DOI: 10.5061/dryad.cnp5hqcc5
title: Coherence resonance in a nonlinear aeroelastic system

description: The data set is for the numerical simulation of stochastic sub-critical
 pitch-plunge aeroelastic system. The stochastic differential equations
 (SDEs) are solved in MATLAB. The simulated data is further post-processed
 to prove the manifestation of coherence resonance in the system. The
 measures used to establish the phenomenon are power spectral density
 (PSD), signal-to-noise ratio (SNR), quality factor, correlation time,
 inter-spike interval (ISI) analysis, which is also provided in the
 dataset. The dataset also contains the source code used to simulate the
 system and post-processing codes used to evaluate the measures. Coherence
 resonance is unexplored in the context of aeroelastic/fluid-structure
 interaction systems and can pose danger to the safety of the structure.
 However from the lens of energy harvesting, the amplified power output at
 the system frequency holds a promising outlook.
description: The data was collected by numerically simulating the stochastic
 system in MATLAB. The post-processing was also performed in MATLAB and a
 thorough analysis was done to establish the phenomenon of coherence
 resonance in the stochastic aeroelastic system considered.
description: # Coherence resonance in a nonlinear aeroelastic system
 [https://doi.org/10.5061/dryad.cnp5hqcc5](https://doi.org/10.5061/dryad.cnp5hqcc5) The folders contain the numerical data (.mat files) generated by running the various codes (.m files) in MATLAB. The dataset numerically simulates a stochastic aeroelastic system with pitch and plunge degrees of freedom. The stochastic noise acts on both the pitch and plunge directions as discussed in detail in the manuscript. The data is generated for various values of input noise intensity ($\sigma$) at a specific inlet reduced velocity of ($U=6.05$) by using the file fnc7.m which uses the function file glitter7.m. This data is further post-processed to exhibit the manifestation of coherence resonance in the chosen aeroelastic system by using the remaining .m files. ## Description of the data and file structure **Folders:** 1. **ResultsSDE_Data** :- Contains .mat files that store the raw data obtained from the simulation. The file name of the mat-files follows the following structure: alpha_res_605_sigma_$_%_10_4_add.mat, where $=1,2,3,...,18 and %=1,2,3,...,9 (% is applicable only when $=3,4,5). The data stored in these mat-files are the dimensionless pitch ($\alpha(\tau)$) of the airfoil time-history (stored in the variable name soln which is a 60000001X1 double matrix), directly generated from running the fnc7.m file (which calls the function file glitter7.m). These .mat files are used for further analyses to establish coherence resonance in the aeroelastic system. 2. **SP_TP_NP_SNR_PSD_Data** :- Contains .mat files that have data related to the power spectral densities (PSD) of the pitch time-series stored in alpha_res_605**.mat files and uses them to analyze the PSD. The files are as follows: 1. SNR_1_18_allDATA_30stepsPeak.mat : Contains the variables NP (stores noise power for various noise intensities ($\sigma$) of the PSD in a 18X1 double matrix), PSD_TH (stores the PSD of the pitch data for various noise intensities ($\sigma$) in a 30000001X18 double matrix), SNRRR (stores the signal-to-noise ratio of the PSD for various noise intensities ($\sigma$) in a 18X1 double matrix), SP (stores signal power for various noise intensities ($\sigma$) of the PSD in a 18X1 double matrix), TP (stores total power for various noise intensities ($\sigma$) of the PSD in a 18X1 double matrix), peakPSD (stores the maximum value of PSD for various noise intensities ($\sigma$) in a 18X1 double matrix), peakPSDloc (stores the index of the location of the occurrence of peakPSD for various noise intensities ($\sigma$) in a 18X1 double matrix). Here the noise intensities ($\sigma$) are 1,2,3,4,5,6,...,15,16,17,18 (X10^{-4}). 2. SNR_$*1*$_9_30stepsPeak.mat : Contains the same data and the variables as stored in 1. but here $=3,4,5. and in the matrix size the 18 is replaced by a 9. Here the noise intensities ($\sigma$) are 3.1,3.2,3.3...,3.9,4.1,4.2,...,4.9,5.1,5.2,...5.9 (X10^{-4}). All these 4-files are generated using the alpha_res_605**.mat files and the pow_spec_den_add.m file using MATLAB. 3. SP_NP_TP_SNR_sigma_ALLDATA_30steps_PEAK.mat : Collocates the variables NP, SNRRR, SP, TP as discussed above for all the 45 values of the noise intensities ($\sigma$ stored in sig). 3. **CorrelationTime_Data** :- Contains .mat files that store data regarding the correlation time of the pitch time series obtained from analyzing the data in the alpha_res_605**.mat files and using the code in correlation_time.m. The files are i) taucorr_**.mat that store the variable taucorr (which contain the correlation time for various noise intensities ($\sigma$) in either a 18X1 or a 9X1 double matrix). ii) taucorr.mat which stores the variables taucorr (45X1 double matrix) and sig (45X1 double matrix) which is just a collocation of the correlation time (taucorr) of the pitch time-series at all the 45 values of the noise intensities (sig). 4. **QualityFactor_Data** :- Contains .mat files that store the quality factor of the PSDs that are obtained using the SNR_**.mat files in SP_TP_NP_SNR_PSD_Data folder and the quality_factor.m code. The mat files are i) qf_beta_h_.mat that store the variables beta (product of qf and h), h (peakPSD value), qf (quality factor) in either a 18X1 or a 9X1 matrix for various values of noise intensities. ii) QF_BETA_H_ONE_EIGHTH_ALLDATA.mat which just collocates the above values of beta,h,qf and stores them in variables BETA, h, QF (each of which is a 45X1 double matrix) respectively at various noise intensities sig (45X1 double matrix). 5. **ISI_analysis_Data** :- Contains .mat files that store the inter-spike interval analyses done on the pitch time-series in the alpha_res_605**.mat files and using the code in interspike_analysis.m. The mat files are i) interspike_data_605_**.mat which contain the variables cv (stores the coefficient of variation of the interspike interval distribution), deff (stores the effective diffusion of the spike train), ind (indices where the spike occurs in the alpha time-series), inter (inter-spike intervals), locs (time-location of the occurrence of the spikes in the alpha time-series), pks (local peaks in the alpha time-series), var1 (spike train in a 60000001X1 double matrix). The sizes of the variables ind, inter, locs and pks are dependent on the signal being analysed and are different at different noise intensities. ii) CV_EffDiff.mat contains the variables CV_Final (collocation of the cv values into a 45X1 double matrix), DEff_Final (collocation of the deff values into a 45X1 matrix) for various noise intensities sig (considered sigma values 45X1 matrix). **Codes:** All the codes were written and run using MATLAB. The data files also are stored in the .mat format. The codes are well-commented and can easily be used to generate the data. fn7.m, glitter7.m -----&gt;&gt;&gt;&gt;&gt; Run the fnc7.m file which calls the function glitter7.m file to generate the data by solving the stochastic aeroelastic system to generate the pitch (alpha) time-series. pow_spec_den_add.m -----&gt;&gt;&gt;&gt;&gt; To calculate the Power Spectral Density ,Signal Power, Noise Power, Total Power, SNR (signal-to-noise ratio) of the alpha time series generated by running the fnc7.m file. correlation_time.m -----&gt;&gt;&gt;&gt;&gt; Calculates the correlation time of the alpha time-series generated by running the fnc7.m file. quality_factor.m ----&gt;&gt;&gt;&gt; Calculates the quality factor of the alpha time-series. This .m file analyzes the data generated from the pow_spec_den_add.m file. interspike_analysis.m ----&gt;&gt;&gt;&gt; Performs and stores the ISI Analysis Data on the alpha time-series generated from the fnc7.m file. The codes were run using MATLAB software version R2021a. They can be run in any MATLAB version (preferably &gt;R2021a). The tool-boxes needed to run these codes are : matlab, signal_toolbox.