摘要
鉴于工程材料和地震动的复杂性，抗震试验方法在地震工程领域占有举足轻重的地位。在目前的多种抗震试验方法中，混合试验以其突出的优点更具魅力，比如能以较低的代价完成大型结构的动力响应分析。而实时混合试验方法作为混合试验方法家族的新成员，自从1992年提出以来展示了它独特的性质和分析复杂结构部件尤其是率相关部件的能力。
实时混合试验方法常把原型结构分成多个部分，然后根据对各部分的认知程度选择采用数值方法或者物理试验实时模拟。具体而言，关键、非线性部分或者率相关部分常采用真实的实时试验物理模拟，而其余部分通过求解微分方程同步分析。显而易见，该类方法的挑战在于通过实时加载和实时计算保证不同部分之间的界面耦合。
截至目前，实时混合试验领域已经取得了重要进展。本博士论文主要研究实时混合试验的传递系统控制和时间积分算法。具体而言，本文的研究工作和主要成果总结如下：
本论文首先将基于模型的控制策略-内部模型控制应用于新近设计的高性能试验系统，并且与经典PID/PI控制方法相比较。本研究中电磁式作动器的控制由三个环组成，即转速环、内位移环和外位移环。外位移环采用内部模型控制或者PID/PI调节，其余两环均采用比例控制。为了比较不同的控制方法，分别完成了采用扫频位移信号的真实试验和检验方法鲁棒性能的数值模拟。分析表明，内部模型控制具有更好的鲁棒性能和方便的执行、在线调节特性。对于此类可以简化成一阶模型和纯延迟环节的作动器，内部模型控制和PID控制性能都较好且类似。另外，所完成的实时混合试验表明整个试验系统工作状态良好。
为了准确补偿实时混合试验中的时变时滞，提出并讨论了基于简化作动器模型的在线时滞估计方法。该模型由一个静态增益和纯延迟构成，从而可以导出不同位移量之间的非线性关系。通过引入考虑遗忘因子的递推最小二乘算法进一步发展了基于泰勒级数的估计方法。接着，在纯数值模拟和混合试验中，与另外两种在线估计方法进行了比较。研究表明，所提出的方法具有令人满意的收敛速度、估计精度和可重复性，优于其他两种现有方法。
在认识到现有时滞补偿方法缺点的基础上，我们提出了两种考虑最新位移和速度目标的多项式时滞补偿表达式，通过频响函数和谱稳定性分析了该类方法。为了降低时滞补偿的困难，设计了一种基于时滞过补偿和最优反馈恢复力的新型时滞补偿方法，并完成了检验该方法性能的数值模拟和真实试验。分析表明，所提出的多项式补偿表达式具有较小的位移预测误差，而二阶方法与LSRT2积分算法结合具有略微较大的稳定界限。并且，时滞过补偿方法具有容许时滞变化、减小同步误差和有时提高算法稳定性的能力，能降低时滞补偿的困难。
本论文在积分方法方面发展了等效力控制方法以完成分离质量系统的实时混合试验。等效力控制方法是一种基于隐式积分算法的实时混合试验方法。谱分析表明，与显式积分算法相比，等效力控制方法具有更好的稳定性。认识到二次插值的等效力命令可能导致更大的控制误差，提出了位移修正措施以降低该误差的影响。鉴于实时混合试验内在的特征—界面上多变量耦合，我们把修正方法推广到同时更新位移和加速度的方法。谱稳定性分析和数值模拟表明：（1）同时修正位移和加速度的方法能解除零稳定性的约束和减小算法阻尼；（2）对于多自由度问题该修正方法仍然性能良好。
改进了一种实时混合试验的域间并行算法—IPLSRT2方法。该方法基于Rosenbrock方法（LSRT2）和一个现有的域间并行算法—PLSRT2方法。为了避免或弱化PLSRT2方法的缺点，比如较低的计算效率、位移和速度漂移以及复杂的启动过程，引入了不等级步长的LSRT2方法、速度投影和修正的雅克比矩阵计算方法。为了检验该方法的性能，完成了精度分析、谱稳定性分析、纯数值模拟和真实的实时混合试验。与PLSRT2方法相比，该方法既有优点也有缺点。比如，因为在所有积分点采用速度投影而降低了算法精度。然而，在通常的分析应用中，因积分步长较大，它能提供更准确的位移和速度结果。并且，它减少了A域的计算过程数，提高了A域的计算效率，降低了在实时应用中的执行难度。
Seismic testing methodologies play a significant role in earthquake engineering dueto complexities of engineering materials and ground motion. Among available testingmethods, hybrid simulation is more appealing for its merits, e.g., evaluating dynamicresponses of large scale structures at lower cost. As a novel member of hybrid simu-lation, Real-time Hybrid Simulations (RHS), since its conception in1992, has shownits unique properties and capacity for testing complex structural components, especiallyrate-dependent ones.
RHS often partitions the emulated structure into portions, which are then either nu-merically or physically simulated in real-time according to our knowledge of them. Inparticular, the critical nonlinear and/or rate-dependent parts are often physically modeledwithin a realistic real-time test, while the remainder parts are simultaneously evaluated bysolving diferential equations. Evidently, the challenge of these methods is to enforce thecoupling at the interface between portions via real-time loading and real-time computa-tion.
Heretofore great development of RHS has been attained. This dissertation is devotedto developing RHS in two aspects, namely transfer system control and time integrationalgorithms. In detail, research work and findings are summarized as follows:
The dissertation initially focuses on the implementation of a model-based controlstrategy–internal model control (IMC) and its comparison with the classic PID/PI controlon the lately conceived high performance test system-the TT1test system. The con-trol strategy of the electromagnetic actuators consists of three loops, namely one speedloop and two displacement loops. The outer displacement loop is regulated with IMC orPID/PI whilst the inner two loops with proportional control. In order to compare diferentcontrol strategies, realistic tests with swept sinusoidal waves and numerical simulationsconcentrating on robustness were carried out. Analysis showed that IMC is preferable forits robustness and its ease of implementation and online tuning. Both IMC and PID worksimilarly and well on the actuator which can be simplified into a first-order system plusdead time. In addition, RHS was performed and showed the favorable state of the system.
In order to accurately compensate for a time-varying delay in RHS, online delayestimation methods were proposed and discussed based on a simplified actuator model.The model, consisting of a static gain and dead time, results in nonlinear relationships among diferent displacements. The estimation based on the Taylor series expansion wasfurther developed by introducing the recursive least square algorithm with a forgettingfactor. Then this scheme was investigated and assessed in pure simulations and RHSvia comparison with two other methods. Finally, the proposed scheme was identified tobe satisfactory in terms of its convergence speed, accuracy and repeatability and to besuperior to other methods.
With the insight into the weakness of available compensation schemes in mind, twopolynomial delay compensation formulae considering the latest displacement and veloc-ity targets were proposed. Assessment and comparisons of the formulae by means offrequency response functions and stability analysis were carried out. In order to facilitatedelay compensation, another novel compensation scheme characterized by overcompen-sation and optimal feedback was conceived. Numerical simulations and realistic RHSwas performed to examine the proposed schemes. The analysis revealed that the pro-posed polynomial formulae exhibit smaller prediction errors and the second-order schemewith the LSRT2algorithm is endowed with a somewhat larger stability range. Moreover,the overcompensation scheme was concluded to have the ability of time-varying delayaccommodation, error reduction and sometimes stability improvement.
With regard to time integration algorithms, this dissertation extends the equivalentforce control (EFC) method which is a method of RHS with implicit integrators to RHSon split mass systems. The EFC method for this problem was spectrally analyzed andwas found more satisfactory stability than some explicit integrator. Then larger controlerrors due to quadartically interpolated EF commands were recognized and treated witha proposed displacement correction. In view of the inherent feature of RHS–multiplequantities coupling at the interface, the correction was extended to simultaneously up-date displacement and acceleration. Spectral stability analysis and numerical simulationsdemonstrated that:(1) the correction can remove the constraint of zero-stability to themethod and reduce algorithmic dissipation;(2) it also works well for MDOF systems.
Finally, an inter-field parallel algorithm for RHS, namely IPLSRT2, was developedand analyzed. This method was based on the Rosenbrock (LSRT2) method and a priorinter-filed parallel integrator–PLSRT2. The LSRT2with diferent stage sizes, velocityprojection and modified Jacobian evaluation were introduced to the algorithm in orderto avoid and/or weaken the disadvantages of the PLSRT2method, such as inefcientcomputation, displacement and velocity drifts, and complicated starting procedure. Ac-curacy analysis, spectral stability analysis, pure numerical simulations and realistic RHS were performed to investigate the properties of the IPLSRT2method. Compared with thePLSRT2method, this method exhibits pros and cons. In detail, the method loses the accu-racy order due to the velocity projection applied at all time steps. However, it can providemore accurate displacement and velocity results in common applications where a littlelarger time step is required. In some cases, the proposed method exhibits smaller phaseshifts and dissipation. Moreover, computation efciency in Subdomain A is improved andits implementation in real-time applications is simplified.
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