REAL-TIME HYBRID TESTING FOR SOIL-STRUCTURE … et al__SSI.pdf · ADAPTIVE SIGNAL PROCESSING FRAMEWORK Introduction Numerical formulation of the horizontal SSI problem RTDS of the

REAL-TIME HYBRID TESTING FOR SOIL-STRUCTURE INTERACTION: AN ADAPTIVE SIGNAL PROCESSING FRAMEWORK

Introduction Numerical formulation of the horizontal SSI problem

RTDS of the horizontal SSI problem Application Conclusion

Vasileios K. Dertimanis, Harris P. Mouzakis, Ioannis N. Psycharis

Laboratory for Earthquake Engineering, School of Civil Engineering, National Technical University of Athens, Heroon Polytechniou 9, 15780

Zografou, Athens, Greece

Earthquake Engineering Research Infrastructures, JRC – ISPRA, 28/05/2013



Outline

Outline

First attempt of the LEE – NTUA research team to perform real – time dynamic substructuring (RTDS) tests with shaking table for the SSI problem. The framework was formulated on the basis of adaptive signal processing and parameter estimation techniques:

adaptive signal processing to compensate the dynamics of the shaking table (transfer system) parameter estimation to compensate the total transfer delay

In addition we attempted to introduce two innovative features:

replace the displacement command by acceleration command (wider spectrum) replace conventional load cell feedback sensors by using accelerometers (minimum interference)




Equations of motion Substructuring

Equations of motion


Single DOF lumped mass elastic structure supported on rigid foundation of mass mb

ub(t), u1(t): the displacements of the foundation and the specimen, respectively, relative to the earthquake motion, xg(t). v1(t): displacement of the specimen relative to the foundation. k1, c1: horizontal stiffness and damping of the structure. kx, cx: soil dynamics.




Equations of motion


The two – DOF structural system is described by

+




Substructuring


lumped elastic specimen is the physical substructure foundation and soil dynamics is the numerical substructure (interaction dynamics are shown with red arrows)

numerical substructure (feedback force / provide seismic excitation)

physical substructure (apply seismic excitation / measure force)




Substructuring


The equation that describes the motion of the foundation can be expressed as

where F(t) is the base shear force, given by

The equation that describes the motion of the specimen is

To the left hand side of the latter add and subtract the term

Thus




Substructuring


Summary for the substructuring of the horizontal SSI problem

In view of these equations the following remarks can be made:

1. Shaking table accepts acceleration as reference input.

2. The need for load cell attachment between the physical substructure and the shaking table is relaxed as the base shear force can be measured by simply attaching an accelerometer to the specimen mass (which is known).

3. This concept can be extended to structures of arbitrary DOF, as well as to SSI problems that include rotational DOFs.



General configuration Proposed configuration Adaptive Identification Adaptive Inverse Identification Discretization, specimen identification and predictor design

General configuration


The Aim of a General RTDS configuration is to replicate the output of the numerical model (absolute displacement of the foundation).

Problems: 1. Transfer system dynamics and delay: prevent the command signal to be actually

implemented on the table. A lag between the numerical and the physical substructure is introduced.

2. Feedback Force: the use of load cells for measuring force feedback retains applicability problems.

3. Displacement control mode: eliminates mid – to – high frequency components of the seismic excitation




Proposed configuration


The Aim: of the proposed configuration is to replicate the absolute acceleration of the numerical model (soil & foundation).

The applied solution uses these features: 1. An Adaptive Inverse Controller was used to cancel the transfer system dynamics. The

cascade of the transfer system with the adaptive inverse controller results in a Δ-step delayed impulse response.

2. A Numerical Substructure Predictor was implemented to predict the command to the table at Δ-steps ahead.

3. Use an acceleration Feedback: that eliminates the use of load cells. 4. Use an acceleration control mode that provides a wider frequency range




Adaptive Identification


Aim: specify the unknown dynamics of the transfer system.

x[t]: reference acceleration y[t]: achieved acceleration of the shaking table Employed algorithm: de-correlated LMS filter that adaptively attempts to reduce the total error




Adaptive Identification


Three ways were used to estimate the transfer system delay:

1. From the adaptive identification process (leading zeros of the FIR filter h[t]).

2. From the sample cross—correlation between the reference and the achieved acceleration.

Attention! The cross—correlation method requires Gaussian white noise as a reference

input. Otherwise is invalid.

3. From the inverse discrete Fourier transform of the estimated frequency response function (FRF) between the reference and the achieved acceleration.




Adaptive Inverse Identification


The impulse response of the adaptive inverse controller is the reciprocal of the one that describes the transfer system (including its delay). Yet, since the transfer system is dominated by internal delay, the inverse controller may have difficulty in overcoming it, as it must be a predictor. In addition, if the transfer system is of non – minimum phase (transfer function zeros in the right half of the s-plane or outside the unit circle in the z-plane), then the inverse controller results unstable. Moreover, the disturbance of the transfer system biases the converged solution and prevents the formation of a proper inverse.

To solve these problems we need adaptive inverse identification






Scheme 1 (on – line)

Disadvantage: possibility of slow convergence






Scheme 2 (off – line)

Advantages:

1. Can be run much faster than real time 2. Allows testing of several critical adaptation parameters, such as the choice of the

input signal, the length of the inverse model and the step size.




Discretization, specimen identification and predictor design


Discretization:

refers to the equation that describes the numerical substructure

the bilinear (Tustin) approximation is used, leading to: ab[t]: the discrete – time acceleration of the foundation, relative to the excitation ag[t]: the discrete – time earthquake acceleration (excitation) av[t]: the discrete time acceleration of the specimen, relative to the foundation




Discretization, specimen identification and predictor design


In order to account Delay compensation we have to shift the discrete – time numerical equation Δ time steps forward

It can be seen that only the relative acceleration av of the specimen is unknown. We can use a Predictor, based on the identification of the specimen’s structural parameters, through the following steps:

1. Apply a sine sweep or a Gaussian white noise test and determine the natural frequency and the damping ratio, either parametrically, or non – parametrically.

2. Estimate the stiffness and the damping of the specimen by

3. Design a multi – step predictor on the basis of the identified parameters and the Wold decomposition theorem



Specimen and tests description Results (T=0.5s)

Specimen and tests description


Specimen – to – foundation mass ratio = 4 Two specimen periods: 0.2s and 0.5s.

Fixed – base column that is interconnected to a beam by a hinge Boundary conditions pertain to free rotation around the horizontal axis and free sliding in the horizontal direction Two different orientations of the column are considered two periods







RTDS tests are conducted using a National Instruments RT – Desktop controller, equipped with two DAQ cards. The numerical model have been designed at MATLAB / SIMULINK and subsequently transferred to LABVIEW using the Simulation Interface Toolkit. In any test the sampling frequency is 1kHz. Feedback from the specimen is accomplished by attaching an accelerometer to the beam, right above the hinge.







Conduction of initial tests after specimen installation revealed a strong alteration of the shaking table’s performance, as a result of specimen’s response in both configurations. This is attributed to their mass (comparable to the mass of the shaking table) and geometry, which cause serious affection to the behavior of the shaking table. To this, the corresponding RTDS tests proved extremely demanding, as a lot of effort paid to the compensation of any undesired performance.






Procedure

1. Sine Sweep (four – octave logarithmic, frequency range at [1 16] Hz) and Gaussian White Noise (rms = 0.014g) tests for the specimen’s structural identification

2. Transfer System Adaptive Identification and delay estimation

3. Transfer System Adaptive Inverse Identification (online and offline)

4. Derivation of the overall transfer delay.

5. Predictive delay compensation

6. RTDS execution.




Results (T = 0.5s)


Sine Sweep test (four – octave logarithmic, frequency range at [1 16] Hz)




Results (T = 0.5s)


Transfer system identification: (a) cross – correlation, (b) inverse DFT, (c) decorrelated LMS.




Results (T = 0.5s)


Deccorelated LMS adaptive identification: (a) unfiltered data, order=500, (b) unfiltered data, order=1000, (c) filtered data, order 500.




Results (T = 0.5s)


Adaptive inverse identification: order=500 and (a) delay Δ=10 (0.01s), (b) delay Δ=250 (0.25s).




Results (T = 0.5s)


Convolution between forward and inverse adaptive filters (a) delay Δ=10 (0.01s), (b) delay Δ=250 (0.25s).




Results (T = 0.5s)


Waveform replication test: (a) reference (black) and achieved (red) table acceleration, (b) synchronization plot




Results (T = 0.5s)


RTDS test for sinusoidal input: (a) theoretical (black) and achieved (red) absolute acceleration of the foundation, (b) synchronization plot (c) base shear force.




Results (T = 0.5s)


RTDS test for Kalamata earthquake: (a) theoretical (black) and achieved (red) absolute acceleration of the foundation, (b) synchronization plot (c) base shear force.



Conclusion


Main aim: to develop a framework for effective RTDS of the horizontal SSI problem, based on adaptive signal processing and parameter estimation techniques.

Main features of the design: An adaptive controller is designed and identified, either off – line, or on – line.

Towards this point, an estimate of the transfer system’s impulse response is required. This is a crucial step of the RTDS process and it is considered successful when the cascade of the two estimated FIR models results a delayed version of the unit impulse response (Kronecker’s delta function).

To compensate the effects of the delay, a corresponding predictor is placed prior to the numerical substructure. This predictor handles the part of the relative acceleration of the specimen that cannot be a – priori known.

The process is designed to work in acceleration mode: not only acceleration commands are given to the transfer system, but acceleration feedback is also utilized, dropping the need for load cells.



Conclusion


Problems encountered: It seems that data low – pass filtering strongly alters the adaptation process. Better

models / lower delays occur without filtering (as shake table is a mechanical facility, it acts as a low pass filter itself).

Automatic gain controllers must be placed in the adaptation process, so as to assure that the cascade of the estimated FIR filters is indeed a delayed version of the Kronecker’s delta function.

The identification procedure for the specimen must become systematic… …and so must become the predictor design.

Challenges:

Large scale RTDS tests can be performed in existing shake table facilities It is not necessary to perform analytical modeling of existing elements Currently most sophisticated adaptive signal processing methods are investigated at

LEE – NTUA.




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REAL-TIME HYBRID TESTING FOR SOIL-STRUCTURE … et al__SSI.pdf · ADAPTIVE SIGNAL PROCESSING FRAMEWORK Introduction Numerical formulation of the horizontal SSI problem RTDS of the