With the expansion of power grids, the increasing peak-valley load difference threatens grid security, a challenge addressed by time-of-use pricing which incentivizes load shifting. Since central air-conditioning systems account for over 60% of building energy use, optimizing them for efficiency and cost under time-of-use pricing is crucial. This study presents an integrated optimization framework that coordinates photovoltaic generation, battery storage, and grid power. The approach develops a BES-LSTM forecasting model by using the Bald Eagle Search (BES) algorithm to tune Long Short-Term Memory (LSTM) network parameters for accurate cooling-load prediction. A central air-conditioning water-system energy-minimization model is then formulated and solved with an improved BES algorithm that incorporates adaptive opposition-based learning, logistic chaotic mapping, and Lévy flight. Finally, a daily schedule is optimized by partitioning time according to time-of-use price intervals and treating generation output, battery charge/discharge, and grid draw as decision variables. Simulations demonstrate that the framework reduces the central air-conditioning water system’s total energy consumption by an average of 28.7% and lowers energy costs under time-of-use pricing by 22.38%, achieving both significant energy savings and economic benefits.

Traditional acoustic metamaterials with inherently fixed bandgaps face difficulty in satisfying the dynamic requirements of vibration isolation and vibration attenuation under varying operating conditions, which limits their practical engineering applications. Nonlinear acoustic metamaterials based on effective-negative-mass (ENM) mechanisms provide a promising approach for achieving adaptive vibration attenuation through bandgap regulation. In this study, a temperature-tunable nonlinear local-resonance acoustic metamaterial incorporating shape-memory-alloy (SMA) helical-spring oscillators is proposed. A positive-stiffness nonlinear acoustic metamaterial model is established by combining a nonlinear Duffing oscillator with SMA springs. Based on the ENM local-resonance theory, the governing equations are nondimensionalized, and the first-order perturbation solutions of the acoustic and optical dispersion branches are obtained using the perturbation method. The effects of temperature variation and stiffness ratio on the dispersion characteristics and the starting and cut-off frequencies of the bandgap are theoretically analyzed. The theoretical results show that, as the temperature decreases, the temperature-induced phase transformation of SMA reduces the stiffness of the SMA springs, causing both the starting and cut-off frequencies to decrease and the bandgap to shift toward lower frequencies and become narrower. Furthermore, a five-period finite structure model is established, and the numerical vibration-transmission results verify the theoretical predictions of temperature-dependent bandgap tuning. The dynamic responses further reveal that effective-positive-mass and ENM regions coexist within the bandgap, while a zero-effective-mass state occurs near the bandgap cut-off frequency. These findings demonstrate that the proposed SMA-based nonlinear acoustic metamaterial can actively regulate the low-frequency vibration attenuation range through temperature control, providing a theoretical basis for the design of adaptive acoustic metamaterials for vibration isolation and noise reduction.