Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 4, No. 3, 2022 177 Study on Ceramic Sintering Process Based on Random Forest Runhui He1, Yuna Sheng1, Jianxin Zhang1, Zihan Xu1, Chengrui Li1, Liya Wang1, 2, * 1North China University of Technology, Tangshan, 063210, China 2Tangshan Sanitary Ceramics Quality Intelligent Monitoring Technology Basic Innovation Team, Tangshan, 063210, China * Corresponding author Abstract: While the manufacturing process of ceramics is complex and each link is important to the ceramic, we focus on the sintering process of ceramics and construct models and algorithms to investigate the temperature of the ceramic sintering process in order to improve the yield of the ceramic sinter. We make full use of the ceramic sintering process node temperature and ceramic product problem data, adopt factor analysis for data dimensionality reduction, and use principal component analysis to extract factors to improve efficiency for subsequent optimisation. The random forest algorithm of integrated machine learning is used to investigate the effect of different nodal temperature rates on the ceramic product, and a decision tree is derived to identify the more influential temperature rates. These obtained important temperature factors affecting ceramic sintering can be used as a reference for the ceramic sintering process, thus achieving a study of the temperature of the ceramic sintering process. Keywords: Ceramic sintering, Factor analysis method, Random forest. 1. Introduction The ceramics industry plays an important role in modern construction and everyday life. The variety of forms and complex structures of modern ceramic products, as well as the increasing demands on product quality, have placed new demands on ceramic materials and manufacturing processes. The separation of the product design and manufacturing processes in traditional ceramic manufacturing technology has led to a large number of iterations from product design to the finalisation of the production process; relying on the "experience + experiment" method to develop the process. These have become bottlenecks in the development of ceramic technology, and there is an urgent need to adopt new product development models and technologies to change this situation. With the development of computer technology, ceramic manufacturing technology has changed greatly. The use of computer technology to simulate the ceramic production process can verify the rationality of the production process selection, but also optimize the production process, reduce losses, shorten the development cycle, improve product quality, etc. Random forests are a type of semi-supervised learning, which are efficient to run and easier to use, but decision trees are more likely to cause overfitting, making the trained learning models less generalisable. In order to obtain the correctness of the combination and the diversity of the single- root tree, many scholars have made many researches. Liu abet proposed a random forest algorithm based on multiple fuzzy kernel constraints; Wu Chenwen et al. improved the prediction accuracy through variable prediction and selection; Xla et al. solved the classification problem of incomplete data without attribution by proposing a random forest with surrogate algorithm; Shi Jinyu et al. proposed an improved random forest algorithm to improve the classification accuracy by constructing fuzzy decision trees. 2. Data Pre-processing The data set contains the temperatures of 27 nodes in the ceramic firing process, as well as the five problems of cracking, oxidation, bulging, soiling and wind shock in the production of ceramic products. From the 800,000 data, 560,000 data were randomly selected as the training set and 240,000 data as the test set to investigate the effect of temperature rate on the quality of ceramic products. The processed data are shown in Table 1. Where a positive sign indicates the rate of temperature rise and a negative sign indicates the rate of temperature fall, 0 means the product does not have this problem and 1 means the product has this problem. 3. Factor Analysis Method Factor analysis is an important method of data dimensionality reduction. The principle is to combine some variables with complex relationships (Xi ) into a small number of factors (Fk ) according to the dependencies within the correlation matrix of various indicators, and to use the resulting factors to reflect the main information of the original variables. The mathematical model of factor analysis is used to find the original variables X AF ϵ 1 where F is the extracted common factor; A is the factor loading matrix.ϵ is the special factor. 3.1. Indicator correlation analysis When performing factor analysis on data, we first test whether the data are suitable for factor analysis. The basic logic of factor analysis is to construct a few representative factor variables from the original variables, which requires a strong correlation between the original variables, otherwise factor analysis will not be able to extract the 'common features' between the variables. 178 Table 1. Partial data presentation Kiln car number V1 V2 V3 V4 06080 2.227124464 1.352734610 1.695913540 1.557662630 06081 2.158663761 1.426641993 1.581061737 1.588638055 06082 2.034577636 1.359453215 1.644596840 1.767858508 06083 1.779988723 1.764824962 1.702132689 1.685992475 06084 1.942583953 1.583415125 1.722795668 1.398354660 V5 V6 V7 V8 06080 1.707215787 3.818557288 3.703093038 2.980067668 06081 1.682474525 3.725085829 3.821305758 3.004810595 06082 1.418555999 3.821305758 3.989004355 2.903092049 06083 1.118900655 4.137456954 4.379381012 2.243298260 06084 1.731958725 4.398625333 3.384193372 2.905842185 V9 V10 V11 V12 06080 1.190379300 0.591065279 0.390376679 0.533333981 06081 1.118898972 0.637802680 0.384879717 0.585564991 06082 1.173881789 0.492096896 0.467353942 0.654296838 06083 1.250859079 0.536082463 0.409622644 0.574571084 06084 1.017182108 0.657045346 0.390376651 0.602062502 V13 V14 V15 V16 06080 0.335393835 0.079725771 0.134708561 -0.175945673 06081 0.288659788 0.043988942 0.170445385 -0.065980040 06082 0.203437109 0.085222679 0.148454292 -0.137457042 06083 0.373882494 0.008248770 0.148450911 -0.082474225 06084 0.302405492 0.082474225 0.126458919 -0.148454265 V17 V18 V19 V20 06080 -4.248816697 -5.052194668 -2.083349152 -0.606767866 06081 -4.376313083 -5.002398403 -2.191315898 -0.459079611 06082 -4.076697754 -5.155935819 -2.045361756 -0.574739258 06083 -4.503807525 -4.817739879 -2.112340335 -0.741110777 06084 -4.035259867 -5.155935827 -2.147329401 -0.683280549 V21 V22 V23 V24 06080 -1.887152592 -0.748918179 -1.723222388 -3.852839835 06081 -1.981155256 -0.748918179 -1.723222388 -3.852819835 06082 -1.839264116 -1.008158988 -1.647881796 -3.753789724 06083 -1.754129648 -0.926829196 -1.636660128 -3.577926247 06084 -1.947455677 -0.596423981 -1.667117473 -3.658783330 V25 V26 Burning crack Oxidation 06080 -1.834593429 -1.929634962 0 0 06081 -1.719129458 -2.097201731 0 0 06082 -1.746620865 -2.120765885 1 0 06083 -1.984879597 -2.107674689 0 1 06084 -1.966551991 -2.171304233 0 1 Dirty Wind shock Bulge 06080 0 0 0 06081 0 0 0 06082 0 0 0 06083 0 0 0 06084 0 0 0 179 Figure 1. Correlation heat map A heat map of the correlation coefficients of the variables is shown in Figure 2. The correlation between the variables is strong, with a value of 0.586 for KMO and a significance of 0.00, so factor analysis can be used. 3.2. Factor extraction Factor extraction methods commonly used in factor analysis include the principal component method, the maximum likelihood method and the principal axis factor decomposition method. This method assumes that the variables are linear combinations of factors, and the variance of the original variables is explained by the principal components as much as possible from the overall variance of the original variables, and the proportion of the variance of the original variables explained by each common factor is reduced in turn. The influence factors in the project, the 26 temperature variations affecting ceramic sintering, were brought in to obtain the eigenvalues and the component matrix. The number of principal components was determined based on the total variance explained, and the top 6 factors were selected in order of eigenvalue greater than one, with a cumulative variance explained of 71.230%. 180 Table 2. Initial eigenvalue Composition Total Percentage of variance Cumulative (%) 1 9.107 35.029 35.029 2 3.734 14.36 49.389 3 1.801 6.929 56.318 4 1.548 5.955 62.273 5 1.222 4.701 66.974 6 1.107 4.257 71.23 Table 3. Extract the sum of squares of loads Composition Total Percentage of variance Cumulative (%) 1 9.107 35.029 35.029 2 3.734 14.36 49.389 3 1.801 6.929 56.318 4 1.548 5.955 62.273 5 1.222 4.701 66.974 6 1.107 4.257 71.23 Table 4. Sum of squares of rotational loads Composition Total Percentage of variance Cumulative (%) 1 6.175 23.751 23.751 2 4.584 17.631 41.382 3 2.993 11.511 52.893 4 1.87 7.194 60.087 5 1.688 6.492 66.578 6 1.21 4.652 71.23 A reference line with a value of 1 is set in the gravel plot to obtain 6 components with eigenvalues over 1. It is sufficient to consider only these 6 components. Figure 2. Gravel map 3.3. Factor rotation In order to obtain a clearer meaning of each factor, the Kaiser normalized maximum variance method was used to rotate the factors and to summarize the indicators corresponding to the six factors, and the rotated component loading matrix and component score coefficient matrix are shown in Table. 181 Table 5. Rotated factor component loading factors and score coefficients Indicators Factor component loadings after rotation Factor score coefficient F1 F2 F3 F4 F5 F6 F1 F2 F3 F4 F5 F6 V01 0.243 0.648 -0.388 -0.208 0.116 -0.079 -.016 .147 -.042 -.031 .132 -.081 V02 -0.503 -0.361 0.386 -0.109 0.42 -0.038 -.086 .018 .138 -.180 .203 -.036 V03 -0.357 -0.327 0.673 0.051 0.211 -0.002 -.057 .068 .272 -.099 .072 -.030 V04 -0.339 -0.364 0.386 0.314 0.099 0.115 -.010 -.015 .079 .113 .023 .081 V05 -0.254 -0.302 0.212 0.596 0.049 0.01 .037 -.020 -.029 .346 .018 -.010 V06 -0.082 -0.228 0.193 0.76 -0.103 -0.014 .080 -.013 -.043 .480 -.060 -.038 V07 0.325 -0.277 0.086 -0.637 -0.393 0.023 .006 -.171 .073 -.444 -.284 .072 V08 0.299 0.615 -0.41 -0.297 0.1 -0.013 -.009 .114 -.054 -.087 .120 -.016 V09 0.138 0.73 -0.311 0.126 -0.11 0.149 -.015 .185 -.030 .163 -.001 .084 V10 0.213 -0.372 -0.023 0.027 0.541 -0.495 .097 -.093 -.095 .074 .335 -.382 V11 0.019 0.009 -0.053 -0.053 -0.783 -0.233 -.043 -.040 .030 -.050 -.500 -.194 V12 0.147 0.67 -0.51 -0.118 -0.149 -0.053 -.036 .124 -.098 .025 -.031 -.061 V13 0.018 -0.045 0.031 -0.002 0.197 0.873 .042 -.074 -.058 -.032 .124 .745 V14 0.278 -0.206 0.626 0.017 0.014 -0.068 .059 .034 .267 -.045 -.018 -.072 V15 0.041 0.778 -0.023 -0.228 0.16 -0.121 -.090 .300 .184 -.108 .143 -.157 V16 0.216 0.794 -0.207 -0.118 -0.18 0.189 -.038 .207 .066 -.013 -.053 .117 V17 0.062 -0.083 0.83 0.24 -0.074 0.079 .017 .137 .371 .054 -.075 .014 V18 -0.365 -0.717 -0.159 -0.025 0.229 0.028 .004 -.261 -.228 -.058 .093 .084 V19 -0.774 -0.27 -0.01 -0.052 0.334 -0.042 -.138 -.007 -.038 -.119 .161 -.034 V20 0.794 0.303 -0.215 -0.107 -0.117 -0.046 .136 -.016 -.053 .055 -.017 -.023 V21 0.872 0.103 0.073 -0.176 0.075 -0.052 .163 -.029 .050 -.022 .082 -.024 V22 0.736 0.078 -0.328 -0.129 -0.017 -0.043 .152 -.115 -.158 .043 .035 .005 V23 0.86 0.034 0.096 -0.055 -0.021 0.032 .178 -.058 .030 .047 .020 .047 V24 -0.691 -0.097 -0.057 0.122 -0.057 0.127 -.127 .010 -.046 .002 -.065 .094 V25 -0.756 -0.198 -0.299 0.176 -0.183 -0.064 -.127 -.064 -.178 .062 -.143 -.049 V26 -0.829 -0.209 0.248 0.135 0.049 -0.096 -.158 .071 .100 -.037 -.024 -.110 Based on the matrix of coefficients for the table component scores, the one-way function can be derived as follows: F1 0.016 ∗ V1 0.086 ∗ V2 0.057 ∗ V3 0.01 ∗ V4 0.037 ∗ V5 0.08 ∗ V6 0.006 ∗ V7 0.009 ∗ V8 0.015 ∗ V9 0.097 ∗ V10 0.043 ∗ V11 0.036 ∗ V12 0.042 ∗ V13 0.059 ∗ V14 0.09 ∗ V15 0.038 ∗ V16 0.017 ∗ V17 0.004 ∗ V18 0.138 ∗ V19 0.136 ∗ V20 0.163 ∗ V21 0.152 ∗ V22 0.178 ∗ V23 0.127 ∗ V24 0.127 ∗ V25 0.158 ∗ V26 2 F2 0.147 ∗ V1 0.018 ∗ V2 0.068 ∗ V3 0.015 ∗ V4 0.02 ∗ V5 0.013 ∗ V6 0.171 ∗ V7 0.114 ∗ V8 0.185 ∗ V9 0.093 ∗ V10 0.04 ∗ V11 0.124 ∗ V12 0.074 ∗ V13 0.034 ∗ V14 0.3 ∗ V15 0.207 ∗ V16 0.137 ∗ V17 0.261 ∗ V18 0.007 ∗ V19 0.016 ∗ V20 0.029 ∗ V21 0.115 ∗ V22 0.058 ∗ V23 0.01 ∗ V24 0.064 ∗ V25 0.071 ∗ V26 3 F3 0.042 ∗ V1 0.138 ∗ V2 0.272 ∗ V3 0.079 ∗ V4 0.029 ∗ V5 0.043 ∗ V6 0.073 ∗ V7 0.054 ∗ V8 0.03 ∗ V9 0.095 ∗ V10 0.03 ∗ V11 0.098 ∗ V12 0.058 ∗ V13 0.267 ∗ V14 0.184 ∗ V15 0.066 ∗ V16 0.371 ∗ V17 0.228 ∗ V18 0.038 ∗ V19 0.053 ∗ V20 0.05 ∗ V21 0.158 ∗ V22 0.03 ∗ V23 0.046 ∗ V24 0.178 ∗ V25 0.1 ∗ V26 4 F4 0.031 ∗ V1 0.180 ∗ V2 0.099 ∗ V30.113 ∗ V4 0.346 ∗ V5 0.480 ∗ V6 0.444 ∗ V7 0.087 ∗ V8 0.163 ∗ V9 0.074 ∗ V10 0.05 ∗ V11 0.025 ∗ V12 0.032 ∗ V13 0.045 ∗ V14 0.108 ∗ V15 0.013 ∗ V16 0.054 ∗ V17 0.058 ∗ V18 0.119 ∗ V19 0.055 ∗ V20 0.022 ∗ V21 0.043 ∗ V22 0.047 ∗ V23 0.002 ∗ V24 0.062 ∗ V25 0.037 ∗ V26 5 F5 0.132 ∗ V1 0.203 ∗ V2 0.072 ∗ V3 0.023 ∗ V4 0.018 ∗ V5 0.06 ∗ V6 0.284 ∗ V7 0.12 ∗ V8 0.001 ∗ V9 0.335 ∗ V10 0.5 ∗ V11 0.031 ∗ V12 0124 ∗ V13 0.018 ∗ V14 0.143 ∗ V15 0.053 ∗ V16 0.075 ∗ V17 0.093 ∗ V18 0.161 ∗ V19 0.017 ∗ V20 0.082 ∗ V21 0.035 ∗ V22 0.02 ∗ V23 0.065 ∗ V24 0.143 ∗ V25 0.024 ∗ V26 6 F6 0.081 ∗ V1 0.036 ∗ V2 0.03 ∗ V3 0.081 ∗ V4 0.01 ∗ V5 0.038 ∗ V6 0.072 ∗ V7 0.016 ∗ V8 0.084 ∗ V9 0.382 ∗ V10 0.194 ∗ V11 0.061 ∗ V12 0.745 ∗ V13 0.072 ∗ V14 0.157 ∗ V15 0.117 ∗ V16 0.014 ∗ V17 0.084 ∗ V18 0.034 ∗ V19 0.023 ∗ V20 0.024 ∗ V21 0.005 ∗ V22 0.047 ∗ V23 0.094 ∗ V24 0.049 ∗ V25 0.11 ∗ V26 7 4. Random Forests 4.1. Random forests Each classification tree in a random forest is a binary tree, which is generated based on the principle of top-down recursive splitting, where the training set is partitioned one by one, starting from the root node. In a binary tree, all the training data are concentrated at the root node, and they are 182 divided into left and right nodes, each containing a subset of the training data, according to the principle of the lowest node purity. The nodes continue to be split according to the same rules until the rules are satisfied before stopping further subdivision. If all the classified data on a node are from the same class, then the impurity of this nodel n 0 , in this method, impurity is measured according to the Gini criterion. It is assumed thatP X is the number of samples on node n belonging toX the frequency of the number of samples of class to the total number of training samples, the specific implementation of the random forest training process is as follows. (1) Assuming an initial training set of N, a set of k self-help samples is drawn randomly and with put-back using the bootstrap method, so that k classification trees are constructed, with the samples not drawn each time forming the out-of-bag data. (2) Let there be a total of M feature variables, and at each node of the tree, m features are randomly selected from the overall M feature variables (m M ) at each node, and then select the feature with the best classification ability among the m features based on the criterion of minimum impurity of each node to continue the branching operation. (3) Each tree is allowed to grow to its maximum extent and no pruning is done to them with the aim of minimizing the impurity of the nodes. (4) The resulting multiple trees as a whole form a random forest, and the resulting random forest classifier can then be used to identify and categorise the new data. 4.2. Random forest use The random forest model was implemented in the program to analyse the available data using the random forest algorithm, and the results were tabulated to show the degree of influence of the ceramic products, see Table 3. Table 6. Table of the degree of influence of temperature rate on ceramic products Burning crack Oxidation bulging dirty Wind Surprise F1 0.16714 0.16637 0.17323 0.16675 0.16817 F2 0.17084 0.16703 0.16555 0.17543 0.16680 F3 0.16597 0.16688 0.16254 0.16785 0.16610 F4 0.16642 0.16697 0.16494 0.15997 0.16541 F5 0.16454 0.16658 0.17043 0.16281 0.16626 F6 0.16510 0.16616 0.16331 0.16720 0.16726 5. Experimental Analysis The final results derived from the Random Forest algorithm show that among the five questions for ceramic products, F1 and F2 have a greater weighting, and according to the characteristic weights obtained from the factor analysis method, it can be seen that V1, V9, V15, V16, V20, V21, V22 and V23, the temperature rates of these 8 nodes have a greater degree of influence on the ceramic products. 6. Conclusion In this experiment, by collecting data on 27 nodes of temperature and ceramic product issues during the ceramic firing kiln process, after data pre-processing, checking the correlation of variables, factor analysis method to reduce the dimensionality, the random forest algorithm model was adopted for scientific and objective analysis of the data. Finally the weights of the degree of influence of each temperature node rate on the ceramic product were obtained. It is a reference value for the control of the temperature rate of ceramic firing process. 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