spod_matlab/master/spod.m)
### Using Git in the terminal
git clone https://github.com/SpectralPOD/spod_matlab.git
## Files
| File | Description |
| ------------- |:-------------|
| spod.m | Spectral proper orthogonal decomposition in Matlab |
| example_1.m | Inspect data and plot SPOD spectrum |
| example_2.m | Plot SPOD spectrum and inspect SPOD modes |
| example_3.m | Specify spectral estimation parameters and use weighted inner product |
| example_4.m | Calculate the SPOD of large data and save results on hard drive |
| example_5.m | Calculate full SPOD spectrum of large data |
| example_6.m | Calculate and plot confidence intervals for SPOD eigenvalues |
| jet_data/getjet.m | Interfaces external data source with SPOD() (examples 4-5) |
| utils/trapzWeightsPolar.m | Integration weight matrix for cylindrical coordinates (examples 3-6) |
| utils/jetLES.mat | Mach 0.9 turbulent jet test database |
| LICENSE.txt | License |
## Usage
[L,P,F] = SPOD(X) returns the spectral proper orthogonal decomposition
of the data matrix X whose first dimension is time. X can have any
number of additional spatial dimensions or variable indices.
The columns of L contain the modal energy spectra. P contains the SPOD
modes whose spatial dimensions are identical to those
of X. The first index of P is the frequency and
the last one the mode number ranked in descending order
by modal energy. F is the frequency vector. If DT is not specified, a
unit frequency sampling is assumed. For real-valued data, one-sided spectra
are returned. Although SPOD(X) automatically chooses default spectral
estimation parameters, it is strongly encouraged to manually specify
problem-dependent parameters on a case-to-case basis.
[L,P,F] = SPOD(X,WINDOW) uses a temporal window. If WINDOW is a vector, X
is divided into segments of the same length as WINDOW. Each segment is
then weighted (pointwise multiplied) by WINDOW. If WINDOW is a scalar,
a Hamming window of length WINDOW is used. If WINDOW is omitted or set
as empty, a Hamming window is used.
[L,P,F] = SPOD(X,WINDOW,WEIGHT) uses a spatial inner product weight in
which the SPOD modes are optimally ranked and orthogonal at each
frequency. WEIGHT must have the same spatial dimensions as X.
[L,P,F] = SPOD(X,WINDOW,WEIGHT,NOVERLAP) increases the number of
segments by overlapping consecutive blocks by NOVERLAP snapshots.
NOVERLAP defaults to 50% of the length of WINDOW if not specified.
[L,P,F] = SPOD(X,WINDOW,WEIGHT,NOVERLAP,DT) uses the time step DT
between consecutive snapshots to determine a physical frequency F.
[L,P,F] = SPOD(XFUN,...,OPTS) accepts a function handle XFUN that
provides the i-th snapshot as x(i) = XFUN(i). Like the data matrix X, x(i) can
have any dimension. It is recommended to specify the total number of
snaphots in OPTS.nt (see below). If not specified, OPTS.nt defaults to 10000.
OPTS.isreal should be specified if a two-sided spectrum is desired even
though the data is real-valued, or if the data is initially real-valued,
but complex-valued-valued for later snaphots.
[L,P,F] = SPOD(X,WINDOW,WEIGHT,NOVERLAP,DT,OPTS) specifies options:
OPTS.savefft: save FFT blocks to avoid storing all data in memory [{false} | true]
OPTS.deletefft: delete FFT blocks after calculation is completed [{true} | false]
OPTS.savedir: directory where FFT blocks and results are saved [ string | {'results'}]
OPTS.savefreqs: save results for specified frequencies only [ vector | {all} ]
OPTS.mean: provide a mean that is subtracted from each snapshot [ array of size X | {temporal mean of X; 0 if XFUN} ]
OPTS.nsave: number of most energtic modes to be saved [ integer | {all} ]
OPTS.isreal: complex-valuedity of X or represented by XFUN [{determined from X or first snapshot if XFUN is used} | logical ]
OPTS.nt: number of snapshots [ integer | {determined from X; defaults to 10000 if XFUN is used}]
OPTS.conflvl: confidence interval level [ scalar between 0 and 1 | {0.95} ]
[L,PFUN,F] = SPOD(...,OPTS) returns a function PFUN instead of the SPOD
data matrix P if OPTS.savefft is true. The function returns the j-th
most energetic SPOD mode at the i-th frequency as p = PFUN(i,j) by
reading the modes from the saved files. Saving the data on the hard
drive avoids memory problems when P is large.
[L,P,F,Lc] = SPOD(...) returns the confidence interval Lc of L. By
default, the lower and upper 95% confidence levels of the j-th
most energetic SPOD mode at the i-th frequency are returned in
Lc(i,j,1) and Lc(i,j,2), respectively. The OPTS.conflvl*100% confidence
interval is returned if OPTS.conflvl is set. For example, by setting
OPTS.conflvl = 0.99 we obtain the 99% confidence interval. A
chi-squared distribution is used, i.e. we assume a standard normal
distribution of the SPOD eigenvalues.
## References
[1] Towne, A., Schmidt, O. T., Colonius, T., *Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis*, [arXiv:1708.04393](https://arxiv.org/abs/1708.04393), 2017
[2] Lumley, J. L., *Stochastic tools in turbulence*, Academic Press, 1970
[3] G. A. Bres, P. Jordan, M. Le Rallic, V. Jaunet, A. V. G. Cavalieri, A. Towne, S. K. Lele, T. Colonius, O. T. Schmidt, *Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets*, submitted to JFM, 2017
[4] Schmidt, O. T., Towne, A., Rigas, G., Colonius, T., Bres, G. A., *Spectral analysis of jet turbulence*, [arXiv:1711.06296](https://arxiv.org/abs/1711.06296), 2017
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