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Keywords = least squares (LS)

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17 pages, 5440 KiB  
Article
An Improved Shuffled Frog Leaping Algorithm for Electrical Resistivity Tomography Inversion
by Fuyu Jiang, Likun Gao, Run Han, Minghui Dai, Haijun Chen, Jiong Ni, Yao Lei, Xiaoyu Xu and Sheng Zhang
Appl. Sci. 2025, 15(15), 8527; https://doi.org/10.3390/app15158527 (registering DOI) - 31 Jul 2025
Viewed by 103
Abstract
In order to improve the inversion accuracy of electrical resistivity tomography (ERT) and overcome the limitations of traditional linear methods, this paper proposes an improved shuffled frog leaping algorithm (SFLA). First, an equilibrium grouping strategy is designed to balance the contribution weight of [...] Read more.
In order to improve the inversion accuracy of electrical resistivity tomography (ERT) and overcome the limitations of traditional linear methods, this paper proposes an improved shuffled frog leaping algorithm (SFLA). First, an equilibrium grouping strategy is designed to balance the contribution weight of each subgroup to the global optimal solution, suppressing the local optimum traps caused by the dominance of high-quality groups. Second, an adaptive movement operator is constructed to dynamically regulate the step size of the search, enhancing the guiding effect of the optimal solution. In synthetic data tests of three typical electrical models, including a high-resistivity anomaly with 5% random noise, a normal fault, and a reverse fault, the improved algorithm shows an approximately 2.3 times higher accuracy in boundary identification of the anomaly body compared to the least squares (LS) method and standard SFLA. Additionally, the root mean square error is reduced by 57%. In the engineering validation at the Baota Mountain mining area in Jurong, the improved SFLA inversion clearly reveals the undulating bedrock morphology. At a measuring point 55 m along the profile, the bedrock depth is 14.05 m (ZK3 verification value 12.0 m, error 17%), and at 96 m, the depth is 6.9 m (ZK2 verification value 6.7 m, error 3.0%). The characteristic of deeper bedrock to the south and shallower to the north is highly consistent with the terrain and drilling data (RMSE = 1.053). This algorithm provides reliable technical support for precise detection of complex geological structures using ERT. Full article
(This article belongs to the Section Earth Sciences)
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24 pages, 8255 KiB  
Article
Non-Periodic Reconstruction from Sub-Sampled Velocity Measurement Data Based on Data-Fusion Compressed Sensing
by Jun Hong, Ziyu Chen, Jiawei Lu and Gang Xiao
Fluids 2025, 10(8), 192; https://doi.org/10.3390/fluids10080192 - 26 Jul 2025
Viewed by 187
Abstract
Compressive sensing (CS) is capable of resolving high frequencies from subsampled data. However, it is challenging to apply CS in non-periodic flow fields with multiple frequencies. This study introduces a novel data fusion CS approach aimed at reconstructing temporally resolved flow fields from [...] Read more.
Compressive sensing (CS) is capable of resolving high frequencies from subsampled data. However, it is challenging to apply CS in non-periodic flow fields with multiple frequencies. This study introduces a novel data fusion CS approach aimed at reconstructing temporally resolved flow fields from subsampled particle image velocimetry (PIV) data, integrating constraints derived from a limited number of high-frequency pointwise measurements. The approach combines measurements from particle image velocimetry (PIV), which have high spatial resolution but low temporal resolution, and a few pointwise probes, which have high temporal resolution but low spatial resolution. In the proposed method, proper orthogonal decomposition (POD) is conducted first to the PIV data, thus acquiring spatial modes and low-temporally resolved coefficients. To reconstruct the non-periodic and multiple-frequency coefficients from the PIV data, the traditional CS yields strong high-frequency noise. In this regard, the coefficients obtained from the pointwise measurements using least square (LS) regression can serve as a reciprocal space to suppress the high-frequency noise in the CS reconstruction. Using relaxation factors, the results from LS regression apply the upper and lower boundaries for the CS. By fusing the pointwise measurement and PIV data, the reconstruction performance can be significantly improved. To verify the performance, non-periodic and multiple frequency flow fields in the wake of two cylinders with different diameters are used. Compared to the ground truth, CS and LS reconstruction give an error of about 7% and 13%, respectively. On the other hand, the data fusion CS only has an error of about 2%. The dependency of this method on the number of pointwise probes is also examined. Full article
(This article belongs to the Section Mathematical and Computational Fluid Mechanics)
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17 pages, 3698 KiB  
Article
A Novel Fault Diagnosis Method for Rolling Bearings Based on Spectral Kurtosis and LS-SVM
by Lianyou Lai, Weijian Xu and Zhongzhe Song
Electronics 2025, 14(14), 2790; https://doi.org/10.3390/electronics14142790 - 11 Jul 2025
Viewed by 291
Abstract
As a core component of machining tools and vehicles, the load-bearing and transmission performance of rolling bearings is directly related to product processing quality and driving safety, highlighting the critical importance of fault detection. To address the nonlinearity, non-stationary modulation, and low signal-to-noise [...] Read more.
As a core component of machining tools and vehicles, the load-bearing and transmission performance of rolling bearings is directly related to product processing quality and driving safety, highlighting the critical importance of fault detection. To address the nonlinearity, non-stationary modulation, and low signal-to-noise ratio (SNR) observed in bearing vibration signals, we propose a fault feature extraction method based on spectral kurtosis and Hilbert envelope demodulation. First, spectral kurtosis is employed to determine the center frequency and bandwidth of the signal adaptively, and a bandpass filter is constructed to enhance the characteristic frequency components. Subsequently, the envelope spectrum is extracted through the Hilbert transform, allowing for the precise identification of fault characteristic frequencies. In the fault diagnosis stage, a multidimensional feature vector is formed by combining the kurtosis index with the amplitude ratios of inner/outer race characteristic frequencies, and fault pattern classification is accomplished using a Least-Squares Support Vector Machine (LS-SVM). To evaluate the effectiveness of the proposed method, experiments were conducted on the bearing datasets from Case Western Reserve University (CWRU) and the Machine Failure Prevention Technology (MFPT) Society. The experimental results demonstrate that the proposed method surpasses other comparative approaches, achieving identification accuracies of 95% and 100% for the CWRU and MFPT datasets, respectively. Full article
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31 pages, 853 KiB  
Article
Adversarial Sample Generation Method Based on Frequency Domain Transformation and Channel Awareness
by Yalin Gao, Dongwei Xu, Huiyan Zhu and Qi Xuan
Sensors 2025, 25(12), 3779; https://doi.org/10.3390/s25123779 - 17 Jun 2025
Viewed by 390
Abstract
In OFDM wireless communication systems, low-resolution channel characteristics and noise interference pose significant challenges to accurate channel estimation. To solve these problems, we propose a super-resolution denoising residual network (SDRNet), which combines the advantages of the super-resolution convolutional neural network (SRCNN) and the [...] Read more.
In OFDM wireless communication systems, low-resolution channel characteristics and noise interference pose significant challenges to accurate channel estimation. To solve these problems, we propose a super-resolution denoising residual network (SDRNet), which combines the advantages of the super-resolution convolutional neural network (SRCNN) and the denoising convolutional neural network (DnCNN) to construct a pilot-based OFDM signal model, train SDRNet using OFDM pilot data containing Gaussian noise, and optimize its feature enhancement ability in frequency-selective fading channels. To further explore the role of channel estimation in communication security, we propose a frequency-domain adversarial attack method based on SDRNet output. This method first converts the time-domain signal to the frequency domain by using the Fourier transform and then applies Gaussian noise and selective masking. By integrating the channel gradient information, the adversarial perturbation we generated significantly improves the attack success rate compared with the non-channel awareness method. The experimental results show that SDRNet is superior to traditional algorithms (such as the least square method, minimum mean square error estimation, etc.) in both mean square error and bit error rate. Furthermore, the adversarial samples optimized through channel awareness frequency-domain masking exhibit stronger attack performance, confirming that accurate channel estimation can not only enhance communication reliability but also provide key guidance for adversarial perturbation. The experimental results show that under the same noise conditions, the MSE of SDRNet is significantly lower than that of LS and MMSE. The bit error rate is lower than 0.01 when the signal-to-noise ratio is 10 dB, which is significantly better than the traditional algorithm. The attack success rate of the proposed adversarial attack method reached 79.9%, which was 16.3% higher than that of the non-channel aware method, verifying the key role of accurate channel estimation in enhancing the effectiveness of the attack. Full article
(This article belongs to the Section Communications)
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19 pages, 2053 KiB  
Article
Selecting the Optimal Calculation Method and Chemical Reagents in Surface Energy Tests of Asphalt Materials
by Longchang Niu, Chongzhi Tu and Gongying Ding
Materials 2025, 18(12), 2833; https://doi.org/10.3390/ma18122833 - 16 Jun 2025
Viewed by 273
Abstract
In surface energy tests of asphalt materials, the inaccuracy of the calculation method (e.g., least squares (LS)) and the arbitrary selection of chemical reagent combinations lead to unstable results, threatening the quantitative evaluation of asphalt–aggregate adhesion durability. This study addresses these two scientific [...] Read more.
In surface energy tests of asphalt materials, the inaccuracy of the calculation method (e.g., least squares (LS)) and the arbitrary selection of chemical reagent combinations lead to unstable results, threatening the quantitative evaluation of asphalt–aggregate adhesion durability. This study addresses these two scientific deficiencies with the following findings: (1) when simultaneous equations are used to calculate the asphalt surface energy parameters, the total least squares method should be used instead of the classical least squares method to reduce the fitting error; (2) the selection of the reagent combination should be based on which one is the most rational in terms of the physical characterization, leap degree, abnormal values, and other requirements, and the reagent combination with the fewest abnormal values should be chosen as the best scheme. The results show that (1) compared with the classical least squares method, the total least squares method reduces the fitting error between the calculated and real values of asphalt surface energy parameters and improves the accuracy and stability of the calculation results; (2) the best reagent combination scheme is WFSD (distilled water + formamide + dimethyl sulfoxide + diiodomethane). The calculated values of asphalt surface energy parameters were more accurate and reasonable, and the calculation results had no abnormal values. Compared with WFEG (distilled water + formamide + ethylene glycol + glycerol), the error rate of the reagent combination scheme WFSD in calculating the total surface energy of two kinds of asphalt was reduced by 17.71% and 64.80%, respectively. These findings establish a reliable framework for the accurate quantification of surface energy, addressing the critical issue of reagent-dependent variability in the results and strengthening the scientific basis for evaluating the durability of asphalt pavement. Full article
(This article belongs to the Section Construction and Building Materials)
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15 pages, 12526 KiB  
Article
Research on Registration Methods for Coupled Errors in Maneuvering Platforms
by Qiang Li, Ruidong Liu, Yalei Liu and Zhenzhong Wei
Entropy 2025, 27(6), 607; https://doi.org/10.3390/e27060607 - 6 Jun 2025
Viewed by 330
Abstract
The performance limitations of single-sensor systems in target tracking have led to the widespread adoption of multi-sensor fusion, which improves accuracy through information complementarity and redundancy. However, on mobile platforms, dynamic changes in sensor attitude and position introduce coupled measurement and attitude errors, [...] Read more.
The performance limitations of single-sensor systems in target tracking have led to the widespread adoption of multi-sensor fusion, which improves accuracy through information complementarity and redundancy. However, on mobile platforms, dynamic changes in sensor attitude and position introduce coupled measurement and attitude errors, making accurate sensor registration particularly challenging. Most existing methods either treat these errors independently or rely on simplified assumptions, which limit their effectiveness in dynamic environments. To address this, we propose a novel joint error estimation and registration method based on a pseudo-Kalman filter (PKF). The PKF constructs pseudo-measurements by subtracting outputs from multiple sensors, projecting them into a bias space that is independent of the target’s state. A decoupling mechanism is introduced to distinguish between measurement and attitude error components, enabling accurate joint estimation in real time. In the shipborne environment, simulation experiments on pitch, yaw, and roll motions were conducted using two sensors. This method was compared with least squares (LS), maximum likelihood (ML), and the standard method based on PKF. The results show that the method based on PKF has a lower root mean square error (RMSE), a faster convergence speed, and better estimation accuracy and robustness. The proposed approach provides a practical and scalable solution for sensor registration in dynamic environments, particularly in maritime or aerial applications where coupled errors are prevalent. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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20 pages, 6462 KiB  
Article
Thrust Allocation Control of an Underwater Vehicle with a Redundant Thruster Configuration
by Liping Deng and Jianguo Tao
Mathematics 2025, 13(11), 1766; https://doi.org/10.3390/math13111766 - 26 May 2025
Viewed by 572
Abstract
This paper presents a fault-tolerant thruster configuration scheme and a thrust control allocation strategy for an underwater vehicle. First, to accommodate the vehicle’s flexible spatial motion capabilities and address potential thruster failures, an 8-thruster vector arrangement is designed, and the impact of thruster [...] Read more.
This paper presents a fault-tolerant thruster configuration scheme and a thrust control allocation strategy for an underwater vehicle. First, to accommodate the vehicle’s flexible spatial motion capabilities and address potential thruster failures, an 8-thruster vector arrangement is designed, and the impact of thruster failures on vehicle maneuverability is analyzed. Based on this configuration, a mathematical model of the vector propulsion system is then developed, establishing the relationship between the thrust generated by the individual thrusters and the virtual control forces applied to the vehicle’s 6 degrees of freedom (DOF). Subsequently, a thrust allocation strategy based on quadratic programming (QP) is proposed to optimize thrust allocation, enhancing energy efficiency while satisfying thrust saturation constraints. Finally, simulation results demonstrate that the proposed thruster configuration exhibits strong fault-tolerance. Moreover, compared to the least squares (LS) method based on the pseudo-inverse of the configuration matrix, the QP-based thrust allocation strategy achieves significantly better energy-saving performance. Full article
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24 pages, 6894 KiB  
Article
Early Yield Prediction of Oilseed Rape Using UAV-Based Hyperspectral Imaging Combined with Machine Learning Algorithms
by Hongyan Zhu, Chengzhi Lin, Zhihao Dong, Jun-Li Xu and Yong He
Agriculture 2025, 15(10), 1100; https://doi.org/10.3390/agriculture15101100 - 19 May 2025
Cited by 2 | Viewed by 585
Abstract
Oilseed rape yield critically reflects varietal superiority. Rapid field-scale estimation enables efficient high-throughput breeding. This study evaluates unmanned aerial vehicle (UAV) hyperspectral imagery’s potential for yield prediction at the pod stage by utilizing wavelength selection and vegetation indices. Meanwhile, optimized feature selection algorithms [...] Read more.
Oilseed rape yield critically reflects varietal superiority. Rapid field-scale estimation enables efficient high-throughput breeding. This study evaluates unmanned aerial vehicle (UAV) hyperspectral imagery’s potential for yield prediction at the pod stage by utilizing wavelength selection and vegetation indices. Meanwhile, optimized feature selection algorithms identified effective wavelengths (EWs) and vegetation indices (VIs) for yield estimation. The optimal yield estimation models based on EWs and VIs were established, respectively, by using multiple linear regression (MLR), partial least squares regression (PLSR), extreme learning machine (ELM), and a least squares support vector machine (LS-SVM). The main results were as follows: (i) The yield prediction of oilseed rape using EWs showed better prediction and robustness compared to the full-spectral model. In particular, the competitive adaptive reweighted sampling–extreme learning machine (CARS-ELM) model (Rpre = 0.8122, RMSEP = 170.4 kg/hm2) achieved the best prediction performance. (ii) The ELM model (Rpre = 0.7674 and RMSEP = 187.6 kg/hm2), using 14 combined VIs, showed excellent performance. These results indicate that the remote sensing image data obtained from the UAV hyperspectral remote sensing system can be used to enable the high-throughput acquisition of oilseed rape yield information in the field. This study provides technical guidance for the crop yield estimation and high-throughput detection of breeding information. Full article
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9 pages, 3167 KiB  
Communication
Filter-Assisted Self-Coherent Detection Field Recovery Scheme for Dual-Polarization Complex-Valued Double-Sideband Signals
by Jiahao Huo, Li Han, Peng Qin, Jianlong Tao, Haolin Bai and Xiaoying Zhang
Photonics 2025, 12(4), 343; https://doi.org/10.3390/photonics12040343 - 3 Apr 2025
Viewed by 457
Abstract
In this paper, we have proposed a filter-assisted self-coherent detection (FASCD) scheme that reconstructs the optical field of a dual-polarization complex-valued double-sideband (DP-CV-DSB) signal. At the receiver, the carrier is extracted using an optical bandpass filter (OBPF), and a pair of orthogonal carriers [...] Read more.
In this paper, we have proposed a filter-assisted self-coherent detection (FASCD) scheme that reconstructs the optical field of a dual-polarization complex-valued double-sideband (DP-CV-DSB) signal. At the receiver, the carrier is extracted using an optical bandpass filter (OBPF), and a pair of orthogonal carriers is constructed to achieve polarization-division multiplexing (PDM) by a Faraday rotator mirror (FRM). To address the issue of polarization crosstalk, channel estimation is performed using the least squares (LS) method, and the estimation results are further optimized through the intra-symbol frequency-domain averaging (ISFA) method. We demonstrate the system architecture and algorithms by simulation on a 224 Gbit/s 16-ary quadrature amplitude modulation DSB-PDM-OFDM system. The system performance is improved by 1 dB using the ISFA method. Full article
(This article belongs to the Section Optical Communication and Network)
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20 pages, 3514 KiB  
Article
Optimization of a Time-of-Arrival-Ridge Estimation Iterative Model for Ultra-Wideband Positioning in a Long Linear Area
by Mengqian Li, Mingduo Li, Jinhua Wang, Aoze Duan, Haotian Sun and Qinggang Meng
Sensors 2025, 25(7), 2229; https://doi.org/10.3390/s25072229 - 2 Apr 2025
Cited by 1 | Viewed by 438
Abstract
Ultra-wideband (UWB) technology is widely used for high-precision indoor positioning due to its adaptability to various environments. However, in long linear areas, such as tunnels or corridors, the near-linear deployment of base stations caused by structural constraints significantly degrades UWB localization accuracy, rendering [...] Read more.
Ultra-wideband (UWB) technology is widely used for high-precision indoor positioning due to its adaptability to various environments. However, in long linear areas, such as tunnels or corridors, the near-linear deployment of base stations caused by structural constraints significantly degrades UWB localization accuracy, rendering conventional algorithms ineffective. To address this issue, this study proposes a high-precision UWB+TOA-R positioning algorithm that incorporates Ridge estimation as a constraint condition. The algorithm introduces equivalent weights to refine the iterative computation of Ridge estimation, establishing an iteratively computed TOA-RR solution model. Experiments were conducted in a long linear corridor to compare the performance of three UWB localization models: the TOA-Least Squares (TOA-LS) model, the TOA-Ridge estimation (TOA-R) model, and the proposed TOA-Ridge estimation iterative (TOA-RR) model. The results indicate that the TOA-LS model suffers from significant coordinate distortions due to abnormalities in the inverse matrix of the coefficient matrix, regardless of the initial tag coordinates. The TOA-R model demonstrates improved accuracy and stability, particularly in cases of significant initial deviations, but still exhibits residual errors. In contrast, the TOA-RR model achieves enhanced stability and accuracy, with a positioning error of approximately 0.5 m. This study resolves the challenge of inaccurate UWB localization in long linear areas, providing a robust solution for such environments. Full article
(This article belongs to the Section Navigation and Positioning)
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24 pages, 4972 KiB  
Article
Establishment and Solution Test of Wear Prediction Model Based on Particle Swarm Optimization Least Squares Support Vector Machine
by Xiao Huang, Yongguo Wang and Yuhui Mao
Machines 2025, 13(4), 290; https://doi.org/10.3390/machines13040290 - 31 Mar 2025
Cited by 1 | Viewed by 305
Abstract
Traditional tool wear identification methods are usually based on the framework of “feature extraction + machine learning”, but these methods often have problems of low efficiency and low recognition accuracy. To address these problems, this paper proposes a tool wear state identification model [...] Read more.
Traditional tool wear identification methods are usually based on the framework of “feature extraction + machine learning”, but these methods often have problems of low efficiency and low recognition accuracy. To address these problems, this paper proposes a tool wear state identification model based on particle swarm optimization (PSO) and least squares support vector machine (LS-SVM), namely the PSO-LS-SVM model. By integrating data collected by multiple sensors, key feature information reflecting the tool wear state is extracted; dimensionality reduction techniques such as principal component analysis (PCA) are used to optimize feature vectors to improve the distinguishability of features. The model parameters are optimized by the two-dimensional coordinates (c and g) of the particle swarm algorithm to adapt to the given training sample set. During the training process, the fitness of each particle is calculated and compared with its historical optimal fitness to update the optimal fitness of the particle. This process is iterated until the global optimal solution is found, thereby achieving accurate identification of the tool wear state. Experimental results show that the PSO-LS-SVM model shows high accuracy and good performance in tool wear state identification, which verifies the effectiveness of the algorithm in improving tool efficiency and extending tool life. The study is the first to combine PSO and LS-SVM for tool wear prediction in multi-sensor data fusion. This advanced recognition technology can significantly reduce the waste of resources caused by premature tool replacement, while improving the stability of the machining process and the consistency of the product. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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22 pages, 2984 KiB  
Article
Improved Low-Complexity, Pilot-Based Channel Estimation for Large Intelligent Surface Systems
by Ali Gashtasbi, Mário Marques da Silva and Rui Dinis
Appl. Sci. 2025, 15(7), 3743; https://doi.org/10.3390/app15073743 - 28 Mar 2025
Viewed by 758
Abstract
In Large Intelligent Surface (LIS) systems, achieving accurate channel estimation is essential for enhancing communication quality and system efficiency. The main focus of this study is on using the Least Squares (LS) method to estimate pilot-based channels. It also looks at more advanced [...] Read more.
In Large Intelligent Surface (LIS) systems, achieving accurate channel estimation is essential for enhancing communication quality and system efficiency. The main focus of this study is on using the Least Squares (LS) method to estimate pilot-based channels. It also looks at more advanced methods, like using low-density parity-check (LDPC) codes, antenna selection, and optimized pilot design, to make the method more accurate and effective. We employ orthogonal pilot sequences to reduce signal interference and improve pilot power to enhance estimation performance. Additionally, LDPC codes play a crucial role in eliminating noise and interference effects, thereby improving system reliability. We also propose selective configurations of LIS antennas to balance high performance with reduced computational costs. Collectively, these strategies lead to a significant reduction in the Bit Error Rate (BER) and a remarkable improvement in the overall system performance, offering a practical solution for complex LIS deployments. Full article
(This article belongs to the Special Issue Applications of Wireless and Mobile Communications)
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17 pages, 3957 KiB  
Technical Note
A VCA Combined MHSA-CNN for Aero-Engine Hot Jet Remote Sensing Mixed Spectral Feature Extraction
by Zhenping Kang, Yurong Liao, Xinyan Yang and Zhaoming Li
Remote Sens. 2025, 17(7), 1147; https://doi.org/10.3390/rs17071147 - 24 Mar 2025
Viewed by 382
Abstract
To address the challenges of spectral unmixing and feature extraction in the hot jet mixtures of two types of aero-engine hot jets, Fourier transform infrared spectrometry was employed to precisely measure these mixtures. The collected data encompassed the spectra of hot jets generated [...] Read more.
To address the challenges of spectral unmixing and feature extraction in the hot jet mixtures of two types of aero-engine hot jets, Fourier transform infrared spectrometry was employed to precisely measure these mixtures. The collected data encompassed the spectra of hot jets generated individually by the two distinct engine models, as well as those of the mutually mixed hot jets. In this paper, a mixed spectral unmixing algorithm based on VCA was put forward. Initially, the vertex component analysis (VCA) algorithm was utilized to decompose the mixed spectra. By comparing with the separately measured actual pure spectra, it was found that the mean RMSE of the hot jet pure spectra extracted by VCA for the two engines was 0.34846, and the mean SAM reached 0.00096, thus validating the effectiveness of the algorithm. Subsequently, the least squares (LS) algorithm was applied to ascertain the abundance values of the mixed spectra. Among the mixed samples, the average abundance values of the two pure spectra were 0.78 and 0.22, respectively. To further extract the spectral features after unmixing, an innovative one-dimensional convolutional multi-head self-attention mechanism neural network (MHSA-CNN) algorithm was devised in this study. This algorithm can accurately pinpoint the key wave crests of the features at 2282–2283 cm−1 and 2388–2389 cm−1. The research findings offer crucial technical backing for the intelligent fault diagnosis of aero-engines and contribute to enhancing the accuracy and reliability of engine operating condition monitoring. Full article
(This article belongs to the Special Issue Advancements in AI-Based Remote Sensing Object Detection)
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19 pages, 4427 KiB  
Article
Robust MPS-INS UKF Integration and SIR-Based Hyperparameter Estimation in a 3D Flight Environment
by Juyoung Seo, Dongha Kwon, Byungjin Lee and Sangkyung Sung
Aerospace 2025, 12(3), 228; https://doi.org/10.3390/aerospace12030228 - 11 Mar 2025
Viewed by 646
Abstract
This study introduces a pose estimation algorithm integrating an Inertial Navigation System (INS) with an Alternating Current (AC) magnetic field-based navigation system, referred to as the Magnetic Positioning System (MPS), evaluated using a 6 Degrees of Freedom (DoF) drone. The study addresses significant [...] Read more.
This study introduces a pose estimation algorithm integrating an Inertial Navigation System (INS) with an Alternating Current (AC) magnetic field-based navigation system, referred to as the Magnetic Positioning System (MPS), evaluated using a 6 Degrees of Freedom (DoF) drone. The study addresses significant challenges such as the magnetic vector distortions and model uncertainties caused by motor noise, which degrade attitude estimation and limit the effectiveness of traditional Extended Kalman Filter (EKF)-based fusion methods. To mitigate these issues, a Tightly Coupled Unscented Kalman Filter (TC UKF) was developed to enhance robustness and navigation accuracy in dynamic environments. The proposed Unscented Kalman Filter (UKF) demonstrated a superior attitude estimation performance within a 6 m coil spacing area, outperforming both the MPS 3D LS (Least Squares) and EKF-based approaches. Furthermore, hyperparameters such as alpha, beta, and kappa were optimized using the Sequential Importance Resampling (SIR) process of the Particle Filter. This adaptive hyperparameter adjustment achieved improved navigation results compared to the default UKF settings, particularly in environments with high model uncertainty. Full article
(This article belongs to the Special Issue Advanced GNC Solutions for VTOL Systems)
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21 pages, 1452 KiB  
Article
Estimation of Biresponse Semiparametric Regression Model for Longitudinal Data Using Local Polynomial Kernel Estimator
by Tiani Wahyu Utami, Nur Chamidah, Toha Saifudin, Budi Lestari and Dursun Aydin
Symmetry 2025, 17(3), 392; https://doi.org/10.3390/sym17030392 - 4 Mar 2025
Cited by 2 | Viewed by 938
Abstract
When handling longitudinal data in regression models, we often encounter problems involving two interrelated response variables. These response variables may display an unknown curve shape in their relationship with one predictor variable, referred to as the nonparametric component, while maintaining a linear relationship [...] Read more.
When handling longitudinal data in regression models, we often encounter problems involving two interrelated response variables. These response variables may display an unknown curve shape in their relationship with one predictor variable, referred to as the nonparametric component, while maintaining a linear relationship with other predictor variables, referred to as the parametric component. In such cases, a Biresponse Semiparametric Regression (BSR) approach is a suitable solution. This research aims to estimate the BSR model for longitudinal data using the Local Polynomial Kernel (LPK) estimator by considering a symmetrical variance–covariance matrix estimate validated on simulation data and apply it to a real dataset of Dengue Hemorrhagic Fever (DHF) disease. The parameter estimation method used is a combination of Least Squares (LS) and Weighted Least Squares (WLS). For determining the optimal bandwidth, we use a Generalized Cross–Validation (GCV) method. The simulation study results indicate that with kernel weighting, employing weights derived from the inverse of the variance–covariance matrix significantly enhances the estimation accuracy of the BSR model. In addition, the results of the estimation for modeling the DHF disease, where platelets and hematocrit are response variables, and hemoglobin and examination time are predictor variables, produced an R-Square value of 92.8%. Full article
(This article belongs to the Section Mathematics)
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