In this work, we proposed a sensitivity-enhanced temperature sensor, a compact harmonic Vernier sensor based on an in-fiber Fabry–Perot Interferometer (FPI), with three reflective interfaces for the measurement of gas temperature and pressure. FPI consists of air and silica cavities formulated by single-mode optical fiber (SMF) and several short hollow core fiber segments. One of the cavity lengths is deliberately made larger to excite several harmonics of the Vernier effect that have different sensitivity magnifications to the gas pressure and temperature. The spectral curve could be demodulated using a digital bandpass filter to extract the interference spectrum according to the spatial frequencies of resonance cavities. The findings indicate that the material and structural properties of the resonance cavities have an impact on the respective temperature sensitivity and pressure sensitivity. The measured pressure sensitivity and temperature sensitivity of the proposed sensor are 114 nm/MPa and 176 pm/°C, respectively. Therefore, the proposed sensor combines ease of fabrication and high sensitivity, making it great potential for practical sensing measurements.

The real-time surface thermal monitoring of thermal protection structures (TPSs) is crucial for hypersonic vehicle safety. This study proposes an effective approach for real-time temperature reconstruction by integrating embedded sensor arrays with an enhanced full-time domain inversion algorithm, utilizing the overlapping sliding window method. An array of three evenly spaced sensors is used for TPS monitoring. Notably, the inversion approach eliminates the need for prior knowledge of the TPS’s thermal parameters. It exhibits remarkable practicality with low-frequency sampling requirements (1 Hz) and robust noise resistance. Through numerical simulations and a quartz lamp side heating experiment, it is demonstrated that the window size and data noise have great influence on the temperature reconstruction accuracy, but the window slip step has little influence. The mean relative error of the inversion temperature decreases exponentially as the window size increases, and the optimal window duration is equal to the thermal hysteresis time. The study investigates the impact of three noise filtering methods on the inversion accuracy, finding that the Savitzky-Golay filtering significantly enhances measurement precision, reducing mean relative error from 18.4% to 6.7%. These results highlight the potential of the proposed real-time sensor method for practical engineering applications, offering a reliable and efficient solution for real-time TPS temperature monitoring.

Physics-informed neural networks (PINNs) often struggle to balance multiple loss terms in thermally coupled multiphysics problems. We propose Cooperative Soft-Hard PINNs (s-hPINN/s-HB-PINN), which apply soft constraints to fields with Neumann conditions while enforcing hard constraints on others to balance exact boundary enforcement with training stability. Validated on thermoelasticity and thermal convection, our method reduces training time by approximately 56%. In thermal convection experiments, incorporating partial data further reduces velocity errors by up to 78% compared to standard PINNs. We subsequently assessed the framework’s robustness against varying relative Gaussian white noise levels and different data sampling locations. The result demonstrate that s-HB-PINN maintains high-fidelity predictions even under noise interference, consistently outperforming baseline methods. This confirms that the proposed collaborative strategy offers a superior trade-off between accuracy, efficiency, and robustness in complex multiphysics environments.

As a mesh-free solving paradigm, Physics-Informed Neural Networks (PINNs) demonstrate potential in both forward and inverse problems by embedding physical equations into the loss function. However, they still face challenges in capturing the spatiotemporal evolution of complex physical processes. When applied to time-dependent complex flows, such as high-Reynolds-number cylinder flow, they often rely on supervised data, which is frequently difficult to obtain accurately in practice. To address these issues, this paper proposes a novel unsupervised solving framework—the Adaptive Hard-Constraint Physics-Informed Neural Network (AHC-PINN). This method integrates an adaptive sampling mechanism based on partial differential equation residuals with a hard-constraint strategy. By dynamically evaluating the contribution of collocation points to the loss and incorporating analytically embedded boundary constraints, it directs the network training entirely toward solving the governing equations. Using two-dimensional unsteady cylinder flow as a validation case, experimental results show that AHC-PINN significantly improves the prediction accuracy of wake evolution under unsupervised conditions. Its performance surpasses that of traditional soft-constraint PINNs by an order of magnitude and is even superior to methods using sparse supervised data. Furthermore, through analysis of the PDE loss and gradient distribution, the study explicitly identifies the impact of large-gradient regions on PINN training stability and prediction accuracy, providing a basis for subsequent optimization.

Spectral interrogation of fiber Bragg gratings (FBGs) in the ~850 nm band remains relatively uncommon, largely due to the limited availability of commercial instruments and the restricted applicability of conventional interrogation schemes in this wavelength range. This work presents a practical and high-precision wavelength demodulation method for 850 nm FBG sensing based on an imaging Charge-Coupled Device (CCD) spectrometer. A Czerny–Turner (C–T) optical configuration is employed for spatial spectral dispersion, and the optical system is theoretically analyzed and optimized using ZEMAX to balance spectral resolution, optical throughput, and compactness. A polynomial wavelength–pixel calibration model is established, and Gaussian fitting is adopted for robust peak-position extraction under multimode fiber conditions. Experimental validation is carried out using four serially cascaded FBGs distributed over 830–880 nm. The wavelength–pixel calibration yields an RMS residual of 0.46 nm. Within a strain range of 0–2000 με, the average wavelength demodulation bias of a single FBG is 6.8 pm, with a wavelength demodulation RMS error of 86.9 pm and a measured strain sensitivity of 0.72 pm/με. The results demonstrate that the proposed CCD-based imaging interrogation scheme is feasible for 850 nm FBG sensing and enables accurate wavelength demodulation in this relatively underexplored band. Since the system is implemented using standard off-the-shelf components, it also provides a practical technical route for the deployment of FBG sensing systems in engineering applications.