Engineering Data Analysis OEL Presentation.pptx

It is an engineering data analysis presentation.

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2. ENGINEERING DATA ANALYTICS AND AI OPEN ENDED LABORATORY

3. TOPIC Comparing Conventional (regression based) and Artificial Intelligence (ANN based) Process Modeling Techniques for Engineering Product Design Application: The Case of an Automobile Tyre . 3

4. OUR TEAM 4 MUHAMMAD FURQAN RAMZAN KHAN

5. PROBLEM STATEMENT The tyre industry wants to understand how tyre features, car speed, and temperature affect drag coefficient. They conducted 392 experiments and seek to build regression and neural network models to predict drag coefficient, comparing their effectiveness with standard measures. . 5

6. OBJECTIVES To present basic statistics of raw data visually (measures of spread) and tabularly (measures of central tendency) 2. To develop an effective mixed level full factorial DOE based regression model of your choice using an established software of your choice and effectively present the results visually and orally. 3. 6 To train state of the art ANN model of your choice and effectively present the results visually and orally. 4. To graphically present and defend the best model among regression and ANN based on goodness of fit measures analysis and effectively present the results visually and orally 1.

7. Theoretical background Linear Regression Multiple Regression Polynomial Regression 7 Regression R egression analysis is a statistical method used to model the relationship between a dependent variable (often denoted as Y) and one or more independent variables (denoted as 𝑋1,𝑋2,…,𝑋𝑛​). Types of regression

8. Theoretical background 8 Artificial Neural Network Artificial Neural Networks (ANNs) are computational models inspired by the human brain's structure and functioning. They are used extensively in machine learning and artificial intelligence to model complex patterns and decision-making processes. Basic Structure Neurons The fundamental building blocks of an ANN are neurons, or nodes, which are inspired by biological neurons. Layers An ANN is composed of three layers: Input Layer Hidden Layers Output Layer

9. Theoretical background 9 Weight and Biases Every connection between two neurons has an associated weight that adjusts as the network learns during training. Each neuron can also have a bias, further refining the learning process. Types of Neural Network Feedforward neural network Convolutional neural network Recurrent Neural Network Deep Neural Network

10. Biological resemblance Artificial Neural Networks (ANNs) draw significant inspiration from the biological neural networks found in animal brains. Here’s a closer look at how ANNs are modeled after biological neural systems and the resemblances and differences between them: Biological Inspiration Neurons Biological Neuron Artificial Neuron Synaptic weights Artificial weights 10

11. Biological resemblance Activation and firing Biological Action Potential When the electrical signal within a biological neuron exceeds a certain threshold, it triggers an action potential, causing the neuron to fire and pass the signal along its axon to other neurons Activation Function In ANNs, an activation function determines whether and to what extent a neuron will be activated (or fire). Functions like sigmoid, tanh, or ReLU decide the output of a neuron based on the sum of the weighted inputs and biases, similar to the threshold mechanism in biological neurons. 11

12. Goodness of fit The concept of "goodness of fit" in statistics measures how well a statistical model fits a set of observations. Key Aspects Model Suitability Goodness of fit tests are used to determine whether a specific statistical model is appropriate for a data set. For example, one might test whether data are well-modeled by a normal distribution, a linear regression, or another theoretical distribution. Residual Analysis Residuals, the differences between observed and model-predicted values, are analyzed to assess the fit. A good fit is generally indicated by randomly dispersed residuals around the central line (zero in regression models) without any discernible pattern 12

13. Methods to determine Goodness of fit There are few criteria through which we can check the how effectively our model is predicted: R-Square (Co-efficient of Determination) Root Mean Square Error (RMSE) Mean Square Error (MSE) Mean Absolute Error (MAE) F- Test 13

14. METHODS FORMULAE R-squared: Root Mean Square Error (RMSE): Mean Absolute Error (MAE): R-squared: Root Mean Square Error (RMSE): Mean Absolute Error (MAE):   14

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16. BASIC STATISTICS AND THEIR FORMULAE Mean Median : For odd number of observations: Median : (n+1)/2 2.For even number of observations: Median: n/2 and (n/2)+1 Standard Deviation Variance Range Range = Max Value – Min Value   16

17. Performance Evaluation Table BY training and iterations 17 No of Obs. Number of layers Number of neurons Learning rate R-Squared RMSE 1 5 6 0.2 0.9083 0.0005 2 4 8 0.4 0.8958 0.0004 3 5 6 0.4 0.9123 0.0005 4 3 8 0.2 0.9030 0.0005 5 3 8 0.4 0.9067 0.0004 6 5 8 0.3 0.8978 0.0003 7 3 6 0.3 0.8898 0.0003 8 4 8 0.3 0.8998 0.0005 9 3 10 0.3 0.8890 0.0004 10 5 12 0.3 0.9078 0.0004

18. Performance evaluation regression plots 18 First Iteration Second Iteration

19. RESULTS AND DISCUSSIONS Variable Mean Median Minimum Maximum Range Depth (mm) 9.000 9.000 6.000 12.000 6.000 Width (mm) 9.000 9.000 6.000 12.000 6.000 Temperature (°C) 27.500 27.500 15.000 40.000 25.000 Velocity (m/s) 26.675 27.400 18.600 33.300 14.700 Coefficient of Drag 0.46585 0.46600 0.44184 0.49456 0.05272 BASIC STATISTICS CALCULATIONS ON MINITAB 19 Variable St. Dev. Variance Co. of Var. Sum Sum of Sqrs . Depth (mm) 2.003 4.010 22.25 3528.00 33320.000 Width (mm) 2.003 4.010 22.25 3528.00 33320.000 Temperature (°C) 12.516 156.650 45.51 10780.0 357700.000 Velocity (m/s) 5.722 32.740 21.45 10456.6 291731.300 Coefficient of Drag 0.0140 0.000196 3.01 182.615 85.14873

20. RESULTS AND DISCUSSIONS No of Obs. No. of layers No. of neuron Learning rate R-Sq RMSE 1. 5 6 4 0.912 0.0005 2. 5 12 3 0.907 0.0004 3. 4 12 3 0.915 0.0005 REGRESSION ON MATLAB VS MINITAB 20 Coeff - Terms Co-eff SE Co-eff T-Value P-Value VIF Constant 0.50507 0.00273 185.05 0.00 - Depth (mm) -0.00136 0.000165 -8.27 0.00 1.00 Width (mm) -0.00540 0.000165 -32.67 0.00 1.00 Temperature (°C) -0.00010 0.000026 -3.9 0.00 1.00 Velocity (m/s) 0.00092 0.000058 15.90 0.00 1.00

21. RESULTS AND DISCUSSIONS 21 C Regression Type Value in % MiniTAB R_sq . 0.7839 MATLAB R_sq . 0.9156 Comparison is given in form of table The comparison of the R-squared values between Minitab and MATLAB analyses reveals that the MATLAB analysis yielded a higher R-squared value (0.9156) compared to Minitab (0.7839). Comparison between value of Minitab and MATLAB

22. conclusions Comparison of Techniques Advantages of MATLAB and ANN Implications for Engineering Applications Recommendations for Model Selection Considerations on Data Overfitting

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