The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

State-of-the-Art Review on Advancements of Data Mining in Structural Health Monitoring

In this study, the application of an intelligent digital twin integrated with machine learning for bearing anomaly detection and crack size identification will be observed. The intelligent digital twin has two main sections: signal approximation and intelligent signal estimation. The mathematical vibration bearing signal approximation is integrated with machine learning-based signal approximation to approximate the bearing vibration signal in normal conditions. After that, the combination of the Kalman filter, high-order variable structure technique, and adaptive neural-fuzzy technique is integrated with the proposed signal approximation technique to design an intelligent digital twin. Next, the residual signals will be generated using the proposed intelligent digital twin and the original RAW signals. The machine learning approach will be integrated with the proposed intelligent digital twin for the classification of the bearing anomaly and crack sizes. The Case Western Reserve University bearing dataset is used to test the impact of the proposed scheme. Regarding the experimental results, the average accuracy for the bearing fault pattern recognition and crack size identification will be, respectively, 99.5% and 99.6%.

Bearing Anomaly Recognition Using an Intelligent Digital Twin Integrated with Machine Learning

An integrated approach of Adaptive Neuro-Fuzzy Inference System and Dimension Theory for Diagnosis of Rolling Element Bearing

Most rolling element bearing (REB) fault diagnosis algorithms are evaluated on the Case Western Reserve University (CWRU) bearing dataset for its popularity and simplicity. However, the diagnosis accuracy on CWRU bearing dataset is overly saturated; it is nearly up to 100%. In this study, an input feature mappings (IFMs)-based deep residual network (ResNet) is proposed to conduct detailed and comprehensive fault diagnosis on REB with complicated bearing dataset. Firstly, a new data preprocessing method named as a signal-to-IFMs method is proposed to automatically extract features from raw signals without predefined parameters. Then, a deep ResNet is used as the fault classifier to learn the discriminative features from IFMs and identify the faults of REB. Finally, the proposed model is evaluated on the artificial, real, and mixed damages of the Paderborn university bearing dataset. The proposed method yields the average testing accuracies of 99.7%, 99.7%, and 99.81% in artificial, real, and mixed bearing damages, which outperforms other methods.

Input Feature Mappings-Based Deep Residual Networks for Fault Diagnosis of Rolling Element Bearing With Complicated Dataset

Theoretical and experimental studies to predict vibration responses of defects in spherical roller bearings using dimension theory

The marvelous uniqueness of vibration responses of faulty roller bearings can be simply observed through its vibration signature. Therefore, vibration analysis has been claimed as an effective tool...

An overview of dynamic modeling of rolling-element bearings:

Fault Diagnostics of Roller Bearings Using Dimension Theory

Sandwich panels with cellular material cores are widely used in the aerospace, automotive, and marine industries. Although honeycombs with hexagonal cells are the most frequent shapes for cores, new possibilities in lightweight structures have lately emerged. The present work evaluates the transverse shear modulus of the glass-reinforced polymer honeycomb core (GFRP - HC) and glass-reinforced polymer corrugated bioinspired model (GFRP - CBIM) core. The experimental results from the alternative dynamic technique agreed well with the numerical simulation. In the GFRP sandwich beam with corrugated HC and CBIM's core, numerical free vibration analysis was performed. The CBIM core has a higher natural frequency than the HC core, according to the numerical data. Further, numerical analysis has been performed on the bioinspired cores by varying the side length and edge radius. Modified bioinspired model - 03 core design (MBIM03) appears to be a good option for regular honeycombs used in sandwich composite panels for industrial applications that demand low weight, high rigidity, and a large amount of energy-absorbing capacity. 

Edwin Sudhagar P

Papers

An integrated approach of Adaptive Neuro-Fuzzy Inference System and Dimension Theory for Diagnosis of Rolling Element Bearing

Theoretical and experimental studies to predict vibration responses of defects in spherical roller bearings using dimension theory

An overview of dynamic modeling of rolling-element bearings:

Fault Diagnostics of Roller Bearings Using Dimension Theory

Experimental and numerical study of transverse shear modulus for bioinspired glass fiber‐reinforced polymer sandwich core