Álvaro Alonso, José Luis Ramírez, Jorge Fernández
ARIES Ingeniería y Sistemas
ABSTRACT
After many years of testing civil engineering structures under seismic loading, new available powerful hardware, advanced control systems and simulations allow producing more accurate and therefore reliable test results. This new technologies make possible the so-called real time dynamic substructure test, which, using advanced control algorithms that enable real time system adaptation to the dynamic response of the complete system, and combining numerical models of a structure with specimens, offers a feasible testing ground for full size specimens. Running a virtual pre-test using numerical models for the testing system and the specimen is a new possibility to address control issues offline and thus avoid possible problems.
Furthermore, high-speed communication networks allow geographically distributed coordinated testing, linking the real time test progress taking place in different facilities. This paper reviews the future direction in seismic testing and simulation, highlighting the current limitations and describing the global trend in the research community.
Keywords: real-time hybrid testing, substructuring, geographically distributed testing
INTRODUCTION
In order to understand better the failure mechanisms and collapse processes that happen in various kinds of structures, several experimental procedures are commonly used, having as final goal the understanding of structure behaviour and energy dissipation that will help diminish the hazards associated with large earthquakes. Each test method has its own technique, but to avoid falling into the difficulties arising from the dimension limitations of a model they all search testing specimens with dimensions as close as possible to full-scale structures. These limitations come from the strong non-linear response of most structures under seismic loading, which make the results of scaled test results not very precise.
Quasi-static or traditional pseudo-dynamic reaction wall testing allows specimens to have larger dimensions due to the fact that the inertia effects are not part of the physical system being tested, so the structure is fixed to a strong floor and the loads are applied “stop-and-go” on specific places by actuators. On the other hand, shaking tables do test the inertia effects by subjecting the structure to a dynamic loading that reproduces that from a real earthquake, but most of them have limited specimen dimensions even though they are already quite large and require substantial effort to run. Nowadays, the new testing necessities usually require the use of a shaking table and actuators working together, or even several tables to induce different excitation inputs on multiple supports, like while testing a bridge span.

SUBSTRUCTURE TESTING
To perform reliable tests on structures that cannot be tested full-scale the solution is to do a socalled substructure test. In some laboratories, slow-motion reaction-wall based substructure testing is already well established. This substructuring, also called hybrid testing, consists in dividing the entire structural system into experimental and numerical parts; the latter cover those parts of the structure which can be represented realistically by numerical models, while the experimental parts cover those that cannot be modelled and are consequently represented by physical specimens. Servo-hydraulic actuators provide the forces and displacements at the interface between the two substructures. So as to have the simplest physical model possible the method of division in substructures is applied, which minimizes the specimen size and therefore minimizing the value of the load vector on the substructure of interest. The rest of the deformation values are computer-simulated, which, as they belong to substructures that haven’t reached their elastic limit, have constant values in the stiffness sub-matrices.
Figure 1.
Classification of substructure Tests
There are two main types of substructure tests; pseudo-dynamic and dynamic tests. The first ones are done as discontinuous tests, stopping and going in each time step, while the dynamic tests are done as continuous tests, only modifying the time scale so as to extend or reduce it in comparison to real world time.
In the traditional pseudo-dynamic process the structural displacements due to the earthquake are calculated computationally using a stepwise integration procedure and applied quasi-statically to the test specimen. The resulting resistance forces are measured and fed back to the computational model as part of the input for the next calculation step. In this method all the kinematic effects (inertia, viscosity…) are modeled, because the only measured values that influence the dynamic equation solving are the elements of the load vector, which depend exclusively of the structure deformation in a given instant.

Figure 2.
Substructuring modern methods
Figure 3.
ARIES proposed arquitecture for a Real

Even a well-tuned hybrid system cannot deliver perfect real-time actuation, and therefore the performance of the interface system is vital to minimize typical errors in the timing and amplitude of the imposed displacements, which may cause inaccuracy and possibly instability.
Different control strategies have been used in real-time dynamic substructure testing, being performed with force or displacement control. [Reinhorn et al . 2004, Takahashi & Fenves 2005]
GEOGRAPHICALLY DISTRIBUTED TESTING
Hybrid simulations fall into two categories, depending on the distribution of the structural subassemblies and the different components; local and geographically distributed. In a local hybrid simulation the numerical analysis and the experimental testing are performed at the same location. This allows local high-speed connections between the finite element analysis hardware, the control system, and the data-acquisition system, drastically reducing delays and making it possible to perform real-time substructure testing. On the other hand, in a geographically distributed hybrid simulation various parts of a structure are analysed and tested at different sites. This implies that the analytical and physical portions of the hybrid model are tested in multiple laboratories, needing a wide area network such as the Internet to connect them. This fact makes real-time hybrid simulations very challenging because of the larger delay in the information transfer through these networks as well as breakdowns or information losses, compared to the local high-speed ones.
So far all the geographically distributed tests that have taken place have been done following the pseudo-dynamic method, with a discontinuous stop-and-go at each time step. The main advantage is that it allows the complete software separation between time integration algorithms, communication management and control of the experiment. There is a physical limitation while sharing data between two or more laboratories, and is that the maximum speed of transferring information is the light velocity. This means that running a real-time geographically distributed hybrid test can be limited to a distance of around 300km between the sites. Another difficulty of geographically distributed hybrid testing is the diverse nature of each facility and its researchers, which can have a different testing methodology, culture, language or even local time.
However, breaking a model up into selected subassemblies and distributing them within a network of laboratories and computational sites has some clear benefits: It encourages the collaboration and sharing of resources, including funding and cost, of different facilities, as well as being able to take advantage of and combine the different capabilities available at the various facilities, that might come handy when dealing with solving large and complex problems.
There are some available tools that allow standardization to perform distributed tests:
OpenFresco , developed at UC-Berkeley (USA), is considered as a middleware performing the interface to the Finite Element software and the Control System at the probably several laboratories, therefore providing services needed to carry out hybrid simulations on a local or wide area network. UI-SIMCOR was developed at the University of Illinois at Urbana-
Champaign (USA), and is a hybrid simulation framework that acts as coordinator of several modules that can provide modelling/simulation or be connected to physical instruments. Other tools are ISEE developed at NCREE (Taiwan) or NTCP developed by the NEES consortium
(USA).

ADVANCED ALGORITHMS IN SEISMIC SIMULATION TEST SYSTEMS
The increasing need for testing structures in more and more realistic conditions demands better control algorithms capable to manage harder test requirements. The main features of advanced algorithms in real time seismic simulation fall into two categories: Enhanced accuracy in reference tracking within test duration andt rue multi DOF control minimizing cross talk in test rig.
The first requirement implies building control algorithms capable to take into account, in every moment (adaptive control), significant variations both in specimen under test and test rig dynamic properties. The second one is needed for ensuring that excitation to specimen comes only from the initially specified motion direction, be it translational (X, Y, Z), rotational (Roll,
Pitch, Yaw) or a combination of both. This condition is not easy to achieve, given the fact that in many seismic tables actuators are coupled and motion of one of them has an influence on the response in several DOFs (cross-talk).
Adaptive control algorithms
Many control strategies are based on a linear theory and begin by performing an identification of the whole system impedance matrix; [Z]. Once [Z] has been identified, desired response r is transformed into frequency domain and pre-multiplied by [Z] which leads to drive signals d . d = [Z]· r [1]
This approach works reasonably well for time invariant systems, but loses accuracy with time, since every physical system experiences temporal variation in its properties.
According to this, [Z] matrix needs be checked and updated constantly, so that corrections in drive signals can be calculated and changes in system properties can be accounted for. In this way, adaptive control main idea is to keep on identifying [Z] forever, therefore ensuring adaptation in drive signals. This task of identifying [Z] is accomplished by using different algorithms. For example, in MIMO RANDOM and MIMO REPLICATION tests, well-known algorithms as H1, H2, H3 or Hv can be used. However, it is always necessary to control the new
[Z] estimate to know whether it is better or worse than the previous one. Usually, Multiple
Coherence Function is used for this purpose, so that if it is higher than a certain threshold at a particular line of frequency, the new estimate is accepted at that frequency, but if it is lower than prescribed threshold, then it is rejected.
Reference
[Z]
Initial drive
NEW DRIVE
CALCULATION
Updated drive
SYSTEM
Response
[Z] update
Figure 4.
Generic block diagram for adaptive seismic control
Multi DOF control
As pointed out before, actuators of test rigs are usually coupled, that is, motion in a particular
DOF implies participation of many actuators. This fact implies that a multivariable control scheme must be implemented in order to properly command every actuator movement.

z
Accelerometer 1 (A1)
Ra
Rs
α
Accelerometer 2 (A2)
Actuator 1 (S1) Actuator 2 (S2)
Figure 5.
Simple example of multi-DOF test rig and the simplified control scheme used for control.
Following a linear approach, response in each DOF can be calculated as follows
;
Expressed in matrix notation
[2]
;
!"# $$
[3]
Next figure describes the simplified control block diagram. Drive per DOF is calculated taking into account current DOF response and motion reference.
ACT2DOF Ddof2Dact
A1, A2
[ITM]
Z, α
DOF CONTROL
[Z], adaptive
DZ, Dα
[OTM]
DA1, DA2
DOF ref.
Figure 6.
Simplified control block diagram. Drive per DOF is calculated taking into account current DOF response and motion reference.
Of course, drive per DOF must be decomposed in drives per actuator. This is done by means of another matrix transformation. The strategy described here is purely linear, however and even though it leads to satisfactory results in most cases, non-linear approaches taking into account actuators displacements and velocities are currently being investigated.
)* [4]
In addition, it must be noticed that this matrix control is very powerful and versatile, as it also allows defining customized new DOFs (torsion DOF in tables), weighting unevenly contributions from different accelerometers, account for accelerometers redistribution, etc.

VIRTUAL TESTING IN VIBRATION FACILITIES
Frequently, vibration testing suffers from non-linear responses from the test hardware that might lead to control instabilities that can damage the system, as well as modal coupling between the specimen under test and test rig (seismic table, fixtures, hydraulic actuators and seismic mass, for instance), which is one of the most common factors that alters ideal test conditions. When seismic tables are large, it is very likely that dynamic behavior of table and actuators interferes with modal characteristics of specimen under test, and it gets even worse when the specimen is heavily resonant. Furthermore, sometimes the specimen can even suffer a sudden change in its dynamic response during the shaking, which may cause an un-controllable situation.
Next figures show two modes of a dummy specimen (cylinder) and modal coupling between dummy specimen and seismic table. This modal coupling causes “spurious modes” to appear and shifts specimen modes in frequency, and eventually, a split in eigenfrequencies may also occur. The models presented in figures are not intended to be a faithful representation of an actual test. Their only purpose is to illustrate this phenomena taking place in actual tests.
(1) (2) (3) (4) (5)
Figure 7.
Isolated specimen modes and frequencies: (1) bending mode at 28,25Hz and (2) 125 Hz.
Resulting modes in specimen-table coupled scenario: (3) Spurious coupled bending mode at 17,9 Hz, (4)
Bending mode shifted to 26 Hz and (5) Bending mode shifted to 95 Hz.
Virtual testing consists in building software models representative of the physical behavior of all the subsystems that have an important influence on the performance of the test rig. These are typically the control system, servovalves in the hydraulic system, actuators, seismic table, fixtures and specimen under test.
In this way, a test can be simulated before it takes place, and a series of valuable conclusions can be extracted beforehand:
•
Test engineers can detect, in advance, things that may go wrong while carrying out the test as well as potential difficulties. Virtual testing can reduce test set up time (i.e. selection of control strategy, set up of identification parameters) and assist engineers in the fixtures design process.
•
Analysts are provided with data that will allow them to properly correlate test results with numeric models. This is done by taking out from the former effects that make hypothesis needed by the latter invalid. These unwanted effects are drawn up by means of Virtual Testing.

Usually, the steps that need to be followed when carrying out Virtual Testing are:
•
Identification of the systems having an important contribution in overall system performance: For example, is it possible to neglect the dynamics of the hydraulic power pack?
•
Modeling and calibration of these systems: Great care must be taken while performing a careful calibration of model parameters in order to ensure its validity. It is also quite difficult to find a unique software platform meeting all the requirements for this kind of simulation, since it should allow for implementation and integration of a variety of models such as FEM models, lumped parameters models, discrete time models, multirate and multi-physics simulations, etc. Usually at this stage, specialized software is used for translating FEM models into state-space models with the appropriate outputs
(sensors).
Virtual testing is becoming more and more common within the Civil Engineering testing ground, following the steps of the Aerospace Industry. Nowadays, it is used to improve data coming from test results before correlating them with numerical models of specimens, as well as providing the offline tuning of the identification parameters of the system.
CONCLUSIONS
The present and future direction in seismic testing and simulation has been presented. Online system adaptation to the dynamic response of the test system and virtual pre-testing is day by day getting more common in the seismic engineering community. Although there is still some hardware and control limitations to perform real-time substructure geographically distributed testing, nowadays it relies mostly on the traditional PsD method, great progress is being done.
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