Method for detecting and diagnosing faults

Abstract

Various embodiments are described herein for a system and method for condition monitoring and detecting and diagnosing faults in electromechanical or electrochemical systems and batteries using a frequency-domain statistical analysis framework. The method comprises receiving raw time-domain signals from one or more sensors monitoring the electromechanical or electrochemical system, applying a Short-Time Fourier Transform to convert the time-domain signals into a spectrogram, and segmenting the spectrogram into a plurality of frequency band segments. Each segment is independently analyzed using Principal Component Analysis based Multivariate Statistical Process Control, followed by statistical smoothing of the MSPC outputs. Fault conditions can be classified based on the smoothed statistical indicators, enabling accurate identification of deviations from baseline behavior.

Description

TITLE: METHOD FOR DETECTING AND DIAGNOSING FAULTSFIELD

[0001] The various embodiments described herein generally relate to condition monitoring, fault detection and diagnostic systems and methods thereof.BACKGROUND

[0002] Condition monitoring, fault detection and diagnostic systems play a critical role in ensuring the reliability, safety, and efficiency of complex technologies across a wide range of industries. Mechanical machines, batteries, chemical processes, and other systems are susceptible to faults that can arise from component degradation, environmental conditions, or unexpected operational stresses. Such anomalous operating conditions or faults, if undetected, may result in system downtime, reduced performance, safety hazards, or costly failures. Traditional fault detection approaches often rely on manual inspections, fixed threshold monitoring, or isolated sensors, which may provide incomplete information or delayed response to fault and anomalous conditions.

[0003] There is a growing demand for condition monitoring and diagnostic techniques that can accurately and efficiently identify faults in real time, reduce false positives, and adapt to diverse use-cases spanning fields including, but not limited to, industrial equipment, energy storage devices, and chemical processing plants.

[0004] As an example, the condition monitoring and fault detection and diagnostic system and method described herein can be used to detect degradation and faults in electric motors. Electric motors are extensively utilized across various sectors, including industry, commerce, public services, and household appliances, powering essential systems and equipment like wind turbines, electric propulsion, water pumps, compressors, and machine tools. In both developed and developing nations, electric motors constitute a significant portion of total national power consumption. Statistics reveal that they typically contribute around two-thirds of industrial power consumption andapproximately 40% of overall power consumption in each nation. However, their reliable operation is often compromised by the occurrence of faults, which can lead to safety hazards, increased maintenance costs, and decreased operational efficiency. Among the diverse range of faults observed in electric motors, bearing-related faults account for a significant portion, followed by stator and rotor-related issues.

[0005] Rotor imbalance is identified as a major source of vibration in electric motors, resulting from an unequal distribution of mass around the rotor's center of rotation. This imbalance, whether static or dynamic, generates centrifugal forces and vibrations during motor operation, leading to premature wear and potential catastrophic failures.

[0006] As an another example, the condition monitoring, fault detection and diagnostic system and method described herein can be used to detect faults in energy storage devices. An energy storage device, such as a battery, capacitor, or fuel cell, is a system that stores energy for later use in powering electronic, mechanical, or industrial processes. These devices are critical components in applications ranging from consumer electronics and electric vehicles to renewable energy grids and industrial backup systems. Energy storage devices typically undergo repeated charging and discharging cycles and operate under varying environmental and load conditions, energy storage devices are particularly prone to faults such as capacity fade, thermal runaway, leakage, or internal short circuits. Early detection and accurate diagnosis of such faults are essential to maintain device performance, extend operational lifetime, and, most importantly, ensure safety by preventing hazardous failures that could lead to fire, explosion, or system shutdown.

[0007] It will be appreciated that while the present condition monitoring and fault detection and diagnostic system is described in the context of mechanical machines, energy storage devices, manufacturing, and chemical processes, the disclosed system and method are not limited to these applications. Rather, the principles described herein may be applied to a wide range of other scenarios in which early detection and accurate diagnosis offaults are desirable, including but not limited to industrial automation, manufacturing lines, transportation systems, medical devices, communication networks, and consumer electronics.

[0008] Given the critical importance of condition monitoring and detecting and diagnosing faults, significant research efforts have been directed towards developing effective fault identification methodologies. Various techniques, including hybrid models incorporating fuzzy min-max, neural networks, and classification and regression trees, have been proposed for fault identification and diagnosis in electric motors. Additionally, multiclass support vector machine (SVM) methods have been utilized for mechanical multi-fault classification based on time-domain vibration signals, demonstrating high prediction accuracy under specific operating conditions.

[0009] Efforts to improve fault diagnostics have also led to the integration of advanced techniques such as the Hilbert transform and neural networks for detecting damaged devices. Furthermore, investigations into vibration and current monitoring using multiclass support vector machine (SVM) methods have shown promising results for effective failure prediction. Additionally, the integration of wavelet packet transform (WPT) with SVM has been proposed to enhance fault diagnosis by extracting critical information from raw time series data.

[0010] Despite these advancements, there remains a need for fault detection methodologies that can effectively handle practical system conditions with minimal data or information. Recent research has focused on developing SVM-based fault detection methodologies capable of diagnosing various fault conditions with high accuracy.

[0011] Early detection of anomalies and faults is critically important in preventing more extensive damage and minimizing downtime. Condition monitoring and fault detection and diagnosis (FDD) systems play a vital role in this regard by monitoring systems and identifying anomalies and fault types and their locations. These systems should possess desirable attributes such asquick detection, robustness, adaptability, and the ability to handle multiple faults and anomaly conditions.SUMMARY OF VARIOUS EMBODIMENTS

[0012] In one aspect, in at least one embodiment described herein, there is provided a method for condition monitoring and for detecting and diagnosing faults in an electromechanical or electrochemical system. In at least one embodiment, the method includes receiving raw time-domain signals from one or more sensors, applying a Short-Time Fourier Transform (STFT) to generate a spectrogram, segmenting the spectrogram into multiple frequency bands, and performing Principal Component Analysis (PCA)-based Multivariate Statistical Process Control (MSPC) on each segment. Statistical smoothing is applied to the MSPC output, and fault conditions are classified based on the smoothed indicators. The segmentation from STFT and the frequency segmentation results in a large number of indicators, constituting time and frequency segmentations. Statistical thresholds can be generated base on variability of indicators or in absolute terms. The system is characterized as faulty or non- faulty based on comparison of indicators with respect to statistical thresholds. The system is detected as anomalous or faulty if the indicators exceed their associated thresholds. The fault or anomaly conditions are diagnosed based on the number, pattern, and combination of indicators that exceed their thresholds. The level of severity of the anomaly or fault condition is quantified by the level of indicators that exceed their thresholds. This approach can be applicable to fault diagnostics in a variety of applications, including, but not limited to: rotating machinery, energy storage systems, and chemical process equipment.

[0013] In at least one embodiment, the raw time-domain signal can comprise vibration or acoustic data sampled at a rate sufficient to capture fault- related frequency components. This enables the method to detect subtle anomalies across a wide range of industrial systems.

[0014] In at least one embodiment, the STFT can produce a spectrogram matrix with dimensions corresponding to frequency components and timeobservations, allowing for time-localized frequency analysis critical for identifying transient faults.

[0015] In at least one embodiment, the segmentation step can divide the spectrogram into a plurality of frequency intervals, each analyzed independently to isolate frequency-specific fault signatures.

[0016] In at least one embodiment, the PCA-based MSPC step can include standardizing each frequency segment, applying Singular Value Decomposition (SVD) to extract principal components, selecting components that explain at least 90% of the variance, and computing Hotelling’s T-squared statistics for each segment. This enables robust multivariate fault detection across diverse operational conditions.

[0017] In at least one embodiment, the method can further include constructing a baseline model using healthy system data and comparing test data against this baseline using retained principal components, enhancing fault detection accuracy and consistency.

[0018] In at least one embodiment, statistical smoothing can be performed by applying a number of moving statistics with a window size of any size to the T-squared statistics, improving signal stability and reducing false positives.

[0019] In at least one embodiment, the classification step can include comparing fault signatures across datasets from Original Equipment Manufacturer (OEM) and After-Market (AM) systems, supporting diagnostics across heterogeneous hardware platforms.

[0020] In at least one embodiment, the classification step can identify multiple fault conditions within the electromechanical or electrochemical system, enabling multi-class fault diagnosis for complex industrial assets.

[0021] In at least one embodiment, the method can include visualizing T-squared statistics overtime to identify deviations in specific frequency bands, aiding in intuitive fault localization and trend analysis.

[0022] In at least one embodiment, segmentation boundaries can be predefined or dynamically adjusted based on characteristics extracted from the time-domain signals, allowing adaptive fault detection across varying system behaviors.

[0023] In at least one embodiment, the PCA-based MSPC step can be performed using a sliding window to track fault evolution over time, supporting early detection and predictive maintenance.

[0024] In at least one embodiment, the classification step can employ supervised or unsupervised learning algorithms to label fault types, enabling integration with machine learning frameworks for scalable diagnostics.

[0025] In at least one embodiment, the method can be applied to rotating machinery including electric motors, compressors, and turbines, and is extendable to other industrial systems requiring fault monitoring.

[0026] In at least one embodiment, the condition monitoring and fault detection method can be configured for real-time monitoring and alert generation, supporting continuous system health assessment and rapid response.

[0027] In at least one embodiment, the baseline model can be periodically updated using newly acquired data, allowing the system to adapt to evolving operational conditions and maintain diagnostic accuracy.

[0028] In at least one embodiment, the STFT window can overlap adjacent segments by a predefined number of samples to preserve continuity and improve frequency resolution.

[0029] In at least one embodiment, the method can identify localized anomalies by comparing T-squared statistics across frequency segments, enabling precise fault localization within the system.

[0030] In at least one embodiment, the statistical indicators can be used to generate fault severity scores, providing quantitative metrics for maintenance prioritization and risk assessment.

[0031] In at least one embodiment, the method can be implemented in a computing system comprising a processor and memory storing instructions for executing the steps, enabling deployment in embedded or cloud-based condition monitoring or diagnostic platforms.

[0032] In another aspect, in at least one embodiment described herein, there is provided a system for fault-detection-diagnosis (FDD). In at least one embodiment, the fault-detection-diagnosis (FDD) system can include one or more sensors configured to collect raw time-domain signals from an electromechanical or electrochemical system, a processing unit configured to perform Short-Time Fourier Transform (STFT) on the signals to generate a spectrogram, segment the spectrogram into frequency band segments, apply Principal Component Analysis (PCA)-based Multivariate Statistical Process Control (MSPC) to each segment, apply statistical smoothing to the MSPC output, and classify fault conditions based on the smoothed indicators. A memory can store instructions executable by the processing unit to perform these operations. The system can characterize the electromechanical or electrochemical system as faulty or non-faulty based on statistical thresholds derived from healthy operating data. This architecture is applicable to fault diagnostics across industrial machines, energy storage systems, and chemical processes.

[0033] In at least one embodiment, the sensors can be configured to collect vibration or acoustic data sampled at a rate sufficient to capture fault- related frequency components, enabling high-resolution analysis of mechanical and structural anomalies.

[0034] In at least one embodiment, the processing unit can generate a spectrogram matrix with dimensions corresponding to frequency components and time observations, facilitating time-localized frequency analysis for transient fault detection.

[0035] In at least one embodiment, the processing unit can segment the spectrogram into a plurality of frequency intervals, each analyzedindependently to isolate frequency-specific fault signatures and improve diagnostic precision.

[0036] In at least one embodiment, the processing unit can standardize each frequency segment, apply Singular Value Decomposition (SVD) to extract principal components, select components that account for at least 90% of the variance, and compute Hotelling’s T-squared statistics for each segment. This enables robust multivariate fault detection across diverse operational conditions.

[0037] In at least one embodiment, the processing unit can construct a baseline model using healthy system data and compare test data against the baseline using the selected principal components, enhancing fault detection accuracy and consistency.

[0038] In at least one embodiment, the processing unit can apply a number of moving statistics with a window size of any size to the T-squared statistics to smooth the output, reducing noise and improving the reliability of fault indicators.

[0039] In at least one embodiment, the processing unit can compare fault signatures across datasets from Original Equipment Manufacturer (OEM) and After-Market (AM) systems, supporting diagnostics across heterogeneous hardware platforms.

[0040] In at least one embodiment, the processing unit can identify multiple fault conditions affecting the electromechanical or electrochemical system, enabling multi-class fault diagnosis for complex industrial assets.

[0041] In at least one embodiment, the processing unit can visualize T- squared statistics over time to identify deviations in specific frequency bands, aiding in intuitive fault localization and trend analysis.

[0042] In at least one embodiment, segmentation boundaries can be predefined or dynamically adjusted based on characteristics extracted from the time-domain signals, allowing adaptive fault detection across varying system behaviors.

[0043] In at least one embodiment, the PCA-based MSPC can be performed using a sliding window to track fault evolution over time, supporting early detection and predictive maintenance strategies.

[0044] In at least one embodiment, the classification module can employ supervised or unsupervised learning algorithms to label fault types, enabling integration with machine learning frameworks for scalable diagnostics.

[0045] In at least one embodiment, the system can be configured to monitor rotating machinery including electric motors, compressors, and turbines, and is extendable to other industrial systems requiring fault monitoring.

[0046] In at least one embodiment, the system can be configured to monitor batteries, cells, modules, or packs, (optionally in a manufacturing line), supporting anomaly or fault detection and diagnostics in energy storage or manufacturing applications, where early detection is critical for safety and performance.

[0047] In at least one embodiment, the FDD system can be configured for real-time fault monitoring and alert generation, enabling continuous system health assessment and rapid response to emerging faults.

[0048] In at least one embodiment, the FDD system can be configured for manufacturing line monitoring and alert generation, enabling continuous manufacturing line stability, enabling rapid response to emerging operational variability or faults.

[0049] In at least one embodiment, the baseline model can be periodically updated using newly acquired healthy system data, allowing the system to adapt to evolving operational conditions and maintain diagnostic accuracy.

[0050] In at least one embodiment, the baseline model can be periodically updated using newly acquired manufacturing data, allowing the system to adapt to evolving operational conditions and maintain detection and diagnostic accuracy.

[0051] In at least one embodiment, the STFT window can overlap adjacent segments by a predefined number of samples to preserve continuity and improve frequency resolution in the spectrogram.

[0052] In at least one embodiment, the FDD system can identify localized anomalies by comparing T-squared statistics across frequency segments, enabling precise fault localization within the system.

[0053] In at least one embodiment, the statistical indicators can be used to generate fault severity scores, providing quantitative metrics for maintenance prioritization and risk assessment across industrial domains.

[0054] In another aspect, in at least one embodiment described herein, there is provided a computer-implemented method for fault-detection-diagnosis (FDD). In at least one embodiment, the a computer-implemented method for fault-detection-diagnosis (FDD) can include one or more sensors configured to collect raw time-domain signals from an electromechanical and / or electrochemical system, a processing unit configured to perform Short-Time Fourier Transform (STFT) on the signals to generate a spectrogram, segment the spectrogram into frequency band segments, apply Principal Component Analysis (PCA)-based Multivariate Statistical Process Control (MSPC) to each segment, apply statistical smoothing to the MSPC output, and classify fault conditions based on the smoothed indicators. A memory can store instructions executable by the processing unit to perform these operations. The computer- implemented method can characterize the electromechanical or electrochemical system as faulty or non-faulty based on statistical thresholds derived from healthy operating data. This architecture is applicable to fault diagnostics across industrial machines, energy storage systems, and chemical processes.BRIEF DESCRIPTION OF THE DRAWINGS

[0055] For a better understanding of the various embodiments described herein, and to show more clearly how these various embodiments may be carried into effect, reference will be made, by way of example, to theaccompanying drawings which show at least one example embodiment, and in which:

[0056] Figure 1 illustrates the test setup used in accordance with embodiments of the present invention, including the Belt Starter Generator (BSG) units, sensor placements, and associated instrumentation.

[0057] Figure 2 depicts pulley-unbalance fault conditions at various severity levels, demonstrating the physical configuration used to simulate mechanical imbalance in the system.

[0058] Figure 3 presents the categories of data variability investigated in the study, including BSG-to-BSG differences, teardown effects, bearing type variations, and day-to-day environmental changes.

[0059] Figure 4 provides a close-up view of bearing fault conditions, showing physical damage introduced to simulate inner race, outer race, ball, and grease-related faults.

[0060] Figure 5 offers an overview of the condition monitoring and fault detection and diagnosis method, outlining the sequence of signal processing, feature extraction, and classification steps.

[0061] Figure 6A and 6B show the Short-Time Fourier Transform (STFT) analysis of baseline vibration data, illustrating the time-frequency representation used for subsequent segmentation.

[0062] Figure 7 illustrates the segmentation process applied to the spectrogram, dividing it into multiple frequency bands for independent analysis.

[0063] Figure 8 depicts the PCA-based Multivariate Statistical Process Control (MSPC) technique used to compute Hotelling’s T-squared statistics for each frequency segment.

[0064] Figure 9A shows the STFT spectrogram and Figure 9B PCA- based Hotelling’s T-squared analysis across eight classes, including baseline (0-1 second) and pulley-unbalanced faults (1-8 seconds), with each fault class occupying a distinct time interval.

[0065] Figure 10A-10F illustrate statistical indicators generated using Hotelling’s T-squared statistic, highlighting deviations from baseline behavior.

[0066] Figure 11 presents the first three principal components (PCs) extracted from the feature dataset, showing dominant patterns across data collected on different days.

[0067] Figure 12A and 12B show the confusion matrix for testing and training data related to pulley-unbalance faults, specifically investigating day- to-day variation in fault detection accuracy.

[0068] Figure 13A and 13B show the confusion matrix for pulleyunbalance fault data, evaluating the impact of teardown variation on model performance.

[0069] Figure 14 illustrates a clustering plot of pulley-unbalance data before and after teardown, revealing eight distinct clusters corresponding to different fault conditions.

[0070] Figure 15 shows bearing fault detection results considering both BSG-to-BSG variability and teardown effects, demonstrating the robustness of the diagnostic model.

[0071] Figure 16 illustrates variability between OEM and AM bearings, highlighting differences in fault signatures and diagnostic outcomes.

[0072] Figure 17 presents the total diagnosis accuracy for bearing faults without applying weight factors, serving as a baseline for performance comparison.

[0073] Figure 18 shows the optimized weight factors used to enhance bearing fault diagnosis accuracy, demonstrating improved classification performance.

[0074] Figure 19 illustrates bearing-to-bearing variation in fault detection and diagnosis, emphasizing the importance of accounting for hardware-specific differences in predictive models.

[0075] Figure 20 presents a flowchart showing the steps of the preprocessing method.

[0076] Figure 21 illustrates a flowchart of the algorithm implemented for fault detection in an industrial furnace.

[0077] Figure 22 illustrates an example output generated by the fault detection model.DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] Various apparatuses or processes will be described below to provide an example of an embodiment of each claimed invention. No embodiment described below limits any claimed invention and any claimed invention may cover processes or apparatuses that differ from those described below. The claimed inventions are not limited to apparatuses or processes having all of the features of any one apparatus or process described below or to features common to multiple or all of the apparatuses or processes described below. It is possible that an apparatus or process described below is not an embodiment of any claimed invention. Any invention disclosed in an apparatus or process described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim or dedicate to the public any such invention by its disclosure in this document.

[0079] Furthermore, it will be appreciated that for simplicity and clarity of illustration, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. In addition, numerous specific details are set forth in orderto provide a thorough understanding of the embodiments described herein. However, it will be understood by those of ordinary skill in the art that the embodiments described herein may be practiced without these specific details. In other instances, well- known methods, procedures and components have not been described in detail so as not to obscure the embodiments described herein. Also, the description is not to be considered as limiting the scope of the embodiments described herein.

[0080] Unless otherwise indicated, the definitions and embodiments described in this and other sections are intended to be applicable to all embodiments and aspects of the present disclosure herein described for which they are suitable as would be understood by a person skilled in the art. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting.

[0081] In understanding the scope of the present disclosure, the term “comprising” and its derivatives, as used herein, are intended to be open ended terms that specify the presence of the stated features, elements, components, groups, integers, and / or steps, but do not exclude the presence of other unstated features, elements, components, groups, integers and / or steps. The foregoing also applies to words having similar meanings such as the terms, “including”, “having” and their derivatives. The term “consisting” and its derivatives, as used herein, are intended to be closed terms that specify the presence of the stated features, elements, components, groups, integers, and / or steps, but exclude the presence of other unstated features, elements, components, groups, integers and / or steps. The term “consisting essentially of”, as used herein, is intended to specify the presence of the stated features, elements, components, groups, integers, and / or steps as well as those that do not materially affect the basic and novel characteristic(s) of features, elements, components, groups, integers, and / or steps.

[0082] Terms of degree such as “substantially”, “about” and “approximately” as used herein mean a reasonable amount of deviation of the modified term such that the end result is not significantly changed. These terms of degree should be construed as including a deviation of at least ±5% of the modified term if this deviation would not negate the meaning of the word it modifies. In addition, all ranges given herein include the end of the ranges and also any intermediate range points, whether explicitly stated or not.

[0083] As used in this disclosure, the singular forms “a”, “an” and “the” include plural references unless the content clearly dictates otherwise.

[0084] In embodiments comprising an “additional” or “second” component, the second component as used herein is chemically different from the other components or first component. A “third” component is different from the other, first, and second components, and further enumerated or “additional” components are similarly different.

[0085] The term “and / or” as used herein means that the listed items are present, or used, individually or in combination. In effect, this term means that “at least one of” or “one or more” of the listed items is used or present.

[0086] The abbreviation, “e.g.” is derived from the Latin exempli gratia and is used herein to indicate a non-limiting example. Thus, the abbreviation “e.g.” is synonymous with the term “for example.” The word “or” is intended to include “and” unless the context clearly indicates otherwise.

[0087] It should be noted that the term “coupled” used herein indicates that two elements can be directly coupled to one another or coupled to one another through one or more intermediate elements.

[0088] The present disclosure relates to condition monitoring and detecting and diagnosing faults in devices and provides a method for addressing variability challenges in condition monitoring and fault detection and diagnosis of electrical, mechanical, or chemical devices and systems.

[0089] In an embodiment, the method may also be used in manufacturing processes, indicating the level of variability and stability of the manufacturing process. Variability and stability can be important to the manufacturing process and impact the cost and quality of products. The condition monitoring and fault detection and diagnosis system described herein can be used to provide an indication of variability in parts produced in production lines (such as batteries, battery modules, battery packs).

[0090] Condition monitoring and fault diagnosis methods can be broadly categorized into quantitative model-based, qualitative model-based, and process history-based approaches. While quantitative model-based methods rely on input-output and state-space models, qualitative models focus onunderstanding the physical and chemical aspects of the process. Process history-based methods, on the other hand, utilize historical data for condition monitoring and fault detection and diagnosis, often employing feature extraction techniques to transform historical data into actionable knowledge. Principal Component Analysis (PCA) is a widely used technique for feature extraction, enabling the identification of significant trends in data using a small number of relevant factors.

[0091] To tackle these challenges, a combination of techniques is employed, including time-frequency analysis, multivariate statistical process control, and classification. By leveraging these methodologies, the approach is designed to identify existing faults, thereby enhancing the overall reliability and efficiency of fault diagnostics in practical industrial systems. Variations related to different components, fluctuations in testing, and changes before and after teardowns of devices are analyzed. Addressing these nuances ensures a comprehensive understanding of the factors influencing condition monitoring and fault detection and diagnosis in electrical, mechanical, or chemical devices and systems.

[0092] Rigorous experimentation can be used to provide insights into how these variations impact the performance of condition monitoring and fault detection techniques, offering more reliable guidance by better assessing the strengths and limitations of different methodologies.

[0093] In one aspect, and in at least one embodiment described herein, there is provided a method for detecting and diagnosing faults in an electromechanical and / or electrochemical system.

[0094] As used herein, the term electromechanical system refers to any system, apparatus, or assembly that integrates electrical and mechanical components to perform a functional operation. Electromechanical systems may include, but are not limited to, rotating machinery such as electric motors, generators, and turbines; mechanical transmission components including gears, shafts, pulleys, belts, and couplings; bearing assemblies such as ball bearings, roller bearings, and thrust bearings; actuation systems includingsolenoids, linear actuators, and servo motors; sensor and feedback systems such as vibration sensors, acoustic sensors, temperature sensors, and electrical sensors; and control systems comprising embedded processors, controllers, and software algorithms configured to monitor, regulate, or optimize system performance. Electromechanical systems may be implemented in industrial, automotive, aerospace, consumer electronics, energy, and manufacturing applications, and may operate under varying environmental and load conditions.

[0095] As used herein, the term electrochemical system or energy storage system refers to any system, apparatus, or assembly that stores, manages, or delivers electrical energy through chemical or electrochemical processes. In at least one embodiment, electrochemical systems may include battery packs, battery cells, fuel cells, supercapacitors, power modules, and associated control electronics. Electrochemical systems may also include thermal systems such as heating elements, cooling systems, and furnaces, as well as monitoring and diagnostic subsystems for assessing performance, degradation, and fault conditions. Electrochemical systems may be implemented in industrial, automotive, aerospace, consumer electronics, energy, and manufacturing applications, and may operate under varying environmental and load conditions.

[0096] The method can include receiving raw time-domain signals from one or more sensors positioned to monitor the electromechanical or electrochemical system. These signals may comprise vibration or acoustic data sampled at a rate sufficient to capture fault-related frequency components, thereby enabling the detection of subtle anomalies across a wide range of industrial systems. Upon acquisition, the raw signals can be transformed using a Short-Time Fourier Transform (STFT), which generates a spectrogram matrix with dimensions corresponding to frequency components and time observations. This transformation facilitates time-localized frequency analysis, which is critical for identifying transient fault conditions.

[0097] The spectrogram can then be segmented into a plurality of frequency band intervals. Each segment may be analyzed independently to isolate frequency-specific fault signatures. In at least one embodiment, the segmentation boundaries may be predefined or dynamically adjusted based on characteristics extracted from the time-domain signals, allowing the method to adapt to varying system behaviors. For each frequency segment, Principal Component Analysis (PCA)-based Multivariate Statistical Process Control (MSPC) can be performed. This step may include standardizing the segment, applying Singular Value Decomposition (SVD) to extract principal components, selecting a subset of components that account for at least 90% of the variance, and computing Hotelling’s T-squared statistics. These operations enable multivariate fault detection across diverse operational conditions.

[0098] To enhance the stability of the diagnostic output, statistical smoothing may be applied to the T-squared statistics. In at least one embodiment, this smoothing can be achieved by applying moving statistics with a window size of any number. The smoothed indicators are then used to classify fault conditions. Classification may involve comparing fault signatures across datasets from Original Equipment Manufacturer (OEM) and After-Market (AM) systems, supporting diagnostics across heterogeneous hardware platforms. The classification step can also identify multiple fault conditions, enabling multiclass fault diagnosis for complex industrial assets. In some embodiments, supervised or unsupervised learning algorithms may be employed to label fault types, facilitating integration with machine learning frameworks for scalable diagnostics.

[0099] The method may further include constructing a baseline model using healthy system data and comparing test data against this baseline using retained principal components. This comparison enhances fault detection accuracy and consistency. The baseline model may be periodically updated using newly acquired data to ensure adaptability to evolving operational conditions. Visualization of T-squared statistics overtime may also be included to identify deviations in specific frequency bands, aiding in intuitive faultlocalization and trend analysis. Additionally, the method may identify localized anomalies by comparing T-squared statistics across frequency segments and generate fault severity scores to support maintenance prioritization and risk assessment.

[0100] In at least one embodiment, the method may be implemented in a computing system comprising a processor and memory storing instructions for executing the described steps. The system may be configured for real-time condition and fault monitoring and alert generation, supporting continuous system health assessment. The method is applicable to a wide range of industrial systems, including rotating machinery such as electric motors, compressors, and turbines, as well as energy storage devices and chemical process equipment.

[0101] In another aspect, and in at least one embodiment described herein, there is provided a fault-detection-diagnosis (FDD) system. The FDD system can include one or more sensors configured to collect raw time-domain signals from an electromechanical or electrochemical system, a processing unit configured to perform STFT to generate a spectrogram, segment the spectrogram into frequency band segments, apply PCA-based MSPC to each segment, apply statistical smoothing to the MSPC output, and classify fault conditions based on the smoothed indicators. A memory may store instructions executable by the processing unit to perform these operations. The system can characterize the electromechanical or electrochemical system as faulty or non- faulty based on statistical thresholds derived from healthy operating data. This architecture is broadly applicable to fault diagnostics across industrial machines, energy storage systems, and chemical processes.

[0102] In some embodiments, the system may include one or more sensors configured to detect and / or measure various physical, chemical, or environmental parameters. The sensors may be of any suitable type, including, without limitation, optical sensors, acoustic sensors, pressure sensors, temperature sensors, chemical sensors, biosensors, capacitive sensors, resistive sensors, piezoelectric sensors, magnetic sensors, motion sensors,inertial sensors, gyroscopes, accelerometers, proximity sensors, imaging sensors, voltage sensors, current sensors, or combinations thereof. The sensors may be provided in any number, arrangement, or combination as appropriate for the intended application, and the present disclosure is not limited to any particular sensor type, configuration, or quantity.

[0103] In some embodiments, when adapted for detecting faults in a battery use-case, the system may use at least two sensors, including but not limited to one voltage sensor and one current sensor connected through Nl DAQ systems. In another example, when adapted for detecting faults in a chemical processing use-case such as a furnace, the system may use at least one acoustic sensor, including but not limited to a microphone. In yet another example, when adapted for detecting faults in a rotational machine use-case, the system may use at least four sensors, including but not limited to two triaxial accelerometers providing six vibration channels, and two microphones for capturing sound of the machine, resulting in a total of eight channels.Experimental setup and data

[0104] For the purpose of illustrating the development and validation of the fault detection algorithm, an electrical motor was selected as an example system. The motor provides a well-defined platform for demonstrating the principles of fault detection and diagnosis, given its widespread use and susceptibility to common issues such as bearing wear, insulation breakdown, and rotor imbalance. However, it will be understood that the use of an electrical motor is provided merely as an illustrative example. The underlying methods and systems described herein are not limited to this particular application and may be adapted for diagnosing faults in a variety of other domains, including mechanical, chemical, and energy storage systems, among others.

[0105] In accordance with embodiments of the present invention, three Belt Starter Generators (BSGs) are utilized for the development and validation of a data-driven fault detection and diagnosis (FDD) method. Referring to Figure 1 , the HT-250 Belt Starter Generator (BSG) tester is depicted, representing one of the BSG units employed in the experimentation. The motorand associated test cell are instrumented to facilitate the measurement of key motor parameters. A three-axis accelerometer, designated as accelerometer #1 , is affixed to the motor for the purpose of capturing vibration data specific to the BSG. A second accelerometer of identical specification, referred to as accelerometer #2, is mounted on the BSG tester to acquire vibration data pertaining to the test cell. Additionally, two microphones are employed to record acoustic signals. Microphone #1 is positioned within the BSG tester to detect sound emissions originating from the BSG, while microphone #2 is located externally to the test cell to capture ambient environmental sound data.

[0106] In a first testing procedure, two distinct test conditions are executed: a healthy (no-fault) condition and a pulley-unbalanced fault condition. The fault condition is implemented across seven discrete severity levels, ranging from low to high. For each condition, one second of data is acquired. Each one-second interval comprises 48,000 data points per channel for both sound and vibration sensors. The pulley-unbalanced fault condition is simulated by affixing screws of varying sizes at a radial offset of 28.575 mm from the center of the pulley, as illustrated in Figure 2.

[0107] Figure 3 illustrates four categories of variability examined in accordance with the present invention, each of which influences the operational performance and reliability of the systems under investigation: BSG Variability, Variability Before and After Teardown, Bearing Variability, and Day-to-Day Variations.

[0108] BSG Variability pertains to the analysis of data variability across three distinct Belt Starter Generators (BSGs). Comparative evaluation of performance metrics and fault detection outcomes among the BSG units enables assessment of the influence of unit-specific characteristics on system behavior and data consistency.

[0109] Variability Before and After Teardown addresses the changes in system performance and diagnostic metrics observed prior to and subsequent to teardown procedures. Such analysis facilitates evaluation of the impact of maintenance and repair activities on overall system reliability.

[0110] Bearing Variability encompasses the differences between original equipment manufacturer (OEM) bearings and After-Market (AM) bearings. The invention investigates the operational and diagnostic implications of bearing type selection, with emphasis on reliability and maintenance considerations.

[0111] Day-to-Day Variations involves the assessment of performance fluctuations attributable to varying environmental conditions, including but not limited to temperature and humidity. The invention examines the extent to which such daily variations affect system operation and the precision of fault detection mechanisms.

[0112] In accordance with embodiments of the present invention, an extensive dataset pertaining to pulley unbalance severity was generated through test procedures utilizing BSG #1 and BSG #2. The dataset comprises measurements corresponding to seven distinct severity levels of pulley unbalance, ranging from mild to severe, thereby offering a comprehensive representation of real-world fault scenarios. For BSG #1 , data acquisition was performed both prior to, and subsequent to, teardown operations, enabling longitudinal analysis of the pulley system’s operational behavior and degradation characteristics over time.

[0113] A diverse dataset of bearing faults was compiled using BSG #3 and BSG #2. This dataset encompasses seven fault types, including faults associated with the inner race, outer race, ball elements, and grease degradation. Fault simulation procedures, illustrated in Figure 4, involved subjecting multiple bearings to controlled damage conditions. The bearing under test was located at the front end of the BSG. Faults were introduced by creating apertures in the inner and outer race tracks as well as in the ball bearings, thereby replicating physical damage. Each faulty bearing incorporated at least two fault conditions. Healthy bearings, designated as “OEM” and “AM,” remained unaltered and retained their original lubricant composition.

[0114] Moreover, the bearing faults dataset included data collected from both After-Market (AM) and Original Equipment Manufacturer (OEM) bearings,thereby facilitating comparative analysis of fault signatures between these two bearing types. The comprehensive nature of the dataset ensures inclusion of a wide range of fault scenarios, which contributes to the development, validation, and refinement of fault detection and diagnosis methodologies applicable to rotating machinery.

[0115] In at least one embodiment, a pre-processing method is described herein. Figures 5 provide details of the pre-processing method. The preprocessing method was developed to improve the accuracy of detecting and diagnosing pully-imbalanced and bearing faults. The method is a combination of short-time Fourier transform (STFT) and Principal Component Analysis (PCA) based Multivariate Statistical Process Control (MSPC) with a sliding window method. The pre-processing method consists of the following steps: time-frequency analysis, segmentation, PCA-based Multivariate Statistical Process Control (MSPC) with a sliding window, statistical analysis, and classification.

[0116] The short-time Fourier transform (STFT) serves to examine how the frequency composition of a signal, which may vary over time, evolves. The square of the magnitude of the STFT is referred to as the spectrogram, a representation of the signal's frequency behavior across time.

[0117] STFT of a signal involves sliding an analysis window, denoted as g(n) and of length M, along the signal. At each position, the discrete Fourier transform (DFT) is computed for the windowed segment. The window advances over the original signal in intervals of f? samples, resulting in an overlap of L = M - R samples between adjacent segments. To mitigate spectral artifacts, most window functions taper off towards the edges. The DFT of each windowed segment contributes to a complex-valued matrix containing magnitude and phase information across time and frequency.

[0118] Each column (indexed by m of the STFT matrix X( ) = [%!( ) X2( / ) ^( / ) ■ ■■ ^ / <( / ) ] corresponds to the DFT of the windowed data centered around time mR:

[0119] In the first step of the proposed method, STFT with a Hanning window is applied to raw time-domain data of sound and vibration to have frequency components with respect to time. It can be appreciated that any suitable Hanning window length can be utilized. Figure 6 shows an example of using STFT to convert a vibration signal in the time domain.

[0120] In the second step of the pre-processing method, a segmentation process is applied to the frequency components derived from the Short-Time Fourier Transform (STFT) of the data. The objective of the segmentation step is to divide the frequency range into smaller segments, enabling a detailed analysis of frequency-specific variations and anomalies. Segmenting the frequency range allows for a focused examination of specific frequency bands, which is essential for identifying and understanding fault characteristics in rotating machinery and similar systems.

[0121] For example, certain anomalies may manifest only in specific frequency bands, making it crucial to analyze these bands independently. This isolation enables more accurate detection and classification of faults that would otherwise be obscured in broader-spectrum analysis. Furthermore, smaller frequency segments increase the sensitivity of the analysis, aiding in the detection of subtle changes and variations that could be indicative of underlying issues. This heightened sensitivity is particularly valuable in early-stage fault detection, where signal deviations may be minimal.

[0122] Segmentation also provides insights into the behavior of different frequency components, facilitating targeted interventions and control measures. By understanding how specific frequencies respond under various fault conditions, more effective diagnostic and maintenance strategies can be developed.

[0123] In at least one embodiment, the STFT output can be a matrix where the rows represent frequency components, and the columns represent timeobservations. For example, an STFT output of size 129x374 indicates 129 frequency components across 374 time observations. In the proposed method, the segmentation process Figure 7 divides the frequency range into smaller intervals, each containing a specified number of frequency components. In at least one embodiment, the specified number can be obtained through a trial- and-error process to achieve high accuracy for classification. In the embodiments described herein, let Nfbe the total number of frequency components, and let the data be segmented into Kfsegments, with each segment containing m frequency components.

[0124] For instance, if Nf= 129 and the number of segments Kf= 43, then each segment will have 3 frequency components (m=3). The segmentation boundaries are defined as:Zj = 1 + (Z — 1) x m (1-2)Uj = i x m (1-3) where ltand utrepresent the lower and upper bounds of the i-th frequency segment, respectively.

[0125] For each segmented frequency band, a series of analytical steps are independently applied to ensure precise characterization of system behavior. The analysis steps include standardization, singular value decomposition (SVD), principal component analysis (PCA), and the calculation of the T-squared statistic. By performing these operations separately for each frequency segment, a focused and granular analysis of the data can be performed. The results from all segments are subsequently integrated to produce a comprehensive overview of the process behavior over time, capturing both localized and system-wide variations.

[0126] The process begins by extracting the relevant segment from the baseline or healthy dataset. For each segment, the mean and standard deviation are computed to establish the statistical parameters necessary for normalization. The segment is then standardized to ensure consistency in scaleand distribution, which is critical for subsequent dimensionality reduction techniques.

[0127] Following standardization, singular value decomposition (SVD) is performed to obtain scores, loadings, and eigenvalues. These outputs are used to conduct principal component analysis (PCA), which identifies the principal components that capture the most significant variance within the data. The percentage of variance explained by each principal component is calculated, and the number of components that collectively explain more than 90% of the variance is determined. This threshold ensures that the dimensionality reduction retains the most informative aspects of the signal.

[0128] Once the principal components are established, the T-squared statistic is calculated for the baseline data to quantify the multivariate distance of each observation from the mean. The same analytical process is then applied to the test data. Importantly, the T-squared statistic for the test data is computed using the loadings derived from the baseline dataset, allowing for consistent comparison and fault detection. The methodology for calculating the T-squared statistic and the detailed procedures for both baseline and test data are further elaborated in the following section. Calculating T-squared and the different processes for baseline and test data are elaborated further in the following section.

[0129] Turning now to the PCA-based Multivariate Statistical Process Control (MSPC) with a sliding window step, Statistical Process Control (SPC), including Multivariate Statistical Process Control (MSPC), is important to condition monitoring in various industries like manufacturing and FDD. MSPC schemes primarily concentrate on assessing the stability of process means. They utilize statistical metrics such as the Squared Prediction Error (SPE) and Hotelling’s T2statistic, which are derived from process variables. In MSPCA, process mean's stability is built using Hotelling's T2statistic and the original K registered (typically product quality or dimension) variables.T2= z - fi)TS z - (1-4)Where S is an estimate of the in-control covariance matrix Y,z is a vector of measurements, and p is the in-control mean vector.

[0130] To understand the PCA-based MSPC technique, a GUI-based model can be used. The performance of the in-control process can be modelled using historical reference data collected under normal operating conditions. This historical database analysis effectively improves process understanding and detects past process faults (out-of-control samples). A historical database can be considered as a collection of N multivariate observations (objects or samples) on K variables (online process measurements, dimensional variables, or product quality data), organized in an (NxK) data matrix z. The z variables are frequently pre-processed by mean-centering and scaling to unit variance. PCA can be used to reduce the process's dimensionality by compressing the high-dimensional original data matrix X into a low-dimensional subspace of dimension A (A < rank(X)), in which most of the data variability is explained by a smaller number of latent variables that are orthogonal and linear combinations of the original ones. This is accomplished by decomposing X into a collection of A rank-one matrices.

[0131] P (K x A) is the loading matrix containing the loading vectors Pa, which are the eigenvectors equivalent to the A largest eigenvalues of the covariance matrix of the original pre-treated data set X. These identify the orientation of the largest variance of the new latent A -dimensional subspace.

[0132] T N x A) is the score matrix that holds the coordinates of the original observations' orthogonal projection onto the latent subspace. The columns taof the score matrix T(ta= XPa represent the new latent variables with variances given by their respective eigenvalues (la). The most important information from the original K variables is captured in these new latent variables and, as a result, can estimate (reconstruct) X with minimum meansquare error, X* = TPT. Matrix E = N x K incorporates the residuals (statistical noise) or knowledge that the PCA model does not describe.

[0133] From the scores and residual connected from each observation, an important static called Hotelling's T is obtained. Thestatic for the i -th observation is as follows:

[0134] Where 0(A x A) is the covariance matrix of T (diagonal matrix of the highest A eigenvalues {A1;... ,2^}). Hotelling's T; shows the expected squared Mahalanobis distance from the centre of the latent subspace to the projection of observation onto this subspace when a diminished subspace with A components is used rather than on the original variables space.

[0135] New process observations can be monitored in real-time after obtaining the reference PCA model and the control limits for the multivariate control charts. When a new observation ztvector becomes available, pre- processed, and projected onto the PCA model, resulting in scores and residuals from which Hotelling's T; value is calculated, as shown in Figure 8.

[0136] A sliding window with a width of 0.6 kHz can be applied to the output of the Short-Time Fourier Transform (STFT). This window size corresponds to three frequency components in the STFT output. For example, the original STFT matrix, which has 129 frequency components (rows) across 374 time observations (columns), is segmented into 43 smaller segments. Each segment represents a frequency band of 0.6 kHz.

[0137] Using the healthy data, a baseline model can be constructed through the Multivariate Statistical Process Control (MSPC) method. This model serves as a reference for detecting deviations in test data. After segmentation, the baseline model's output is a matrix with dimensions of 43 segments by 374 data points. Each entry in this matrix represents a segment's behavior over time.

[0138] Hotelling's T-squared statistic is employed to measure the deviation of each segment from the corresponding segment in the baseline model. This statistic helps identify significant variations that may indicate potential faults. The calculation of the T-squared statistic involves several steps: Standardization, Singular Value Decomposition (SVD), Principal Component Analysis (PCA), and T-Squared Calculation. This process is applied separately to both baseline (healthy) and test datasets to ensure consistency and reliability in fault detection.

[0139] First, each segment of the baseline and test data is standardized. Standardization transforms the data such that each feature has a mean of zero and a standard deviation of one. This step is essential to eliminate scale differences across variables and to prepare the data for dimensionality reduction techniques.

[0140] Following standardization, Singular Value Decomposition (SVD) is performed on the data. SVD decomposes the standardized dataset into scores, loadings, and eigenvalues, which are then used to conduct Principal Component Analysis (PCA). PCA identifies the principal components that capture the most significant variance in the data. Only those components that explain the majority of the variance are retained for further analysis. For example, only the components that are contributing to over 90% of the total can be retained.

[0141] Using the retained principal components, the T-squared statistic is computed for each segment. The T-squared statistic measures the multivariate distance of each observation from the mean, effectively quantifying how far a data point deviates from the expected baseline behavior. The same procedure is applied to the test data, with the T-squared values calculated using the loadings derived from the baseline dataset. This ensures that deviations in the test data are evaluated relative to the healthy system profile.

[0142] The results of the T-square calculation can be visualized by plotting the T-squared statistic over time for each frequency segment. For instance, Figure 9 illustrates the Hotelling's T-squared index for the first frequency band(0 to 0.6 kHz). This figure shows the deviations of different faults from the baseline. Faults 1 and 2 do not show significant deviations from the baseline, indicating that they do not affect the first frequency band markedly. On the other hand, fault 7 shows a substantial deviation from the baseline, indicating a significant anomaly in the first frequency band. The indicators extracted by this method for each condition provide a detailed view of how different faults affect various frequency bands. By examining these indicators, specific frequency ranges where deviations occur can be pinpointed, enabling targeted analysis and diagnostics.

[0143] The PCA-based Hotelling index for 43 segments is generated in the previous session. The statistical analysis step applies a number of moving statics with window of any number to the Hotelling index. This step aims to get smoother indices from the Hotelling index, as shown in Figure 10. The feature dimension for sound and vibration data is 43 segments x 8 channels x 5 moving indices.

[0144] In the culmination of the process, the extracted features are utilized as inputs for the classification models. Classification methodologies such as support vector machines classifier can be applied across diverse datasets. This approach ensures not only effective feature representation but also robust model performance. In the final step of the proposed method, the extracted features are used as input for the Support Vector Machine (SVM) model. In this embodiment, the input matrix for training consists of 1720 features and 2992 observations. The 1720 features are derived from reshaping the data from 8 sensors, 43 Hotelling's T-squared statistics, and 5 descriptive statistics. The 2992 observations correspond to 8 classes with 374 observations each, obtained after applying the Short-Time Fourier T ransform (STFT) with a window size of 256.

[0145] For the SVM model, a kernel SVM with 1000 iterations can be used utilized. Kernel SVMs are advantageous when dealing with non-linear data, as they can effectively map the input features into a higher-dimensional space where a linear separation becomes possible.

[0146] The SVM model uses a hinge loss function during the fitting process.The hinge loss function is defined as:where y is the actual class label and (%) is the predicted class label. This loss function is pivotal in maximizing the margin between different classes, thus enhancing the classifier's ability to generalize to unseen data.

[0147] In one embodiment, the regularization strength, denoted as A, is set to 0.000334. Regularization helps prevent overfitting by penalizing overly complex models. The parameter A controls the trade-off between achieving a low training error and minimizing model complexity:where m is the number of training examples, b is bias, xtis the feature vector, and w is the weight vector. By setting A to 0.000334, the model strikes a balance between fitting the training data well and maintaining a simpler, more generalizable model.

[0148] In accordance with embodiments of the present invention, the proposed approach emphasizes feature extraction as the primary objective, rather than direct classification or artificial intelligence (Al)-based decisionmaking. The features extracted through the described methodology are designed to serve as indicators of system behavior and may optionally be utilized as inputs to anomaly detection algorithms or machine learning (ML) models for advanced classification and predictive diagnostics. However, the feature outputs themselves are sufficiently informative to support binary decision-making, such as pass / fail determinations, without requiring further Al- based interpretation.

[0149] Pass / fail thresholds are established using control limits derived from baseline (healthy) operating data. Specifically, statistical indices such as Hotelling’s T-squared (T2) statistic are employed, wherein control limits aredefined at predetermined confidence levels (e.g., 95% or 99%). Measurements that fall within these control limits are classified as pass, indicating healthy operation, while those that exceed the limits are classified as fail, signifying a potential fault condition.

[0150] To complement this framework, additional statistical measures such as the three-sigma rule and z-score thresholds may be applied to individual features. These measures can help reinforce the decision-making process by providing alternative or supplementary criteria for identifying deviations from normal behavior. Furthermore, the frequency region in which a deviation occurs offers diagnostic insight beyond binary classification, enabling identification of fault types based on the spectral location of the abnormality.

[0151] This dual capability ensures that the system not only provides direct pass / fail decisions based on statistically grounded thresholds but also generates structured feature outputs that are compatible with more sophisticated Al or ML frameworks. As such, the invention supports both immediate fault detection and scalable integration into predictive maintenance systems.

[0152] The proposed method also provides a method of analysis to show how different variabilities within the dataset can affect model performance.

[0153] In accordance with embodiments of the present invention, one significant advantage of the proposed method lies in the comprehensive and diverse dataset collected to support fault detection and diagnosis. The dataset includes measurements from multiple Belt Starter Generators (BSGs) under varying fault conditions. For pulley unbalance faults, data was acquired from BSG #1 and BSG #2 across seven distinct severity levels, simulating real-world mechanical imbalance scenarios. For bearing faults, data was collected from BSG #2 and BSG #3, encompassing seven fault types and incorporating both Original Equipment Manufacturer (OEM) and After-Market (AM) bearings. This extensive and heterogeneous dataset enables rigorous evaluation of diagnostic techniques under realistic operating conditions. More broadly, the methodology for data acquisition and fault simulation is applicable to any industrial system,including rotating machinery, energy storage devices, and chemical processing equipment, where diverse fault scenarios are be captured to ensure robust model development.

[0154] A second advantage of the invention is its ability to detect and diagnose pulley-unbalanced faults with high reliability across varying conditions. The analysis accounts for two key sources of variability: differences between individual BSG units and variations introduced by teardown procedures. Data was collected using multiple BSGs under both healthy and faulty conditions, allowing the model to assess how hardware-specific differences influence fault detection outcomes. Teardown procedures, which involve disassembling equipment for inspection and reassembly, can introduce inconsistencies in fault manifestation. By incorporating these factors into the analysis, the invention ensures that the developed fault detection and diagnosis (FDD) techniques remain accurate and consistent across different operational and maintenance scenarios. This approach generalizes to any industrial diagnostic system where equipment variability and maintenance-induced changes may affect fault signatures.

[0155] The third advantage pertains to the detection and diagnosis of bearing faults under a wide range of operating conditions. The invention investigates multiple sources of variability, including differences between BSG units, teardown effects, and bearing type (OEM vs. AM). The results demonstrate that the proposed diagnostic framework is capable of accurately identifying bearing faults regardless of these variations. This robustness supports improved maintenance strategies and contributes to reduced downtime in industrial systems. The methodology is broadly applicable to fault diagnostics in other domains, such as electric motors, compressors, turbines, and battery systems, where component-level variability and operational diversity are needed to ensure reliable fault identification.

[0156] In accordance with embodiments of the present invention, the following section presents experimental results related to the detection and diagnosis of pulley unbalance faults, including an analysis of associatedvariations such as differences between Belt Starter Generators (BSGs). The methodologies and findings described herein are broadly applicable to fault diagnostics in a wide range of industrial systems, including rotating machinery, energy storage devices, and chemical processing equipment, where variability in hardware, operating conditions, and maintenance procedures may influence fault manifestation and detection accuracy.

[0157] The robustness of the proposed diagnostic model was demonstrated through its consistent performance across datasets collected from different BSG units and on different days. Feature vectors extracted from sensor data were used as inputs to a Support Vector Machine (SVM) model implemented. To evaluate generalization capability, the model was trained on data from BSG #1 and tested on data from BSG #2. This cross-unit validation confirmed the model’s ability to accurately predict fault conditions in previously unseen data, thereby verifying its reliability and adaptability. Default SVM parameters included a linear kernel, a regularization parameter (C) of 1 , and an optimization tolerance (TolFun) of 1e-3, with parameter tuning available based on dataset characteristics and optimization requirements. Such a framework is readily transferable to other industrial domains where fault detection models must generalize across different equipment units or operational environments.

[0158] Principal Component Analysis (PCA) was employed to reduce dimensionality and identify dominant patterns within the extracted feature space. The first three principal components (PCs) captured the primary axes of variability across datasets collected from different BSGs, revealing consistent structural trends in the data. These components facilitated interpretation of the underlying fault characteristics and enhanced the model’s diagnostic capability. The model achieved 100% detection accuracy and 95.7% diagnosis accuracy for pulley unbalance faults, underscoring its effectiveness in distinguishing between healthy and faulty conditions. In industrial applications, the ability to reliably separate healthy operation from fault states is often more critical than distinguishing between fault severity levels. For example, minormisclassifications between adjacent fault classes (e.g., fault 1 and fault 2) may be acceptable if the system consistently identifies the presence of a fault. This principle applies broadly to fault diagnostics in complex systems such as battery packs, compressors, and chemical reactors, where early and accurate fault detection is essential for operational safety and maintenance planning.

[0159] The Model Performance for the BSG tear-down variability analysis was conducted to assess the impact of BSG teardown on detection and diagnosis results. Remarkably, the invention revealed that the process of tearing down the BSG did not affect the accuracy of detection and diagnosis. By training the model using data collected before the teardown, the testing accuracy achieved using data collected after the teardown was significantly high. Notably, the invention achieved an exceptional 100% detection accuracy and an 97.2% (see Figure 13) diagnosis accuracy, reinforcing the robustness and reliability of the model in handling the variability of BSG operating conditions. These findings hold great promise in enhancing the effectiveness of fault detection and diagnosis techniques in industrial applications. Figure 14 shows the first three principal components of the extracted features for two sets of data. One is related to the first day of testing before the teardown, the second one is related to the dataset collected on day #2 after the teardown. Figure 14 shows that these two datasets are consistent, with each class forming a distinct cluster.

[0160] In accordance with embodiments of the present invention, a comprehensive dataset comprising at least seven bearing fault combinations was collected to facilitate the evaluation of the fault detection and diagnosis model. The dataset includes variations in fault type, bearing condition, and operating environment, thereby enabling a robust assessment of the model’s performance under diverse scenarios.

[0161] In at least one embodiment, the method also considers variabilities such as tear-down effects and differences between OEM and AM bearings and investigated model performance under different operating conditions (load and RPM). By including diverse fault manifestations andcombinations, the model's ability to accurately detect and diagnose bearing faults is thoroughly assessed, enhancing its reliability and practical applicability in industrial machinery maintenance. Moreover, the methodology employed for dataset generation is broadly applicable to fault diagnostics across a wide range of industrial domains. Whether applied to rotating machinery, energy storage systems, or chemical processing equipment, the approach supports the development of scalable and generalizable fault detection models.

[0162] Figure 15 showcases the healthy data collected from different days of testing and various BSGs, along with data representing bearing faults. Figure 15 further shows that the healthy and faulty data form two distinct clusters, simultaneously depicting the variations in healthy and faulty conditions. The model achieved an impressive 100% detection accuracy for this type of bearing fault, successfully accounting for two sources of variability: BSG-to-BSG variation and teardown variability. This noteworthy result highlights the model's ability to extract meaningful features from the data, demonstrating its robustness and reliability in detecting bearing faults amidst complex and diverse data variations.

[0163] Figure 16 illustrates distinct clusters for both OEM and AM bearings. This underscores the significance of considering the OEM and AM bearings as two categories separately for the purposes of bearing fault detection and diagnosis. The observed variability in the data indicates that the performance characteristics and fault patterns may vary between OEM and AM bearings. Taking this variation into account can help develop accurate and reliable detection and diagnosis models, ensuring effective maintenance and optimal performance of machinery that relies on different types of bearings.

[0164] In accordance with embodiments of the present invention, the method further considers bearing fault detection and diagnosis across various operating conditions. The training data is collected on a different day than the testing data. Specifically, the model is trained using data from day #1 and tested on data from day #2. This setup enables the understanding of day-to-day variations in model performance.

[0165] In at least one embodiment, a weighted average accuracy can be used to report the final diagnosis accuracy, as this approach accounts for the variability in performance across different scenarios. The variations in detection and diagnosis performance at various RPM and load conditions can be common, necessitating optimization to calculate the appropriate weight factors. Figure 17 illustrates the total diagnosis accuracy of the model without considering weight factors. In at least one embodiment, higher RPM and load conditions showed increased accuracy levels, influenced by complex interactions between mechanical stress, lubrication, and temperature affecting the manifestation of bearing faults. By employing optimization techniques, weight factors can be derived (Figure 18), highlighting the significance of considering specific conditions for diagnosing various faults. Remarkably, the highest performance of 99.94% across all fault types was observed at 40 Nm and 1000 RPM, highlighting the importance of tailoring diagnostic approaches to specific operating conditions to enhance fault detection accuracy.

[0166] The variations in fault manifestation across different operating conditions, particularly with respect to lubricant faults and ball bearing faults, can be attributed to several factors. At lower RPM (Revolution Per Minute) levels, the lubrication process may be less efficient, leading to inadequate distribution of lubricant within the bearing assembly. As a result, lubricant- related faults may be less pronounced due to reduced friction and wear, masking their visibility in fault detection. Similarly, ball bearing faults may exhibit lower intensity at lower RPM as the reduced rotational speed lessens the dynamic forces acting on the bearings, thereby mitigating the severity of defects and preventing their detection at these operating conditions. Understanding these nuances in fault behavior across different operating conditions is critical for devising effective condition monitoring and fault detection and diagnosis strategies, as it allows maintenance personnel to focus on targeted inspections and corrective measures, perform preventative maintenance, thereby optimizing machinery performance and ensuring reliability in various operational scenarios.

[0167] In accordance with embodiments of the present invention, the method considers the bearing-to-bearing variation in bearing fault detection, involving at least four sets of data collected from four different AM bearings over at least two separate days. In one embodiment, two sets of data can be used for training the model, while the other two sets can be kept as blind data for testing purposes. As depicted in Figure 18, the healthy bearing data forms a single cluster, indicating consistent behavior across all healthy bearings. In contrast, the faulty bearing data forms two distinct clusters (Figure 19), suggesting varying severity levels of bearing faults introduced in different bearings. This observation highlights the model's capability to detect and diagnose these changes effectively, as it discerns the differing fault patterns resulting from various bearing conditions. This ability to handle bearing-to- bearing variation demonstrates the model's robustness and reliability in addressing real-world scenarios, making it a promising tool for accurate and dependable bearing fault detection and diagnosis.

[0168] The methodology employs techniques including time-frequency analysis, multivariate statistical process control, and classification to enhance fault diagnostics in industrial systems. Key strengths of this method include consideration of variability within the dataset, such as differences between bearing types, fluctuations across BSGs and testing days, and changes before and after teardowns. Another advantage of the method includes the demonstration of robustness with a 100% detection rate across diverse scenarios.

[0169] For bearing faults, the model achieved a diagnosis accuracy of 99.94%, compared to 80% with the CNN-SVM model, indicating better handling of day-to-day variability. Results also show that healthy data using AM and OEM bearings form distinct clusters, highlighting the need to consider such variability when developing fault detection and diagnosis models. The model's performance across different operating conditions (RPM and torque) was also investigated, revealing the highest accuracy at 2000 RPM and 40 Nm. Additionally, the model’s performance in detecting and diagnosing pulleyunbalance and bearing faults remains unaffected by tear-down and BSG-to- BSG variability. These findings underscore the importance of addressing variability to improve diagnostic accuracy and reliability in practical applications.

[0170] Moreover, the methodology employed for dataset generation is broadly applicable to fault diagnostics across a wide range of industrial domains. Whether applied to rotating machinery, energy storage systems, or chemical processing equipment, the approach supports the development of scalable and generalizable fault detection models. By capturing multiple fault modes and operational variations, the invention provides a foundation for predictive maintenance and reliability optimization in complex industrial systems.

[0171] In at least one embodiment, a flowchart showing the steps of the preprocessing method is shown in Figure 20. The process begins with extracting a segment from baseline or healthy data (200 and 210), followed by computing the mean and standard deviation of the segment (220). The segment is then standardized to have zero mean and unit variance (230). Singular Value Decomposition (SVD) is performed to obtain scores, loadings, and eigenvalues (240), and the percentage of variance explained by each principal component is calculated (250). The system then determines the number of principal components that account for at least 90% of the variance (260), and computes Hotelling’s T-squared statistic for the baseline data (270). The same process is applied to the test data (280), and the T-squared statistic for the test data is computed using the loadings derived from the baseline (290). This process enables consistent comparison between healthy and test data segments to identify deviations indicative of faults.

[0172] Figure 21 illustrates the flowchart of the algorithm implemented for fault detection in an industrial furnace. Time-domain microphone signals, recorded at multiple locations of the furnace, were provided by the collaborating company for analysis. In at least one embodiment, the deviations from a predefined baseline operating condition was determined. The feature extraction procedure applied herein is consistent with that described in Figure 20. Thealgorithm quantifies the deviation of incoming samples from the baseline, and such deviations are subsequently utilized to detect faults. The model demonstrated a detection accuracy of 99% under a challenging operating condition characterized by substantial noise.

[0173] In at least one embodiment, Figure 21 , showing the flowchart of the model for detecting furnace faults can be also applicable to that of the battery case. However, instead of microphone data, current data is acquired by the sensors.

[0174] In at least one embodiment, the electromechanical or electrochemical system is considered to be in a fault condition when the indicators produced by the method exceed their respective derived or predefined statistical limits. Conversely, the system is considered healthy when the indicators remain within those statistical limits.

[0175] Figure 22 illustrates an example output generated by the fault detection model. In one embodiment, fault detection thresholds were set at approximately 10 for HSN1 and 4 for HSN2, where HSN1 and HSN2 represent the mean deviation indicators for the two lowest frequency bands. Any data point exceeding these thresholds is flagged as faulty.

[0176] At least some of the elements of the various embodiments of the ingestible medical device described herein that are implemented via software may be written in a high-level procedural language such as object oriented programming or a scripting language. Accordingly, the program code may be written in C, C++or any other suitable programming language and may comprise modules or classes, as is known to those skilled in object oriented programming. Alternatively, or in addition, at least some of the elements of the embodiments of the ingestible medical device described herein that are implemented via software may be written in assembly language, machine language or firmware as needed. In either case, the program code can be stored on a storage media or on a computer readable medium that is readable by a general or special purpose programmable computing device having a processor, an operating system and the associated hardware and software thatis necessary to implement the functionality of at least one of the embodiments described herein. The program code, when read by the computing device, configures the computing device to operate in a new, specific and predefined manner in order to perform at least one of the methods described herein.

[0177] Furthermore, at least some of the methods described herein are capable of being distributed in a computer program product comprising a computer readable medium that bears computer usable instructions for one or more processors. The medium may be provided in various forms such as, but not limited to, one or more diskettes, compact disks, tapes, chips, USB keys, external hard drives, wire-line transmissions, satellite transmissions, internet transmissions or downloads, magnetic and electronic storage media, digital and analog signals, and the like. The computer useable instructions may also be in various forms, including compiled and non-compiled code.

[0178] While the applicant's teachings described herein are in conjunction with various embodiments for illustrative purposes, it is not intended that the applicant's teachings be limited to such embodiments. On the contrary, the applicant's teachings described and illustrated herein encompass various alternatives, modifications, and equivalents, without departing from the embodiments, the general scope of which is defined in the appended claims.

Claims

CLAIMS:1 . A method for condition monitoring and detecting and diagnosing faults on an electromechanical and / or electrochemical system, comprising: receiving raw time-domain signals from one or more sensors collecting data from the electromechanical or electrochemical system; applying a Short-Time Fourier Transform (STFT) to the timedomain raw signals to generate a spectrogram; segmenting the spectrogram into a plurality of frequency band segments; performing Principal Component Analysis (PCA)-based Multivariate Statistical Process Control (MSPC) on each of the plurality of frequency band segments; applying statistical smoothing to the MSPC output; and classifying fault conditions based on the smoothed statistical indicators; wherein the electromechanical or electrochemical system is characterized as having a fault when indicators generated by the method exceed their derived or specified statistical limits, and the electromechanical or electrochemical system is characterized as not having a fault when the indicators are within their corresponding derived or specified statistical limits.

2. The method of claim 1 , wherein the raw time-domain signal comprises vibration or acoustic data sampled at a rate sufficient to capture fault- related frequencies.

3. The method of claim 1 , wherein the STFT produces a spectrogram matrix with dimensions corresponding to frequency components and time observations.

4. The method of claim 1 , wherein the segmentation step divides the spectrogram into a plurality of frequency intervals, each analyzed independently.

5. The method of claim 1 , wherein the PCA-based MSPC step comprises:standardizing each frequency segment; applying Singular Value Decomposition (SVD) to the standardized frequency segments to extract principal components (PC’s); selecting a portion of the principal components that account for at least 90% of the variation in the standardized frequency segments; computing Hotelling’s T-squared statistics for each of the standardized frequency segments using the selected principal components.

6. The method of claim 5, further comprising constructing a baseline model using healthy system data and comparing test data against the baseline using the retained principal components.

7. The method of claim 5, wherein the statistical smoothing step comprises applying a number of moving statistics to the T-squared statistics.

8. The method of claim 1 , wherein the classification step comprises comparing fault signatures across Original Equipment Manufacturer (OEM) and After-Market (AM) electromechanical or electrochemical system datasets.

9. The method of claim 1 , wherein the classification step identifies multiple fault conditions to the electromechanical or electrochemical system.

10. The method of claim 5, further comprising visualizing the T-squared statistics over time to identify deviations in specific frequency bands.

11. The method of claim 1 , wherein the segmentation boundaries are predefined or dynamically adjustable based on characteristics from the time-domain signals.

12. The method of claim 1 , wherein the PCA-based MSPC step is performed using a sliding window to track fault evolution over time.

13. The method of claim 1 , wherein the classification step employs supervised or unsupervised learning algorithms to label fault types.

14. The method of claim 1 , wherein the method is applied to rotating machinery including electric motors, compressors, and turbines.

15. The method of claim 1 , wherein the fault detection method is configured for real-time monitoring and alert generation.

16. The method of claim 1 , wherein the baseline model is periodically updated using newly acquired data.

17. The method of claim 1 , wherein the STFT window overlaps adjacent segments by a predefined number of samples to preserve continuity.

18. The method of claim 1 , wherein the method identifies localized anomalies by comparing T-squared statistics across frequency segments.

19. The method of claim 1 , wherein the statistical indicators are used to generate fault severity scores.

20. The method of claim 1 , wherein the method is implemented in a computing system comprising a processor and memory storing instructions for executing the steps.

21. A fault-detection-diagnosis (FDD) system for detecting and diagnosing faults in an electromechanical or electrochemical system, comprising: one or more sensors configured to collect raw time-domain signals from the electromechanical or electrochemical system; a processing unit configured to: apply a Short-Time Fourier Transform (STFT) to the raw time-domain signals to generate a spectrogram; segment the spectrogram into a plurality of frequency band segments; perform Principal Component Analysis (PCA)-based Multivariate Statistical Process Control (MSPC) on each of the plurality of frequency band segments; apply statistical smoothing to the MSPC output; and classify fault conditions based on the smoothed statistical indicators; anda memory storing instructions executable by the processing unit to perform the above operations; wherein the electromechanical or electrochemical system is characterized as having a fault when indicators generated by the method exceed their derived or specified statistical limits, and the electromechanical or electrochemical system is characterized as not having a fault when the indicators are within their corresponding derived or specified statistical limits.

22. The FDD system of claim 21 , wherein the sensors are configured to collect vibration or acoustic data sampled at a rate sufficient to capture fault-related frequencies.

23. The FDD system of claim 21 , wherein the processing unit generates a spectrogram matrix with dimensions corresponding to frequency components and time observations.

24. The FDD system of claim 21 , wherein the processing unit segments the spectrogram into a plurality of frequency intervals, each analyzed independently.

25. The FDD system of claim 21 , wherein the processing unit: standardizes each frequency segment; applies Singular Value Decomposition (SVD) to the standardized frequency segments to extract principal components; selects a portion of the principal components that account for at least 90% of the variation in the standardized frequency segments; computes Hotelling’s T-squared statistics for each of the standardized frequency segments using the selected principal components.

26. The FDD system of claim 25, wherein the processing unit constructs a baseline model using healthy system data and compares test data against the baseline using the selected principal components.

27. The FDD system of claim 25, wherein the processing unit applies moving statistics with a window size of any numberto the T-squared statistics to smooth the output.

28. The FDD system of claim 21 , wherein the processing unit compares fault signatures across Original Equipment Manufacturer (OEM) and After-Market (AM) electromechanical or electrochemical system datasets.

29. The FDD system of claim 21 , wherein the processing unit identifies multiple fault conditions affecting the electromechanical or electrochemical system.

30. The FDD system of claim 25, wherein the processing unit visualizes the T-squared statistics overtime to identify deviations in specific frequency bands.31 . The FDD system of claim 21 , wherein the segmentation boundaries are predefined or dynamically adjustable based on characteristics of the timedomain signals.

32. The FDD system of claim 21 , wherein the PCA-based MSPC is performed using a sliding window to track fault evolution over time.

33. The FDD system of claim 21 , wherein the classification module employs supervised or unsupervised learning algorithms to label fault types.

34. The FDD system of claim 21 , wherein the system is configured to monitor rotating machinery including electric motors, compressors, and turbines.

35. The FDD system of claim 21 , wherein the FDD system is configured to monitor batteries.

36. The FDD system of claim 21 , wherein the FDD system is configured for real-time fault monitoring and alert generation.

37. The FDD system of claim 21 , wherein the baseline model is periodically updated using newly acquired healthy system data.

38. The FDD system of claim 21 , wherein the STFT window overlaps adjacent segments by a predefined number of samples to preserve continuity.

39. The FDD system of claim 21 , wherein the FDD system identifies localized anomalies by comparing T-squared statistics across frequency segments.

40. The FDD system of claim 21 , wherein the statistical indicators are used to generate fault severity scores.

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