Multi-objective Optimization of Thermal and Sound Insulation Properties of Basalt and Carbon Fabric Reinforced Composites Using the Taguchi Grey Relations Analysis

ABSTRACT In this study, an experimental investigation was conducted to explore the thermal and acoustic insulation capabilities of basalt fabric and carbon fabric-reinforced composite materials. The relationship between fabric additive ratios and sound and thermal absorption qualities has been studied. The resin is mixed with two distinct mineral powder additions. Taguchi Grey Relations Analysis optimization approach was utilized to discover the composite material with the optimum sound and thermal insulation qualities. The Taguchi Method Experimental Design L18 (mixed 3–6 levels) was chosen. Fabric (six levels), Al2O3 (alumina) filler (three levels), and SiC (silicon carbide) filler (three levels) were chosen as test parameters as input variables based on the experimental design. Sound Transmission Loss and Thermal Conduction Coefficient were chosen as the output parameters to be optimized as response variables. The study’s findings led to the identification of optimal samples for thermal conductivity coefficient and sound transmission loss testing, as well as confirmation tests for these samples. Using the Taguchi Grey Relational Analysis, the best input parameters were discovered to be 30% carbon, 0% Al2O3, and 5% SiC for the best Thermal Conductivity Coefficients (W/mK) and Sound Transmission Loss (dB). As a result of the confirmation test, an improvement of 0.15 was found.


Introduction
The manufacture of composite materials has increased significantly in recent years. This type of composite is employed in a variety of sectors and technologies. This substance has taken the role of old-style manufacturing. Glass and carbon fibers are the most commonly utilized materials in composite technology. However, today's glass fiber production requires elements that are

Material
Plain-woven basalt and carbon textiles weighing 200 g/m 2 were employed as composite reinforcing material in the investigation. Because basalt is a very strong material, its use has increased in recent years. These two materials were chosen in order to compare this material with carbon, which is the strongest material used in this field. Basalt is also used as a thermal insulation material. Gümülcine et al. (2013) suggested that basalt fibers are generally used as reinforcing material for composite materials with their excellent mechanical properties, in the fire protection sector due to their nonflammability and ability to retain their properties at high temperatures, as an insulator with their heat and sound insulation properties, and in corrosive environment applications due to their excellent chemical resistance.
Reinforcement fabrics were used at three different percentages: 30, 40, and 50 in composite. Figure 1 shows reinforcement materials and selected composite plates. Mineral powder components, SiC (micro powder, 3µ) and Al 2 O 3 (nano powder, 28ƞm), are used as particle additives. The matrix was epoxy resin (Propox 300 L-laminating epoxy set-LR 300/LH300-15 kg), and the accelerator was cobalt. The resin accelerator percent ratio is 75:25.
SiC (micro powder) was employed in three different proportions (0, 5, and 10) and Al 2 O 3 (nano powder) in three different proportions (0, 2, and 4). These ratios are decided according to the literature and blended manually. The composite samples are produced using hand lay-up technique. It is known that composite materials are based on the weight ratio of the reinforcing resin. The porosity of the reinforcing fabrics was not evaluated in this study, but the m 2 weights of the carbon and basalt fabrics were chosen the same (200 g/m 2 ) to ensure the weight equality of the reinforcing fabrics in the composite.

Method
The Taguchi Grey Relations Analysis method was used as a multi-objective optimization method in the study. With this method, the composite sheet that will provide the optimization of both sound and thermal absorption properties (equal weight) has been investigated. MINITAB 16® package program was used in the application of the method. Experimental Design was chosen Taguchi L18-mixed 3-6 levels (Minitab Inc 2000). This design was chosen because of our test parameters and their levels. The Taguchi method states that instead of trying all combinations of the experiments, using orthogonal arrays, the factor levels that give the best performance characteristics can be found. Orthogonal arrays are expressed as a number of matrix. Each row represents the levels of the selected factors, and each column represents the factors considered. Generally, two-and three-level orthogonal arrays are used according to the experimental design. The most commonly used 2-level orthogonal arrays are L4, L8, L12, and L32. The most used three-level are L9, L18, L27. There are also orthogonal arrays, such as L18, L36, and L54, where both levels can be mixed. In our study, since the fabric factor is six levels, Al 2 O 3 filler is three levels and the SiC filler is three levels, the L18 experiment plan was chosen in the mixed design suggested by the Taguchi experimental plan.
The test parameters (Input Variables) were determined as fabric (six levels), Al 2 O 3 filler (three levels), and SiC filler (three levels) according to the experimental design. As a result of the experiments made according to the experimental design, the output parameters (response variables) to be optimized were decided as sound transmission loss and thermal conductivity coefficient. The input parameters and their levels are shown in Table 1. According to Table 1, if a full factorial experiment design is used, the number of experiments will be 54.
The number of experiments was reduced to 18 with the Taguchi Method used in the study. Table 1 shows L18 orthogonal layout in Taguchi experimental design and Table 2 shows the experimental plan. Table 2 contains the codes of experimental plan and the factor levels corresponding to the codes. According to the experimental design given in Table 2, the production of composite plates was carried out using the hand lay-up method. The hand lay-up method used for composite production has been one of the production methods that has been widely used in low production quantities. This method is the process of giving the shape of the mold for fibers/fabrics placed in a mold with resin with a roller or brush ( Figure 2).
After sample production, the samples were cut in the laser cutting device in the dimensions specified in the test standards. Thermal and sound absorption tests were applied to the produced composite samples. These were the outputs for the study. Sound transmission loss is the result of materials with sound absorbing properties. It is the value in decibels (dB) of the insulation level of sound waves coming on it. Determination of Heat Conduction Coefficient is the value that shows how much a material transmits heat, and this value is different for each material.
Sound transmission loss tests (ASTM E-2611:2009) was used for sound absorption (a fourmicrophone impedance tube). The larger the measured value in these tests, the higher the sound absorption value. The standard of "Thermal Performance of Building Materials and Products -Determination of Thermal Resistance by Means of Guarded Hot Plate and Thermal Flow Meter Methods (TS EN 12667)" was used for thermal absorption property of the composite plates. The determination of the thermal transfer coefficient of the composite plates was made by the Thermtest device at Erciyes University (Kayseri/Türkiye). The lower the measured value, the better the thermal insulation.

The Taguchi Grey Relations Analysis method
Grey Relations Analysis method based on Taguchi Method is applied to cases where more than one performance characteristics need to be optimized together (multi-objective optimization). Steps and formulas used in this method; 1. Experimental Design and Its Application 2. Determination of the Reference Series n: experiment number 1,2. . ..n 3. Normalization of data: In the case of "the larger-the better," normalization is as follows. (2) x i ðkÞ: After normalization i. series and k. value x 0 k ð Þ : the k. value in reference series x j k ð Þ : k. value in j. value Δ oi ðkÞ: k. value in the series 5. Obtaining the Grey Relations coefficient matrix of the series with the distance matrix is calculated as follows: ; x i ðkÞ ð Þ: Grey relational coefficient at point k �: a coefficient between (0,1) Δ min : Minimum value in the series Δ max : Maximum value in the series Δ oi ðkÞ: k. value in the series Table 2. Experimental plan for selected experimental design L18 (mixed 3-6 levels).

Experiment No
6. Weighting of normalized data (w) and determination of the degree of Grey relations If the effects of the response variables on performance are equal, the Grey relations degree is calculated as Equation 5: If the effects of the response variables on performance are not equal, the Grey relations degree is calculated as Equation 6:  Sarpkaya and Sabır 2016;Özgür, and Sabır 2015).

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The Larger À The Better y i : Experimental results, n: Experiment number η : Grey relations degree predicted by optimum design η m : Mean Grey relations degree η i : The value of calculated new factor levels in optimum combination

The results of the Taguchi Grey R analysis method
In this study, Grey Relations Analysis method based on Taguchi Method was applied. Experimental Design L18 (mixed 3-6 levels) was chosen, and results are given in Table 3. The first row is factors affecting the process (A, B, and C) and the response variables are sound transmission loss and heat conduction coefficient. The first column in Table 4 is the number of experiments. The last two columns are the experimental results for L18 (mixed 3-6 levels) Taguchi Experimental Design (Step 1).
Step 2. Determination of the Reference series. Using Equation 1, the reference series for the two performance output variables are determined in Table 4.
Step 3. Data Normalization. The normalization matrix for outputs can be seen in Table 4 (Eq. 2) Step 4. Using equation, Distance matrix is calculated in Table 4.
Step 5. Grey relational coefficient matrix of the Distance matrix calculated is obtained with Eq. 4 (Table 5)  Step 6: Performance outcomes were calculated as equally (0,5-0,5) weighted. Applying Equation 5, Grey Relational Degree is calculated. In Table 5, Grey relational degree and ranking are seen. In the table, the experiment with the highest Grey relational degree is 10th experiment. Figure 3 shows Grey relational degree graph. Grey relation degree of Experiment No. 10 is the highest.
Step 7. After steps 1-6, new levels of experimental factors are calculated. Table 6 shows Calculated new Factor levels. As seen from the table, the difference between the levels of factor A (Fabric) is the biggest, and this factor is understood as the most influential parameter. Figure 4 shows the graph of the parameter levels. Optimal parameter levels are seen as A4B1C2. (This combination is not included in the experimental plan.) Step 8. ANOVA test. The ANOVA test results are given in Table 7. As seen in the table, the highest F value is Factor A (Fabric). The second F value is Factor B (Al 2 O 3 Filler), and the third F value is Factor C (SiC Filler). Factor A (Fabric), which has the highest F value, is the most effective factor. Contribution (%) values also support that. The highest contribution (%) value, respectively, is Factor A (Fabric), Factor B (Al 2 O 3 Filler), and Factor C (SiC Filler). This value shows that when the thermal and sound insulation values are evaluated together, the most effective factor is Factor A (Fabric).
Step 9: The final step is applying the Taguchi Method and confirmation test. In Table 8, S/N Ratio of Grey Relational Degree is seen (Equation 7 and was calculated by using MINITAB 16® package program). When Table 8 is examined, it is seen that the lowest S/N value is in sample 10. It means that when the heat transmission coefficient and sound transmission loss values are evaluated together, the most optimum sample is sample number 10.
Confirmation Test: According to the Grey Relation Taguchi test results, when the heat and sound insulation properties were examined together, it was concluded that the most optimum sample is the sample containing 30% carbon, 0% Al 2 O 3 and 5% SiC.
When the analyzes are examined, it is seen that the sample moves away from the optimum situation with the increase in the amount of fabric in the composite, and the most optimal samples are the samples containing 30% fabric (basalt and carbon).
In addition, it was concluded that adding Al 2 O 3 (alumina) as a filling material into the composite negatively affects the thermal and sound insulation properties of the composite. It is thought that the reason for this situation may be that the nano Al 2 O 3 material creates gaps in the composite and the passage of heat and sound through these gaps becomes easier. This situation also supports the literature. It is known that the heat conduction properties of Al 2 O 3 material are not good. For the confirmation test, a sample containing 30% carbon fiber, 0% Al 2 O 3 , and 5% SiC suggested by the method was produced, and measurements were made for the heat conductivity coefficient and    sound transmission loss values. The Grey Relationship Degree was calculated for the estimation and the experiment. Improvement in Grey Relationship Rating was also found. These findings are seen collectively in Table 9. Experiment (4) (A2B1C1) is chosen as the initial design. Grade of Grey Relations = 0.55 calculated for this experiment. The average Grey Relationship Grade for weighting coefficient of thermal conduction is 0.5 and the sound conduction loss 0.5 is η m , 0,65 (Table 5) Optimum levels of factors are η A4 ¼ 0; 8111, η B1 ¼ 0; 6791 ve η C2 ¼ 0; 6566.

Initial Process Parameter
Optimum Process Parameter Step 5: Weight Determination (It is calculated for 0,5-0,5) Step 6: ð0; 61 þ 0; 78Þ=2 ¼ 0; 70 The difference between the Grey Relationship Degree (0,70) calculated for the experiment performed at the optimum process parameters and the Grey Relationship Degree (0,55) calculated for the Initial process parameters gives the improvement in the Grey Relationship Degree. This value is seen as 0,15 in Table 9.
Since the optimum experimental plan (A4B1C2) suggested by the Grey Relationship Analysis for the confirmation test was not included in the experimental plan, the experiment of A4B1C2 was carried out under the recommended conditions under the operating conditions. As a result of the experiment, thermal conductivity coefficient output in the test for the confirmation test is 0,033 W/ mK and the sound transmission loss is 2753 dB. In a study by Ovalı (2015), it was observed that the heat transmission coefficient value increased with the increase in filling materials above a certain level. The reason for this situation was thought to be related to the thermal permeability properties of the filling materials used.

Conclusion
In this study, 18 different composite containing basalt and carbon fabric at the rate of 30%, 40%, and 50%, Al 2 O 3 (Alumina) at the rates of 0%, 2%, and 4% and SiC (Silicon carbide) at the rates of 0%, 5%, and 10% were produced in accordance with the Taguchi orthogonal experiment design. Thermal conductivity coefficient and sound absorption tests were performed on the basalt and carbon reinforcement epoxy composite samples. Obtained test results were analyzed with L18 (mixed 3-6 levels) orthogonal experiment design using the Taguchi Method Based on Grey Relationships. From the Grey Taguchi analysis, it was concluded that the most optimum sample in terms of thermal transmission coefficient and sound transmission loss values was the sample containing 30% carbon, 0% Al 2 O 3 and 5% SiC. It is also concluded that when the heat conductivity coefficient is low and the sound transmission loss value is high, it is concluded that the optimum sample is the 30% carbon containing samples.
It can be thought that the reason for the high thermal and sound properties of the sample containing 0% Al 2 O 3 is the change in the porous structure. It was thought that the reason for the optimum sample was that the sample containing 0% Al 2 O 3 might be that the heat conduction properties of Al 2 O 3 are not very good. In addition, it can be concluded that the rate of filling materials increases above a certain level as a result of inhomogeneously spreading of the filling materials on the composite surface, which facilitates the passage of heat through the composite surface. It was also shown that when the heat conductivity coefficient is low and the sound transmission loss value is high, the 30% carbon-containing samples are the best. As seen in Tables 6 and 7, as a result of the Grey relations analysis performed for the effect of the factors that will optimize the heat and sound insulation together in the study, Al 2 O 3 Filler is the second most effective factor and SiC Filler is the third most effective factor. As a result of the confirmation test, after the combination suggested from Grey Taguchi was produced, heat and sound insulation tests were performed. An improvement degree was found of 0.15.
The density of the composites also is important data. Future studies that can be added to the model and the effect can be examined. Composite materials produced within the scope of the study can be used as heat and sound insulation materials in buildings, automotive, aerospace, defense, and construction industries and in areas where sound insulation is required, thanks to their heat and sound insulation properties and high mechanical properties.

Highlights
• This study is an experimental study examining the optimization of both sound and heat insulation properties of basalt and carbon fabric-reinforced composite plates, which are materials with superior physical and mechanical properties, using a multi-objective decision method. • In this study, powder substances, such as Al 2 O 3 and SiC, were added to the epoxy matrix, as well as basalt and carbon fabric reinforcements, to reveal the effect of these substances on the optimum heat and sound absorption properties. • Taguchi Grey Relations Analysis method was used as a multi-objective optimization method and thus the optimum composite plate that could be analyzed statistically with fewer samples could be determined experimentally. • By performing verification experiments based on Grey Relations, the accuracy and improvement of the optimum results obtained can be demonstrated. • The study includes experiments in which optimum results named "Confirmation Test" are verified and also shows the proportional values of the improvements obtained.