Geopsy: Structure spectrum - Revision history

Clotaire Michel: /* Background */

2010-03-21T15:26:19Z

Background

Clotaire Michel: /* Results */

2010-03-21T11:29:32Z

Results

Clotaire Michel: /* Pre-Processing */

2010-03-21T11:28:02Z

Pre-Processing

Clotaire Michel at 11:19, 21 March 2010

2010-03-21T11:19:43Z

Clotaire Michel at 16:20, 12 March 2010

2010-03-12T16:20:17Z

Clotaire Michel: New page: '''Structure spectrum''' is an advanced signal processing tool aiming at computing the Transfer function of a system, i.e. to deconvolve signals, mainly civil engineering...

2010-03-12T15:53:36Z

New page: '''Structure spectrum''' is an advanced signal processing tool aiming at computing the Transfer function of a system, i.e. to deconvolve signals, mainly civil engineering...

New page

'''Structure spectrum''' is an [[Geopsy: Tools|advanced signal processing tool]] aiming at computing the Transfer function of a system, i.e. to deconvolve signals, mainly civil engineering structures.

==Background==
, i.e. the solution of the homogeneous equation

ATTENTION no Transfer function, good in frequency, not in amplitude (Konno et Omachi)

==Pre-Processing==
Before starting the ''Structure spectrum'' toolbox, the signals should be rearranged by pairs. In the pre-processing toolbox (see below), check-boxes allow to discard Z, N or E components, therefore simplifying this procedure. Moreover, in case of odd number of signals, the last one is removed. The toolbox will compute the Transfer function between the first and the second signal, i.e. the spectral ratio of the second over the first signal. In a building, the bottom recording should therefore be placed first and the top recording second.

When starting the ''Structure spectrum'' toolbox using the [[Geopsy: Tools|Menu Tools]] or using the [[Geopsy: Toolbar|Toolbar]], a pop-up menu allows several pre-processing:
*''Excludes components''. 3 check boxes allow to discard Vertical and/or North and/or East components. This is to help the rearrangement of signals.
*''Third signal operation''. A third signal is added to each pair of signals that will be used in the deconvolution (see [[#Deconvolution|Deconvolution]]). Two possibilities are offered:
**''Difference'' computes the difference signal 1 minus signal 2 for each pair of signals. For bottom and top recordings in a building, this corresponds to the relative motion of the structure (see [[#Background|Background]])
**''Average'' computes the average of each pair of signals. It seems to be an obsolete option.

computes the transfer functions between signals in the active [[Geopsy: Signal Viewer|signal viewer]].

@@ Line 19: / Line 19: @@
 In the case of a building excited by an earthquake, the recorded signal at the top <math>u_t(t)</math> of the building is the sum between the response to the earthquake (relative motion) <math>u_r(t)</math> and the ground motion <math>u_g(t)</math>:
-<math>u_t(t)=u_g(t)+u_r(t)=u_g(t)+\ddot(u)_g\otimes h(t)</math>
+<math>u_t(t)=u_g(t)+u_r(t)=u_g(t)+\ddot{u}_g(t)\otimes h(t)</math>
 It is therefore necessary to deconvolve the relative motion <math>u_r(t)=u_t(t)-u_g(t)</math> instead of the total recorded motion <math>u_t(t)</math>. <math>u_r(t)</math> can also be seen as the solution of the homogeneous equation of motion.

@@ Line 45: / Line 45: @@
 ==Results==
 Starting the processing creates a new [[SciFigs: Graphic sheet|graphic sheet]] with 4 different resulting spectral ratios. Calling c1 the first and c2 the second signal of each pair, the computed spectral ratio are:
 *<math>\frac{c2-c1}{c1}</math>. This is the ratio between the relative motion and the input signal, therefore the estimate of the transfer function of the structure.

← Older revision		Revision as of 11:28, 21 March 2010
Line 28:		Line 28:

	==Pre-Processing==		==Pre-Processing==
		+	[[Image:EQrec.png\|thumb\|right\|250px\|Recordings of an earthquake at the bottom and top of a structure]]
		+	[[Image:EQrecdiff.png\|thumb\|right\|250px\|Created signal viewer with the difference top-bottom (relative motion).]]
		+
	Before starting the ''Structure spectrum'' toolbox, the signals should be rearranged by pairs. In the pre-processing toolbox (see below), check-boxes allow to discard Z, N or E components, therefore simplifying this procedure. Moreover, in case of odd number of signals, the last one is removed. The toolbox will compute the Transfer function between the first and the second signal, i.e. the spectral ratio of the second over the first signal. In a building, the bottom recording should therefore be placed first and the top recording second.		Before starting the ''Structure spectrum'' toolbox, the signals should be rearranged by pairs. In the pre-processing toolbox (see below), check-boxes allow to discard Z, N or E components, therefore simplifying this procedure. Moreover, in case of odd number of signals, the last one is removed. The toolbox will compute the Transfer function between the first and the second signal, i.e. the spectral ratio of the second over the first signal. In a building, the bottom recording should therefore be placed first and the top recording second.

@@ Line 1: / Line 1: @@
-'''Structure spectrum''' is an [[Geopsy: Tools|advanced signal processing tool]] aiming at estimating the Transfer function of a system, i.e. to deconvolve signals, mainly in civil engineering structures.
+'''Structure spectrum''' is an [[Geopsy: Tools|advanced signal processing tool]] aiming at estimating the Transfer function of a system by computing the spectral ratio between the input and the output signals.
 ==Background==
-, i.e. the solution of the homogeneous equation
+Considering a linear system with an input signal (e.g. the ground motion) and an output signal (e.g. the recording at the top of a building), system identification aims at estimating the parameters of the linear system (filter), called Transfer Function. The characteristic values of a linear filter are its poles (peaks) and zeros. In the time domain, the response y(t) of a linear system with a transfer function h(t) to a given input signal x(t) is written using the convolution product:
-Warning no real Transfer function, good in frequency, not in amplitude (Konno et Omachi)
+<math>y(t)=x(t) \otimes h(t)</math>
 ==Pre-Processing==
@@ Line 13: / Line 33: @@
 *''Excludes components''. 3 check boxes allow to discard Vertical and/or North and/or East components. This is to help the rearrangement of signals.
 *''Third signal operation''. A third signal is added to each pair of signals that will be used in the deconvolution (see [[#Deconvolution|Deconvolution]]). Two possibilities are offered:
-**''Difference'' computes the difference signal 1 minus signal 2 for each pair of signals. For bottom and top recordings in a building, this corresponds to the relative motion of the structure (see [[#Background|Background]])
+**''Difference'' computes the difference signal 2 minus signal 1 for each pair of signals. For bottom and top recordings in a building, this corresponds to the relative motion of the structure (see [[#Background|Background]])
 **''Average'' computes the average of each pair of signals. It seems to be an obsolete option.
-After clicking ''OK'', the processing toolbox appears.
+Clicking ''OK'' creates a new  [[Geopsy: Signal Viewer|signal viewer]] with the initial signals and the resulting third signal and the processing toolbox appears.
 ==Processing Toolbox==
 The processing toolbox is the same used for H/V and Spectrum and is described [[Geopsy:_H/V_and_Spectrum_Toolboxes|there]].
 ==Results==