Accurate ranging and real-time temperature monitoring are essential for metrology and safety in electrical conduit applications. This paper proposes an acoustic time-of-flight (TOF) estimation method based on the digital lock-in filtering (DLF) technique for conduit ranging and thermometry. The method establishes the relationship between the frequency and the time domain by applying a linear frequency modulated Chirp signal as the sound source and using the DLF technique to extract the first harmonic of the characteristic frequencies of the transmitted and received signals. Acoustic TOF estimation in the conduit is then achieved by calculating the mathematical expectation of the time difference between each characteristic frequency in the time-frequency relationship of the two signals. The experimental results with enhanced noise interference on different conduit lengths and various temperature conditions, proved that the proposed DLF method can establish a robust linear time-frequency relationship according to the characteristics of the Chirp signal, and the measurement accuracy of TOF has also been confirmed. Compared to the conventional method, the DLF method provides the lowest absolute error and standard deviation for both distance and temperature measurements with an enhanced robustness.

A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10⁻¹⁷ for arbitrary α_L/α_G ratios. In particular, the accuracy reaches an astonishing 10⁻³⁴ (quadruple precision) in the domain 0 ≤ α_L/α_G ≤ 0.2371 ∪ α_L/α_G ≥ 33.8786.

Data generated during the shutdown or start-up processes of wind turbines, particularly in complex wind conditions such as offshore environments, often accumulate in the low-wind-speed region, leading to reduced multivariate power estimation accuracy. Therefore, developing efficient filtering methods is crucial to improving data quality and model performance. This paper proposes a novel filtering method that integrates the control strategies of variable-speed, variable-pitch wind turbines, such as maximum-power point tracking (MPPT) and pitch angle control, with statistical distribution characteristics derived from supervisory control and data acquisition (SCADA). First, thresholds for pitch angle and rotor speed are determined based on SCADA data distribution, and the filtering effect is visualized. Subsequently, a sliding window technique is employed for the secondary confirmation of potential outliers, enabling further anomaly detection (AD). Finally, the performance of the power estimation model is validated using two wind turbine datasets and two machine learning algorithms, with results compared with and without filtering. The results demonstrate that the proposed filtering method significantly enhances the accuracy of multivariate power estimation, proving its effectiveness in improving data quality for wind turbines operating in diverse and complex environments.

A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument y ≤ 0.1. Error analysis and run-time tests in double-precision arithmetic reveals that in the real and imaginary parts, the proposed algorithm provides an average accuracy exceeding 10⁻¹⁵ and 10⁻¹⁶, respectively, and the calculation speed is as fast as that reported in recent publications. An optimized MATLAB code providing rapid computation with high accuracy is presented.

The increasing deployment of turbines installed offshore is critical for sustainable energy development, yet accurate performance assessment remains challenging due to complex environmental influences, diverse turbine control strategies, and issues with data quality. Traditional performance metrics and power curve models often fail to provide reliable cross-turbine comparisons because they neglect multivariate environmental factors and turbine-specific biases. To address these limitations, this study develops a novel multivariate environmental factor-driven power assessment framework employing segmented long short-term memory (LSTM) models. A hybrid data cleaning method, combining bidirectional quartile analysis with the power curtailment detection, is proposed to effectively identify outliers, including subtle anomalies within typical data ranges. Samples are segmented based on rated wind speed to reflect differences in control strategies, and turbine-specific operational parameters are excluded to ensure unbiased comparisons among turbines. The proposed method achieves substantial improvements in predictive accuracy, with decreases of 9.39% in mean absolute error (MAE) and 11.75% in root mean square error (RMSE), compared to conventional binning approaches. When applied to three 5.5 MW offshore wind turbines, the proposed method reveals significant differences among the units. Turbine A demonstrates the highest performance, while turbines B and C exhibit reductions of 14.35% and 8.29%, respectively. Operational state analysis shows that turbine B experiences substantially longer maintenance durations, indicating severe faults that adversely affect its operational reliability and power output. These findings provide valuable insights for maintenance prioritization and performance benchmarking among wind turbines.