The matching of power performance parameters of marine diesel based on orthogonal principal component analysis

To solve the problem of combining the operating parameters of marine diesel engines after modification. The 4190ZLC-2 type marine medium-speed engine produced by Jinan Diesel Engine Plant is used as the research object. The AVL_FIRE software is used to construct a dual-fuel combustion chamber model and verify the accuracy of the model. The orthogonal test method was used to simulate the combustion parameter matching the indicated power research objective. The method of principal component analysis was used for screening and comprehensive analysis. The results show that among the principal components affecting the indicated power, the cumulative contribution of the first two principal components reaches 99.90%, which basically contains all the information of the five indicators affecting the indicated power of diesel engine and can reflect the combination of power parameters of dual-fuel diesel engine. The study’s results can provide useful references for matching the influencing parameters of the indicated power.


Introduction
When multi-parameter optimization is carried out in diesel engines, the orthogonal experimental design [1] is commonly used to reduce the number of tests and the analysis and calculation costs.However, many factors affect the indicated power of diesel engines, and experiments will still face many experimental data analyses.Principal component analysis (PCA) is a multivariate statistical analysis method that transforms a group of variables originally related to each other into a series of linearly independent principal components based on the correlation between variables.These principal components are highly synthesized and generalized from the raw data, which can simplify the evaluation of diesel engines indicating power factors and provide most of the original information [2].Venkatanarayana et al. [3] used Taguchi's PCA to optimize the performance parameters of methyl esterdiesel engines.Orthogonal-principal meta-analysis is a method of dimensionality reduction calculation based on orthogonal experimental design data to extract the main influencing factors [4].This article mainly simulates the operating parameters of the oil extractor in CHEMKIN and Fire software; After the orthogonal experimental design is used for design, the data dimensionality reduction is carried out by using PCA, and the low-dimensional parameters affecting the indicated power of marine diesel engines are obtained, which provides a useful reference for analyzing and optimizing the relevant parameters of the indicated power.

Combustion chamber modeling
This paper selects the existing exhaust gas turbocharged four-stroke 4190Z L C-2 marine medium-speed diesel engine in the laboratory as the research object, whose basic parameters are as follows: cylinder bore×stroke of 190 mm×210 mm, rated power of 220kW@1000r/min, compression ratio of 14:1.Based on its structural parameters and operating parameters, import AUTO-CAD, the two-dimensional combustion chamber is drawn, resulting in a longitudinal 1/2 cross-section (Figure1), and then the threedimensional mesh is automatically generated through the ESE module of AVL-FIRE for meshing and checking.Since there are eight nozzles in the cylinder of the 4190Z L C-2 diesel engine, which are symmetrically distributed, only 1/8 of the combustion chamber is simulated and calculated to simplify the simulation calculation (Figure 2).In this paper, the diesel engine is studied with the intake valve closed (594 °CA) to the exhaust valve open (841 °CA) [5][6].

Module selection
In this paper, based on the methanol/diesel dual fuel combustion model, select each sub-module.The kε two-equation model is chosen as the turbulent flow model.The KH-RT model of the multi-orifice fuel injector is selected.The Enable model is used to explain the gas phase pulse velocity.Walljet1 model was selected as the droplet-hitting-the-wall model.The evaporation model is a multi-component model.In Figure 3, the mixing ratio is set to 0. Compared with the diesel engine data, the results show that the test value and the simulation value curve are consistent, the error between the test value and the simulation value of the pure diesel engine is within 5%, and the model is basically correct, which can be used for simulation calculation research.

Principal component analysis
The principal component analysis is a linear combination of a few principal components (synthetic variables) representing a raw variable using dimensionality reduction techniques.To achieve the most efficient dimensionality reduction, the information contained in these principal components (in the sense of linear relations) should be made unrelated.The specific steps [7] are as follows:  (1) The range normalization method is used to standardize the factors affecting the indicated power [8], and the calculation formula is as follows: (2) The correlation coefficient matrix R = (r ij )p×p, and r ij is evaluated as follows. ) where r ij is the correlation coefficient between the ith indicator and the jth indicator of the standardized data, r ij = r ji , r ii = 1.
(3) The eigenvalues λ1, λ2...λp of the matrix R are calculated and the values are ranked in order of magnitude to find the corresponding eigenvectors.After that, the contribution rate and cumulative contribution rate of the eigenvalues are calculated, where the first principal component y1 has the largest contribution rate, indicating that it has the strongest ability to explain the original variables x1, x2, ..., xp, while y2, y3...yp have the decreasing ability to explain in descending order.The formula for the cumulative contribution is as follows.

Selection of test factors and determination of orthogonal test table
In this paper, five elements were selected: methanol substitution rate x1, EGR rate x2, intake pressure x3, intake temperature x4 and injection advance angle x5, each corresponding to four levels.The indicated power was used as the diesel engine dynamics evaluation index, keeping the rated speed constant and pursuing the maximum and minimum results respectively, and the factor level table is shown in Table 1

Orthogonal tables, table header design, and extreme difference analysis
According to the number of factors to draw an orthogonal table (Table 2), the number of levels and the orthogonal table corresponding to the number of groups, choose L16(4 5 ) orthogonal table to arrange the test [10].The analysis of polar differences method has the characteristics of easy operation and intuitive image, and is a standard method for orthogonal tests, and its calculation formula is: max , , , min , , ,

Analysis of extreme differences
Table 2 shows the influence of each level factor on the indicated power obtained by the extreme difference analysis method, where k1 to k4 denotes the average value of the indicated power for each level factor at the same level, R denotes the extreme difference value of each level factor on the indicated power, and the drastic difference value R can accurately represent the influence of each group of parameters on the indicated power at different levels.The order of their influence is intake air temperature < intake pressure < injection advance angle < methanol replacement rate < EGR rate.After that, the principal component analysis method is used to reduce the fractal dimension of the orthogonal test data to achieve the result of simplifying the parameters.

Correlation coefficient matrix
Correlation analysis is a quantitative analysis of different variables to determine whether there is a closer relationship between them and the degree of closeness of the relationship.In this paper, the factors affecting the indicated power were subjected to correlation analysis, and the correlation coefficient matrix between the factors was calculated, and the results are shown in Table 3. substitution rate and the EGR rate.With the increase of the methanol blending ratio, the low calorific value of the fuel mixture decreases, the stall period is prolonged, and the indicated power gradually decreases.And as the EGR rate increases, the oxygen content in the cylinder gradually decreases, the combustion is insufficient, and the pressure peak gradually decreases, reducing the indicated power.On the contrary, as the injection advance angle increases, the stall period is long, the mixture quality is high, the in-cylinder combustion is optimized, the in-cylinder pressure and temperature are raised, and the combustion is more adequate, so there is a strong negative correlation between the injection advance angle and the methanol substitution rate.And after that, it is necessary to condense the information carried by the data through principal component analysis to prevent the effect of multivariate covariance.

Eigenvalues and principal component contribution rates
Table 4 shows the eigenvalues, contribution rates and cumulative contribution rates of the correlation matrix calculated for the five factors affecting the indicated power.According to the principal component theory, if the incremental contribution of m principal components reaches 80%, or if the eigenvalues of m principal components are more significant than 1, the explanatory power of the first m principal components is sufficient to replace the explanatory power of the original index.Therefore, only the first two principal components can be taken for data extraction.
To further explain the specific factors that each principal component can express and calculate the correlation of each principal component with an element and the correlation of each principal component with the indicated power, it is necessary to calculate further the eigenvalues of the principal components and the loading distribution to explain further the applicability and the selection of the principal components.

Principal component analysis
To give the expression of principal components and determine the number of principal components, 2 eigenvalues and 2 corresponding eigenvectors of the correlation matrix R were calculated, and 2 principal components were selected with a cumulative contribution rate of more than 85%, which can represent all the information of 5 indicators.The selected principal components and the corresponding eigenvectors are shown in Table 5, from which the relationships between the first two principal components and the variables are as follows.
Y2 = -0.0211x1-0.1820x2-0.24557x3-0.8157x4+0.4906x5 From Table 5 and Equations 5 and 6, the cumulative contribution of the first principal component is 79.59% and Y1 has a moderately favorable loading on x1, x2 and an average loading on x3.The large (small) value of Y1 means that there is a tendency to have large (small) values on variables x1, x2, and a tendency to have small (large) values on variable x3 therefore, the first principal component is called Methanol substitution rate, EGR rate and injection advance angle principal component.In the second principal component, y2 has a large negative load on x4 and a medium load on x5.The large (small) value of y2 means that the variable x4 tends to have a small (large) value and the variable x5 tends to have a large (small) value.This principal component mainly reflects the principal components of intake air temperature and intake air pressure, so the second principal component is also known as the principal component of intake air pressure and intake air temperature.

Conclusion
In this paper, orthogonal tests and PCA principal component analysis were used to vary five parameters: methanol substitution rate, EGR rate, injection advance angle, intake air temperature and intake air pressure.The experimental conclusions are as follows.
(1) By principal component feature analysis, the five original indicators were dimensional zed and two principal components were obtained, which together retained 99% of the impact indication power information of the foremost indicators (2) The first principal component mainly reflects the methanol substitution rate, EGR rate and injection advance angle principal components.The second principal component mainly reflects the intake pressure and intake temperature principal components.

Figure 3 .
Figure 3.Comparison of simulated and measured pressure curves and heat release rate curves

Figure 1 .
Figure 1.Schematic diagram of center section 1/2 of the combustion chamber

Table 2 .
Orthogonal test table and extreme difference analysis table Test Group

Table 3 ,
there is a correlation between x1 and x2, x3 and x5 with correlation coefficients of 0.9867, -0.9601 and 0.8575, respectively.There is a powerful positive correlation between the methanol

Table 5 .
Results of the first 2 principal component loads of R