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Keywords = Monte-Carlo method

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38 pages, 2692 KB  
Article
Observability- and Identifiability-Guided Sensor-Set Design for Digital-Twin-Assisted Consolidated Bioprocessing
by Mark Korang Yeboah, Nana Yaw Asiedu and Ahmad Addo
Sensors 2026, 26(12), 3948; https://doi.org/10.3390/s26123948 (registering DOI) - 21 Jun 2026
Abstract
Consolidated bioprocessing (CBP) is difficult to monitor because enzyme production, lignocellulose degradation, sugar release, and fermentation occur simultaneously under sparse measurement, feedstock variability, and plant–model mismatch conditions. This study proposes a computational sensor-set design framework for digital-twin-assisted CBP monitoring. A five-state virtual plant, [...] Read more.
Consolidated bioprocessing (CBP) is difficult to monitor because enzyme production, lignocellulose degradation, sugar release, and fermentation occur simultaneously under sparse measurement, feedstock variability, and plant–model mismatch conditions. This study proposes a computational sensor-set design framework for digital-twin-assisted CBP monitoring. A five-state virtual plant, consisting of active biomass, cellulolytic enzyme activity, residual insoluble substrate, soluble sugar, and ethanol, was used to evaluate all 16 ethanol-mandatory measurement packages formed from ethanol, sugar, biomass, enzyme, and residual-substrate proxy channels. Candidate sensor sets were assessed using finite-difference output sensitivities, Fisher-information-based state-observability and parameter-identifiability analyses, eigenvalue and parameter-correlation diagnostics, and paired Monte Carlo unscented Kalman filter soft-sensing reconstruction. Within the tested five-state virtual-plant benchmark and with the specified excitation schedule, noise assumptions, burden indices, and scoring objective, ethanol-only sensing provided the weakest support for state-aware CBP digital-twin reconstruction. At a 6h sampling interval, the state-observability log-pseudodeterminant increased from 4.18 with ethanol-only sensing to 8.56 after adding soluble sugar and to 16.42 with full-proxy monitoring. The ethanol–sugar–biomass–substrate package also gave strong reduced state-observability performance, with log-pseudodeterminants of 15.12, 13.76, and 12.51 at 6, 12, and 24h, respectively. Biomass and enzyme proxies contributed strongly to parameter learning, and the ethanol–sugar–biomass–enzyme package gave the strongest active parameter-identifiability performance, with log-pseudodeterminants of 10.82, 9.06, and 6.67 at 6, 12, and 24h, respectively. In the paired soft-sensing analysis, full-proxy monitoring reduced the mean latent-state RMSE from 1.1899 to 0.3756, followed by ethanol–biomass–enzyme–substrate with 0.3843 and ethanol–sugar–biomass–substrate with 0.4121. The primary aggregate ranking identified ethanol–sugar–biomass–substrate as the best overall package, with a sensor-value score of 0.8432 and a burden index of 7.0, followed by full-proxy monitoring with a score of 0.8173 and a burden index of 10.0. Robustness tests showed that ethanol–sugar–biomass–substrate remained top-ranked under uniform noise scaling, full UKF missingness, delay and bias stress test conditions, most scoring-weight scenarios, and all tested sensor-specific burden workflows. Full-proxy monitoring remained a close competitor under independent sensor-specific noise variation conditions and became top-ranked for some alternative operating trajectories. The proposed framework provides a simulation-based method for prioritizing informative measurement packages before implementing CBP digital twins in laboratory and pilot-plant settings. Full article
(This article belongs to the Special Issue Soft Sensors and Sensing Techniques (2nd Edition))
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26 pages, 30333 KB  
Article
Interpretable Attribution of Sentinel-1/2 and Environmental Covariates for Compositionally Closed Soil Mapping and Uncertainty Quantification
by Wenhao Wang, Chao Dong, Bin Zhao, Yanling Li, Zhuoran Wang and Chunyan Chang
Remote Sens. 2026, 18(12), 2051; https://doi.org/10.3390/rs18122051 (registering DOI) - 21 Jun 2026
Abstract
Soil particle size fractions (PSFs)—sand, silt, and clay—are fundamental determinants of soil hydrological behavior, nutrient retention, and erodibility, yet their spatial prediction remains challenging due to the compositional nature of the data, unquantified prediction uncertainty, and limited interpretability of machine learning models. This [...] Read more.
Soil particle size fractions (PSFs)—sand, silt, and clay—are fundamental determinants of soil hydrological behavior, nutrient retention, and erodibility, yet their spatial prediction remains challenging due to the compositional nature of the data, unquantified prediction uncertainty, and limited interpretability of machine learning models. This study develops an integrated compositional mapping framework incorporating multi-source Sentinel-1/2 and topographic covariates, coupling the isometric log-ratio (ILR) transformation with Quantile Regression Forests (QRFs), a Monte Carlo simulation (MCS)-based latent-to-physical space uncertainty propagation strategy, and a Wrapper-SHAP attribution method to jointly address these challenges. The framework was evaluated across regional croplands in the central Shandong mountain-hilly region of China, using an elevation-stratified spatial cross-validation. Validations achieved R2 values of 0.72, 0.61, and 0.59 for sand, silt, and clay, respectively, and a global Aitchison distance of 0.34. Critically, the MCS error propagation strategy effectively compensated for the probability distribution shift introduced by non-linear ILR back-transformation. This ensured that all predicted compositions strictly satisfied compositional closure and the [0, 100%] constraint, while aligning the prediction interval coverage probability (PICP) of each fraction closely with the 90% nominal level. Wrapper-SHAP overcame direct attribution limitations in compositional models, revealing the predictive associations of these multi-source covariates: high remote sensing-derived Bare Soil Index (BSI) and Moisture Stress Index (MSI) values primarily exhibited strong predictive associations with sand enrichment, whereas their lower values, combined with elevated Normalized Difference Moisture Index (NDMI), Enhanced Vegetation Index (EVI), and anthropogenic indicators, favored silt and clay accumulation. The proposed framework provides a transferable methodological reference for remote sensing-integrated compositional soil mapping with reliable uncertainty estimates and interpretable driver identification at regional scales. Full article
14 pages, 2041 KB  
Article
Research on Detection Performance of NaI(Tl) Detector Based on Monte Carlo Method
by Qingbo Du, Yapeng Yang, Xiaoyu Zhao, Qi Lv, Yuyao Tang, Jiapeng He, Yier Liu and Guoqiang Li
Sensors 2026, 26(12), 3913; https://doi.org/10.3390/s26123913 (registering DOI) - 19 Jun 2026
Viewed by 64
Abstract
The NaI(TI) detector is highly favored in gamma radiation detection and widely applied in fields such as environmental radiation monitoring, nuclear medicine, and laboratory gamma-ray spectroscopy. Its detection performance determines the results of quantitative gamma-ray detection, making it a crucial indicator in detector [...] Read more.
The NaI(TI) detector is highly favored in gamma radiation detection and widely applied in fields such as environmental radiation monitoring, nuclear medicine, and laboratory gamma-ray spectroscopy. Its detection performance determines the results of quantitative gamma-ray detection, making it a crucial indicator in detector design and development. This study employs the Monte Carlo method and utilizes TopMC 1.0 software to establish a NaI(TI) detector model. First, the effects of crystal size, ray energy, cladding thickness, and distance on the detector’s detection efficiency were investigated. Subsequently, the energy resolution and peak-to-total ratio of the detector were simulated and calculated, with comparisons made to experimental values. The results indicate that all three detection efficiencies of the NaI(TI) detector are positively correlated with crystal size and exhibit an initial increase followed by a decrease with rising gamma-ray energy. Both the absolute detection efficiency and full-energy peak detection efficiency first increase and then decrease with increasing cladding thickness, while showing a negative correlation with detection distance. The intrinsic detection efficiency is almost unaffected by cladding thickness and initially rises before declining with increasing detection distance. The simulated values of energy resolution closely match experimental values, improving with higher gamma-ray energy. The deviation between simulated and experimental values for different source peak-to-total ratios remains within 6.25%, verifying the model’s reliability and the accuracy of simulation data. These findings provide valuable references and guidance for optimizing detection performance, conducting source-free efficiency calibration, and structural design of NaI(TI) detectors. Full article
(This article belongs to the Special Issue Nuclear Radiation Detectors and Sensors)
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26 pages, 1991 KB  
Article
The Maximal Almost Sure Lyapunov Exponent of Three-Dimensional Linear Stratonovich Stochastic Differential Equations
by Jianyue Su and Ziying He
Mathematics 2026, 14(12), 2207; https://doi.org/10.3390/math14122207 (registering DOI) - 19 Jun 2026
Viewed by 165
Abstract
The sign of the maximal almost sure Lyapunov exponent determines the stability of stochastic systems, while its numerical computation for three-dimensional linear Stratonovich stochastic differential equations remains challenging due to the failure of classical two-dimensional strategies. The spherical angular motion of 3D systems [...] Read more.
The sign of the maximal almost sure Lyapunov exponent determines the stability of stochastic systems, while its numerical computation for three-dimensional linear Stratonovich stochastic differential equations remains challenging due to the failure of classical two-dimensional strategies. The spherical angular motion of 3D systems produces a Fokker–Planck equation with intractable mixed partial derivatives, preventing conventional analytical solutions. This paper develops a unified computational framework for three-dimensional linear Stratonovich stochastic systems using analytical derivation for degenerate cases and physics-informed neural network (PINN) approximation for general non-degenerate scenarios. For degenerate systems, we reduce the coefficient matrix to a lower triangular form via orthogonal transformation and establish tight upper bounds based on the logarithmic growth property of the Wiener process, yielding closed-form expressions for the maximal almost sure Lyapunov exponent under all parameter sign configurations. For non-degenerate systems, we reformulate the Fokker–Planck equation in spherical coordinates and construct a customized PINN with trigonometric encoding to enforce periodic boundary conditions. The network is trained by joint loss functions of equation residuals, boundary constraints and normalization consistency, and the converged stationary density is substituted into the Furstenberg–Khasminskii formula to calculate the exponent via Gauss–Legendre quadrature. Monte Carlo simulations confirm the accuracy and robustness of the proposed method, which reliably identifies the sign of the maximal almost sure Lyapunov exponent even in near-critical regimes. Numerical experiments on a 3D stochastic Hopf bifurcation model show that noise negatively shifts the bifurcation point, with the offset linearly proportional to the squared noise intensity. This work extends Lyapunov stability analysis from two-dimensional to three-dimensional linear Stratonovich stochastic systems, offering an effective tool for stability evaluation of general three-dimensional stochastic dynamical models. Full article
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37 pages, 21335 KB  
Article
A New Reparameterized Weibull-Type Distribution for Asymmetric Lifetime Data: Inference, Simulation, and Applications
by Ahmed Elshahhat, Heba S. Mohammed, Osama E. Abo-Kasem and Asmaa Abdel-Hakim
Symmetry 2026, 18(6), 1057; https://doi.org/10.3390/sym18061057 - 19 Jun 2026
Viewed by 64
Abstract
This article presents a comprehensive inferential and applied investigation of the newly reparameterized Z-Weibull (ZW) distribution, a flexible Weibull-type lifetime model capable of accommodating both bounded and unbounded support regimes as well as a wide variety of hazard rate shapes. Unified frequentist and [...] Read more.
This article presents a comprehensive inferential and applied investigation of the newly reparameterized Z-Weibull (ZW) distribution, a flexible Weibull-type lifetime model capable of accommodating both bounded and unbounded support regimes as well as a wide variety of hazard rate shapes. Unified frequentist and Bayesian inference procedures are developed for complete and censored samples using maximum likelihood, maximum product spacing, and Markov chain Monte Carlo methods. Theoretical properties of the estimators and their associated interval estimates are established, while extensive Monte Carlo simulations assess their finite-sample performance under diverse parameter configurations and censoring schemes. The results indicate that Bayesian spacing-based procedures generally provide more accurate estimation, lower bias, and improved interval performance than competing classical methods. Applications to biomedical survival and climatological datasets, together with comparisons against several Weibull-type and exponential-based competitors, demonstrate the superior flexibility and goodness-of-fit of the ZW model. These findings highlight the practical value of the reparameterized ZW distribution as a unified and effective tool for modeling complex lifetime and reliability data arising in survival, environmental, and engineering studies. Full article
20 pages, 386 KB  
Article
Classical Estimation Methods and Optimality of Sampling Plans Under Progressive Type-I Censoring Scheme with Application to Reliability Data
by Ahmed R. El-Saeed
Axioms 2026, 15(6), 459; https://doi.org/10.3390/axioms15060459 (registering DOI) - 18 Jun 2026
Viewed by 87
Abstract
In this paper, the maximum product spacing method of estimation has been investigated under progressive Type-I censoring scheme. This estimation method has not previously been considered in the life-testing literature, particularly under this censoring scheme. The optimality of the sampling plans under progressive [...] Read more.
In this paper, the maximum product spacing method of estimation has been investigated under progressive Type-I censoring scheme. This estimation method has not previously been considered in the life-testing literature, particularly under this censoring scheme. The optimality of the sampling plans under progressive Type-I censoring was studied using different criteria and proposed censoring plans. The applicability of the distribution was examined using the Chen distribution, which is capable of modeling various reliability behaviors. A Monte Carlo simulation was conducted to assess the efficiency of the maximum product spacing method and the optimality of the sampling plans. Finally, an engineering application was analyzed considering progressive Type-I censoring. Full article
(This article belongs to the Special Issue Recent Developments in Statistical Research)
18 pages, 4201 KB  
Article
A Multi-Modal AI System for Detecting Pedestrians Lying on the Road: Simulation-Based Safety and Injury Risk Analysis
by Nick Barua and Masahito Hitosugi
Vehicles 2026, 8(6), 136; https://doi.org/10.3390/vehicles8060136 - 18 Jun 2026
Viewed by 182
Abstract
Introduction: Pedestrians lying on the road—collapsed through medical emergency, intoxication, or displacement following a prior collision—represent a disproportionately lethal and underaddressed category in road traffic safety. Forensic database analyses derived from Japan’s national police records document a fatality rate of 33.0% for collisions [...] Read more.
Introduction: Pedestrians lying on the road—collapsed through medical emergency, intoxication, or displacement following a prior collision—represent a disproportionately lethal and underaddressed category in road traffic safety. Forensic database analyses derived from Japan’s national police records document a fatality rate of 33.0% for collisions involving pedestrians lying on the road, more than double the rate for upright pedestrian collisions. Standard Advanced Driver-Assistance Systems (ADAS) yield a True Positive Rate (TPR) of only 21.4% for detecting pedestrians lying on the road under night conditions—a classification gap of 73.3 percentage points. Methods: In simulation trials, we evaluated the Advanced Falling Object Detection System (AFODS—where “falling object” denotes the low-profile human form at road level, distinguishing the prone pedestrian from the upright postures addressed by conventional ADAS) on a composite dataset of 3200 annotated fall events and 12,000 negative samples (training/validation), with 320 independent controlled simulation trials used for performance evaluation, spanning real-world, forensic-reconstruction, and Total Human Body Model for Safety (THUMS)-validated synthetic scenarios. No physical prototype has been evaluated; all performance data are derived from simulation, and 37.5% of positive samples are synthetically generated. These simulation conditions represent a first feasibility demonstration pending real-world hardware validation. This paper introduces three original contributions absent from prior work: a three-stage quantitative injury-risk model, a formal ISO 26262 Hazard Analysis and Risk Assessment (HARA), and a medicolegal SHAP interpretability framework. The injury-risk model translated detection latency via impact velocity to Head Injury Criterion (HIC) and estimated fatal injury probability (AIS ≥ 5); these model outputs should be interpreted as exploratory estimates pending ATD validation. Reporting follows principles consistent with the TRIPOD statement. Results: Under clear daytime conditions, AFODS demonstrated a TPR of 98.2% (95% CI: 97.4–98.8%) in simulation, decreasing to 95.6% under night dry-road conditions and 89.4% under night rain. The system achieved an AUC of 0.981 and a mean end-to-end latency of 46.5 ms, representing a 76.8 percentage-point improvement in simulation over the monocular RGB baseline (p < 0.001). The injury-risk model projects a reduction in estimated fatal head injury probability from 66.2% (Monte Carlo mean) (no detection, 50 km/h full-speed impact) to 0.7% under AFODS worst-case night/rain conditions, and to ≈0% under clear daytime simulation conditions. Conclusions: A 73.3 percentage-point classification gap places pedestrians lying on the road outside the effective detection envelope of current ADAS, compounded by the systematic exclusion of non-upright postures from regulatory test protocols and benchmark datasets. AFODS supports proof-of-concept feasibility under simulation conditions. Three translational steps are required: prototype validation on real-world hardware using instrumented Anthropomorphic Test Devices (ATDs); prone-posture biomechanical injury modelling using HIC and BrIC criteria; and regulatory extension of pedestrian AEB test standards to non-upright scenarios. Full article
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25 pages, 13672 KB  
Article
Seismic Fragility Assessment of Reinforced Concrete Bridge Under Near-Fault Pulse-like Ground Motions Considering Structural Parameter Uncertainties
by Zekai Ma, Chao Yin, Jiagu Chen and Jiaxu Li
Coatings 2026, 16(6), 730; https://doi.org/10.3390/coatings16060730 (registering DOI) - 18 Jun 2026
Viewed by 75
Abstract
Near-fault pulse-like ground motions (NFPLGMs) impose concentrated energy demands that can severely damage bridges, yet their scarcity and the influence of structural parameter uncertainties are often neglected in seismic fragility assessments. This study proposed a synthesis method for NFPLGMs by superposing low-frequency pulse [...] Read more.
Near-fault pulse-like ground motions (NFPLGMs) impose concentrated energy demands that can severely damage bridges, yet their scarcity and the influence of structural parameter uncertainties are often neglected in seismic fragility assessments. This study proposed a synthesis method for NFPLGMs by superposing low-frequency pulse components (extracted via the Gabor wavelet transform and low-pass filtering) with high-frequency stochastic components based on an evolutionary power spectrum. A three-span reinforced concrete bridge was modeled in OpenSeesPy, and Incremental Dynamic Analysis (IDA), together with a quadratic response surface model, were used to plot seismic fragility curves. The damping ratio (ξ), elastic modulus of steel reinforcement (Es), yield strength of steel reinforcement (fy), diameter of longitudinal reinforcement (D), and peak ground acceleration (PGA) were treated as random variables. Sensitivity indices were computed using Monte Carlo sampling (n = 10,000). Results show that ξ most strongly affects the displacement ductility ratio of the bridge pier (ud) (variation of up to 32.6%), while Es dominates the shear deformation of the bridge bearing (d) (variation of up to 43.8%). Neglecting structural parameter uncertainties overestimates median PGA thresholds (mR) for different damage states by 1.5%–36.1%, and replacing NFPLGMs with ordinary ground motions overestimates seismic capacity by 1.7%–36.6%. The bridge bearing is consistently more vulnerable than the pier, with a collapse probability of 0.9566 at PGA = 1.0 g. These findings highlight the necessity of incorporating both NFPLGM characteristics and structural parameter uncertainties into bridge seismic fragility assessment. On the other hand, when seismic retrofitting of bridges is carried out using coating materials, priority should be given to more vulnerable components, such as bridge bearings, to improve the utilization efficiency of limited resources. Full article
(This article belongs to the Special Issue Surface Treatments and Coatings for Asphalt and Concrete)
23 pages, 5270 KB  
Article
Constraint-Adjusted Nonparametric Inference for Residual-Life Functionals Under Stochastic Precedence
by Abdulmajeed A. R. Alharbi
Mathematics 2026, 14(12), 2196; https://doi.org/10.3390/math14122196 - 18 Jun 2026
Viewed by 126
Abstract
Nonparametric inference for residual-life functionals is a fundamental problem in mathematical statistics, reliability theory, and survival analysis, particularly in studies with limited sample sizes where empirical plug-in estimators may exhibit substantial sampling variability. In comparative lifetime analysis, additional qualitative information is often available [...] Read more.
Nonparametric inference for residual-life functionals is a fundamental problem in mathematical statistics, reliability theory, and survival analysis, particularly in studies with limited sample sizes where empirical plug-in estimators may exhibit substantial sampling variability. In comparative lifetime analysis, additional qualitative information is often available regarding the relative behavior of two populations; however, such information is frequently too weak to justify classical stochastic dominance assumptions. Stochastic precedence provides a natural and interpretable framework for representing this partial ordering through a pairwise probabilistic constraint. This paper develops a constraint-adjusted nonparametric inference framework for estimating the mean residual life (MRL) and quantile residual life (QRL) functions under stochastic precedence information. The proposed approach replaces the ordinary empirical distribution function in standard residual-life plug-in estimators with a constraint-adjusted empirical distribution function that enforces the stochastic precedence relation at the sample level. The adjustment is governed by a data-driven scaling factor and is asymptotically negligible, thereby preserving the large-sample behavior of the ordinary empirical estimators while incorporating meaningful structural information in finite samples. Strong consistency of the proposed MRL and QRL estimators was established under mild regularity conditions. A Monte Carlo study based on Weibull and gamma lifetime models demonstrates that in the simulation settings considered, the proposed estimators provide improved finite-sample stability and generally achieve smaller mean squared errors than their ordinary empirical counterparts, especially for small and moderate sample sizes. The methodology is further illustrated using survival data from patients with squamous cell carcinoma of the oropharynx, highlighting its practical relevance in biomedical survival analysis. The proposed method offers a flexible, interpretable, and computationally simple framework for nonparametric inference with structured lifetime data under weak stochastic ordering information. Full article
(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)
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47 pages, 3664 KB  
Review
A Critical Review of Risk Assessment and Control Strategies for Ammonia Storage and Handling in Maritime Decarbonisation
by Zahra Barbari, Saleh S. Meibodi, Jinoop Arackal Narayanan, Soheil Mohtaram, Mohammad Ja’fari and Sina Rezaei Gomari
J. Mar. Sci. Eng. 2026, 14(12), 1124; https://doi.org/10.3390/jmse14121124 - 18 Jun 2026
Viewed by 241
Abstract
Ammonia is a promising zero-carbon energy carrier for maritime decarbonisation, but its deployment is limited by safety risks that are not adequately addressed by conventional marine fuel safety frameworks. This study critically reviews safety assessment, risk management and control strategies for ammonia storage [...] Read more.
Ammonia is a promising zero-carbon energy carrier for maritime decarbonisation, but its deployment is limited by safety risks that are not adequately addressed by conventional marine fuel safety frameworks. This study critically reviews safety assessment, risk management and control strategies for ammonia storage and handling in maritime applications using a PRISMA-informed literature synthesis. Evidence is analysed across hazard characterisation, storage configurations, transfer operations, risk assessment methods, mitigation barriers and regulatory frameworks. The review shows that ammonia safety is governed by coupled release–exposure–barrier interactions shaped by storage condition, tank configuration, pressure–temperature behaviour, material compatibility, transfer mode, ventilation, ship geometry and human intervention. Existing methods, including HAZID, HAZOP, risk matrices and QRA, support hazard screening and prioritisation, but remain limited in representing flashing two-phase releases, dense gas dispersion, confined-space accumulation, exposure duration, ventilation effectiveness and safeguard timing under maritime conditions. CFD, FTA, Bayesian approaches and Monte Carlo analysis offer higher analytical resolution, but their reliability is constrained by limited validation data, uncertain leak-frequency inputs and simplified assumptions for human exposure and emergency response. Effective risk control therefore requires a toxicity-centred barrier strategy linking containment integrity, ammonia-compatible materials, gas and process monitoring, emergency shutdown, ventilation, water-based mitigation, PPE, competency-based training and emergency planning. Current regulatory and classification guidance provides an essential foundation but remains fragmented and insufficiently aligned with ammonia-specific requirements for exposure modelling, safety-zone definition and approval pathways. This review contributes a maritime-specific synthesis of ammonia storage and handling safety by connecting hazard behaviour, storage design, transfer operations, risk assessment limitations, control-barrier logic and regulatory approval needs. The findings highlight the need for validated source-term models, full-scale release and dispersion data, exposure-based safety criteria and harmonised regulatory pathways to support the safe and scalable use of ammonia in maritime decarbonisation. Full article
(This article belongs to the Special Issue Alternative Fuels for Marine Engine Applications)
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35 pages, 14335 KB  
Article
Comprehensive Assessments of the Bilal Extended Model with Applications in Mechanical Engineering and Health Insurance
by Ahmed Elshahhat and Eslam Abdelhakim Seyam
Mathematics 2026, 14(12), 2176; https://doi.org/10.3390/math14122176 - 17 Jun 2026
Viewed by 84
Abstract
A recent generalized Bilal (G-Bilal) model demonstrates remarkable flexibility in capturing a wide spectrum of failure behaviors, including monotonic and non-monotonic (upside-down bathtub-shaped) hazard patterns, outperforming several existing models such as the Weibull, gamma, and exponential families. This paper develops several inferential frameworks [...] Read more.
A recent generalized Bilal (G-Bilal) model demonstrates remarkable flexibility in capturing a wide spectrum of failure behaviors, including monotonic and non-monotonic (upside-down bathtub-shaped) hazard patterns, outperforming several existing models such as the Weibull, gamma, and exponential families. This paper develops several inferential frameworks for different G-Bilal parameters of life using samples gathered by improved Type-II adaptive progressive censoring. This enhanced design ensures optimal control of test duration while maintaining high inferential precision. Expressions for the model parameters, reliability, and hazard rate functions are derived, followed by the development of maximum likelihood (ML) and maximum product of spacing (MPS) estimators with their asymptotic confidence intervals using the observed Fisher information with the delta approach. Furthermore, Bayesian estimators and two associated credible intervals are proposed under independent gamma priors and computed through Markov iterations, with both ML and MPS posteriors considered. Extensive Monte Carlo experiments confirm the consistency, robustness, and precision of the proposed estimators, with Bayesian spacing-based methods exhibiting superior accuracy and coverage. The model’s practical potential is further verified through two real applications: one involving mechanical system lifetimes and another analyzing health insurance premium data, representing physical and actuarial domains, respectively. Using the introduced censoring, the proposed G-Bilal model outperforms all competing models in terms of goodness-of-fit and reliability estimates in both cases. The results underscore the G-Bilal model’s adaptability, computational stability, and empirical superiority, establishing it as a powerful tool for modern reliability and actuarial risk assessments. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
37 pages, 2447 KB  
Article
A Comparative Study of Robust and Improved Shrinkage Estimators Under Multicollinearity and Outliers Using Multiple Performance Criteria with Application to Health Data
by Nusrat Yasmin, B. M. Golam Kibria and Zoran Bursac
Stats 2026, 9(3), 62; https://doi.org/10.3390/stats9030062 - 17 Jun 2026
Viewed by 89
Abstract
Multicollinearity reduces the reliability of ordinary least squares by increasing variances and creating unstable estimates. This issue has led to biased and penalized regression methods like ridge-, Liu- and Stein-type estimators. Here, we build existing ridge-type approaches by introducing improved ridge and Liu-type [...] Read more.
Multicollinearity reduces the reliability of ordinary least squares by increasing variances and creating unstable estimates. This issue has led to biased and penalized regression methods like ridge-, Liu- and Stein-type estimators. Here, we build existing ridge-type approaches by introducing improved ridge and Liu-type estimators, along with robust variants to handle outliers. We investigate their theoretical properties regarding bias, variance, and mean squared error. We also evaluate their performance through Monte Carlo simulations with different levels of multicollinearity and data contamination. By using several evaluation criteria, including mean squared error, akaike information criterion, mean absolute deviation, and mean absolute percentage error, along with an average-rank comparison framework applied here for the first time, we further validate our results with two health-related datasets. The findings show that the strong estimators provide more stable estimates and improved predictive performance, particularly when dealing with severe multicollinearity and outliers. Full article
21 pages, 1608 KB  
Article
Distributed Jamming Method for ASLC Systems Based on Random Phase Perturbation
by Liang Qi and Jianjiang Zhou
Sensors 2026, 26(12), 3857; https://doi.org/10.3390/s26123857 - 17 Jun 2026
Viewed by 229
Abstract
Adaptive Sidelobe Cancellation (ASLC) is a core technology for modern radar systems to suppress active sidelobe jamming. From the perspective of disrupting the ASLC system’s ability to stably track the jamming direction, this paper proposes a distributed jamming method based on random phase [...] Read more.
Adaptive Sidelobe Cancellation (ASLC) is a core technology for modern radar systems to suppress active sidelobe jamming. From the perspective of disrupting the ASLC system’s ability to stably track the jamming direction, this paper proposes a distributed jamming method based on random phase perturbation. The method employs two spatially separated jamming sources that simultaneously transmit coherent signals. By actively applying controllable random jumps to the relative phase between the two sources, the equivalent wavefront direction of the synthesized signal at the radar receiver changes rapidly, forming a non-stationary jamming that destroys the null-tracking capability of ASLC. An analytical model of the ASLC cancellation ratio (CR) under random phase perturbation is established, with a focus on analyzing the effects of time synchronization accuracy and phase synchronization accuracy on jamming performance. Monte Carlo simulation results show that the proposed method can reduce the average ASLC CR from 26.80 dB to 20.29 dB (a decrease of 6.51 dB). Under identical conditions, this performance is comparable to asynchronous blinking jamming while requiring no precise timing matching, and outperforms multi-source saturation jamming in resource efficiency (two vs. four jammers). This study provides promising simulation-level evidence for the effectiveness of the proposed jamming method. The quantitative results and sensitivity analyses offer a simulation-level theoretical reference for parameter design of distributed cooperative jamming. Further validation in semi-physical simulations or field trials is necessary before claiming engineering readiness. Full article
(This article belongs to the Section Radar Sensors)
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20 pages, 7195 KB  
Article
A Method for Propagating Uncertainty of LiDAR Measurements to QSM-Derived Tree Metrics
by Vincent B. Verhoeven, Eric Casella, Markku Åkerblom and Pasi Raumonen
Remote Sens. 2026, 18(12), 2005; https://doi.org/10.3390/rs18122005 - 16 Jun 2026
Viewed by 115
Abstract
Forests constitute a large part of the global vegetation biomass, and various ecological metrics such as biodiversity and carbon stock can be determined by scanning them using LiDAR. LiDAR data is, however, inherently uncertain due to the finite beamwidth, and this uncertainty is [...] Read more.
Forests constitute a large part of the global vegetation biomass, and various ecological metrics such as biodiversity and carbon stock can be determined by scanning them using LiDAR. LiDAR data is, however, inherently uncertain due to the finite beamwidth, and this uncertainty is propagated to any metrics derived from it. This study presents a methodology to propagate this uncertainty to tree metrics derived from quantitative structure models (QSMs), such as volume. First, the point cloud uncertainty is quantified using the laser beamwidth and an initial geometry estimate to create the so-called fuzzy cloud. This fuzzy cloud is then sampled iteratively using the Monte Carlo method until the variance estimate has converged. As a case study, we applied this method to three trees of varying size and present a selection of metrics for the trees as a whole, different branch orders and distributions along their heights. We show that the number of scanning locations has a large effect on both the volume and its uncertainty. We attained convergence at a 5% variance threshold within 30 iterations. Full article
(This article belongs to the Section Forest Remote Sensing)
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27 pages, 21143 KB  
Article
A Hybrid Machine Learning Method for Dynamic Monitoring of CO2 Sequestration Using Pulsed Neutron Logging
by Tianyang Jiao, Xiaying Li, Juntao Liu, Liyuan Sheng, Yixin Zhang, Bin Lei, Jiarong Guo, Fangyang Yao, Fujun Long, Di Wu, Haoyu Zhang, Xin Tong and Zhiyi Liu
Energies 2026, 19(12), 2848; https://doi.org/10.3390/en19122848 - 16 Jun 2026
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Abstract
This study proposes a hybrid machine learning model based on full-spectrum pulsed neutron logging data to address the monitoring challenges of Carbon Capture, Utilization, and Storage (CCUS) under complex geological conditions. Traditional interpretation models for sequestered CO2 saturation (e.g., macroscopic capture cross-section [...] Read more.
This study proposes a hybrid machine learning model based on full-spectrum pulsed neutron logging data to address the monitoring challenges of Carbon Capture, Utilization, and Storage (CCUS) under complex geological conditions. Traditional interpretation models for sequestered CO2 saturation (e.g., macroscopic capture cross-section model, characteristic peak count model, and ratio model) heavily rely on prior parameters such as porosity, formation water salinity, and lithology. Acquiring these parameters in real time during practical engineering is often costly and difficult. To reduce the rigid dependence of accurate CO2 saturation monitoring on complex prior parameters like porosity and salinity under heterogeneous geological settings, this research focuses on the Pearl River Mouth Basin, a core carbon sequestration target area in the Guangdong-Hong Kong-Macao Greater Bay Area, based on the evaluation results of offshore carbon sequestration macro-regions in China. Taking the primary reservoirs of the Enping and Wenchang Formations as typical geological prototypes, a high-fidelity, full-spectrum neutron–gamma response database was constructed using Monte Carlo simulations. Two machine learning strategies are proposed: a direct regression model (NMF+SVR) and a joint model (NMF+SVC/KMeans+SVR). Based on Monte Carlo simulated data, experimental results demonstrate that, compared with traditional petrophysical baseline models and simple machine learning models, the proposed joint learning method effectively reduces the dependence of CO2 saturation monitoring on lithology and porosity. Furthermore, it is proven that even with a single-detector tool configuration, the method exhibits high prediction accuracy under complex lithological conditions. Notably, the two-step joint model achieves a Root Mean Square Error (RMSE) as low as 4.200%, significantly outperforming traditional physics-based models and single machine learning models such as MLP and RF. This study provides a physically interpretable and accurate technical reference for applying machine learning to pulsed neutron-logging-based CO2 geological sequestration monitoring. Full article
(This article belongs to the Special Issue Advances in the Development of Geoenergy: 3rd Edition)
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