Plot fitting and equation of El Centro earthquake wave data

Hello, I need to know how to get the mathematical formula for the set of data points for El Centro earthquake wave [see attached Excel file], I have tried using trend-line of MS Office Excel 365, applying polynomial of 6th order, but the result is not good as the R square value = 0.0006 Please find the attached file, I am looking forward to hearing from you.

Best regards

Ahmad Ibrahim

Answer 1

[John D'Errico]

You must admit, that this is just a bit funny. Before you EVER do anything with your data, PLOT IT FIRST. If you learn nothing else from this exercise, learn that.

quake = xlsread('El_Centro_Data');
plot(quake(:,1),quake(:,2))

Then think about what you see.

Does this seriously look like a polynomial? Polynomials look like straight lines, quadratics, smooth things, nice, smooth curves. Now, look again. Be serious. How ell do you expect a straight line, a quadratic polynomial, or even a 6th order polynomial will fit that data? An R^2 of 0.0006 seems about right.

Don't just throw any random model at any arbitrary set of data and expect anything of value to drop out the end.

A better model for this data than a polynomial might be random noise. Well, not quite. There is some signal there. So you might better concentrate on things like a Fourier transform, since it is designed to extract information from signals like this. Except your data is not equally spaced. But I'd want to look in that direction.

[Ahmad Ibrahim]

Thanks for your response. Actually I am trying to simulate a 4.5 Hz geophone accelerometer sensor by applying Butterworth low pass filter with cutoff frequency of 10 Hz. by applying 1,2,3,...,n order of Butterworth filter I will get different pattern of response spectra which may have overshoots or undershoots. My target is to get filtered output without over/under shoots.

Geophone MATLAB Code:

===================================================================================== % AC-23 poles and zeros, 0.2 Hz version % LG20020913 SR20040402

% The geophone is a 4.5 Hz SM-6 Model B % constants m = 0.0111; % mass in kg w0 = 2*pi*4.5; % natural frequency B0 = 0.56; % open circuit damping sens = 28.8; % open circuit sensitivity Rb = 470; % Resistance of one branch in bridge, if bridge is balanced V = 13.83; % amplification of differential bridge amplifier stage

Bc = sens^2 * (V+1) / (2 * Rb * 2 * w0 * m) ; % damping caused by geophone coil current Btot = B0 + Bc; % Total damping

w = 2 pi logspace(-3, 4, 1000);

%transfer function of output voltage (TP1, [V])/ground acceleration [m/s^2]

K = 6.28; B = [V * sens / w0^2 / 2 * K 0]; A = [1/w0^2 2*Btot/w0 1];

H = freqs(B, A, w);

loglog (w/2/pi, abs(H)); title ('AC-23'); xlabel('[Frequency in Hz]') ylabel('[Relative Response to acceleration]') grid on;

================================================================================== Kindly find the Geophone system and block diagram.

Answer 2

[suha salman]