Early Fault Research Articles

The Uncertainty Evaluation of Determining the Trace H2S in SF6/N2 Insulating Gas Mixture by Cavity Ring-Down Spectroscopy

Abstract H2S is one of the most important characteristic components of sulfur hexafluoride gas insulated electrical equipment. The detection of trace H2S is of great significance for early fault diagnosis of such equipment. Based on the 1578 nm wavelength distributed feedback diode laser (DFB-DL), cavity ring-down spectroscopy (CRDS) can effectively measure the concentration of trace H2S in SF6/N2 gas mixtures. Starting from the principle of methodology, this article establishes a mathematical model for evaluating the measurement uncertainty of CRDS and analyzes its sources of uncertainty: gas constant R1 , temperature T, Avogadro constant NA , gas pressure p in the optical cavity, volume V of the optical cavity, speed c of light, the absorption cross-section parameter σ(ν) of H2S molecules in the laser frequency ν, the ring-down time τ with absorption sample H2S and the ring-down time τ0 without absorption sample. After evaluating the uncertainty components, it was found that the main component was σ(ν) and the secondary components were τ and τ0. The H2S content in the 80% SF6-20% N2 mixed gas measured is (7.64 ± 0.12) × 10−6 mol/mol.

Enhancing Predictive Maintenance in Contour Cutting Machines: A Similarity-Based Approach for Band Blade Remaining Useful Life Estimation and Early Fault Detection

Anticipating the Remaining Useful Life (RUL) of cutting tools is crucial for optimising operational efficiency, ensuring safety, and minimising maintenance costs. This paper addresses the unresolved challenge of unexpected band blade failures in contour cutting machines within the foam and plastic industry, where such failures disrupt production, lead to material wastage, and pose operational hazards. Band blades circulate continuously at very high speeds during operation, and no classic sensor technology can be applied to them. Any information required to estimate the condition of the band blades must be acquired externally. Using similarity-based prediction models, a strategy for estimating band blades' effective RUL is proposed. Historical failure data is systematically collected from a contour-cutting machine operating under various load conditions using multiple contact and non-contact sensors mounted on the machine. Features are extracted and processed from the mounted sensors in both time and frequency domains using classical condition monitoring techniques. The classification of damaged and undamaged states of the blade is performed using bagged decision trees, which consider predefined health levels of the band blade during test runs. Degradation trends are generated for a test set of blade failures, and a similarity model is trained on this data to determine the remaining life. Different features are selected based on their prognostic capabilities to optimise the proposed algorithm's performance. The developed model is tested on new data, demonstrating efficacy in predicting band blades' health status and RUL with good accuracy. This research contributes to cutting tool condition monitoring and predictive maintenance by offering a novel and reliable approach for early fault detection and estimation of the RUL of band blades in contour cutting machines, mitigating disruptions, reducing material wastage, and enhancing overall operational efficiency. The procedures are validated in situ with a latest generation's real contour-cutting machine.

An early-fault diagnostic method based on phase plane for lithium-ion batteries under complex operation conditions

Timely and accurate diagnosis of lithium-ion battery faults is crucial for ensuring the safety of electric vehicles. While incremental capacity (IC)-based diagnostic methods are effective, they can only be employed under charging conditions. To address this issue, a fault diagnostic method based on phase plane analysis is proposed to extend the application to various operating conditions. In a phase plane, the battery voltage is plotted on the x-axis, while the differential in voltage is plotted on the y-axis. During charging, diagnostic vectors indicating the occurrence and type of faults are extracted from the trajectories in the phase plane. Under complex operating conditions, early faults can be detected based on the morphological and scale deviation of the trajectories. Experimental results have shown that the proposed method can effectively detect minor faults. The fault detection rate and detection accuracy rate under charging conditions are 96.25 % and 97.73 %, respectively, which are 17.5 % and 8.54 % higher than those of the IC-based diagnostic method. Furthermore, the fault detection rate and accuracy rate under UDDS (Urban Dynamometer Driving Schedule) are 91.76 % and 97.23 %, respectively. Additionally, the diagnostic speed of the proposed method is twice as fast as that of the IC-based method.

Diagnosis of Rotor Component Shedding in Rotating Machinery: A Data-Driven Approach.

The potential for rotor component shedding in rotating machinery poses significant risks, necessitating the development of an early and precise fault diagnosis technique to prevent catastrophic failures and reduce maintenance costs. This study introduces a data-driven approach to detect rotor component shedding at its inception, thereby enhancing operational safety and minimizing downtime. Utilizing frequency analysis, this research identifies harmonic amplitudes within rotor vibration data as key indicators of impending faults. The methodology employs principal component analysis (PCA) to orthogonalize and reduce the dimensionality of vibration data from rotor sensors, followed by k-fold cross-validation to select a subset of significant features, ensuring the detection algorithm's robustness and generalizability. These features are then integrated into a linear discriminant analysis (LDA) model, which serves as the diagnostic engine to predict the probability of rotor component shedding. The efficacy of the approach is demonstrated through its application to 16 industrial compressors and turbines, proving its value in providing timely fault warnings and enhancing operational reliability.

Implementation and Possibilities of Fuzzy Logic for Optimal Operation and Maintenance of Marine Diesel Engines

This paper explores the implementation and possibilities of utilizing fuzzy logic theory for optimal operation and early fault detection in marine diesel engines. It emphasizes its role in managing the complexity and ambiguity inherent in engine performance and preventive maintenance. Preventive maintenance is crucial for ensuring the reliability and longevity of marine diesel engines. Implementing fuzzy logic control (FLC) systems can enhance the preventive maintenance strategies for these engines, leading to reduced downtime, lower maintenance costs, and improved overall performance. Through a comprehensive literature review and analysis of a case study, this paper demonstrates the adaptability, effectiveness, and transformative potential of fuzzy logic systems. Focusing on applications such as engine speed control, performance improvements, and early fault detection, the paper highlights the implementation of fuzzy logic for enhanced predictive capabilities. The study aims to offer a flexible approach to engine management through fuzzy logic, laying the way for significant improvement in optimal marine diesel engine operation.

Intelligent fault detection of photovoltaic panel using neural networks

This research primarily aims to leverage artificial neural network technology for diagnosing power output issues in photovoltaic (PV) panels stemming from fluctuations in solar irradiance and temperature. The proposed diagnostic approach relies on constructing a reference model that captures the expected normal operating behavior of the PV panel under fault-free conditions. This reference model is then compared against the actual power output, and the difference, known as the residual, is analyzed to detect potential faults. The neural network is trained using real-world data inputs like solar irradiance and temperature measurements, with the sole output being the power produced by the PV panel. Through training, the neural network learns to map the complex non-linear relationships between environmental inputs and expected power output, effectively modeling the PV system's intrinsic behavior under healthy conditions. Results demonstrate the neural network-based approach's remarkable ability to diagnose faults with high accuracy while avoiding potential non-linear complications. This intelligent monitoring system provides a reliable protocol for early fault detection through training on actual measurements, eliminating the need for complex mathematical models. Consequently, it streamlines the maintenance process by negating intricate procedures to identify PV panel issues. The neural network effectively learns the mapping between environmental conditions and expected power output through exposure to real-world data during training. By analyzing deviations from this learned mapping, represented by the residual signal, the approach can reliably detect anomalies indicative of faults or performance degradation in the PV system. This data-driven nature allows the system to adapt to site-specific characteristics and capture non-linear effects without explicit modeling.

Complex Segment Linkage Along the Sevier Normal Fault, Southwestern Utah

Abstract Major normal fault systems are composed of segments that link as displacement accumulates, with linkage zone characteristics that reveal fault zone evolution. The steeply west-dipping Sevier fault zone in southwestern Utah, displays a complex fault network that developed between two long (>10 km), en echelon segments near the town of Orderville. Geologic map data and cross-sections of the transfer zone between the Mt. Carmel segment in the south and the Spencer Bench segment in the north reveal more than ten normal faults and four relay ramps displaying a range of geometries, including two relay ramps that display ramp-parallel folds. We suggest that transfer zone deformation was initially dominated by faults subparallel to the primary segments with later cross-faults that hard-linked these faults across most of the transfer zone. When the transfer zone was a soft-linked system, a displacement deficit likely existed relative to fault segments to the north and south. This early fault configuration would have reduced the efficiency of slip propagation associated with major earthquakes (>M7.0). In contrast, the present-day transfer zone, with a complex but hard-linked fault network, shows displacements that transition smoothly from the higher displacement (~800 m) southern segment to the lower displacement (~400 m) northern segment. That transition, combined with extensional strain within the zone, suggests that the Orderville fault network would be unlikely to impede propagation associated with future major earthquakes. The kinematic model of fault evolution presented here has implications for those investigating geothermal energy potential, groundwater flow, natural gas and oil reservoirs, mineral deposit formation, or seismic hazards.

Outlier detection in temporal and spatial sequences via correlation analysis based on graph neural networks

Outlier detection is essential for identifying patterns that deviate from expected normal representations in data. Real-world challenges such as the lack of labeled data, noise, and high dimensionality significantly impact the effectiveness of existing methods. Understanding the temporal or spatial correlation of normal data is crucial for detecting or forecasting anomalous patterns. In this paper, we introduce UOSC-GNN, a novel Unsupervised Outlier detection architecture by Sequential Correlation analysis with Graph Neural Network. The architecture includes a deviation generation module to measure the variance between expected and actual states of sequential data. This module incorporates a Generic Feature Extraction component to extract intrinsic features from outliers and normal instances tailored to specific tasks, and an Expected State Estimator component based on Graph Neural Network to learn sequential patterns. To ensure the forecast of outliers with high confidence and improve alarm accuracy, an Outlier Probability Assessment module is introduced. This module combines a rule-based index derived from expert knowledge and a statistical index calculated based on generated deviations. Our method is evaluated on two real-world tasks: medical imaging analysis utilizing spatial-related data and early fault detection of instruments leveraging temporal-related data. The results show that our method triggers alarms about 70 min earlier than the best models on the run-to-failure bearing dataset and achieves an accuracy of 92.82% and a sensitivity of 88.51% on the wireless capsule endoscopy image dataset, outperforming traditional outlier detection algorithms consistently.

Wind turbine gearbox oil temperature feature extraction and condition monitoring based on energy flow

Supervisory Control and Data Acquisition (SCADA) data is widely used for wind turbine gearbox condition monitoring (WTGCM) due to its easy access and low cost, thus ensuring the safe and reliable operation of wind turbine gearboxes. However, existing WTGCM methods based on SCADA overlook the fundamental thermal physics and sensor failure. To effectively address the challenges of weak feature generalization and numerous false alarms, we propose a highly robust WTGCM method based on energy flow. Firstly, based on the principles of thermal balance and wind energy conversion, a feature extraction method considering the physical change process of oil temperature is proposed. Secondly, the performance of different feature extraction methods is quantitatively analyzed using data evaluation criteria. The reasons why different feature extraction methods have different effects are revealed through dimensionality reduction analysis. Finally, we compare the proposed method with other feature extraction methods using four models to validate the excellent performance of the proposed method in the early fault warning. The results demonstrate that the proposed method reduces the average root mean square error by 18.21% during the healthy operation of the wind turbine gearboxes. Moreover, the proposed method performs excellently in early warning of mechanical and sensor faults, significantly reducing the number of false alarms. The average warning time for mechanical faults is 32.56 h earlier.

Performance degradation assessment of rolling bearing under vibration signal monitoring based on optimized variational mode decomposition and improved fuzzy support vector data description

Performance degradation assessment methods for rolling bearings under vibration signal monitoring typically involve extracting signal degradation features and inputting them directly into unoptimized assessment models. However, this method often fails to characterize degradation trends and detect early faults in bearings effectively. Moreover, it is susceptible to interference from outliers and false signal fluctuations, posing challenges for accurate performance degradation assessment. To solve the above problems, a novel performance degradation assessment method of rolling bearings based on optimized variational mode decomposition to construct the maximum information degradation feature set and improved hippopotamus optimization algorithm optimized fuzzy support vector data description is proposed. This method effectively suppresses the signal degradation feature pollution caused by the redundancy of irrelevant frequency components, realizes the screening of effective degradation feature sets, and further improves the accuracy of bearing performance degradation assessment. Through experimental verification, this research method uses early healthy rolling bearing samples to establish an assessment model, which can adaptively determine the starting point and degradation trend of bearing degradation. In comparison with other methods for performance degradation assessment under vibration monitoring, it offers distinct advantages.

Adaptive Low-Rank Tensor Estimation Model Based Multichannel Weak Fault Detection for Bearings.

Multichannel signals contain an abundance of fault characteristic information on equipment and show greater potential for weak fault characteristics extraction and early fault detection. However, how to effectively utilize the advantages of multichannel signals with their information richness while eliminating interference components caused by strong background noise and information redundancy to achieve accurate extraction of fault characteristics is still challenging for mechanical fault diagnosis based on multichannel signals. To address this issue, an effective weak fault detection framework for multichannel signals is proposed in this paper. Firstly, the advantages of a tensor on characterizing fault information were displayed, and the low-rank property of multichannel fault signals in a tensor domain is revealed through tensor singular value decomposition. Secondly, to tackle weak fault characteristics extraction from multichannel signals under strong background noise, an adaptive threshold function is introduced, and an adaptive low-rank tensor estimation model is constructed. Thirdly, to further improve the accurate estimation of weak fault characteristics from multichannel signals, a new sparsity metric-oriented parameter optimization strategy is provided for the adaptive low-rank tensor estimation model. Finally, an effective multichannel weak fault detection framework is formed for rolling bearings. Multichannel data from the repeatable simulation, the publicly available XJTU-SY whole lifetime datasets and an accelerated fatigue test of rolling bearings are used to validate the effectiveness and practicality of the proposed method. Excellent results are obtained in multichannel weak fault detection with strong background noise, especially for early fault detection.

Fault system dynamics and their impact on ordovician carbonate karst reservoirs: Outcrop analogs and 3D seismic analysis in the Tabei region, Tarim Basin, NW China

The Tabei Uplift in the Tarim Basin of NW China represents an area with significant hydrocarbon exploration potential. This paper describes the effects of multi-phase faults on structural and hydrocarbon systems in the Tabei Uplift utilizing high-quality 3-D seismic, geological outcrops and drilling and production data. The interpretation and analysis of 10 fault systems from the Cambrian through the Cretaceous, shows that the deep, middle and shallow faults developed in four stages: the Early Caledonian, Mid-Late Caledonian, Hercynian and Himalayan. Specifically, the Early Caledonian fault system is favorable for the hydrocarbon expulsion of Cambrian source rocks, while Mid-Late Caledonian strike-slip faults facilitate hydrocarbon migration and accumulation. Hercynian and Himalayan strike-slip faults were formed as a result of the reactivation of the Mid-Late Caledonian strike-slip faults and have a destructive effect on the older oil reservoirs. Similarly, Permian volcanic activity also caused varying degrees of damage to Ordovician reservoirs. Oil production along fault zones more than 100 km show that the complex fracture-vuggy (FV) structure is more likely to trap oil and gas when it is damaged than the simple FV structure. Fault-controlled, fracture-vuggy carbonate reservoirs (FVCRs) were classified into six grades, which correlate to the productivity of oil wells in the region. Using this classification system, several drilling locations were selected and resulted in 80% success rate. This classification provides a novel approach for assessing the interplay between fault activity and reservoir formation, enhancing the prediction of hydrocarbon potential in varying strike-slip fault zones. This analysis not only refines our understanding of the region's geodynamic history but also aids in optimizing exploration and development strategies.

Kinematic Evolution of the Santa Bárbara System in the Foreland of the Central Andes of Northwestern Argentina (26°S)

AbstractCompared to the thin‐skinned Subandean foreland fold‐and‐thrust belt of northern Argentina and Bolivia, the tectonically active morphotectonic province of the Santa Bárbara System in the Andean broken foreland of northwestern Argentina is characterized by a temporally and spatially disparate deformation style. Although there is no well‐defined orogenic deformation front associated with the uplift of these basement‐cored, reverse‐fault bounded mountain ranges, there has been an overall eastward trend in Andean compressional deformation since the Miocene. While reactivation of basement anisotropies, such as early Paleozoic metamorphic fabrics and Cretaceous normal faults, has been proposed to have profoundly affected deformation processes in the Santa Bárbara System, other mechanisms involving Mesozoic and Cenozoic cover rocks may also have played an important role in orogenic deformation in this sector of the Andean foreland. We present structural field observations, interpretations of seismic reflection profiles, and kinematic modeling from the basins bordering the Candelaria Range in the southern sector of the Santa Bárbara System at 26°S. Our analysis features a 110‐km‐long structural cross section that images and links deep‐seated structures with shallow neotectonic faults. We find that regional shortening has been facilitated by several faults associated with a regional detachment at a depth of 23 km, resulting in total horizontal shortening of about 17% (18.4 km). While the deep‐seated first‐order structures seem closely linked to seismogenic processes in the Andean foreland, shallow second‐order structures within the sedimentary cover modify the intermontane landscapes and appear to be associated with aseismic creep.

Three-dimensional structural models, evolution and petroleum geological significances of transtensional faults in the Ziyang area, central Sichuan Basin, SW China

With drilling and seismic data of Transtensional (strike-slip) Fault System in the Ziyang area of the central Sichuan Basin, SW China plane-section integrated structural interpretation, 3-D fault framework model building, fault throw analyzing, and balanced profile restoration, it is pointed out that the transtensional fault system in the Ziyang 3-D seismic survey consists of the northeast-trending FI19 and FI20 fault zones dominated by extensional deformation, as well as 3 sets of northwest-trending en echelon normal faults experienced dextral shear deformation. Among them, the FI19 and FI20 fault zones cut through the Neoproterozoic to Lower Triassic Jialingjiang Formation, presenting a 3-D structure of an “S”-shaped ribbon. And before Permian and during the Early Triassic, the FI19 and FI20 fault zones underwent at least two periods of structural superimposition. Besides, the 3 sets of northwest-trending en echelon normal faults are composed of small normal faults arranged in pairs, with opposite dip directions and partially left-stepped arrangement. And before Permian, they had formed almost, restricting the eastward growth and propagation of the FI19 fault zone. The FI19 and FI20 fault zones communicate multiple sets of source rocks and reservoirs from deep to shallow, and the timing of fault activity matches well with oil and gas generation peaks. If there were favorable Cambrian–Triassic sedimentary facies and reservoirs developing on the local anticlinal belts of both sides of the FI19 and FI20 fault zones, the major reservoirs in this area are expected to achieve breakthroughs in oil and gas exploration.

Particle accelerator power system early fault diagnosis based on deep learning and multi-sensor feature fusion

Particle accelerators play a crucial role in scientific research and industrial applications, and enhancing their reliability, ensuring stable operation, and reducing downtime caused by faults are essential for achieving research goals. This paper introduces a novel particle accelerator fault diagnosis method based on deep learning and multi-sensor feature fusion. The approach employs one-dimensional convolution to extract signals from multiple sensors and achieves comprehensive feature fusion of multi-sensor data, effectively overcoming the limitations of individual sensors. It combines 1d convolutional neural networks (1D-CNN) and long short-term memory networks (LSTM) to enhance spatiotemporal feature extraction. This approach efficiently extracts features from multiple sensors while concurrently reducing data length and training time. The study uses real signals from particle accelerators and aims to achieve early detection of faults by identifying abnormal signals preceding accelerator malfunctions. Comparative analysis with other machine learning models and the use of multiple evaluation metrics validate the effectiveness and generalizability of this method. The research provides a better performance fault diagnosis model with significant implications for reducing downtime, troubleshooting faults, and improving the reliability of particle accelerators.

Fault diagnosis method of rolling bearing based on MSSA-VMD algorithm

Abstract Early fault signals of rolling bearings are affected by environmental noise, which makes it challenging to extract fault characteristics. In this paper, a bearing fault diagnosis method based on Sparrow Search Algorithm (SSA) and Variable Modal Decomposition (VMD) is proposed to achieve adaptive signal decomposition and feature extraction. First, the fusion shock index is constructed based on the envelope spectrum pulse factor and correlation coefficient to measure the shock fault components. Then, the VMD parameters are adaptively optimized by the improved sparrow search algorithm MSSA, and the fusion shock index is established as the optimal modal component selection method of the fitness function. Finally, the envelope spectrum of the signal after noise reduction is analyzed to extract the fault characteristic frequency. By analyzing the bearing outer ring fault signal and inner ring fault signal under strong noise, the results show that this method can adaptively determine the mode number and penalty factor of VMD, effectively extract the fault signal characteristics, and realize rolling bearing fault diagnosis.

A Deep Learning-based Fault Detection and Classification in Smart Electrical Power Transmission System

Progressively, the energy demands and responsibilities to control the demands have expanded dramatically. Subsequently, various solutions have been introduced, including producing high-capacity electrical generating power plants, and applying the grid concept to synchronize the electrical power plants in geographically scattered grids. Electrical Power Transmission Networks (EPTN) are made of many complex, dynamic, and interrelated components. The transmission lines are essential components of the EPTN, and their fundamental duty is to transport electricity from the source area to the distribution network. These components, among others, are continually prone to electrical disturbance or failure. Hence, the EPTN required fault detection and activation of protective mechanisms in the shortest time possible to preserve stability. This research focuses on using a deep learning approach for early fault detection to improve the stability of the EPTN. Early fault detection swiftly identifies and isolates faults, preventing cascading failures and enabling rapid corrective actions. This ensures the resilience and reliability of the grid, optimizing its operation even in the face of disruptions. The design of the deep learning approach comprises a long-term and short-term memory (LSTM) model. The LSTM model is trained on an electrical fault detection dataset that contains three-phase currents and voltages at one end serving as inputs and fault detection as outputs. The proposed LSTM model has attained an accuracy of 99.65 percent with an error rate of just 1.17 percent and outperforms neural network (NN) and convolutional neural network (CNN) models.

Edge Machine Learning-Enabled Predictive Fault Detection System for Conveyor Belt Maintenance Optimization in Industrial Settings

Digital transformation is essential for industrial and manufacturing sectors, especially in conveyor belt systems. On the other hand, Innovative electronic components and software applications offer opportunities for advanced fault prediction, minimizing operational disruptions, reducing inefficiencies, and enhancing overall industrial efficiency. Efficient conveyor belt systems are crucial for industrial operations, requiring early fault detection to prevent costly downtime and ensure safety. The utilization of embedded machine learning via the Edge Impulse platform enhances data collection and spectral feature extraction using wavelet approximation. This article presents a novel methodology for predictive fault detection in conveyor belt systems employing edge machine learning. Leveraging the ESP32 microcontroller and accelerometer sensor for real-time vibration data capture, a four-layer Artificial Neural Network (ANN) model, trained on 336 feature samples, is deployed via Edge Impulse and TensorFlow scripts. TensorFlow Lite compresses the model for microcontroller integration. The ESP32 microcontroller, acting as an edge device, achieves real-time predictions with 97.5% accuracy and 0.20 minimal loss. This work promises significant strides in predictive maintenance, offering cost savings, operational reliability, and efficiency gains in industrial settings, revolutionizing maintenance strategies.

Early-Stage Fault Diagnosis of Motor Bearing Based on Kurtosis Weighting and Fusion of Current-Vibration Signals.

To solve the problem of a low signal-to-noise ratio of fault signals and the difficulty in effectively and accurately identifying the fault state in the early stage of motor bearing fault occurrence, this paper proposes an early fault diagnosis method for bearings based on the Differential Local Mean Decomposition (DLMD) and fusion of current-vibration signals. This method uses DLMD to decompose the current signal and vibration signal, respectively, and weights the decomposed product function (PF) according to the kurtosis value to reconstruct the signal, and then fuses the reconstructed signals to obtain the current-vibration fusion signal after normalization, and then analyzes the fusion signal spectrally through the Hilbert envelope spectrum. Finally, the fusion signal is analyzed by the Hilbert envelope spectrum, and a clear fault characteristic frequency is obtained. The experimental results demonstrate that compared to traditional bearing fault diagnosis methods, the proposed method significantly improves the signal-to-noise ratio of fault signals, effectively enhances the sensitivity of early-stage fault detection in motor bearings, and improves the accuracy of fault identification.

On the design of Optimal Health Indicators for early fault detection and their statistical thresholds

This research presents a method for developing optimal health indicators for early fault detection in machine condition monitoring. The devised health indicators are optimal in the Neyman–Pearson sense, as they maximize the probability of detection while maintaining a constant false alarm rate. They are generated through a generalized likelihood ratio test that involves the probability density functions representing the healthy and faulty states. The essence of the approach lies in establishing a framework that defines optimal health indicators as functions of the partial derivatives of the healthy probability density function and a modulation function, representing the distortion of the probability density function in the faulty state. Specific modulation functions lead to the recovery of several traditional health indicators, including kurtosis, skewness, the crest factor, the clearance factor, the smoothness factor, the shape factor, the impulse factor, ℓp/ℓq-norms, the negentropy, among others. New health indicators are also derived. As the proposed optimal health indicators asymptotically follow a chi-squared distribution, they come with a statistical threshold. The study comprehensively outlines the methodology, with its performance assessed through simulated and experimental signals. The results reveal that the early transition from healthy to faulty can be well detected via the established optimal health indicators and their thresholds.