# Performance Evaluation of an Improved ANFIS Approach Using Different Algorithms to Predict the Bonding Strength of Glulam Adhered by Modified Soy Protein–MUF Resin Adhesive

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{3}, pH of 2.5–4 and concentration of 36–38 made by Mojalali Co., Tehran, Iran), NaOH (40%), butanol and ammonium chloride (20%) were used.

#### 2.2. Methods

#### 2.2.1. Experimental Design

#### 2.2.2. Making the Protein Adhesive

#### 2.2.3. Making the Melamine–Urea–Formaldehyde Resin

#### 2.3. Manufacturing Glulam

^{2}adhesive (based on oven-dried substance) uniformly on two upper and lower surfaces of the middle layer (among a total of 3 layers) and placing it between two boards, the layers were placed under a hydraulic press at a temperature according to the experimental design for 60 s/mm at a pressure of 30 kg/cm

^{2}.

#### 2.4. Model Development

#### 2.4.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)

^{1}

_{i}is the membership grade of a fuzzy set (P

_{i}) and determines a range in which the input x meets the quantity P and μ

_{pi}is the membership function (MF). Gaussian2mf, a famous membership function was chosen, which is expressed as follows:

_{i},b

_{i},c

_{i}} is the set of the consequent parameters.

_{R}, PSO, DE and GA, to ensure the bonding strength prediction error.

#### 2.4.2. Ant Colony Optimization (ACO_{R})

_{R}algorithms have a wide range of applications due to their ability to solve both static and dynamic problems. These algorithms use a discrete structure to determine the solution. The discrete structure concept in an ACO

_{R}means that each decision variable is divided into a certain number of states within a defined range. In order to ensure that the variable space is discrete, a limitation is imposed on the algorithm that decreases the optimality precision. However, by dividing the space between the decision variables to a large degree, the solution precision is increased, and the program time increases accordingly. Furthermore, as the system becomes more complicated, the precision may decrease. To solve this problem, ACO

_{R}was generalized in the continuous space so that the algorithm would move in the R space and the continuity would be met using a probability density function. Socha and Dorigo proposed the Gaussian function. A Gaussian function cannot create several maxima [36]. Therefore, the kernel Gaussian function (sum of single Gaussian functions) was used, which is defined for the i-th decision variable as follows:

^{l}, μ

^{l}

_{i}and σ

^{l}

_{i}must be defined, and k is the number of single Gaussian functions. The decision variables related to the i-th solution are denoted by b

^{l}

_{1}and b

^{l}

_{2}, and the n-th decision variable is denoted by b

^{l}

_{n}, the value of which is calculated for each solution (h(b

^{l})). The number of solutions is k. Then, the solutions are arranged in descending order based on quality and are saved. Then, for each b

^{l}, a weight (w) is determined, the value of which is proportional to the quality of the related solution, where w

^{1}≥ w

^{2}≤ … ≥ w

^{k}is calculated as follows:

^{l}

_{i}is equal to b

^{l}

_{l}for the solution l and the i-th variable. σ

^{l}

_{i}is the standard deviation between all k values of the i-th variable relative to b

^{l}

_{i}and is calculated as follows:

#### 2.4.3. Particle Swarm Optimization (PSO)

_{1}is the local weight; c

_{2}is the global weight; p

_{best}and g

_{best}are the best positions of particles and swarms, respectively; and rand is a random value.

#### 2.4.4. Differential Evaluation (DE)

_{i}

_{,G + 1}, and r

_{1}, r

_{2}and r

_{3}are the arbitrary selection numbers ∈[1,2,3,…,]…NP. The trial vector is determined by a combined process (crossover operation) that uses a combination of the mutated vector parameters and other predetermined vector parameters:

_{j}

_{,G + 1}is the trailer vector, x

_{i}

_{,G}is the target vector, rand b(j) denotes the j-th uniform random evaluation (∈∈[0,1]), rnbr(i) is a random value index (∈∈[1,2,3,…,d]) and CR is a crossover constant determined by the user. Finally, the trial vector is used as the target value of the next generation in the selection process and offers the lowest-cost function value compared to the target vector. Since each population must act as the target vector, NP tasks are considered a single generation procedure.

#### 2.4.5. Genetic Algorithm

_{i}, c

_{i}} or μ

_{pi}in Equation (5) are related to the membership functions that can be optimized by the evolutionary algorithms. Any of these parameters contains N genes, where N is the number of the membership functions. The consequent parameters {P

_{i}, Q

_{i}, c

_{i}} in Equation (3) can be trained by the optimization algorithm. In the Results section, the genes (I + 1) × R produce each chromosome. The objective function of the evolutionary algorithms used is the root mean square error (RMSE). To solve the mentioned optimum problem using the ANFIS-GA, the weight (μ

_{pi}) of the fuzzy antecedent parameters is tuned by the GA algorithms like linear parameters such as Q, P and c.

#### 2.5. Performance Evaluation

^{2}), root mean square error (RMSE), mean absolute error (MAE) and sum square error (SSE), were used to analyze the performance of the new models in the following examined forms:

_{i}and $\overline{x}$ are the observed and mean values, respectively; and y

_{i}and ȳ are the related predicted and mean values, respectively. As R

^{2}increases and approaches 1, the predicted values approach the experimental values, showing the high performance of the model in predicting the response with high precision. As the errors decrease to a minimum, the model under examination offers a more precise prediction of the response being examined.

## 3. Results and Discussion

#### 3.1. Accuracy of the Predicted Values Obtained by the Approaches

^{2}equal to 0.9809 for the training dataset and 0.8108 for the testing datasets, meaning that the model achieved excellent training of the outputs so that 98.09% and 81.08% of the estimated values agree with the measured values for the training and testing datasets, respectively.

^{2}, three other statistical indices that compare the deviation between the actual and estimated values, i.e., RMSE, MAE and SSE, are given in Table 3 to compare the performance of the developed prediction models. In addition to confirming the higher precision of the ANFIS-GA model to predict the output using R

^{2}(Figure 2), the errors estimated by RMSE, MAE and SSE have lower values (0.3366, 0.2082 and 3.8523, respectively) than the ANFIS (0.7192, 0.3575 and 17.5885, respectively), ANFIS-ACOR (0.4711, 0.3636 and 7.5470, respectively), ANFIS-DE (0.6157, 0.4905 and 12.8904, respectively) and ANFIS-PSO (0.3535, 0.2135 and 4.2479, respectively) models. Using different hybrids of the ANFIS model, the errors were decreased, with the most limited decrease associated with the using the GA model (Figure 3). More than 70% of the errors produced range from −5% to 5% in the model developed with the GA, while in the basic ANFIS and ACOR models, the errors are distributed in a wider range from −40% to 60%. Hence, the hybrid ANFIS-GA model can be used to predict the response values with the highest precision among tested models. The random division of data into two testing and training phases led to an overfitting problem because the classic training algorithms are generally very dependent on the training datasets and cannot offer an acceptable performance in the testing phase (Figure 3). Unlike the classic ANFIS model, the hybrid ANFIS algorithms showed reliable performance in the testing and training phases. The best hybrid methods prevent the system from falling into overfitting and local optima [42]. The performance of the GA method may be due to the ability of the algorithm to model a complex phenomenon. The weak performance of other optimization methods such as PSO may be due to the weakness of the algorithms to solve hard problems compared to GA [43] because the simple PSO structure cannot precisely optimize the bonding strength values. Furthermore, the classic ANFIS model that uses gradient-based training techniques including backpropagation requires many burden values to be optimized and trained when the number of inputs is increased [41].

#### 3.2. Optimized Values of the Preferred Approach

## 4. Conclusions

_{R}, ANFIS-PSO, ANFIS-DE and ANFIS-GA models were developed to predict the bonding strength of glulam made with MUF-modified soy protein adhesive. A three-factor, three-level CCD design was used to make the test samples to compare the prediction precision of the response under examination obtained by all applied methods. After designing and testing the systems, the predictability of all five models was compared using statistical criteria, i.e., R

^{2}, RMSE, MAE and SSE. After determining the best model in terms of precision in estimating the response, it was used to determine the optimum level of the variables used to achieve the highest bonding strength. The results indicate that by combining the basic ANFIS model with other algorithms, the accuracy of the response estimation can be generally increased. The combination of the genetic algorithm with the ANFIS model resulted in a more accurate response estimation compared to combinations with other algorithms, with an R

^{2}of 0.9809, RMSE of 0.3366, MAE of 0.2082 and SSE of 3.8523. Hence, the optimization method has had a higher prediction accuracy. Based on the developed model, the optimum input values to produce glulam with a maximum bonding strength (7.76 MPa) were a minimum MR value (1.68:1), a maximum WR value (60:40) and a maximum press temperature value (180 °C).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Cheng, H.; Dowd, M.K.; He, Z. Investigation of modified cottonseed protein adhesives for wood composites. Ind. Crops Prod.
**2013**, 46, 399–403. [Google Scholar] [CrossRef] - Kumar, R.; Choudhary, V.; Mishra, S.; Varma, I.K.; Mattiason, B. Adhesives and plastics based on soy protein products. Ind. Crops Prod.
**2002**, 16, 155–172. [Google Scholar] [CrossRef] - Hettiarachchy, N.; Kalapathy, U.; Myers, D. Alkali-modified soy protein with improved adhesive and hydrophobic properties. J. Am. Oil Chem. Soc.
**1995**, 72, 1461–1464. [Google Scholar] [CrossRef] - Yang, G.; Yang, B.; Yuan, C.; Geng, W.; Li, H. Effects of preparation parameters on properties of soy protein-based fiberboard. J. Polym. Environ.
**2011**, 9, 146–151. [Google Scholar] [CrossRef] - Taghiyari, H.R.; Hosseini, S.B.; Ghahri, S.; Ghofrani, M.; Papadopoulos, A.N. Formaldehyde emission in micron-sized wollastonite-treated plywood bonded with soy flour and urea-formaldehyde resin. Appl. Sci.
**2020**, 10, 6709. [Google Scholar] [CrossRef] - Pereira, F.; Pereira, J.; Paiva, N.; Ferra, J.; Martins, J.M.; Magalhaes, F.D.; Carvalho, L. Natural additive for reducing formaldehyde emissions in urea-formaldehyde resins. J. Renew. Mater.
**2016**, 4, 41–46. [Google Scholar] [CrossRef] - Sun, X.; Bian, K. Shear strength and water resistance of modified soy protein adhesives. J. Am. Oil Chem. Soc.
**1999**, 76, 977–980. [Google Scholar] [CrossRef] - Huang, W.; Sun, X. Adhesive properties of soy proteins modified by urea and guanidine hydrochloride. J. Am. Oil Chem. Soc.
**2000**, 77, 101–104. [Google Scholar] [CrossRef] - Yapici, F.; Senyer, N.; Esen, R. Comparison of the multiple regression, ANN, and ANFIS models for prediction of MOE value of OSB panels. Wood Res.
**2016**, 61, 741–754. [Google Scholar] - Alhijazi, M.; Safaei, B.; Zeeshan, Q.; Asmael, M.; Harb, M.; Qin, Z. An experimental and metamodeling approach to tensile properties of natural fibers composites. J. Polym. Environ.
**2022**, 30, 4377–4393. [Google Scholar] [CrossRef] - Nazerian, M.; Naderi, F.; Partovinia, A.; Papadopoulos, A.N.; Younesi-Kordkheili, H. Developing adaptive neuro-fuzzy inference system-based models to predict the bending strength of polyurethane foam-cored sandwich panels. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl.
**2022**, 236, 3–22. [Google Scholar] [CrossRef] - Papadopoulos, A.N. Advances in Wood Composites. Polymers
**2020**, 12, 48. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wong, Y.J.; Mustapha, K.B.; Shimizu, Y.; Kamiya, A.; Arumugasamy, S.K. Development of surrogate predictive models for the nonlinear elasto-plastic response of medium density fibreboard-based sandwich structures. Int. J. lightweight Mater.
**2021**, 4, 302–314. [Google Scholar] [CrossRef] - Jamali, F.; Mousavi, S.R.; Peyma, A.B.; Moodi, Y. Prediction of compressive strength of fiber-reinforced polymers-confined cylindrical concrete using artificial intelligence methods. J. Reinf. Plast. Compos.
**2022**, 41, 679–704. [Google Scholar] [CrossRef] - Karaboga, D.; Kaya, E. Training ANFIS by using and adaptive and hybrid artificial bee colony algorithm (aABC) for the identification of nonlinear static systems. Arab. J. Sci. Eng.
**2019**, 44, 3531–3547. [Google Scholar] [CrossRef] - Al-Musawi, A.A.; Alwanas, A.A.H.; Salih, S.Q.; Ali, Z.H.; Tran, M.T.; Yaseen, Z.M. Shear strength of SFRCB without stirrups simulation: Implementation of hybrid artificial intelligence model. Eng. Comput.
**2020**, 36, 1–11. [Google Scholar] [CrossRef] - Jayaram, M.A.; Nataraja, M.C.; Ravi Kumar, C.N. Design of high performance concrete mixes through particle swarm optimization. J. Intell. Syst.
**2010**, 19, 249–264. [Google Scholar] [CrossRef] - Flint, M.; Grünewald, S.; Coenders, J. Ant colony optimization for ultra high performance concrete structures. In Designing and Building with UHPFRC; Toutlemonde, F., Resplendino, J., Eds.; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar] [CrossRef]
- Quaranta, G.; Fiore, A.; Marano, G.C. Optimum design of prestressed concrete beams using constrained differential evolution algorithm. Struct. Multidiscipl. Optim.
**2014**, 49, 441–453. [Google Scholar] [CrossRef] - Coello Coello, C.A.; Christiansen, A.D.; Hernández, F.S. A simple genetic algorithm for the design of reinforced concrete beams. Eng. Comput.
**1997**, 13, 185–196. [Google Scholar] [CrossRef] - Elbaz, K.; Shen, S.L.; Sun, W.J.; Yin, Z.Y.; Zhou, A. Prediction model of shield performance during tunneling via incorporating improved particle swarm optimization into ANFIS. IEEE Access
**2020**, 8, 39659–39671. [Google Scholar] [CrossRef] - Babanezhad, M.; Behroyan, I.; Nakhjiri, A.T.; Marjani, A.; Rezakazemi, M.; Shirazian, S. High-performance hybrid modeling chemical reactors using differential evolution based fuzzy inference system. Sci. Rep.
**2020**, 10, 21304. [Google Scholar] [CrossRef] [PubMed] - Jing, H.; Rad, H.N.; Hasanipanah, M.; Armaghani, D.J.; Qasem, S.N. Design and implementation of a new tuned hybrid intelligent model to predict the uniaxial compressive strength of the rock using SFS-ANFIS. Eng. Comput.
**2021**, 37, 2717–2734. [Google Scholar] [CrossRef] - Penghui, L.; Ewees, A.A.; Beyaztas, B.H.; Qi, C.; Salih, N.Q.; Al-Ansari, N.; Bhagat, S.K.; Yaseen, Z.M.; Singh, V.P. Metaheuristic optimization algorithms hybridized with artificial intelligence model for soil temperature prediction: Novel model. IEEE Access
**2020**, 8, 51884–51904. [Google Scholar] [CrossRef] - Bui, Q.T.; Van Pham, M.; Nguyen, Q.H.; Nguyen, L.X.; Pham, H.M. Whale optimization algorithm and adaptive neuro-fuzzy inference system: A hybrid method for feature selection and land pattern classification. Int. J. Remote Sens.
**2019**, 40, 5078–5093. [Google Scholar] [CrossRef] - Zhang, S.; Bui, X.N.; Trung, N.T.; Nguyen, H.; Bui, H.B. Prediction of rock size distribution in mine bench blasting using a novel ant colony optimization-based boosted regression tree technique. Nat. Resour. Res.
**2020**, 29, 867–886. [Google Scholar] [CrossRef] - Jaafari, A.; Zenner, E.K.; Panahi, M.; Shahabi, H. Hybrid artificial intelligence models based on a neuro-fuzzy system and metaheuristic optimization algorithms for spatial prediction of wildfire probability. Agric. For. Meteorol.
**2019**, 266–267, 198–207. [Google Scholar] [CrossRef] - Elbaz, K.; Shen, S.L.; Zhou, A.; Yuan, D.J.; Xu, Y.S. Optimization of EPB shield performance with adaptive neuro-fuzzy inference system and genetic algorithm. Appl. Sci.
**2019**, 9, 780. [Google Scholar] [CrossRef][Green Version] - Sari, P.a.; Suhatril, M.; Osman, N.; Muazu, M.A.; Katebi, J.; Abavisani, A.; Ghaffari, N.; Chahnasir, E.S.; Wakil, K.; Khorami, M.; et al. Developing a hybrid adoptive neuro-fuzzy inference system in predicting safety of factors of slopes subjected to surface eco-protection techniques. Eng. Comput.
**2020**, 36, 1347–1354. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Melini, W.H.; Mohtar, H.W.; Ameen, A.M.S.; Ebtehaj, I.; Razali, S.F.M.; Bonakdari, H.; Salih, S.Q.; Al-Ansari, N.; Shahid, S. Implementation of univariate paradigm for streamflow simulation using hybrid data-driven model: Case study in tropical region. IEEE Access
**2019**, 7, 74471–74481. [Google Scholar] [CrossRef] - Varnamkhasti, M.J. A hybrid of adaptive neuro-fuzzy inference system and genetic algorithm. J. Intell. Fuzzy Syst.
**2013**, 25, 793–796. [Google Scholar] [CrossRef] - Varnamkhasti, M.J. ANFISGA-adaptive neuro-fuzzy inference system genetic algorithm. Glob. J. Comput. Sci. Technol.
**2011**, 11, 15036870. [Google Scholar] - Yuan, Z.; Wang, L.N.; Ji, X. Prediction of concrete compressive strength: Research on hybrid models genetic based algorithms and ANFIS. Adv. Eng. Softw.
**2014**, 67, 156–163. [Google Scholar] [CrossRef] - Jiang, K.; Zhang, J.; Xia, S.; Ou, C.; Fu, C.; Yi, M.; Li, W.; Jing, M.; Lv, W.; Xiao, H. Improve performance of soy protein adhesives with a low molar ratio melamine-urea-formaldehyde resin. J. Phys. Conf. Ser.
**2020**, 1549, 032083. [Google Scholar] [CrossRef] - Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man. Cybern.
**1985**, 15, 116–132. [Google Scholar] [CrossRef] - Socha, K.; Dorigo, M. Ant colony optimization for continuous domains. Eur. J. Oper. Res.
**2008**, 185, 1155–1173. [Google Scholar] [CrossRef][Green Version] - Kennedy, J.; Eberhart, R. A new optimizer using particles swarm theory. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4–6 October 1995. [Google Scholar]
- Liu, X.; Hussein, S.H.; Ghazali, K.H.; Tung, T.M.; Yaseen, Z.M. Optimized adaptive neuro-fuzzy inference system using metaheuristic algorithms: Application of shield tunnelling ground surface settlement prediction. Complexity
**2021**, 2021, 6666699. [Google Scholar] [CrossRef] - Mohandes, M.A. Modeling global solar radiation using Particle Swarm Optimization (PSO). Sol. Energy
**2012**, 86, 3137–3145. [Google Scholar] [CrossRef] - Catalao, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F. Hybrid wavelet-PSO-ANFIS approach for short-term electricity prices forecasting. IEEE Trans. Power Syst.
**2011**, 26, 137–144. [Google Scholar] [CrossRef] - Shihabudheen, K.V.; Pillai, G.N. Recent advances in neuro-fuzzy system: A survey. Knowl. Based Syst.
**2018**, 152, 136–162. [Google Scholar] [CrossRef] - Kisi, O.; Azad, A.; Kashi, H.; Saeedian, A.; Hashemi, S.A.A.; Ghorbani, S. Modeling groundwater quality parameters using hybrid neuro-fuzzy methods. Water Resour. Manag.
**2019**, 33, 847–861. [Google Scholar] [CrossRef] - Azad, A.; Manoochehri, M.; Kashi, H.; Farzin, S.; Karami, H.; Nourani, V.; Shiri, J. Comparative evaluation of intelligent algorithms to improve adaptive neuro-fuzzy inference system performance in precipitation modelling. J. Hydrol.
**2019**, 571, 214–224. [Google Scholar] [CrossRef] - Armaghani, D.J.; Asteris, P.G.A. Comparative study of ANN and ANFIS models for the prediction of cement-based mortar materials compressive strength. Neural Comput. Applic.
**2021**, 33, 4501–4532. [Google Scholar] [CrossRef] - Mercy, L.J.; Prakash, S. Experimental investigation and neuro fuzzy modeling of inplane shear strength for self-healing GFRP. Transac. Ind. Inst. Met.
**2016**, 69, 1483–1491. [Google Scholar] [CrossRef] - Wang, D.; Sun, X.S. Low density particleboard from wheat straw and corn pith. Ind. Crops Prod.
**2002**, 15, 43–50. [Google Scholar] [CrossRef] - Bacigalupe, A.; He, Z.; Escobar, M.M. Effects of rheology and viscosity of bio-based adhesives on bonding performance. In Bio-Based Wood Adhesives; CRC Press: Boca Raton, FL, USA, 2017; pp. 293–309. [Google Scholar] [CrossRef]
- Chang, Q. Rheology Properties. In Colloid and Interface Chemistry for Water Quality Control; Elsevier: Amsterdam, The Netherlands, 2016; pp. 61–77. [Google Scholar] [CrossRef]
- Bacigalupe, A.; Molinari, F.; Eisenberg, P.; Escobar, M.M. Adhesive properties of urea-formaldehyde resins blended with soy protein concentrate. Adv. Compos. Mater.
**2020**, 3, 213–221. [Google Scholar] [CrossRef] - Zhang, X.; Ding, Y.; Zhang, G.; Li, L.; Yan, Y. Preparation and rheological studies on the solvent based acrylic pressure sensitive adhesives with different crosslinking density. Int. J. Adhes. Adhes.
**2011**, 31, 760–766. [Google Scholar] [CrossRef] - Bacigalupe, A.; Poliszuk, A.K.; Eisenberg, P.; Escobar, M.M. Rheological behavior and bonding performance of an alkaline soy protein suspension. Int. J. Adhes. Adhes.
**2015**, 62, 1–6. [Google Scholar] [CrossRef] - Kamoun, C.; Pizzi, A.; Garcia, R. The effect of humidity on crosslinked and entanglement networking of formaldehyde-based wood adhesives. Eur. J. Wood Wood Prod.
**1998**, 56, 235–243. [Google Scholar] [CrossRef] - Rachtanapun, P.; Heiden, P. Thermoplastic polymers as modifiers for urea-formaldehyde (UF) wood adhesives. II Procedures for the preparation and characterization of thermoplastic-modified UF wood composites. J. Appl. Polym. Sci.
**2003**, 87, 898–907. [Google Scholar] [CrossRef] - Wang, F.; Wang, J.; Chu, F.; Wang, C.; Jin, C.; Wang, S.; Pang, J. Combinations of soy protein and polyacrylate emulsions as wood adhesives. Int. J. Adhes. Adhes.
**2018**, 82, 160–165. [Google Scholar] [CrossRef] - Fink, J.K. Urea/formaldehyde resins. In Reactive Polymers Fundamentals and Applications; William Andrew Publishing: New York, NY, USA, 2013; pp. 179–192. [Google Scholar]
- Wei, X.; Wang, X.; Li, Y.; Ma, Y. Properties of a new renewable sesame protein adhesive modified by urea in the absence and presence of zinc oxide. RSC Adv.
**2017**, 7, 46388. [Google Scholar] [CrossRef][Green Version] - Norstrom, E.; Demircan, D.; Fogelström, L.; Khabbaz, F.; Malmström, E. Green binders for wood adhesives. Appl. Adhes. Bond. Sci. Technol.
**2017**, 1, 13–70. [Google Scholar] [CrossRef][Green Version] - Vnucec, D.; Kutnar, A.; Gorsek, A. Soy-based adhesives for wood-bonding—A review. J. Adhes. Sci. Technol.
**2017**, 31, 910–931. [Google Scholar] [CrossRef] - Sun, X.S. Thermal and mechanical properties of soy proteins. In Bio-Based Polymers and Composites; Wool, R., Sun, X.S., Eds.; Elsevier Inc.: Amsterdam, The Netherlands, 2005; pp. 292–326. [Google Scholar]
- Migneault, S.; Koubaa, A.; Riedl, B.; Nadji, H.; Deng, J.; Zhang, S.Y. Potential of pulp and paper sludge as a formaldehyde scavenger agent in MDF resins. Holzforschung
**2011**, 65, 403–409. [Google Scholar] [CrossRef] - Li, C.; Li, H.; Zhang, S.; Li, J. Preparation of reinforced soy protein adhesive using silane coupling agent as an enhancer. Bioresources
**2014**, 9, 5448–5460. [Google Scholar] [CrossRef][Green Version] - Abdullah, Z.A.; Park, B.D. Influence of acrylamide copolymerization of urea–formaldehyde resin adhesives to their chemical structure and performance. J. App. Polym. Sci.
**2010**, 117, 3181–3186. [Google Scholar] [CrossRef] - Qu, P.; Huang, H.; Wu, G.; Sun, H.; Chang, Z. The effect of hydrolyzed soy protein isolate on the structure and biodegradability of urea– formaldehyde adhesives. J. Adhes. Sci. Technol.
**2015**, 29, 502–517. [Google Scholar] [CrossRef] - Luo, J.; Luo, J.; Bai, Y.; Gao, Q.; Li, J. A high performance soy protein-based bio-adhesive enhanced with a melamine/epichlorohydrin prepolymer and its application on plywood. RSC Adv.
**2016**, 6, 67669–67676. [Google Scholar] [CrossRef] - Zhang, L.; Zhang, B.; Fan, B.; Gao, Z.; Shi, J. Liquefaction of soybean protein and its effects on the properties of soybean protein adhesive. Pigment. Resin Technol.
**2017**, 46, 399–407. [Google Scholar] [CrossRef]

**Figure 2.**Comparison of the estimated and actual values for the (

**a**) training dataset and (

**b**) testing dataset.

**Figure 4.**Comparison of the actual direct effects of the independent variable on the bonding strength of glulam with ANFIS, ANFIS-ACO

_{R}, ANFIS-PSO, ANFIS-DE and ANFIS-GA.

**Figure 8.**Comparison of the interactive effect of MR × WR, MR × TEM and WR × TEM on the real and estimated values of the bonding strength estimated by the ANFIS-GA model.

**Figure 9.**Three-dimensional plot of the interactive effect of the independent variables on the bonding strength according to the ANFIS-GA approach: (

**a**) WR × MR, (

**b**) MR × Tem and (

**c**) WR × Tem.

No | x1 (MR) | x2 (WR) | x3 (TEM) | No | x1 (MR) | x2 (WR) | x3 (TEM) |
---|---|---|---|---|---|---|---|

1 | 1.93:1 (1) | 20 (−1) | 140 (−1) | 18 | 1.805 (0) | 40 (0) | 160 (0) |

2 | 1.68:1 (−1) | 40 (0) | 160 (0) | 19 | 1.805 (0) | 40 (0) | 160 (0) |

3 | 1.805:1 (0) | 40 (0) | 140 (−1) | 20 | 1.805 (0) | 40 (0) | 160 (0) |

4 | 1.93:1 (1) | 60 (1) | 140 (−1) | 21 | 1.68 (−1) | 60 (1) | 180 (1) |

5 | 1.93:1 (1) | 40 (0) | 160 (0) | 22 | 1.805 (0) | 40 (0) | 160 (0) |

6 | 1.68:1 (−1) | 20 (−1) | 140 (−1) | 23 | 1.68 (−1) | 20 (−1) | 180 (1) |

7 | 1.805:1 (0) | 40 (0) | 160 (0) | 24 | 1.93 (1) | 60 (1) | 140 (−1) |

8 | 1.68:1 (−1) | 20 (−1) | 180 (1) | 25 | 1.93 (1) | 60 (1) | 180 (1) |

9 | 1.93:1 (1) | 20 (−1) | 180 (1) | 26 | 1.68 (−1) | 60 (1) | 140 (−1) |

10 | 1.805:1 (0) | 40 (0) | 160 (0) | 27 | 1.805 (0) | 20 (−1) | 160 (0) |

11 | 1.68:1 (−1) | 20 (−1) | 140 (−1) | 28 | 1.805 (0) | 20 (−1) | 160 (0) |

12 | 1.93:1 (1) | 20 (−1) | 180 (1) | 29 | 1.93 (1) | 40 (0) | 160 (0) |

13 | 1.68:1 (−1) | 60 (1) | 140 (−1) | 30 | 1.805 (0) | 40 (0) | 180 (1) |

14 | 1.805:1 (0) | 60 (1) | 160 (0) | 31 | 1.93 (1) | 60 (1) | 180 (1) |

15 | 1.805:1 (0) | 60 (1) | 160 (0) | 32 | 1.93 (1) | 20 (−1) | 140 (−1) |

16 | 1.805:1 (0) | 40 (0) | 140 (−1) | 33 | 1.805 (0) | 40 (0) | 180 (1) |

17 | 1.68:1 (−1) | 60 (1) | 180 (1) | 34 | 1.68 (−1) | 40 (0) | 160 (0) |

No | Ex. | ANFIS | ACOR | PSO | DE | GA | No | Ex. | ANFIS | ACOR | PSO | DL | GA |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 4.71 | 2.11 | 3.74 | 4.94 | 3.76 | 4.93 | 18 | 5.02 | 5.45 | 5.40 | 5.49 | 5.77 | 5.49 |

2 | 5.13 | 5.15 | 5.10 | 5.13 | 5.37 | 5.16 | 19 | 5.7 | 5.45 | 5.40 | 5.49 | 5.77 | 5.49 |

3 | 4.94 | 4.54 | 4.38 | 4.94 | 4.42 | 4.92 | 20 | 5.6 | 5.45 | 5.40 | 5.49 | 5.77 | 5.49 |

4 | 5.03 | 5.03 | 5.65 | 5.19 | 4.84 | 5.19 | 21 | 7.82 | 7.75 | 7.18 | 7.75 | 7.08 | 7.75 |

5 | 5.7 | 5.75 | 5.70 | 5.80 | 5.43 | 5.80 | 22 | 5.08 | 5.45 | 5.40 | 5.49 | 5.77 | 5.49 |

6 | 2.49 | 2.72 | 3.02 | 2.95 | 3.13 | 2.95 | 23 | 4.98 | 4.98 | 5.07 | 4.98 | 5.39 | 4.95 |

7 | 5.5 | 5.45 | 5.40 | 5.49 | 5.77 | 5.49 | 24 | 5.36 | 5.03 | 5.65 | 5.19 | 4.84 | 5.18 |

8 | 4.24 | 4.98 | 5.08 | 4.99 | 5.39 | 4.95 | 25 | 6.67 | 6.10 | 7.66 | 6.80 | 6.65 | 6.79 |

9 | 5.54 | 5.66 | 5.75 | 5.59 | 6.16 | 5.60 | 26 | 5.14 | 5.14 | 5.12 | 5.26 | 5.33 | 5.24 |

10 | 5.8 | 5.45 | 5.40 | 5.49 | 5.77 | 5.49 | 27 | 4.15 | 4.39 | 4.38 | 5.38 | 5.76 | 5.29 |

11 | 2.95 | 2.72 | 3.02 | 2.95 | 3.13 | 2.95 | 28 | 4.63 | 4.39 | 4.38 | 5.38 | 5.76 | 5.29 |

12 | 5.66 | 5.66 | 5.75 | 5.59 | 6.16 | 5.60 | 29 | 5.8 | 5.75 | 5.70 | 5.79 | 5.43 | 5.79 |

13 | 5.38 | 5.14 | 5.12 | 5.26 | 5.33 | 5.24 | 30 | 6.03 | 6.03 | 6.42 | 6.07 | 6.71 | 6.07 |

14 | 6.10 | 6.10 | 6.42 | 6.20 | 5.89 | 6.20 | 31 | 6.92 | 6.10 | 7.66 | 6.80 | 6.65 | 6.79 |

15 | 6.3 | 6.10 | 6.42 | 6.20 | 5.89 | 6.20 | 32 | 4.94 | 2.11 | 3.74 | 4.93 | 3.76 | 4.93 |

16 | 4.15 | 4.54 | 4.38 | 4.94 | 4.42 | 4.93 | 33 | 6.13 | 6.03 | 6.42 | 6.07 | 6.71 | 6.07 |

17 | 7.69 | 7.75 | 7.18 | 7.75 | 7.08 | 7.75 | 34 | 5.18 | 5.15 | 5.10 | 5.13 | 5.37 | 5.16 |

Source | ANFIS | ANFIS-ACOR | ANFIS-DE | ANFIS-PSO | ANFIS-GA | |
---|---|---|---|---|---|---|

R^{2} | Test dataset | 0.4715 | 0.8870 | 0.4635 | 0.7798 | 0.8108 |

Training dataset | 0.9655 | 0.8664 | 0.7664 | 0.9810 | 0.9809 | |

RMSE | 0.7192 | 0.4711 | 0.6157 | 0.3535 | 0.3366 | |

MAE | 0.3575 | 0.3636 | 0.4905 | 0.2135 | 0.2082 | |

SSE | 17.5885 | 7.5470 | 12.8904 | 4.2479 | 3.8523 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nazerian, M.; Naderi, F.; Papadopoulos, A.N. Performance Evaluation of an Improved ANFIS Approach Using Different Algorithms to Predict the Bonding Strength of Glulam Adhered by Modified Soy Protein–MUF Resin Adhesive. *J. Compos. Sci.* **2023**, *7*, 93.
https://doi.org/10.3390/jcs7030093

**AMA Style**

Nazerian M, Naderi F, Papadopoulos AN. Performance Evaluation of an Improved ANFIS Approach Using Different Algorithms to Predict the Bonding Strength of Glulam Adhered by Modified Soy Protein–MUF Resin Adhesive. *Journal of Composites Science*. 2023; 7(3):93.
https://doi.org/10.3390/jcs7030093

**Chicago/Turabian Style**

Nazerian, Morteza, Fatemeh Naderi, and Antonios N. Papadopoulos. 2023. "Performance Evaluation of an Improved ANFIS Approach Using Different Algorithms to Predict the Bonding Strength of Glulam Adhered by Modified Soy Protein–MUF Resin Adhesive" *Journal of Composites Science* 7, no. 3: 93.
https://doi.org/10.3390/jcs7030093