This study investigates the hydrodynamics of the net system of the bottom-mounted aquaculture farms located in the Bohai Sea, addressing the growing demand for high-quality aquatic products and the limitations of coastal aquaculture. Based on the validation part, the established lumped-mass method integrated with the finite element method ABAQUS/AQUA was employed to evaluate the structural responses of the net system with three arrangement schemes under diverse environmental loads. The hydrodynamic loads on net twines are modeled with Morison formulae. With the motivation of investigating the trade-offs between volume expansions, load distributions, and structural reliabilities, Scheme 1 refers to the baseline design enclosing the basic aquaculture volume, while Scheme 2 targets to increase the aquaculture volume and utilization rate and Scheme 3 seeks to optimize the load distributions instead. The results demonstrate that Scheme 1 provides the optimal balance of structural safety and functional efficiency. Specifically, under survival conditions, Scheme 1 reduces peak bottom tension rope loads by 14% compared to Scheme 2 and limits maximum netting displacement to 4.0 m. It is 21.3% lower than Scheme 3, of which the displacement is 5.08 m. It has been confirmed that Scheme 1 effectively minimizes collision risks, whereas the other schemes exhibit severe collisions. Scheme 1 trades off maximum volume expansion for optimal load management, minimal deformation, and the highest overall structural reliability, making it the recommended design. These findings offer valuable insights for the design and optimization of net systems in offshore aquaculture structures serviced in comparable offshore regions.

Caputo fractional derivatives describe causal power-law memory, whereas the fractional Fourier transform represents continuous rotations in the time–frequency plane. This study derives an Abel–Gaussian-regularized coupling for endpoint-compatible causal signals. Unlike a direct composition of the two operators, the coupling is induced by embedding the causal Caputo convolution into a chirp-conjugated fractional convolution compatible with the adopted transform phase convention. Evaluation of the two transform branches shows that their quadratic phases cancel the additional convolution phase. On a compactly supported smooth core, removal of the regularization yields a rotation–memory–rotation factorization in which the fractional-memory multiplier acts at the ordinary Fourier node and the outer rotation maps the weighted spectrum to the prescribed fractional domain. At the discrete level, modulo-four reduction of the transform order is kept separate from decomposition of the derivative order, while a one-sided Grünwald–Letnikov approximation preserves causal history accumulation. Numerical experiments confirm fixed-spectral rotation identities and forward–inverse reconstruction at double-precision roundoff, approximately first-order convergence to an analytic Caputo reference, and decreasing low-frequency discrepancies under grid refinement. Further tests distinguish the effects of the sampling interval, observation length, fractional order, and nonzero endpoint traces. Exact boundary-term retention preserves the finite record, whereas compatible tapering produces a modified surrogate. For the tested dense implementations, the spectral implementation is faster than the direct full-history Grünwald–Letnikov implementation, while the shared dense operators dominate the storage requirements.

Tethered unmanned surface vehicle (USV) and remotely operated vehicle (ROV) systems are widely used in deep-sea inspection, observation, and intervention tasks. During cooperative operations, the USV must follow the mission trajectory of the ROV while avoiding surface obstacles and maintaining a prescribed tether-related safety envelope. This study proposes a multi-objective nonlinear model predictive control (NMPC) framework for USV-side cooperative tracking and dynamic obstacle avoidance in tethered USV-ROV operations. The framework integrates the predicted three-dimensional ROV trajectory, USV nonholonomic motion, surface-obstacle avoidance, straight-line tether-length-related geometric constraints, and control-smoothness regulation into a unified receding-horizon optimization problem. Sequential Least Squares Programming is used to compute the online control sequence. Numerical simulations include obstacle-free tracking under bounded ocean-current disturbances and heterogeneous surface–underwater obstacle scenarios. The results show that the proposed controller provides improved tracking performance and maintains the straight-line tether-length proxy below the prescribed limit in the tested simulations. The current-disturbance results further indicate preliminary disturbance-rejection capability under bounded time-varying ocean currents. The study provides a controller-level numerical framework for cooperative tracking and surface obstacle avoidance in tethered USV-ROV operations.