Adaptive linear quadratic regulator for optimal structural control based on wavelet transform and genetic algorithm

Abstract

PurposeIn real life, excitations are highly non-stationary in frequency and amplitude, which easily induces resonant vibration to structural responses. Conventional control algorithms in this case cannot guarantee cost-effective control effort and efficient structural response alleviation. To this end, this paper proposes a novel adaptive linear quadratic regulator (LQR) by integrating wavelet transform and genetic algorithm (GA).Design/methodology/approachIn each time interval, multiresolution analysis of real-time structural responses returns filtered time signals dominated by different frequency bands. Minimization of cost function in each frequency band obtains control law and gain matrix that depend on temporal-frequency band, so suppressing resonance-induced filtered response signal can be directly achieved by regulating gain matrix in the temporal-frequency band, leading to emphasizing cost-function weights on control and state. To efficiently subdivide gain matrices in resonant and normal frequency bands, the cost-function weights are optimized by a developed procedure associated to genetic algorithm. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structures subjected to near- and far-fault ground motions are studied.FindingsResonant band requires a larger control force than non-resonant band to decay resonance-induced peak responses. The time-varying cost-function weights generate control force more cost-effective than time-invariant ones. The scheme outperforms existing control algorithms and attains the trade-off between response suppression and control force under non-stationary excitations.Originality/valueProposed control law allocates control force amounts depending upon resonant or non-resonant band in each time interval. Cost-function weights and wavelet decomposition level are formulated in an elegant manner. Genetic algorithm-based optimization cost-efficiently results in minimizing structural responses.

Multiscale stochastic optimal control of hysteretic structures based on wavelet transform and probability density evolution method

“…In general, the conventional optimal control algorithm computes optimal control force by employing dynamic properties of a nondestructive and intact structure, which leads to producing an ideal optimal control force that disqualifies for practical implementation since the structural properties naturally fall off with respect to the structure’s service time. On another note, the real-life external stochastic excitations are highly non-stationary in amplitude and frequency, which inevitably induces resonant vibrations of the structure to turn out during the structure’s service time (Chha and Peng, 2023). To this end, this paper proposes a modified control law that computes optimal control forces based on the actual dynamic properties of the structure and temporal frequency bands.…”

“…In the real world, frequency non-stationary characteristics of stochastic ground motions are unavoidable and have a significant effect on structural behaviors, which often induces resonance phenomenon in structural vibrations throughout the service time of the structural systems. Recent studies proved that optimal control algorithms based only on the time domain cannot ensure the cost-effectiveness of energy consumption versus control efficacy (Chha and Peng, 2022, 2023). The first disadvantage of those control algorithms is that their control laws generate control forces that do not reflect the actual control effort demands between resonant and non-resonant vibrations, which mostly leads to increasing the responses of the structure due to unreasonable large control effort for non-resonant vibration.…”

“…The first disadvantage of those control algorithms is that their control laws generate control forces that do not reflect the actual control effort demands between resonant and non-resonant vibrations, which mostly leads to increasing the responses of the structure due to unreasonable large control effort for non-resonant vibration. For example, Chha and Peng found that the non-resonant vibration can be effectively suppressed by less control effort, while an adequately large control effort was needed to decay the resonant vibration (Chha and Peng, 2023). They showed that this allocation technique of control forces between both generic vibrations is superior to the control law of time-based optimal controllers which mostly increases structural responses and requires an inappropriately large control force.…”

Adaptive semiactive control of structure with magnetorheological dampers using wavelet packet transform

“…To achieve effective response reductions along with the economic damping force of MR damper, the proposed multiscale control algorithm allocates the major control force in the resonant band and sufficiently minor control force in the non-resonant band. In this regard, manipulation of cost-function weights on state and control is able to regulate the control forces in both frequency bands (Chha and Peng, 2022;Fitzgerald et al, Table 4. Frequency sub-bands (Hz) at the depth j of wavelet packet tree per ground motion.…”