├── .gitignore ├── LICENCE.txt ├── README.md ├── analyze_record.m ├── classification_algo.m ├── classify_record_main.m ├── cont_wavelet_trans.m ├── example1.AT2 ├── example2.AT2 ├── find_Ipulse.m ├── find_Tp.m ├── make_plot.m └── parseAT2.m /.gitignore: -------------------------------------------------------------------------------- 1 | # asv files 2 | *.asv 3 | *.mat -------------------------------------------------------------------------------- /LICENCE.txt: -------------------------------------------------------------------------------- 1 | Copyright (c) 2012 Shrey K. Shahi, Jack W. Baker 2 | 3 | Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: 4 | 5 | The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 6 | 7 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | Pulse classification algorithm 2 | =============================== 3 | 4 | This set of Matlab scripts and functions implements the Shahi and Baker (2012) multi-component pulse classification algorithm. 5 | 6 | Contents 7 | ======== 8 | 9 | classify_record_main : This scripts is the one that calls other functions to classify a ground motion as a pulse/non-pulse and then compute the Ipulse and Tp values. 10 | 11 | classification_algo.m : This defines the function that selects the prospective pulses for classification 12 | 13 | analyze_record.m : This defines the main classification function that classified each prospective pulse 14 | 15 | find_Ipulse.m : Defines the function to find if the ground motion is classified as pulse-like or non-pulse-like 16 | 17 | find_Tp.m : Defines the function to compute the pulse period. Outputs -999 if the ground motion is non-pulse. 18 | 19 | make_plot.m : Defines the function to make a plot showing the velocity time-history of the original ground motion (in the orientation from which pulse was extracted), the extracted pulse and the residual ground-motion. 20 | 21 | cont_wavelet_trans.m : This funtion is used to perform the continuous wavelet transform 22 | 23 | parseAT2.m : This function parses the NGA West2 AT2 files. 24 | 25 | example1.AT2 , example2.AT2 : Example time-histories (recorded components of the Imperial Valley(1979) El centro Array #4 recording) used for demonstration. 26 | 27 | References 28 | =========== 29 | 30 | Shahi S.K., and Baker J.W. (2013). "An efficient algorithm to identify strong velocity pulses in multi-component ground-motions". Bulletin of the Seismological Society of America (under review) 31 | -------------------------------------------------------------------------------- /analyze_record.m: -------------------------------------------------------------------------------- 1 | % Function to classify an extracted pulse as pulse-like or non pulse-like 2 | % 3 | % Input 4 | % 5 | % signal : the velocity time history of original ground motion 6 | % col, row : location of the identified pulse 7 | % scales: scales at which wavelet transform was computed 8 | % wname : name of the wavelet used for wavlet analysis 9 | %%%%%%%%%%%%%%% 10 | % 11 | % Output 12 | % 13 | % pulse_data : A structure with details about the classification results. 14 | %%%%%%%%%%%%%%%% 15 | 16 | function pulse_data = analyze_record(signal,dt,col,row,scales,wname) 17 | 18 | num_coefs = 10; % number of wavelet coefs used to construct the pulse 19 | 20 | % refine the scales to get a better resolution of pulse (zoom in) 21 | 22 | num_scales = length(scales); 23 | scales = [scales(max(1, row-1)): scales(min(num_scales, row+1))]; 24 | cwt_coefs = cwt(signal,scales, wname); 25 | z=abs(cwt_coefs(:,col)); % only use the coefficients at the same time as the original pulse 26 | row = find(z==max(z)); 27 | pulse_scale = scales(row); 28 | 29 | time = dt:dt:length(signal)*dt; 30 | wtype = wavemngr('type',wname); 31 | iter = 4; 32 | 33 | switch wtype 34 | case 1 , [nul,psi,xval] = wavefun(wname,iter); 35 | case 2 , [nul,psi,nul,nul,xval] = wavefun(wname,iter); 36 | case 3 , [nul,psi,xval] = wavefun(wname,iter); 37 | case 4 , [psi,xval] = wavefun(wname,iter); 38 | case 5 , [psi,xval] = wavefun(wname,iter); 39 | end 40 | 41 | 42 | resid_th = signal; 43 | pulse_th = zeros(size(signal)); 44 | 45 | for i = 1:num_coefs 46 | [coefs(1,i), ~, col(1,i), Tp] = fn_extract_one_wavelet(resid_th, dt, pulse_scale, col(1)); 47 | 48 | % compute the residual 49 | basis = xval.*(pulse_scale); 50 | basis = basis + (col(1,i) - median(basis)); 51 | basis = basis.*dt; 52 | y_vals = psi * coefs(1,i) / sqrt(pulse_scale); 53 | delta = basis(2) - basis(1); 54 | num_pads = ceil((max(time) - max(basis))/delta); 55 | final_basis = [0:delta:min(basis-0.00001) basis (max(basis)+delta:delta:max(basis)+delta*num_pads)]; 56 | final_yvals = [zeros(size(0:delta:min(basis-0.00001))) y_vals zeros(1,num_pads)]; 57 | pulse_th = pulse_th + interp1(final_basis,final_yvals,time); 58 | pulse_th(find(isnan(pulse_th))) = 0; 59 | resid_th = signal - pulse_th; 60 | end 61 | 62 | % Check if the pulse is late 63 | 64 | signal_E = cumsum(signal.^2)/(sum(signal.^2))*100; 65 | pulse_E = cumsum(pulse_th.^2)/(sum(pulse_th.^2))*100; 66 | index = find(pulse_E <= 5); 67 | lateTime = signal_E(index(end)); 68 | 69 | late = lateTime >= 17; 70 | 71 | % sum of the coefficients of the DWT of the original signal and the final 72 | % residual. This sum is also equal to the energy of the ground motion. 73 | pulse_data.dwt_orig = sum(sum(abs(dwt(signal,wname)))); 74 | pulse_data.dwt_resid = sum(sum(abs(dwt(resid_th,wname)))); 75 | pulse_data.dwt_squared_orig = sum(sum( dwt(signal,wname).^2 )); 76 | pulse_data.dwt_squared_resid = sum(sum( dwt(resid_th,wname).^2 )); 77 | 78 | % compute the "Pulse Indicator" based on the PGV ratio and energy ratio 79 | PGV = max(abs(signal)); 80 | PGV_resid = max(abs(resid_th)); 81 | pgvRatio = PGV_resid/PGV; 82 | energyRatio = pulse_data.dwt_squared_resid/pulse_data.dwt_squared_orig; 83 | pc = 0.63*pgvRatio + 0.777*energyRatio; % the principle component 84 | % center the variables 85 | P = (pc-1.208421)/0.2462717; 86 | V = (PGV-11.58861)/18.88015; 87 | pulse_indicator = -7.817 - 0.5679*P^2 - 0.1516*V^2 - 3.0253*P -1.7396*V -2.7156*P*V; 88 | 89 | % identify whether the record contains a significant pulse 90 | is_pulse = (pulse_indicator>0) & ~late; 91 | 92 | 93 | % build a structure to hold the decomposition data 94 | pulse_data.dt = dt; % time step of the ground motion recording 95 | pulse_data.num_pts = length(signal); % number of points in the recording 96 | pulse_data.Tp = Tp; % pulse period 97 | pulse_data.wavelet_name = wname; % name of the wavelet used for analysis 98 | pulse_data.pulse_scale = pulse_scale; % scale at which the largest wavelet was found 99 | pulse_data.rows = col; % rows where wavelets were extracted 100 | pulse_data.coefs = coefs; % coefficients for the extracted wavelets 101 | pulse_data.PGV = PGV; % Peak ground velocity of the original ground motion 102 | pulse_data.PGV_resid = PGV_resid; % Peak ground velocity of the residual ground motion 103 | pulse_data.delta_energy_t= delta; % if this is negative, then the pulse is late-arriving 104 | pulse_data.late = late; % is the pulse late arriving 105 | pulse_data.pulse_indicator = pulse_indicator; % the score from the logistic regression used for classification 106 | pulse_data.is_pulse = is_pulse; % classification of the record 107 | pulse_data.signal = signal; 108 | pulse_data.pulse_th = pulse_th; 109 | pulse_data.resid_th = resid_th; 110 | 111 | % function to extract one wavelet 112 | 113 | function [coef, pulse_scale, col, Tp] = fn_extract_one_wavelet(signal, dt, pulse_scale, pulse_row) 114 | % defined parameters 115 | Tp_min = 0.25; % minimum period to consider for pulses 116 | Tp_max = 15; % maximum period to consider for pulses 117 | row_range = 10/25; % range of row locations in which to look for supplementary wavelets 118 | wname = 'db4'; % use Daubechies Wavelet of fourth order for the transform 119 | 120 | % set the scales at which to perform the CWT 121 | % scale and range of rows to consider are already known 122 | scales = pulse_scale; 123 | row_indices = [max(1, pulse_row - ceil(scales*row_range)) : min(length(signal), pulse_row + ceil(scales*row_range))]; 124 | % peform the Continuous Wavelet Transform 125 | cwt_coefs = cwt(signal,scales, wname); 126 | 127 | % find max coefficient 128 | 129 | z=max(max(abs(cwt_coefs(1,row_indices)))); 130 | row = 1; 131 | col = find(z==(abs(cwt_coefs(1,:)))); 132 | 133 | % the value of the coeficient associated with the extracted pulse 134 | coef = cwt_coefs(row, col); 135 | 136 | % pulse period (Tp) 137 | Tp = 1./scal2frq(pulse_scale,wname,dt); 138 | 139 | 140 | 141 | 142 | -------------------------------------------------------------------------------- /classification_algo.m: -------------------------------------------------------------------------------- 1 | % Implementation of the stratified classification algorithm 2 | %%%%%%%%%%%%%%%% 3 | % 4 | % Inputs 5 | % 6 | % signal1 , signal2 : Velocity time histories from 2 orthogonal components 7 | % dt : the time difference two consecutively recorded data points 8 | %%%%%%%%%%%%%%%%% 9 | % 10 | % Outputs 11 | % 12 | % pulse_datas : Cell with 5 slots with information about 5 potntial pulses 13 | % rotAngles : Orientations from which the 5 pulses are extracted 14 | % selectedCol, selectedRow : Indicates the scale and time at which each pulse 15 | % was extracted 16 | %%%%%%%%%%%%%%%%% 17 | 18 | 19 | function [pulse_datas,rotAngles,selectedCol,selectedRow] = classification_algo(signal1,signal2,dt) 20 | 21 | % Initialize the variables 22 | pulse_datas = cell(1,5); 23 | rotAngles = cell(1,5); 24 | selectedCol = cell(1,5); 25 | selectedRow = cell(1,5); 26 | 27 | % setup wavelet analysis 28 | wname = 'db4'; 29 | TpMin = 0.25; 30 | TpMax = 15; 31 | numScales = 50; 32 | scaleMin = floor(TpMin/1.4/dt); 33 | scaleStep = ceil((TpMax/1.4/dt - scaleMin)/numScales); 34 | scaleMax = scaleMin + numScales*scaleStep; 35 | scales = scaleMin:scaleStep:scaleMax; 36 | 37 | % Perform continuous wavelet transform on both components 38 | coefs1 = cont_wavelet_trans(signal1, dt, scales, wname); 39 | coefs2 = cont_wavelet_trans(signal2, dt, scales, wname); 40 | 41 | 42 | maxCoefs = (coefs1.^2 + coefs2.^2); 43 | 44 | for i = 1:5 45 | %pulse extraction 46 | maxCoef = max(max(maxCoefs)); 47 | col = find(max(maxCoefs) == maxCoef); 48 | row = find(max(maxCoefs,[],2) == maxCoef); 49 | maxDir = atan(coefs2(row,col)/coefs1(row,col)); 50 | signal = signal1*cos(maxDir(1))+signal2*sin(maxDir(1)); 51 | pulse_data = analyze_record(signal,dt,col,row,scales,wname); % classify the pulse. 52 | pulseScale = scales(row); 53 | 54 | % record the data about the extracted pulse 55 | pulse_datas{i} = pulse_data; 56 | rotAngles{i} = maxDir; 57 | selectedCol{i} = col; 58 | selectedRow{i} = row; 59 | 60 | % block out the region surrounding the extracted pulse so that pulse from a different time - freq region is selected 61 | blockMin = col-10/25*pulseScale; 62 | blockMax = col+10/25*pulseScale; 63 | idx = find(([1:length(signal1)] > blockMin).*([1:length(signal1)] < blockMax) == 1); 64 | maxCoefs(:,idx) = 0; 65 | end 66 | -------------------------------------------------------------------------------- /classify_record_main.m: -------------------------------------------------------------------------------- 1 | % Main pulse classification script 2 | % 3 | %%%%%%%%%%%%%%%%%% 4 | 5 | clear all 6 | clc 7 | 8 | filename1 = './example1.AT2'; 9 | filename2 = './example2.AT2'; 10 | 11 | disp('Starting computations'); 12 | 13 | [A1,dt,NPTS,errCode] = parseAT2(filename1); 14 | signal1 = cumsum(A1)' .* dt .* 981; % convert acc (in g) to velocity (in cm/s) 15 | [A2,dt2,NPTS2,errCode2] = parseAT2(filename2); 16 | signal2 = cumsum(A2)' .* dt2 .* 981; % convert acc (in g) to velocity (in cm/s) 17 | 18 | if(errCode == -1) 19 | % Error in reading the file (File not found), skip the record 20 | disp('File not found'); 21 | return; 22 | end 23 | 24 | if(abs(NPTS-NPTS2) > 20) 25 | % If the difference between number of points recorded in two 26 | % orientation is greater than 20 then skip 27 | disp('NPTS1 ~= NPTS2'); 28 | return; 29 | end 30 | 31 | if(NPTS ~= NPTS2) 32 | % If number of points recorded in the two orientation differ from 33 | % one another curtail the longer record to match the length of 34 | % shorter record 35 | if(NPTS < NPTS2) 36 | A2 = A2(1:length(A1)); 37 | signal2 = signal2(1:length(signal1)); 38 | else 39 | A1 = A1(1:length(A2)); 40 | signal1 = signal1(1:length(signal2)); 41 | end 42 | end 43 | 44 | if(dt ~= dt2) 45 | % if the reported dt in the timehistory file in both orientations 46 | % is different skip the record. 47 | disp('dt1 ~= dt2'); 48 | return; 49 | end 50 | 51 | 52 | if(length(A1) == length(A2)) 53 | % Check if the length of records are the same. 54 | [pulseData, rotAngles,selectedCol,selectedRow] = classification_algo(signal1,signal2,dt); 55 | fn = './classification_result.mat'; 56 | save(fn,'pulseData','rotAngles','selectedCol','selectedRow'); 57 | else 58 | disp('length(A1) ~= length(A2), even though the NPTS are same'); 59 | return; 60 | end 61 | 62 | Ipulse = find_Ipulse(pulseData); 63 | Tp = find_Tp(pulseData); 64 | make_plot(pulseData); 65 | 66 | 67 | -------------------------------------------------------------------------------- /cont_wavelet_trans.m: -------------------------------------------------------------------------------- 1 | % This function returns the continuous wavelet transform coeficients for 2 | % the input signat at the specified time and scales 3 | function [cwt_coefs] = cont_wavelet_trans(signal, dt, scales, wname) 4 | 5 | time = dt:dt:length(signal)*dt; 6 | wtype = wavemngr('type',wname); 7 | cwt_coefs = cwt(signal,scales,wname); -------------------------------------------------------------------------------- /example1.AT2: -------------------------------------------------------------------------------- 1 | PACIFIC ENGINEERING AND ANALYSIS STRONG-MOTION DATA 2 | IMPERIAL VALLEY 10/15/79 2316, El Centro Array #4, 140 3 | ACCELERATION TIME HISTORY IN UNITS OF G, PGA= .48431 G, PGV= 39.6246 CM/SEC, PGD= 25.1238 CM 4 | NPTS= 7818, DT= .0050 SEC, 0 POLE @ 40.00000 HZ, -5 POLE @ .05000 HZ, ACAUSAL 5 | -.2964875E-03 -.2947976E-03 -.2930890E-03 -.2913476E-03 -.2895808E-03 6 | -.2877795E-03 -.2859462E-03 -.2840880E-03 -.2821785E-03 -.2802475E-03 7 | -.2782998E-03 -.2763195E-03 -.2743063E-03 -.2722672E-03 -.2702156E-03 8 | -.2681598E-03 -.2660949E-03 -.2640236E-03 -.2618759E-03 -.2594433E-03 9 | -.2567847E-03 -.2540372E-03 -.2511881E-03 -.2481103E-03 -.2447385E-03 10 | -.2410470E-03 -.2370663E-03 -.2327336E-03 -.2280035E-03 -.2228099E-03 11 | -.2172414E-03 -.2132983E-03 -.2127135E-03 -.2134133E-03 -.2138399E-03 12 | -.2182114E-03 -.2254742E-03 -.2184232E-03 -.1984221E-03 -.1814274E-03 13 | -.1876928E-03 -.2101430E-03 -.2293225E-03 -.2416083E-03 -.2554308E-03 14 | -.2738956E-03 -.2863207E-03 -.2787845E-03 -.2624686E-03 -.2507519E-03 15 | -.2428478E-03 -.2316776E-03 -.2144888E-03 -.1936609E-03 -.1718116E-03 16 | -.1490684E-03 -.1241968E-03 -.9636245E-04 -.6587485E-04 -.4962771E-04 17 | -.8642723E-04 -.1546392E-03 -.2146364E-03 -.2627827E-03 -.3172779E-03 18 | -.3876289E-03 -.4635136E-03 -.5304799E-03 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-------------------------------------------------------------------------------- /find_Ipulse.m: -------------------------------------------------------------------------------- 1 | function isPulse = find_Ipulse(pulseData) 2 | 3 | % Check if any prospective pulse was classified as pulse 4 | isPulse = 0; 5 | for j = 1:5 6 | buff = pulseData{j}; 7 | if(buff.is_pulse == 1) 8 | isPulse = 1; 9 | end 10 | end -------------------------------------------------------------------------------- /find_Tp.m: -------------------------------------------------------------------------------- 1 | % Returns the Tp of the first potential pulse which is classified as 2 | % pulse-like . Returns -999 if the ground motion is not pulse-like 3 | 4 | function Tp = find_Tp(pulseData) 5 | 6 | Tp = -999; 7 | for j = 1:5 8 | buff = pulseData{j}; 9 | if(buff.is_pulse == 1) 10 | Tp = buff.Tp; 11 | return; 12 | end 13 | end -------------------------------------------------------------------------------- /make_plot.m: -------------------------------------------------------------------------------- 1 | % Makes the plot of original ground motion, extracted pulse and residual 2 | % ground motion 3 | 4 | function [] = make_plot(pulseData) 5 | 6 | for j = 1:5 7 | buff = pulseData{j}; 8 | if(buff.is_pulse == 1) 9 | signal = buff.signal; 10 | pulse_th = buff.pulse_th; 11 | resid_th = buff.resid_th; 12 | record_dt = buff.dt; 13 | 14 | np = length(signal); 15 | time = record_dt:record_dt:record_dt*np; 16 | 17 | fig = figure(); 18 | subplot(3,1,1) 19 | plot(time, signal, '-k') 20 | legend('Original ground motion') 21 | set(gca, 'xticklabel', []) 22 | yl= [-max(abs(get(gca, 'ylim'))) max(abs(get(gca, 'ylim')))]; 23 | set(gca, 'ylim', yl) 24 | 25 | subplot(3,1,2) 26 | 27 | plot(time, pulse_th, '-r') 28 | legend('Extracted pulse') 29 | 30 | hy = ylabel('Velocity [cm/s]'); 31 | set(gca, 'xticklabel', []) 32 | set(gca, 'ylim', yl) 33 | 34 | subplot(3,1,3) 35 | plot(time, resid_th , '-k') 36 | legend('Residual ground motion') 37 | hx = xlabel('Time [s]'); 38 | set(gca, 'ylim', yl) 39 | 40 | break; 41 | end 42 | end -------------------------------------------------------------------------------- /parseAT2.m: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % Parser for NGA West2 AT2 files 3 | % --------------------------------- 4 | % Input : Full path of the file to be parsed 5 | % 6 | % Outputs: 7 | % -Acceleration time history (Acc) 8 | % -Time step used for recording (record_dt) 9 | % -Number of recorded points (NPTS) 10 | % -error code to indicate if the file was not present (errCode) 11 | % --errCode = 0 if successful, -1 if File not found 12 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 13 | 14 | function [Acc,record_dt,NPTS,errCode] = parseAT2(filename) 15 | file_in = fopen(filename, 'r'); 16 | if(file_in == -1) 17 | Acc = -1; 18 | record_dt = -1; 19 | errCode = -1; 20 | NPTS = -1; 21 | else 22 | for j=1:3 23 | ans = fgetl(file_in); 24 | end 25 | [a1 ans] = fscanf(file_in, '%5c', 1); 26 | [NPTS ans] = fscanf(file_in, '%s', 1); 27 | NPTS = str2double(NPTS(1:end-1)); 28 | [a3 ans] = fscanf(file_in, '%s', 1); 29 | [record_dt ans] = fscanf(file_in, '%f', 1); 30 | ans = fgetl(file_in); 31 | [Acc, np] = fscanf(file_in, '%f'); 32 | fclose(file_in); 33 | errCode = 0; 34 | end --------------------------------------------------------------------------------