Calibration Guide for Wireless Sensors. Shinae Jang Jennifer Rice

Transcription

1 Calibration Guide for Wireless Sensors Shinae Jang Jennifer Rice November, 2009

2 Contents Introduction Static Method for Sensor Board Calibration Dynamic Method for Sensor Board Calibration Running the example calibration Comparing your own files Conclusion Appendix A A.1. RunCalibration.m MATLAB code A.2. Calibration.m MATLAB code A.3. Sync_func.m MATLAB code November

3 Introduction This guide describes both static and dynamic methods to determine calibration constants for wireless sensors. The raw outputs of the sensor board are the ADC values from the QF4A512. To convert the raw data to units of acceleration, the scale and offset values must be determined for each sensor as follows: Acceleration = (ADC values offset)/scale The scale and offset are known as the calibration constants, which can be utilized to obtain the physical acceleration. The scale allows conversion from the raw ADC values to acceleration. The offset is the mean of the ADC values. Nominal calibration constants are usually given in a sensor s data sheet; however, inherent differences in electronic components and manufacturing dictate that the calibration constants should be determined for each channel of a sensor to achieve a high quality of measured data. Because the SHM A sensor board can measure DC signals, the earth s gravitation can be used to perform straightforward sensor board calibration. This static approach is described in the first section of this guide. Subsequently, the guide describes how to compare wireless sensor data to data from a reference sensor for the purpose of dynamic calibration. November

4 1 Static Method for Sensor Board Calibration Set the Imote2/sensor board stack on a flat surface. Use a level to check that the z axis is experiencing 1g and the x and y axes are experiencing 0g. Measure data from each of the three channels with no excitation and then calculate the mean values of each channel. Turn the Imote2/sensor board stack on its side so that the x axis experiences 0g and the y and z axes experience 0g and repeat the measurements. Turn the stack a final time so that the y axis experiences 1g and the other two axes experience 0g and take a final set of measurements (as illustrated in Fig. 1). z = 1g y = 0g y = 0g x = 1g x = 0g y = 1g Figure 1. Illustration of accelerometer orientation for SHM A sensor board. For each axis, subtract the value mean 0g value from the mean 1g value to get the scale factor. The offset for each axis is the mean value of the 0g reading for that axis. For example, the mean 0g reading for the x axis is and the mean 1g reading for the x axis is then the scale and offset are calculated as follows: The x acceleration, x accel, is then calculated as: scale x = x 1g x 0g = = 5800 offset x = x 0g = x accel = (x ADC 14700)/5800 November

5 2 Dynamic Method for Sensor Board Calibration The calibration constants for an accelerometer may also be calculated through dynamic testing. This method requires the use of a reference accelerometer for which the calibration constants are known. Place the Imote2/sensor board stack so that one of the measurement axes is aligned with the direction of the shaking motion, collect data from both the wireless and the reference sensors, and store the data in text files. This section describes how to compare the data from the wireless sensor to the reference sensor. The results obtained from this method should correspond to those calculated using the static method described in the previous section. 2.1 Running the example calibration This section describes how acquired data from wireless and reference sensors can be compared. The main challenge with making this comparison arises from the fact that the data from the wireless and the wired sensors are obtained using different data acquisition systems and measurement parameters (e.g., sampling frequencies and data length). In the MATLAB routines described in this section, the time domain data from both systems are matched by finding the time offset that maximizes the cross correlation between the two signals. Subsequently, the data from the wired and wireless sensors can be compared in the frequency domain (i.e., power spectral density, coherence, and transfer function). This approach is realized in RunCalibration.m, an executable file that employs the subfunctions contained in the files Calibration.m and sync_func.m. In these files, the output files from both the wired and wireless sensors are assumed to be saved as text files. In the wired data file, wired.txt, the first column is the time vector and the second column is the acceleration vector as shown in Fig. 2. Figure 2. Data from reference sensor. In the wireless data file, wireless.txt, the first column is the node ID, the second column is the timestamp from when the RemoteSensing command was issued, and the third column is the acceleration data as shown in Fig. 3. November

6 Figure 3. Data from wireless sensor. Open the executable m file, RunCalibration.m (see Fig. 4). (1) Input the calibration constants: Input the calibration constants obtained from the static procedure offset : mean value scale : sensitivity (2) Input the wired sensor information: fs0 : sampling frequency of the wired sensor time0 : time vector of the wired sensor data0 : acceleration of the wired sensor (3) Input the wireless sensor information: filename: wireless.txt The output file from the Imote2 typically has a one line header. This part of the code allows the computer to read the time vector and acceleration vector without the header. fs1 : sampling frequency of the wireless sensor time1 : time stamping of the wireless sensor Time stamping does not start with 0; therefore, the first component should be deducted from the entire time vector. The raw unit, microseconds, has been converted to seconds. data1 : acceleration of the wireless sensor November

7 (1) (2) (3) (4) (5) Figure 4. Source code for Run_Calibration.m. November

8 (4) Select the calibration window These two constants define the size of the data window for the wired sensor data. For example, if a = 0 and b = 6, then the wired data from 0 to 6 seconds is correlated with the wireless sensor data. The calibration window is defined in Calibration.m file (see Fig. 5). Figure 5. Define the calibration window. November

9 (5) Determine maximum correlation Run the Calibration.m file by clicking where indicated in Fig. 6 and find the maximum correlation by changing the wired data window by changing the constants, a and b. Click this! Figure 6. Running the calibration example. The MATLAB command window in Fig. 7 shows the maximum correlation between the wired and wireless sensors at specific points, and based on that point, the data are synchronized. 100% correlation is 1, and 0% correlation is 0. Figure 7. Calibration example output. The output figures are automatically saved in.fig format in the current path (see Figs. 8 10) November

10 Figure 8: Synchronized time histories of the wired and wireless sensor data. The second window can be zoomed to check the accuracy of the synchronization. Figure 9: The top figure is the power spectral density of each data set, which shows good agreement up to 40 Hz in this specific case. The bottom figure is the coherence between the wired and wireless sensor data. The red line is drawn at 0.9 as a reference. November

11 Figure 10: Transfer function between the wired and wireless sensor data. The top figure is the magnitude in db unit, and bottom figure is the phase angle between two signals in degrees. 2.2 Comparing your own files Your own data files can be also compared using RunCalibration.m with an Imote2 output file. The wired data can be stored in various formats such as plain text (.txt), word document (.doc), excel document (.xls), data (.dat), or Matlab structure (.mat,.vna,.vsa,.etc). The sampling frequency, time vector, and data vector should be clearly defined in the original format of the file. For the wireless sensor data from the Imote2, the filename, sampling frequency, time vector, and the data vector should be clearly defined. November

12 3 Conclusion Following the steps outlined in this guide, you should be able to effectively determine the calibration constants for your wireless sensors. The constants obtained from the static procedure provide a quick and easy way to correlate the Imote2 output with physical acceleration data. The dynamic method can be utilized to confirm the quality of the wireless sensor data by comparing it with reference wired sensors. The time domain, frequency domain, and time synchronization comparisons can also be employed to assess the overall quality of the sensors. This user s guide is available at on the ISHMP website. November

13 Appendix A A.1. RunCalibration.m MATLAB code % execution file % Nov by Shinae Jang clear all;close all;clc %calibration offset = 0; scale = 1; %wired sensor load wired.txt fs0 = 256; %Hz time0 = wired(:,1); data0 = wired(:,2); % wireless sensor filename = 'wireless.txt'; fs1 = ; %Hz fid = fopen(filename); C=textscan(fid,'%u %n %n', 'headerlines', 1); NodeID = C{1}; % node id time1 = C{2}; % time stamping time1 = (time1 time1(1))/ ; % subtract DC time, microsec >sec. data1 = (C{3} offset)/scale; % acceleration time history fclose(fid); % calibration window a = 0; b = 6; % run calibration Calibration(fs0, time0, data0, fs1, time1, data1,a,b); November

14 A.2. Calibration.m MATLAB code function []=Calibration(fs0, time0, data0, fs1, time1, data1,a,b) % Calibration of basic/shm a sensorboards % Written by Shinae Jang, November, 2009 % fs0 : sampling frequency of the wired sensor % time0 : time vector for the wired sensor % data0 : data from the wired sensor % % fs1 : sampling frequency of the wireless sensor % time1 : time vector for the wireless sensor % data1 : data from the wireless sensor % a : the constant to define the start of the window % b : the constant to define the end of the window Tind = a*fs0+1:b*fs0; Tsearch = 1; % the window size. [s1,s2,fs,index1,index2,corfun] = sync_func(data1,data0(tind),fs1,fs0,tsearch); t1 = 1/fs*(1:length(s1)); t2 = t1; figure;subplot(2,1,1);plot(t1,s1,t2,s2);legend('wireless','wired'); title('synchronized Time Histories after Synch'); ylabel('mg');grid on; subplot(2,1,2);plot(t1,s1,' x',t2,s2);legend('wireless','siglab'); title('synchronized Time Histories zoomed');xlabel('time (sec)'); ylabel('mg');grid on; savename1 = strcat('timehistory'); saveas(gcf,savename1,'fig'); % PSD, coherence, transfer function nfft = 2^10;window = nfft;numoverlap = nfft/2;%fs = fs3; lg = min(length(s2),length(s1)); [Psl,f1] = cpsd(s2,s2,[],numoverlap,nfft,fs); [Pim,f2] = cpsd(s1,s1,[],numoverlap,nfft,fs); [C,f3] = mscohere(s2(1:lg),s1(1:lg),[],[],nfft,fs); [T,f4] = tfestimate(s2(1:lg),s1(1:lg),[],[],nfft,fs); phase = (180/pi)*angle(T); % PSD and coherence November

15 figure;subplot(2,1,1);plot(f2,db(pim),f1,db(psl));legend('wireless','siglab');title('psd'); ylabel('db');grid%xlabel('freq (Hz)'); axis([0 100 floor(1.1*min(20*log10(pim))) ceil(max(20*log10(pim))+0.2*abs(max(20*log10(pim))))]); subplot(2,1,2);plot(f3,c,f3,0.9*ones(length(f3)));xlabel('f (Hz)');title('Coherence');grid axis([ ]); savename3 = strcat('psd_coherence'); saveas(gcf,savename3,'fig'); % transfer function figure;subplot(2,1,1);plot(f4,db(abs(t)));title('transfer Function');grid;xlim([0 40]);ylabel('dB'); subplot(2,1,2);plot(f4,phase);title('phase');xlabel('freq (Hz)');ylabel('degrees');grid;xlim([0 40])%axis([ ]); savename4 = strcat('xfer'); saveas(gcf,savename4,'fig'); savename5 = strcat('file'); save(savename5,'s1','s2','fs','t1','t2','psl','f1','pim','f2','c','f3','t','f4'); % END of PROGRAM November

16 A.3. Sync_func.m MATLAB code function [s1,s2,fs2,index1,index2,cormax] = sync_func(signal1,signal2,fs1,fs2,tsearch) % Written by Tomonori Nagayama June 2006 % signal1 with sampling frequency fs1; % signal2 with sampling frequency fs2; signal2 is reference with slower % sampling frequency. % Tsearch(s) search Tsearch *2 second for timedelay % s1, s2 synchronized signals % fs2 synchronized frequency % Index1 index for signal1 (start point) % Index2 index for signal2 (start point and end point) % CorMax Correlation Coefficient between s1 and s2 %%%%%% Beginning of Function %%%%%%%%%% % you may need to change FSF FSF = 1; % sampling frequency factor. fs = 50.1 > 10 fs = >100; CorFun = zeros(tsearch*fs2*2+1,1); if fs1< fs2 fprintf('fs1<fs2'); return; end RefSigInd = Tsearch*fs2+1:length(signal2) Tsearch*fs2; RefSig = signal2(refsigind); LenRefSig = length(refsig); SyncSig = resample(signal1,round(fs2*fsf),round(fs1*fsf)); x = RefSig; for cnt1 = 1:Tsearch*fs2*2+1 y = SyncSig(cnt1:LenRefSig+cnt1 1); temp = corrcoef(x,y); CorFun(cnt1) = temp(2,1); end %figure;plot(corfun); [CorMax,Ind1] = max(abs(corfun)); fprintf('maximum correlation : %f\n at index : %d\n',cormax, Ind1); %%%%% End of First Step %%%%%%%%% %%%%% Second step %%%%%%%%%%%%%%% %x = RefSig; SWidth = 2; CorFun = zeros(ceil(fs1/fs2)*2*swidth+1,1); for cnt1 = 1:ceil(fs1/fs2)*2*SWidth+1 temp2 = ceil(ind1*fs1/fs2) SWidth*ceil(fs1/fs2)+cnt1 1; November

17 y1 = resample(signal1(temp2:length(signal1)),round(fs2*fsf),round(fs1*fsf)); y = y1(1:length(x)); temp = corrcoef(x,y); CorFun(cnt1) = temp(2,1); end %figure;plot(corfun); [CorMax,Ind2] = max(abs(corfun)); fprintf('maximum correlation : %f\n at index : %d\n',cormax, Ind2); temp2 = ceil(ind1*fs1/fs2) SWidth*ceil(fs1/fs2)+Ind2 1; y = resample(signal1(temp2:length(signal1)),round(fs2*fsf),round(fs1*fsf)); y = y(1:length(x)); temp = corrcoef(x,y); if temp(2,1)<0 y = y; end CorMax = temp(2,1); Index1 = temp2; Index2 = [RefSigInd(1) RefSigInd(length(RefSigInd))]; % t = 1/fs2*(1:length(x)); % y =y*std(x)/std(y); %figure;plot(t,x,t,y); s1 = y; s2 = x; November

18 Information provided in this document is connected to the Illinois Structural Health Monitoring Project (ISHMP) software toolsuite developed at the University of Illinois at Urbana Champaign. This software is copyrighted in the name of the Board of Trustees of the University of Illinois. THE UNIVERSITY OF ILLINOIS MAKES NO REPRESENTATIONS ABOUT THE SUITABILITY OF THE SOFTWARE FOR ANY PURPOSE. IT IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY. For inquiries, please contact: Professor B.F. Spencer, Jr. University of Illinois at Urbana Champaign Department of Civil and Environmental Engineering 2213 Newmark Civil Engineering Laboratory, MC North Mathews Ave Urbana, IL USA Or visit: November