Equipment health management is implemented in the industry to maximize the lifetime of components, identify the type and severity of anomalies, and predict the remaining useful life of a component or system. Health management has three main aspects: diagnostics, prognostics, and decision-making. The diagnostics part involves the fault detection process, which also includes the classification of the type of fault. Prognostics is the prediction of the remaining useful life based on current conditions such as loading and environmental factors. The decision-making process ensures scheduled repair actions, reduction in operational costs, and prevention of catastrophic failures. The following figures illustrate various gear defects caused by fatigue: (a) a single tooth with a 2 mm crack, (b) multiple cracks located on five teeth denoted with numbers 1, 6, 10, 15, and 19, (c) and the sizes of the five tooth cracks ranging from 0.5 mm to 2.5 mm.

Gear vibrational signals contain significant information about the gear dynamics; therefore, the majority of diagnostic approaches are based on them. Any gear failure modes such as wear, cracks, and pitting cause a change in the dynamics of the system and the vibrational signal. Thus, vibration signals are used in gear diagnostics, which can be classified into three main categories:

In this approach, a virtual dynamic system is built to mimic the actual physical system. Based on the laws of physics and engineering knowledge, a set of equations is solved to assess the health of the gears. This approach is recommended when equipment testing is not available and high accuracy is needed.

To detect faults, the output of the physics-based model is compared with the sensor data output. Faults will appear in the vibration signal, depending on the type of fault. These anomalies can manifest as changes in the gear mesh frequency, amplitude modulation, and frequency modulation. For example, a defect on the gear tooth surface will affect the gear mesh stiffness.

This approach relies on the signal collected during a historical run-to-failure of equipment. The data is collected using suitable sensors and processed using a data acquisition system, which converts the analog sensor data to digital values that can be utilized to extract valuable information.

The section of suitable sensors and data acquisition is critical in this method. Several types of sensors can be used, such as accelerometers for measuring vibration levels, acoustic emission sensors for measuring stress waves, and sound microphones for measuring noise. The choice of sensor depends on requirements and limitations, such as cost, location, accuracy, environment, and frequency range.

The hybrid approach combines both the physics-based and data-driven approaches. Diagnostics can be performed by fusing the system equation with the collected data from the actual physical system, utilizing machine learning algorithms such as artificial neural networks (ANN) and support vector machines (SVM).

It is expected that the prediction accuracy and effectiveness in this approach are better when sufficient data is available.

Hybrid diagnostic algorithm for gear cracks:

Vibration signals are a primary resource in fault diagnostics of rotating machinery since they provide valuable information about the health state of equipment. Various conventional techniques have been developed for fault diagnostics; however, these techniques face many challenges, since they were designed for linear models and the nature of the systems is inevitably nonlinear.

Traditional diagnostic methods generally do not consider the effects of nonlinearity in diagnostics, resulting in a lack of general applicability and ineffective prediction for complex engineering systems. This lack of consideration raises safety concerns in addition to high maintenance costs. Therefore, it is critically important to incorporate knowledge about the nonlinear aspects of a system into diagnostic reasoning to ensure safe and efficient operation.

I am working on advancing diagnostic approaches applied to real-world dynamic systems from two perspectives. Firstly, I concentrate on extracting knowledge from the nonlinear aspects of engineering systems, such as limit cycles, chaos, and bifurcation, to enhance the performance of diagnostic algorithms. Secondly, I aim to address the limitations of classic pure data-driven approaches, which often require large amounts of data, lack interpretability, and raise safety concerns. To tackle these issues, I am developing hybrid models that integrate physics-based and data-driven techniques. This approach combines the strengths of both approaches, leveraging the physics-based models for interpretability and safety considerations while utilizing the data-driven models to enhance performance and handle complex real-world dynamics.

Nonlinear dynamics and machine/deep learning are principal aspects of my study, to characterize the nature of the dynamic system, phase space trajectories are constructed and used for information extraction, kernel density function and orthogonal bases are examples of the tools we use to reconstruct the phase space, where most of the details and characteristics are reserved and converted to informative features.

After obtaining informative features, we develop classifiers to detect faults in industrial equipment, healthy and faulty signals are divided into N number of segments, where the size of the segments is determined by the correlation between the healthy and faulty samples. The data samples are normalized, shuffled, and divided into training and testing sets with various ratios depending on the application. Finally, we deploy experimental data to minimize the loss function and increased the accuracy of the classifier.

The top right picture depicts Phase space of the pinion (a) healthy, (b) faulty with 1.3 mm tooth crack, and (c) defective with 3.1 mm tooth crack.

The bottom left image shows velocity of a pinion (a) healthy and (b) faulty with a crack depth of 1.3 mm (c) faulty with a crack depth of 3.1 mm.

The bottom right picture displays density plot of a displacement of healthy gear fitted by Legendre polynomial.

1. Ahmad Alqawasmi, Turki Haj Mohamad, Amirhassan Abbasi, Prashant N Kambali, C Nataraj, Integration of Nonlinear Dynamics and Machine learning for Diagnostics of a Single-Stage Gear Box.
2. Zihan Liu, T Haj Mohamad, Shahab Ilbeigi, C Nataraj, Early Detection of Cracks in a Gear-Train System Using Proper and Smooth Orthogonal Decompositions.
3. T Haj Mohamad, Amirhassan Abbasi, E Kim, Chandrasekhar Nataraj, Application of deep CNN-LSTM network to gear fault diagnostics.
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6. CA Kitio Kwuimy, PK Kankar, Y Chen, Z Chaudhry, C Nataraj,Development of recurrence analysis for fault discrimination in gears .