Development of Machine Learning Algorithms for Application in Major Performance Enhancement in the Selective Catalytic Reduction (SCR) System

Abstract

Machine learning is used in this study to deal with the reduction in the design period and major performance improvement of the selective catalyst reduction system. The selective catalyst reduction system helps in the reduction in NOx emission in the diesel engine. The existing methods for the design and performance improvement of selective catalyst reduction systems tend to be inefficient, due to layout changes that require modification when mounting a vehicle based on previously designed models. There are some factors that can affect the design of the diesel engine selective catalyst reduction system that can be identified by applying an optimized design. The Taguchi orthogonal array design is used with the eight factors and three levels of the main design factors. The distance of the urea injector, the distance of the mixer, the inflow angle of the exhaust gas, the angle of the urea injector, the angle of the mixer, the mounting angle in the direction of rotation of the mixer inside the selective catalyst reduction pipe, the number of mixer blades, the and bending angle of the mixer blade are identified as the eight major factors involved. These factors can also be considered manufacturing factors and can be established through machine learning. Machine learning has the advantage of being more efficient compared to other methods in determining the relationship between the data for each mutual factor. Machine learning can help in reducing processing time, which can further decrease the cost of the design analysis and improve the performance of the selective catalyst reduction system. This study shows that the results are statistically significant as the p values of the mixer blade number and cone length are lower than 0.05.

1. Introduction

Selective catalytic reduction (SCR) has a significant use in NO_x removal from stationary sources. This technology is being offered to the diesel vehicle industry and is regarded as one of the best technologies to use for reaching strict NO_x reduction requirements [1]. However, currently, some studies have shown that the uniformity of ammonia is very crucial for the reduction in the NO_x emissions by SCR [2,3,4,5,6]. The uniformity of NH₃ distribution before reaching the catalytic converter has an important influence on NOx conversion efficiency and catalyst life. A low concentration of NH₃ leads to a low conversion efficiency of NO_x, and too much NH₃ leads to crystallization and NH₃ leakage [7]. The increasing ammonia uniformity is affected by major parameters, which can be analyzed using a machine learning algorithm.

Machine learning is a subset of artificial intelligence (AI) that has garnered increasing interest in engineering applications over the past few years [8,9,10]. Machine learning has been recently used for developing and predicting certain objectives for engineering applications. There are several diversified engineering applications in which machine learning methods have been used in recent times, such as the prediction of the octane number of gasoline oil [11], the energy management of the Atkinson cycle engine [12], the study of the characteristics of mortars [13,14], the study of cement-based composite [15], the forecasting of the compression strength of alkaline-activated slag concretes [16], the study of the permeability of nano silica–rice husk ash ternary-blended concrete [17], the estimation of the cost–time overrun of building projects [18], the estimation of the performance of the biomass-derived bimetallic catalyst of the hydrogen-based SCR system [19], and the identification of flooded areas [20].

In machine learning, algorithms are trained to identify patterns and correlations in massive data sets and to make the most accurate decisions and forecasts based on this research. The more data to which machine learning applications have access, the more accurate they become [21]. The Taguchi method was used to determine a suitable number of neurons in a single hidden layer of machine learning [22,23,24].

Here, in this work, the major design factors of the SCR were analyzed using the Taguchi method to investigate the flow uniformity (UI) of the SCR system when the urea is blown. However, the main study—related to the development of machine learning algorithms—will mainly be analyzed in subsequent, future work. The analysis of the design factors and flow uniformity helps in reducing the cost and in improving the performance of the SCR system. To the best of our knowledge, many works have been conducted on the SCR system to date; however, these works have mainly focused on only certain parts of the SCR system, but not the entire SCR system as a whole. Herein, we consider the full size of the SCR system, from the inlet to the outlet.

2. Methodology

2.1. Configuration of Machine Learning System

As mentioned earlier, design factors can be analyzed using the Taguchi Method. This research focuses on identifying three major steps, namely, Taguchi’s parameter design, machine learning modeling, and an optimization technique. Figure 1 shows the flow chart for the development of the major performance prediction process of the SCR system proposed in this study. Before starting to design an experiment using the Taguchi method, we have to define the object of the research, the constraint factors, the major control factors, and the noise factor of this study [25,26]. The object of this study was to analyze the flow uniformity of the SCR by optimizing the major parameter. The constraint factors of this study defined the constrained-response surface optimization methods and Taguchi’s method in order to investigate the significant factors and to determine the optimum factor level in order to improve the uniformity of the ammonia. The distance of the urea injector, the distance of the mixer, the inflow angle of the exhaust gas, the angle of the urea injector, the angle of the mixer, the mounting angle, the number of mixer blades, the bending angle of the mixer blades, the distance of the mixer, and the length of the SCR cone are the main controls factors that can increase the flow uniformity of the ammonia. Meanwhile, some factors cannot be controlled and should be defined in as noise factors.

2.2. Taguchi Parameter Design

In the Taguchi parameter design, management factors are defined by developing an internal/external arrangement, which is then used to generate important management factors in an internal/external intersecting arrangement [27,28]. Using the signal-to-noise ratio, a Taguchi orthogonal matrix is applied to arrange the design of the factors and levels. Using ANOVA, the statistically significant differences between the two groups after evaluating the design mixture are analyzed.

2.3. Machine Learning Modelling

As shown in Figure 1, the development process of a machine learning model involves several steps, such as first regression, data analysis, second Bayesian optimization, the optimization of a sparse Gaussian process, algorithm application, and algorithm validation [29,30]. The first regression helps in the identification of independent and dependent variables; data analysis represents the analysis of the first regression process. The second Bayesian optimization is generally composed of an acquisition function, a surrogate model, and an objective function, and its main purpose is to find a globally optimal solution, rather than a local optimal solution [31]. The optimization of a sparse Gaussian process represents the machine learning model that estimates the objective function, mainly utilizing the Gaussian process and configuring the process for regression problems, classification problems, and dimensionality reduction problems. The composition of the surrogate model is carried out during the algorithm application step. The derivation/and verification of the optimization results based on established processes and algorithms are studied during the algorithm validation process.

2.4. SCR System Major Design Factors Analysis and Taguchi Orthogonal Array Design

There are countless factors to consider when designing an SCR system. The urea slip rate, urea deposit, NOx purification rate, UI, and pressure and temperature distribution in the SCR system can be factors to consider when designing an SCR system [24,32]. The manufacturing of SCR systems generally requires the consideration of several variables such as material parameters, design parameters, and manufacturing method parameters. These variables help to establish the process for the constraint function, as well as the objective function. During the development of the optimal design, when several types of multiple variables are considered, the degree of freedom of design increases. With the increase in the degree of freedom of design, the product performance also improves; however, the time and cost required for design also increase. To reduce this time and cost, it is essential to identify design variables that produce a major contribution to change in performance. Thus, in this work, only design factors that represent the shape of the SCR system are considered.

Table 1. Layout, major design factors, and shape characteristics of the major design factors of the SCR system.

No.	Classification	Major Design Factors	Unit	Detailed Description
1	Inlet of SCR System	Distance between Urea Injector and Mixer	mm
2		Inflow Angle of Exhaust Gas	deg.
3		Angle of Urea Injector and Mixer	deg.
4	Mixer	Mounting Angle in the Direction of Rotation of the Mixer inside the SCR Pipe	deg.
5		Number of Mixer Blade	No.
6		Bending Angle of Mixer Blade	deg.
7	SCR System	Distance of Mixer and SCR Catalyst	mm
8		Length of SCR Cone	mm

shows the layout, major design factors, and shape characteristics of the major design factors of the SCR system. The distance between the urea injector and the mixer, the inflow angle of the exhaust gas, and the angle between the urea injector and the mixer can be classified as the design factors for the inlet of the SCR system. The mixer design factors are mainly the mounting angle in the direction of rotation of the mixer inside the SCR pipe, the number of mixer blades, and the bending angle of the mixer blade. Similarly, the distance of the mixer and SCR catalyst and the length of the SCR cone are classified as the SCR system. Due to the nature of the design, the eight factors are mutually correlated with each other, and the Taguchi method design factor approach explores the size and dimensions of the design space for surrogate model-based optimization; then, it allows a substitute model to be constructed to fit both.

The Taguchi method uses orthogonal arrays in a statistical way to explore the effects of multiple variables simultaneously. In particular, the design of experiment (DOE) is a methodology for planning and executing a series of experimental processes with a few conditions. Firstly, when there are many factors, a fractional factorial design including all factors can be easily deployed while reducing the number of experiments. Secondly, accurate balance can be achieved in the arrangement of experiments, that is, when the effect of one factor is calculated, there is no bias with respect to the effect of another factor. Lastly, it is easy to calculate the factor change from the experimental data, so it is easier to prepare an analysis of the variance table.

Figure 2 shows the efficiency evaluation and distribution of signal-to-noise ratio of Taguchi. A signal factor is a factor determined by a user to obtain a desired output. Depending on the signal factor, the output (response) has a linear, proportional relationship. The noise factor is an uncontrollable factor and appears as a dispersion in quality characteristics. Since the noise factor has a great influence on the quality characteristics, the level setting of the control factor is determined according to the influence of the noise factor, and the influence of the noise factor must be reduced to expect good quality characteristics. The control factor is a variable whose center or level can be freely determined by the user. When all of the signal factors, noise factors, and control factors are selected, a response is calculated by statistical calculation or using Minitab software.

When the orthogonal arrangement of Taguchi’s experimental design method is applied with the 8 factors and 3 levels of the main design factors, a total of 27 experiments occur, and a total of 27 modeling configurations are required, including the layout model of the SCR system, which is the standard. As already mentioned in Table 1, the structural design according to the orthogonal arrangement design was carried out based on the three-region design area, in consideration of the layout and shape factors.

Table 2. Major design factors of 3 sets.

No.	Major Design Factors	Unit	Sets
			Set 1	Set 2	Set 3
1	A: Distance of Urea Injector and Mixer	mm	95	85	75
2	B: Inflow Angle of Exhaust Gas	deg.	114	109	104
3	C: Angle of Urea Injector and Mixer	deg.	115	110	105
4	D: Mounting Angle in the Direction of Rotation of the Mixer inside the SCR Pipe	deg.	10	0	−10
5	E: Number of Mixer Blade	No.	8	6	4
6	F: Bending Angle of Mixer Blade	deg.	125	120	115
7	G: Distance of Mixer and SCR Catalyst	mm	187	167	147
8	H: Length of SCR Cone	mm	186	166	146

shows the appropriate range that affects the flow uniformity (UI) when designing the SCR system. The experimental plan was applied as a data pre-processing process before applying the machine learning process to 3 levels for each factor. The category for each factor can be arranged alphabetically, where A indicates the distance of the urea injector and the mixer, B indicates the inflow angle of the exhaust gas, C indicates the angle of the urea injector and the mixer, D indicates the mounting angle in the direction of rotation of the mixer inside the SCR pipe, E indicates the number of mixer blades, F indicates the bending angle of the mixer blade, G indicates the distance of the mixer and the SCR catalyst, and H indicates the length of the SCR cone. All of these factors are evaluated between three sets (Set 1, Set 2, and Set 3) of values, for example, factor A, which corresponds to the distance of the urea injector and the mixer, is varied to 95 mm, 85 mm, and 75 mm, respectively. Similarly, all other factors are varied across three sets of values, as shown in Table 2.

2.5. Application of Taguchi’s Orthogonal Matrix

2.5.1. Composition of Structural Design by Major Design Factors

The Taguchi orthogonal array (Taguchi OA) produced using Minitab Statistical Software (S/W) is shown in

Table 3. Application of Taguchi’s orthogonal matrix for 8 factors in 3 levels in the SCR System.

	Major Design Factors	A	B	C	D	E	F	G	H
Number of Experiments
Case 1		1	1	1	1	1	1	1	1
Case 2		1	1	1	1	2	2	2	2
Case 3		1	1	1	1	3	3	3	3
Case 4		1	2	2	2	1	1	1	2
Case 5		1	2	2	2	2	2	2	3
Case 6		1	2	2	2	3	3	3	1
Case 7		1	3	3	3	1	1	1	3
Case 8		1	3	3	3	2	2	2	1
Case 9		1	3	3	3	3	3	3	2
Case 10		2	1	2	3	1	2	3	1
Case 11		2	1	2	3	2	3	1	2
Case 12		2	1	2	3	3	1	2	3
Case 13		2	2	3	1	1	2	3	2
Case 14		2	2	3	1	2	3	1	3
Case 15		2	2	3	1	3	1	2	1
Case 16		2	3	1	2	1	2	3	3
Case 17		2	3	1	2	2	3	1	1
Case 18		2	3	1	2	3	1	2	2
Case 19		3	1	3	2	1	3	2	1
Case 20		3	1	3	2	2	1	3	2
Case 21		3	1	3	2	3	2	1	3
Case 22		3	2	1	3	1	3	2	2
Case 23		3	2	1	3	2	1	3	3
Case 24		3	2	1	3	3	2	1	1
Case 25		3	3	2	1	1	3	2	3
Case 26		3	3	2	1	2	1	3	1
Case 27		3	3	2	1	3	2	1	2

. The letters A to H indicate the parameters and the numbers 1, 2, and 3 indicate the level of each design factor. When eight factors and 3 levels are orthogonally arranged, 27 experimental points appear, as shown in Table 3. If there are three or more factors, a factorial design can analyze all factors by reducing the possible number of experiments. During the determination of the effect of each factor, there is no singularity about the influence of other factors, and it is possible to accurately arrange experiments according to the factors.

Figure 3 shows the factors related to the shape of the SCR system (A, B, C, G, and H), the factors related to the bending angle of the mixer blades (F), the mounting angle in the rotation direction of the mixer in the pipe (D), and the factors related to the number of mixer blades (E). It shows a total of 27 design images completed through the structural design of 3 areas. For example, case 1 in Figure 3 is inserted based on the 3-level values for each of the 8 factors presented in Table 2 to the experimental reference point indicated by the orthogonal arrangement method in case 1 given in Table 3. In particular, in case 1, the distance between the urea injector and the mixer (A) is 95 mm, the inflow angle of the exhaust gas (B) is 114 deg, the angle of the urea injector and the mixer (C) is 115 deg, the mounting angle in the direction of rotation of the mixer inside the SCR pipe (D) is 10 deg, the number of mixer blades (E) is 8, the bending angle of the mixer blade (F) is 125 deg, the distance of mixer and the SCR catalyst (G) is 187 mm, and the length of the SCR cone (H) is 186 mm.

This work mainly focuses on the Taguchi method and the results from this work can be utilized by machine learning in the second study.

Table 4. Specific settings for Taguchi and machine learning methods.

No	Classification	Taguchi	Machine Learning
1	Design of Experiments	OA (Orthogonal Array)	OLHD (Optimal Latin Hypercube Design)
2	Global Metamodel	One-Shot	Sequential Sampling
3	Number of Experiments	27 EA	At least 80 EA
4	Analysis Type	Signal-to-Noise Ratio, ANOVA	EDT (Ensemble of Decision Trees), Kriging
5	Purpose	Estimation of Probability of Failure	Estimation of Prediction of Success

shows the specific settings for the Taguchi method and the machine learning methods used in this study and the subsequent study. The design of the experiments is carried out using the Taguchi method with orthogonal array (OA), while using the machine learning technique with optimal Latin hypercube design (OLHD). In the Taguchi method, the global metamodel is generally one-shot, while in machine learning, it is conducted using sequential sampling. The Taguchi method utilizes 27 experiments and the machine learning requires a minimum of 80 experiments. The analysis methods applied to the Taguchi method are signal-to-noise ratio and ANOVA. Furthermore, the ensemble of decision trees (EDT) and the Kriging model are applied to the machine learning method.

2.5.2. Injection Analysis Model and Boundary Conditions

In order to verify and evaluate the correlation between the flow uniformity (UI) of each factor and the influence of a total of 27 design models that have been designed, injection analysis is performed. The distance between the urea injector and the mixer, the exhaust gas inlet angle, the angle between the urea injector and the mixture rotational mounting angle of the mixer inside the SCR pipe, the number of mixer blades, the mixer blade bending angle, the mixer and the SCR catalyst setting distances, and the length of the SCR cone as variable factors. STAR-CCM+, of SIEMENS, which is a commercial computational fluid dynamics (CFD) code, was used, and the CFD analysis is the same as the pre-processing and test conditions for modeling the flow space required for analysis by creating a three-dimensional shape or importing an already designed shape into a program. A solver that simulates by setting initial conditions, boundary conditions, and physical modeling to implement the corresponding physical phenomenon was created in a 3D virtual model.

It consists of a post-processing process. STAR-CCM+ is an integrated CAE analysis software that can execute pre-processing, solver, and post-processing in one frame. The numerical analysis results conducted using STAR-CCM+ will be used as the basic data for the optimization design of the SCR system shape in the future. The uniformity of flow of NH₃ through the catalyst shear is an important index affecting NO_x conversion efficiency and catalyst lifetime and chemical reaction activation time. As an index indicating the flow uniformity, the flow uniformity index (γ) proposed is used [34], and it is designed as in Equation (1).

$$\mathsf{\gamma } = 1 - \frac{1}{2n}{\displaystyle \sum _{i=0}^n\frac{\sqrt{{\left(C_i - \overline{C}\right)}^2}}{\overline{C}}}$$

(1)

where n is the total number of SCR catalyst cells, $\overline{C}$ is the average concentration in the SCR cross-sectional area, and C_i is the local concentration in the catalyst lattice i. To check whether the flow uniformity is improved according to the application of each design factor, the flow uniformity results of all 27 experimental points on the orthogonal array are required. The closer the flow uniformity index to 1, the more uniform the concentration distribution of NH₃. In other words, as the average concentration in SCR cross-sectional area reaches close to the local concentration, flow uniformity is achieved. In this study, when analyzing NH₃ flow uniformity injection, exhaust pressure analysis at the SCR carrier inlet, including velocity flow uniformity, was also performed. Additionally, the multi-component governing equation for the combination of different gases in the SCR system can also help in determining the flow uniformity parameter as follows [35]:

$$\frac{{\delta }_{{\rho }_j{\alpha }_j}{Y}_{j,i}}{\delta t} + \nabla ·\left({\rho }_j{\alpha }_j{Y}_{j,i}{\nu }_j\right) = \nabla ·\left({\rho }_j{\alpha }_j{D}_j\nabla Y_{j,i}\right) + S_{j,i} + m_{j,i}$$

(2)

where Y_j,i is the mass fraction of species i in j phase, D_j is the mass diffusivity numbers of the molecular particle and gas turbulent in the SCR system, ρ_j is the density of j phase, α_j is the volume fraction of phase j, ν_j is the velocity of phase j, S_j,i is the general mass source, and m_j,i is the mass transfer coefficient of the species i in phase j.

Figure 4 shows the CFD model of the SCR system. It demonstrates the values calculated during injection analysis using SIEMENS STAR-CCM+ and shows example images performed according to each factor level, such as the shape of the SCR system and mixer, and the urea injection angle, as shown in Table 2. During the operation of the engine, as the RPM increases, the flow rate in the SCR system increases, so the mass fraction and particle temperature of NH₃ also increase. In this study, all of the structure design models of 27 types for the Taguchi orthogonal array were applied in the same CFD analysis time. However, CFD training time means the time it takes from modelling grid generation (mesh) to performing CFD to produce the final results. The training time used for the CFD simulation was 1 day per model.

The analysis boundary conditions for performing the injection analysis are shown in

Table 5. Boundary conditions of CFD in the SCR System, geometrical and functional data of urea injector nozzle holes for the dosing of the SCR system, parameters for CFD spray initialization and mesh modelling information.

Boundary conditions of CFD in the SCR System
No.	Classification	Design Factors				Unit	Value
1	Material	Shell Material in CFD Modeling				SUS	436 L
2	SCR Inlet Condition	Mass Flow of Exhaust Gas				kg/h	316
3		Exhaust Gas Temp.				Max, °C	411
4		Turbo-Charger				Max, RPM	203,000
5		Engine RPM				RPM	3000
6	Urea Injection	Adblue				mg/s	105
7		Urea Injection				mg/Injection	30.6
8		Injection Duration				msec	81.6
9	SCR Outlet Condition	Pressure of Exhaust Gas				kPa	9.8
Geometrical and functional data of urea injector nozzle holes for the dosing of the SCR system
No.	Classification					Unit	Value
1	Number					No.	3
2	Hole Diameter					μm	120
3	Diameter at Hole Center Positions					mm	1.9
4	Circumferential Distribution					deg.	120
5	Static Mass Flow					Kg/h	3.2
Parameters for CFD spray initialization
No.	Classification					Unit	Value
1	Equivalent Spray Type					Type	3 Hole Full Cone Spray
2	Cone Angle					deg.	7
3	Spray Angle					deg.	7
4	Estimated Initial Droplet Velocity					m/s	24
5	Droplet Diameter, SMD					μm	100
Mesh modelling information
Analysis Tool	Mesh Type	Volume (Total Mesh Quantity)	Base Mesh Size	Surface Mesh Size	Number of Prism Layers	Prism Layer Thickness	Fine Mesh
Star-CCM + V12.04	Polyhedral	1,041,308	4 mm	50~100% (Compared Base Mesh Size)	3	25% (Compared Base Thickness)	Surface: 25% Prism: 12.5%

, which shows the geometrical and functional data of the urea injector nozzle holes for dosing of the SCR system. Table 5 also describes the parameters for CFD spray initialization and mesh modeling information. However, it is regrettable that the detailed analysis boundary condition of the SCR system split analysis applied in this study is a modified design part of the SCR system being developed by a related company. The boundary conditions for CFD were set based on experimental values, and the engine conditions were set based on engine operation at EOP5 (EOP: engine operating point) of 3000 RPM. The exhaust gas mass flow rate is currently 316 kg/h, the exhaust gas inlet temperature is 411 °C, the urea injection amount is 30.6 mg/Injection, the urea injection period is 81.6 ms/Hz, and the exhaust gas outlet pressure is 9.8 kPa. However, in the CFD model, all shell materials were designated as SUS 436 L, and numerical analysis was performed.

Table 6. Comparison result of UI-related NH3 spray time of the design factors of Case 01 in CFD.

Spray Time	81.7 ms		300 ms
Simulation Model for Case 01
CFD Results
	Velocity UI: 0.982	NH3 UI: 0.964	Velocity UI: 0.982	NH3 UI: 0.963
Analysis Time of CFD	1 day		2 to 3 days

shows the comparison results of the uniformity index-related NH₃ spray time of design factors of case 1. After the start of the NH₃ injection, the time required for reaching the steady state of both the NH₃ mass fraction and uniformity index is known as the spray time. NH₃ uniformity (UI) is a numerical representation of how uniformly the exhaust gas containing NO_x passes through the SCR catalyst carrier in a state where urea is evenly absorbed in the SCR catalyst carrier. The values of NH₃ UI can be calculated by the equation described elsewhere [36,37]. The cumulative NH₃ UI shows the result of NH₃ distribution in the SCR catalyst layer and the closer this value is to the NH₃ UI value, the greater the NO_x reduction effect becomes. The analysis time of CFD indicates the time taken from the modeling grid generation (mesh) work to the final result during CFD analysis. When the NH₃ spray time is 81.7 ms, the NH₃ UI value is 0.964 and the analysis period of CFD is 1 day; meanwhile, when the NH₃ spray time is 300 ms, the NH₃ UI value is 0.963 and the analysis period of CFD is 2 to 3 days. The reason for this analysis is to reduce the time to perform CFD by figuring out in advance the time it takes to perform all 27 modeling CFDs. In order to reduce the time it takes to perform CFD, the time it took for the normal uniformity index (UI) values to be calculated through the representative model of case 1 of the 27 models in the orthogonal array was analyzed. The uniformity index and analysis time of CFD are the main performance indicators for the SCR system.

3. Results and Discussion

3.1. Numerical Analysis and Orthogonal Analysis Results

Figure 5 shows the process carried out to reduce the CFD analysis time through the case 1 values in Table 6. The green line in the graph indicates the accumulation of NH₃ UI (or UI NH₃ Monitor), and the blue line indicates NH₃ mass fraction (or NH₃ AvgSrt Monitor). As shown in Figure 4, the uniformity index is applied when the performance of CFD of the SCR system involves the accumulation of UI (one cycle: 300 ms), and in this case, the analysis time for case 1 takes about 2 to 3 days. However, due to the nature of this study, if it takes about 3 days to analyze case 1, other problems arise in the process. From the start to the end of the spraying, as shown in the plots in Figure 5, a process was conducted to reduce the CFD analysis time by comparing the UI values of 50 ms, 81.7 ms, and 300 ms. When the times of spraying were 50 ms, 81.7 ms, and 300 ms, the UI value was analyzed to extract the equivalent values. At 50 ms, 81.7 ms, and 300 ms, the UI values were 0.964, 0.964, and 0.963, respectively. The CFD analysis time proceeded through 81.7 ms; after the end of spraying of urea, the NH₃ UI value curve also changes due to a rapid decrease in NH₃ mass fraction. In general, the stabilization of the injection amount compared to the injection time of urea during the actual vehicle and UI test evaluation reaches stabilization after a certain period in the initial injection, and CFD also stabilizes after an unstable time after the initial injection of urea. Therefore, the UI value and NH₃ mass fraction go through the process of sudden increase and decrease in values during the initial period. From Figure 5, it can be concluded that with an increase in NH₃ mass fraction, the NH₃ uniformity index also reaches to a maximum value and continues to maintain the saturation level even after the end of spraying takes place.

Table 7. CFD results of Taguchi’s orthogonal matrix.

Analysis			CFD Results		H	G	F	E	D	C	B	A	No.
Average	Standard Deviation	Signal-to-Noise Ratio	Velocity UI	NH3 UI	Length of SCR Cone (mm)	Distance of Mixer and SCR Catalyst (mm)	Angle of Mixer and SCR Catalyst (deg.)	Number of Mixer Blade (No.)	Mounting Angle in the Direction of Rotation of the Mixer inside the SCR Pipe (deg.)	Angle of Urea Injector and Mixer (deg.)	Inflow Angle of Exhaust Gas (deg.)	Distance of Urea Injector and Mixer (mm)
0.97	0.01273	−0.23886	0.98	0.96	186	187	125	8	10	115	114	95	Case 1
0.96	0.03111	−0.33428	0.99	0.94	166	187	120	6	0	115	114	95	Case 2
0.91	0.11031	−0.90526	0.99	0.83	146	187	115	4	−10	115	114	95	Case 3
0.97	0.01131	−0.2297	0.98	0.97	166	167	125	8	10	110	109	95	Case 4
0.96	0.02899	−0.32886	0.98	0.94	146	167	120	6	0	110	109	95	Case 5
0.93	0.08839	−0.69396	0.99	0.87	186	167	115	4	−10	110	109	95	Case 6
0.97	0.01556	−0.25729	0.98	0.96	146	147	125	8	10	105	104	95	Case 7
0.98	0.01909	−0.21795	0.99	0.96	186	147	120	6	0	105	104	95	Case 8
0.94	0.07778	−0.62888	0.99	0.88	166	147	115	4	−10	105	104	95	Case 9
0.97	0.02828	−0.27011	0.99	0.95	186	187	115	6	10	105	109	85	Case 10
0.92	0.0997	−0.78643	0.99	0.85	166	187	125	4	0	105	109	85	Case 11
0.97	0.01414	−0.23912	0.98	0.96	146	187	120	8	−10	105	109	85	Case 12
0.97	0.02121	−0.26768	0.99	0.96	166	167	115	6	10	115	104	85	Case 13
0.92	0.09617	−0.7859	0.99	0.85	146	167	125	4	0	115	104	85	Case 14
0.98	0.00707	−0.22025	0.98	0.97	186	167	120	8	−10	115	104	85	Case 15
0.97	0.02334	−0.29077	0.98	0.95	146	147	115	6	10	110	114	85	Case 16
0.94	0.07849	−0.62501	0.99	0.88	186	147	125	4	0	110	114	85	Case 17
0.97	0.01131	−0.24756	0.98	0.96	166	147	120	8	−10	110	114	85	Case 18
0.93	0.08344	−0.6545	0.99	0.87	186	187	120	4	10	110	104	75	Case 19
0.98	0.00707	−0.19356	0.98	0.97	166	187	115	8	0	110	104	75	Case 20
0.96	0.0297	−0.32464	0.99	0.94	146	187	125	6	−10	110	104	75	Case 21
0.93	0.08273	−0.65833	0.99	0.87	166	167	120	4	10	105	114	75	Case 22
0.97	0.01131	−0.2297	0.98	0.97	146	167	115	8	0	105	114	75	Case 23
0.97	0.02334	−0.24596	0.99	0.96	186	167	125	6	−10	105	114	75	Case 24
0.93	0.0799	−0.66431	0.99	0.88	146	147	120	4	10	115	109	75	Case 25
0.97	0.00849	−0.22932	0.98	0.97	186	147	115	8	0	115	109	75	Case 26
0.97	0.01909	−0.27157	0.98	0.96	166	147	125	6	−10	115	109	75	Case 27

shows the results of a numerical study of the number of trials for a total of 27 modeling configurations using the orthogonal arrangement of the Taguchi design of experiments with eight major design parameters (A–H) at three levels. Before building the performance prediction process using a surrogate machine learning model, the Minitab Taguchi design computes the response to the signal-to-noise ratio and the average, which are then analyzed using analysis of variance (ANOVA). The CFD findings in the table are calculated after producing the modeling mesh and configuring the boundary conditions for CFD analysis. The corresponding UI value is then determined following the convergence of the equations of NH₃ UI and velocity UI on CFD. In Taguchi’s method, the signal-to-noise ratio is defined as a method for identifying control factors that minimize the effects of uncontrollable factors (noise factors) to minimize variations in a product or process. The control for factor setting that minimizes the effect is shown. This study’s signal-to-noise ratio characteristic is a tower characteristic [33,38,39] and it is defined in Equation (3).

$$\frac{S}{N} = -10\times \log \left[\frac{\Sigma \left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$Y^2$}\right.\right)}{n}\right]$$

(3)

where Y is the response (or characteristic value) for a given combination of factor levels, and N is the number of factor-level combination responses.

Analysis of variance is a statistical analysis technique that compares and contrasts the means of two or more groups. In other words, analysis is a technique for determining the statistical significance of a difference in the means of two or more groups. ANOVA is essentially a subset of regression analysis.

Table 8. Response for the signal-to-noise ratio.

Level	A	B	C	D	E	F	G	H
1	−0.3858	−0.3945	−0.3926	−0.4197	−0.7114	−0.4121	−0.3814	−0.4473
2	−0.4148	−0.4126	−0.3987	−0.4146	−0.2835	−0.3961	−0.4067	−0.402
3	−0.4261	−0.4195	−0.4353	−0.3924	−0.2317	−0.4184	−0.4385	−0.3773
Delta	0.0403	0.025	0.0426	0.0273	0.4797	0.0222	0.0571	0.07
Ranking	5	7	4	6	1	8	3	2

shows the response for the signal-to-noise ratio for each parameter at each level. Delta ranking is a value that measures the size of the effect by obtaining the difference between the maximum and minimum average of the parameter. The number of mixer blades (E) is the highest delta ranking with a value of 0.4797, followed by the length of the SCR cone (H), the distance of the mixer and the SCR catalyst (G), the angle of the urea and the mixer (C), the distance of the urea injector and the mixer (A), the mounting angle in the direction of rotation of the mixer inside the SCR pipe (D), the inflow angle of the exhaust gas (B), and the bending angle of mixer blade (F), with delta values of 0.07, 0.0571, 0.0426, 0.0403, 0.0273, 0.025, and 0.0222, respectively.

Table 9. ANOVA for the signal-to-noise ratio.

Classification	DF	Seq SS	Adj SS	Adj MS	F	p
A	2	0.00779	0.00779	0.003896	1.7	0.232
B	2	0.003	0.003	0.0015	0.65	0.541
C	2	0.00957	0.00957	0.004784	2.09	0.175
D	2	0.00379	0.00379	0.001894	0.83	0.466
E	2	1.24757	1.24757	0.623785	272.04	0
F	2	0.00237	0.00237	0.001185	0.52	0.612
G	2	0.01475	0.01475	0.007374	3.22	0.083
H	2	0.02268	0.02268	0.011342	4.95	0.032
Residual Error	10	0.02293	0.02293	0.02293
Total	26	1.33445

shows the ANOVA for the signal-to-noise ratio. The p value is the probability of measuring the evidence against the null hypothesis, and the smaller the p value, the greater the influence of the design variable/factor against the null hypothesis. The F value is a test statistic used to determine whether a term is associated with a response. If the F value is large, it means that the effect of the terms or design variables/factors is large. Seq SS (sequential sum of square) is a measure of the variability of the different components of a model. Minitab S/W does not use Seq SS to calculate p value when analyzing a design. Adj SS (adjusted mean sum of squares) is a measure of the variability of the different components of a model. Minitab S/W uses Adj SS and Adj MS (adjusted mean sum of squares) to calculate the p value for a term. The detailed formulas for the calculation of Seq SS, Adj SS, and Adj MS can be referred to from the Minitab source [40]. The degree of freedom (DF) is the number of samples analyzed in this study and can be calculated using Equation (4) [41,42].

$$DF = N-1$$

(4)

where DF is the degrees of freedom and N is the number of samples. The p values of E and H are less than 0.05, which means that there is a statistical correlation between the response characteristics and terms. The F values of E and H are also larger than the values of A, B, C, D, F, and G, as shown in the figure. The variability of the different components of a model can be computed by knowing the value of the adjusted sum of squares It can be concluded that the influence of design variables/parameters is large.

The response for the average for each parameter at each level is shown in

Table 10. Responses for the averages.

Level	A	B	C	D	E	F	G	H
1	0.9588	0.9581	0.9583	0.9557	0.9278	0.9566	0.9591	0.9529
2	0.9562	0.9563	0.9574	0.9562	0.9684	0.9577	0.9569	0.9573
3	0.9551	0.9557	0.9542	0.9581	0.9738	0.9558	0.9541	0.9598
Delta	0.0037	0.0024	0.0041	0.0023	0.0459	0.0019	0.005	0.0068
Ranking	5	6	4	7	1	8	3	2

. Delta ranking produces a value that measures the size of the effect by obtaining the difference between the maximum and minimum averages of the parameter. The number of mixer blades (E) has the highest delta ranking, with a value of 0.459, followed by the length of the SCR cone (H), the distance of the mixer and the SCR catalyst (G), the angle of the urea and the mixer (C), the distance of the urea injector and the mixer (A), the inflow angle of the exhaust gas (B), the mounting angle in the direction of rotation of the mixer inside the SCR pipe (D), and the bending angle of the mixer blade (F), with delta values of 0.0068, 0.05, 0.041, 0.0037, 0.0024, 0.0023, and 0.0019, respectively.

Table 11. ANOVAs for the averages.

Classification	DF	Seq SS	Adj SS	Adj MS	F	p
A	2	0.000066	0.000066	0.000033	1.89	0.202
B	2	0.000028	0.000028	0.000014	0.8	0.478
C	2	0.000084	0.000084	0.000042	2.42	0.139
D	2	0.000027	0.000027	0.000014	0.78	0.484
E	2	0.011354	0.011354	0.005677	326.16	0
F	2	0.000016	0.000016	0.000008	0.47	0.64
G	2	0.000113	0.000113	0.000057	3.25	0.082
H	2	0.000215	0.000215	0.000108	6.18	0.018
Residual Error	10	0.000174	0.000174	0.000017
Total	26	0.012077

shows the average of the ANOVAs. In Table 9, parameter H has the smallest p value 0.018, followed by parameter G. These parameters have p values lower than 0.05, which means there is less than 5% of a risk in these conclusions [27]. Since the p values of E and H are lower than 0.05, there is a statistical correlation between the response characteristics and terms, compared to the other parameters (A, B, C, D, F, and G).

Figure 6 shows the main effect of the signal-to-noise ratio of each parameter on its level. This indicates that parameter E is slightly increased, from around 0.7 to 0.1, which means that factor E on level 3 has the biggest effect on the response characteristic. Figure 7 illustrates the biggest effect of each factor on the average at each level. This indicates that factor E on level 3 has the biggest effect on the average design and this increases extremely from level 1 to level 2, with values of 0.92 to 0.97, respectively. The main effects plot depicts how much each factor influences the response characteristics, including the signal-to-noise ratio, mean, and standard deviation. There is a sizeable effect if the line is not horizontal, and it can be seen that the levels of the factors have different effects on the characteristics. The magnitude of the biggest effect increases as the perpendicularity of the marked point increases, which shows that the line is not parallel with the X-axis [29,43].

3.2. Cross-Validation of PIAno S/W versus Taguchi Orthogonal Array Design Analysis Results to Verify the Reliability of the Main Effect Diagram of the Signal-to-Noise Ratio for Each Factor

The process of this study increased the reliability of the primary results using Minitab S/W, a traditional statistical tool, for the extraction of major design factors/variables and analysis of correlations with factors in the primary study, and in the secondary research, machine learning. After analyzing the biggest effect of the parameters at each level, the cross-validation of PIAnO is required. PIAnO S/W is based on the optimal metamodel creation (product design optimization) of an artificial intelligence (AI) platform developed by PIDOTECH.

Figure 8 shows the degree to which each design factor/parameter affects the response characteristics (i.e., signal-to-noise ratio, average, slope, and standard deviation) using Minitab S/W, and a lower figure indicates PIAno S/W cross-validation. The upper graph in Figure 8 is the main effect diagram of the analysis values of the Taguchi orthogonal array design in Minitab, and the lower graph is the main effect diagram analyzed by PIAnO S/W. It can be seen that both tools show the same effect in the main effect plot of the signal-to-noise ratio for each factor. Although the mini-tab of the upper graph that applies traditional statistical analysis and the PIAnO S/W of the lower graph that applies machine learning techniques are somewhat different in their purposes of use, the biggest effect of each factor is the same as the results are extracted. This information will be considered in the secondary research on the development of a performance prediction process based on PIAnO S/W when building some processes and applying algorithms [31].

4. Conclusions

The purpose of this study was to develop a major performance prediction process that can be used in the design of an SCR system using machine learning techniques. In the first study, the main factors affecting the flow uniformity of the SCR system during urea injection were analyzed using Minitab’s Taguchi technique, a traditional statistical analysis method for the examination of major design factors. A total of 27 injection analysis experiments occur when the Taguchi orthogonal array design is used with the eight factors and three levels of the main design factors of the present work. The number of mixer blades (E) has the highest delta ranking, with a value of 0.459, followed by the length of the SCR cone (H), the distance of the mixer and the SCR catalyst (G), the angle of the urea and the mixer (C), the distance of the urea injector and the mixer (A), the inflow angle of the exhaust gas (B), the mounting angle in the direction of rotation of the mixer inside the SCR pipe (D), and the bending angle of the mixer blade (F), with delta values of 0.0068, 0.05, 0.041, 0.0037, 0.0024, 0.0023, and 0.0019, respectively. The p values of the mixer blade number and cone length are less than 0.05, indicating that this result is statistically significant. The number of mixer blades has the greatest influence in the main effect diagram for the signal-to-noise ratio and average, and the part where four blades are used must be reanalyzed in the later analyses of machine learning algorithms.

In this work, statistical methods were used, and it is difficult to prove the reliability of the results obtained from these methods. Moreover, the introduction of another statistical method will not further help in securing reliability in the result. Thus, in the second study, additional research and analysis using PIAnO S/W will be conducted when developing the process using a machine learning algorithm. The factors and their main effects that are produced by the close optimization in sequential order using the Kriging model and ensemble of decision tree will be reanalyzed in the future work. In order to validate the statistical reliability of the main effect plot, it can be shown that the main effect plot for the signal-to-noise ratio is the same when performing both the cross-validation of the PIAnO S/W and the Taguchi orthogonal array design analysis.