¶ 相关文件：
¶ PDT recommendations；Pseudo Dynamic Testing.ppt；Servotest PDT scheme.doc
¶ 1. Servotest PDT scheme
Pseudo-dynamic testing in the Pulsar environment
¶ 1.1 Principle
The computational element to the Pseudo-dynamic test (PDT) method involves a stepwise resolving of forces generated in the theoretical structure by a ground excitation. The dynamic forces are calculated using Mass and Damping Matrices, whereas the static Restoring forces are measured experimentally.
Ma(t) + Cv(t) + r(t) = F(t)
where:
M = Mass Matrix
a = Acceleration Vector
C = Damping Matrix
v = Velocity Vector
r = Restoring Forces (measured with load cells)
F = External Excitation Forces so F = - M g where g is the ground acceleration time history.
Figure 1: PDT test setup
By modeling the dynamic elements of the above equation, it is possible to perform the experimental part of the test in ‘slow-motion’ in the computers virtual timeframe. This not only reduces hydraulic power requirements, but also allows for better observation of the onset of structural damage. In some cases, it is possible to incorporate multiple elements of a structure into the model, leaving only a small proportion of the structure to be tested experimentally, again reducing experimentation costs.
A discrete time-integration is required in order to transform the modal acceleration and velocity vectors into modal displacements which are then applied to the structure.
¶ 1.2 The method
The Newmark algorithms assume that:
M_a^(m+1) + C_v^(m+1) + r^(m+1) = F^(m+1)
d^(m+1) = d^m + Tv^m + T^2 [(0.5 - b)*a^m + b*a^(m+1)]
v^(m+1) = v^m + T[(1 - y)*a^m + y*a^(m+1)]
where a^(m+1), v^(m+1) and d^(m+1) are the acceleration, velocity and displacement vectors respectively, at time equal to (m+1)*T; and b and y are parameters selected by the user for stability and accuracy.
When b = 0 the next displacement is no longer a function of the next (unknown) acceleration so the integration method becomes explicit and if b = 0 and y = 0.5 the popular central difference scheme is recovered, ie:
d^(m+1) = d^m + T*v^m + 0.5*T^2*a^m
v^(m+1) = v^m + 0.5*T*(a^m + a^(m+1))
¶ 1.3 Energy dissipation
Normally, viscous damping is very small compared to hysteretic damping. This is due to inelastic deformation and damage to the structural materials and represents the major source of energy dissipation [Shing et al, 1984]. This would be very difficult to model but fortunately this is not required as this information is contained in the measured restoring forces.
¶ 1.4 Continuous pseudo-dynamic testing
The conventional pseudo-dynamic method would require that, at each step, the actuators be ramped to the new desired position and held there while the new restoring forces be measured and used in the calculation of the next displacements.
The drawbacks of this technique are the load relaxation phenomenon occurring during the hold periods and the long time it takes to complete a test.
Servotest implement the so-called continuous procedure [Casciati et al, 2006] whereby the servo-controller moves the actuator in such a way that the specimen follows very accurately the target displacement (due to the lack of discontinuities in the motion). The forces are measured at every control sample period (typically 1ms) and the equations of motion are integrated on the fly at the same rate. The next displacement is determined and the motion proceeds without interruption. To do so, for each g^m discrete value of ground acceleration, a sequence of N acceleration values is computed by interpolation between g^m and g^(m+1) (that is g0^m, g1^m, …,gn^m, …, g_N-1 ^m), as shown in Figure 2 .
Figure 2: The continuous PDT procedure
The choice of N depends on the application, particularly the nodal masses, and obviously affects the time scale expansion factor which is given by:
Example: the earthquake record may be sampled at 200 Hz (so T = 5 ms) and the control system would normally run at 1kHz (so t = 1 ms)
In these conditions, for a time scale expansion factor of 500 (each second of earthquake would take 500 seconds to test) we need N = 2500.
¶ 1.5 The algorithm
The algorithm can be summarised as follows:
- gn^m is read and the external forces are computed using Fn^m = - Mg.
- The restoring forces rn^m are measured.
- an^m and vn^m are computed by direct integration
- The next displacements d_n+1 ^m are computed
- d_n+1 ^m are imposed on the structure
- Wait for end of control sampling time t (1 or 2 ms typically) before going to step 1.
¶ 1.6 Practical considerations
The experience gained so far has shown that it is the attention to the PDT method’s experimental implementation that ultimately leads to good results [Magonette et al, 1998]. The effects of experimental errors are much more severe in PDT testing than in any other testing methods. Incorrect displacements generate erroneous restoring forces which in turn lead to incorrect displacement targets, hence the error propagation.
Displacement transducers: The displacement transducers within the actuators are only used to connect the actuators to the specimen. Once this is done the control loop switches to external incremental (digital) transducers whose reference is independent of the strong wall on which the actuators are attached (see Figure 3). This eliminates the unavoidable errors due to finite bearing and strong wall stiffness.
Furthermore, because the specimens are stiff (especially at the start of the test) very little displacement produces a lot of reaction force. For this reason and the nature of PDT algorithms which makes them prone to displacement error propagation [Casciati et al, 2006] it is imperative to use transducers with a 1 or 2 micron resolution.
Figure 3: Measuring structural position using incremental transducers with separate reference
Load cells: Because the load cells are used to measure the restoring forces at each of the N sub-steps of the continuous PDT procedure any noise tends to be filtered out by the smoothing effect of the averaging. The main requirement for the load cells is that their hysteretic rate be less than 0.1%.
Actuators: There must be no friction coming from the actuators because this would prevent the accurate displacement control required for the tests. All actuators must be fitted with hydrostatic bearings.
Servo-valves: In the continuous PDT experiment the displacement command changes by a few microns and the valve has to react to this change to minimise the error. So the valves must have as high a bandwidth as possible, and be as small as possible to minimise the noise.
The full scale PDT control system
A separate real time processor (Master) is used to hold the user’s simulation/control algorithms and any sub-structuring model. The high speed communication between this PC and the Pulsar DSP is done via a hardware link whose only task is to send the transducer signals from Pulsar to the Master, wait for the algorithm to update the commands and send the new commands back to Pulsar within 1 ms or 2 ms.
In the case of very large sub-structure models it may be necessary to use multiple processors running in parallel, each simulating one part of the sub-structure. For example these could be Finite Element models of the individual piers of a suspended bridge. These parallel processors (called slaves) are connected to the Master using standard LAN equipment.
A visualisation PC is also connected to the Master for the purpose of on-line monitoring and graphing. This allows the Master to be totally devoted to the highly demanding real time algorithms and models.
Figure 4: PDT implementation using external simulation processors
The simplified PDT implementation
In the case of smaller systems with a reduced number of nodes and no sub-structuring involved it may be possible to perform the pseudo-dynamic test within the Pulsar controller itself. This is done by downloading the PDT algorithm onto a DSP Socket running within the real time Pulsar control system (normally at 1 kHz).
The algorithm is normally written in C and compiled into DSP using a Texas Instrument compiler.
Note: If the user prefers to use a flow diagram editor to implement the PDT algorithm, then Matlab, Simulink and Real Time Workshop will need to be purchased, as well as the TI compiler.
In this configuration the on-line monitoring and graphing are performed by the Pulsar front end PC (see Figure 5).
Figure 5: Simplified PDT implementation
¶ 1.7 References
Shing, P. and Mahin, S. (1984). Pseudodynamic Test Method for Seismic Performance Evaluation: Theory and Implementation. Report UCB/EERC-84/01, Earthquake Engineering Research Center, University of California, Bekerley, USA.
Magonette, G. and Negro, P. (1998). Verification of the Pseudodynamic Test Method. Journal of the European Association for Earthquake Engineering 1.
Casciati, F., Magonette, G. and Marazzi, F. (2006). Technology of Semiactive Devices and Applications in Vibration Mitigation. John Wiley & Sons Ltd.
¶ 2. PDT Recommendations
These are our current recommendations & strategy based on what I learnt at ISPRA.
The full scale PDT control system hasn’t been implemented yet (we’re waiting for the first order to implement it as it’s going to be a lot of work) , nor costed. Beijing Highway and Shenzhen Uni will both get the simplified version.
The simplified version uses Sockets but does not require Matlab, Simulink or RTW. The TI compiler is necessary.
Also below is a note I sent recently on the importance of using independent incremental transducers. In Mr Magonette’s own words “without these it’s pointless to even start the test”.
In pseudo-dynamic testing the displacement command is modified by just a few microns at each step (every ms). So it is vital the displacement transducer used as feedback measure accurately the actual movement of the structure, and just that. The actuator’s internal LVDT does not have the resolution necessary to do this and furthermore it measures not just the structure deflection but also the few microns going into the strong wall motion, the bearing play and so on. As a result the measured reaction force will be less than what it should have been for a particular specimen stiffness and the next displacement command will be wrongly increased by the PDT algorithm. This will inevitably lead to instability.
The only solution is to use external incremental transducers with 1 or 2 micron resolution connected to a reference frame that is independent of the strong wall. This should be explained to customers when they purchase a PDT system, along with other Servotest recommendations detailed in the attached document.
If they choose to ignore these recommendations it becomes their problem, not ours.
The Shenzen University scope of supply, as far as I can see, does not include external displacement transducers at all. Is this correct (Brian?) or are they providing their own? In which case we need to know this because the software needs to switch the feedback to these when the test starts.