#### Abstract

Because of its excellent thermal, mechanical, and electrical properties, graphene has been used in a variety of functional coatings. Noncovalent bond functionalization and covalent bond functionalization are the most common graphene surface functionalization methods. Polymer modification, for example, can be used to give graphene and its derivatives new structure, morphology, and properties. The basic structure and predictive control principle of neural networks are discussed in this study, and a high thermal resistance porous graphene structure is reversely designed using machine learning. The effect of a graphene defect modification prediction model based on a GA (genetic algorithm) and improved BPNN (BP neural network) algorithm is investigated. The RMSE predicted by submodels 1–4 decreases by 13.26%, 3.86%, 11.71%, and 19.63%, respectively, according to the simulation results. The BPNN graphene defect modification prediction model optimized by GA has a better training and prediction effect than before optimization.

#### 1. Introduction

Because graphene is made up of six-membered benzene rings, it has extremely stable chemical properties. Graphene is the thinnest two-dimensional material ever discovered [1]. Graphene nanocomposites have a wide range of applications in electronics, polymers, automobiles, biopharmaceuticals, and other fields [2, 3]. Understanding the basic elastic parameters of graphene is critical to comprehending its mechanical properties. Since the discovery of graphene, academic circles in the United States and abroad have conducted extensive research on its elastic properties. Experiments, molecular dynamics, quantum mechanics, and other methods are currently used in research. However, because graphene is inert, the interaction of Van der Waals forces causes irreversible aggregation, making it difficult to dissolve in water or common organic solvents, and even more difficult to compound with organic or inorganic materials [4]. One of the main research topics is how to improve graphene’s compatibility with solvents and polymer matrix.

Some preliminary results have been achieved in the application of graphene in the fields of conductive, thermal conductive, anticorrosive, antistatic, and flame retardant functional coatings. In order to make the sensor specific, the traditional method of graphene biochemical sensor is to modify some molecules on the sensor surface [5], such as some atoms, chemical functional groups, metal nanoparticles, enzymes, biomolecules, and polymerases. Pazhooh et al. designed a method for detecting the electrical quantity of single-base hybrid DNA molecules by using graphene transistors grown based on CVD [6]; Bakasova et al. invented a method of photochemical synthesis of chlorine-doped graphene that can be printed without damage [7]. They covered the surface of graphene with an aluminum/titanium metal layer as a mask against chlorine penetration, which protected some graphene areas from photochlorination during doping. Patan uses a Bayesian network and rough set reduction in mathematical statistics to analyze and process defect data and effectively analyze and manage software test data, which can further play a guiding role in testing [8]. Wu et al. used the overall data quality index, the confidence degree of uncertain data, and the evidence theory to process uncertain data and applied it in the process of complex data preprocessing [9]. He et al. proposed a prediction model of graphene defect modification based on the combination of particle swarm optimization algorithm and naive Bayes. In the research, aiming at the discretization of entropy, the expected quotient of attributes is used to guide particle swarm optimization to optimize the segmentation points, so as to find the segmentation points intelligently and quickly [10].

Due to the interaction of van der Waals forces between graphene sheets, stacking of bonds, and the formation of graphene dispersions, graphene can form agglomerates on its own, and the surface free energy is minimised. Graphene is found in very small quantities. Hydrogen bonds have a lot of energy, according to studies, and breaking them causes new substances to form. The artificial neural network [11] with self-learning, self-organization, and self-adaptive abilities can process discrete data accurately to solve the above problems, but there is no clear mathematical relationship between the known factors and the experimental results. The relationship between known factors and experimental results is established, and the multivariate relationship is nonlinearly mapped to create the prediction model. In this study, a neural network is used to develop a graphene defect modification prediction method that can automatically learn the mapping relationship between multidimensional input feature vectors and their corresponding output vectors in samples and produce reasonable results. The main innovations of this study are as follows:(1)In this study, CNN is used to study the high thermal resistance structure of porous graphene. The learning samples of the neural network are obtained by the finite element numerical simulation results combined with the local limit strain criterion.(2)GA algorithm is used to make a series of in-depth improvements to BPNN algorithm to reduce the possibility of BPNN algorithm falling to minimum, so as to predict and analyze graphene defect modification more perfectly and obtain more accurate and effective test results.

The following topics are covered in different sections of this study: Section 1 introduces the research background and significance before moving on to the study's main work. Section 2 focuses on related graphene defect modification prediction technologies. Section 3 discusses the research’s specific methods and implementation. Section 4 proves that this research model is superior and feasible. Section 5 is a synopsis and preview of the entire text.

#### 2. Related Work

##### 2.1. Research on Neural Network Predictive Control

A predictive control algorithm based on linear system modeling and optimization is difficult to apply to the controlled object with strong nonlinear characteristics in the industrial process. Karg and Lucia put forward the control system of electric arc furnace based on a neural network and achieved a good control effect [12]. Liu et al. designed a constrained multistep predictive control based on a fuzzy neural network model when studying the linear speed control of sintering production lines [13]. Ma et al. combined neural network predictor with a fuzzy controller, which was applied in the control system of sewage treatment plant [14]. Oguz et al. used the mode of alternating control of fuzzy controller and recurrent neural network for nonlinear model prediction, which made the control system have the advantages of self-adaptability, small overshoot and reduction, and shortened adjustment time [15]. Zhang and Li put forward the formal mathematical description of neurons and the method of network structure and proved that a single neuron can perform logical functions, thus initiating the era of artificial neural network research [16]. Tavakoli and Assadian proposed a neural network predictive control algorithm to solve the time-varying and large time-delay problems in the aluminum electrolysis process and realized the optimal control of aluminum electrolysis process [17].

These successful application practices show that the neural network predictive control method, which combines the advantages of neural network and predictive control, has broad application prospects in industrial processes. Driven by the research trends of various compound intelligent control methods, neural network predictive control will surely develop by leaps and bounds.

##### 2.2. Study on Defect Modification of Graphene

At present, the main method used is to effectively and controllably modify the surface of graphene. There are two main methods for functional modification of graphene, namely, noncovalent bond and covalent bond functional modifications. The functional modification of graphene can improve the dispersibility of graphene and make it uniformly dispersed in the matrix, thus preparing high-quality carbon-polymer nanocomposites.

Refaely-Abramson et al. used conductive polymer polyaniline sulfide as a modifier and prepared a compound with excellent conductivity and water solubility through the interaction between graphene oxide and modifier [18]. Kierdaszuk et al. obtained functionalized graphene oxide through *π*-*π* bond interaction between electron donor material pyrene and acceptor material perylene imide and graphene oxide and then reduced it to prepare functionalized graphene oxide composite film [19]. The experimental results show that there are few defects or oxides on the surface of functionalized graphene, and the film formed by vacuum filtration has good conductivity. Qin et al. prepared amphiphilic functionalized graphene using a polymer as a modifier [20]. In the preparation process, chemical oxidation and ultrasonic stripping were used for the first time. By using the reducibility of sodium borohydride and the catalytic action of dibenzoyl peroxide, styrene, acrylamide, and graphene were copolymerized to obtain functionalized graphene, which improved the solubility of graphene.

Sun et al. proposed that graphite oxide is different from graphene in that the surface of graphite oxide contains oxygen-containing groups such as carboxyl and hydroxyl [21]. Bottcher et al. used Staudenmaier method to prepare graphene. Natural expandable graphite with a fineness of 200 mesh was used as raw material, treated with sulfuric acid, nitric acid, and other oxidants for 96 h, washed with dilute hydrochloric acid and deionized water, dried in vacuum, and rapidly thermally expanded in high-temperature equipment in an argon atmosphere to prepare graphene [22]. Smolsky et al. oxidized graphene with sulfuric acid, nitric acid, and other oxidants, so that active groups such as carboxyl and hydroxyl groups were generated on its molecular surface and then esterified with it with coupling agent KH-560 [23]. Soleimani et al. used graphene oxide at a low price, which was directly used to modify epoxy resin without chemical treatment [24]. Malinsk et al. developed a conductive marine heavy-duty anticorrosion coating with graphene as filler. Experiments show that when graphene is added at 0.6%, combined with a corresponding coupling agent, the comprehensive anticorrosion performance of the coating is greatly improved, and its cost performance is better than that of traditional zinc-rich anticorrosion coatings [25]. Zidong et al. prepared the composites by in-situ emulsification and reduction method. Experiments show that graphene can be uniformly dispersed in a polyurethane matrix, the composites also show excellent mechanical properties and flame retardancy, and the thermal stability is slightly improved [26].

#### 3. Methodology

##### 3.1. Overview of BPNN Algorithm

BPNN (BP neural network) is a multilayer feedforward network. Among artificial neural networks, BPNN has the widest application range. Most of the applied neural network models are BPNN. In the forward network, BPNN occupies an important part. The neural network performs the information processing function of the neural network through the input and output of neurons, the connection mode of neurons, the connection weight of neurons, and the threshold of neurons. BPNN standard includes three layers: IL (input layer), HL (hidden layer), and OL (output layer). Their connection mode is as follows: every neuron in IL and HL is fully connected, every neuron in HL and OL is fully connected, and neurons between layers are not connected. The network structure of three-layer BPNN is shown in Figure 1.

In the figure above, IL has neurons and the input vector is . There are neurons in the hidden layer, neurons in OL, and the output vector is .

The connection weight between IL and hidden layer is , the connection weight between hidden layer and OL is , the threshold of neurons in hidden layer is , and the threshold of neurons in OL is .

The state-space expression of BPNN is as follows:where is the input sample, is the input of HL, is the output result, is the weight connecting IL and HL, is the weight connecting HL and OL, function is the transfer function of HL, using linear transfer function, and function is the transfer function of OL, using the logarithmic transfer function.

In the learning process of BPNN, the expected error and the actual error must also be made clear. Through the error, BPNN can determine whether to continue the superposition calculation or whether to adjust the weights of the neural network. The calculation formula of actual error is as follows:

The above formula is the sum of the square differences between the actual output value and the expected output value, and then the average value is obtained. By calculating and comparing with the expected error , it can be judged whether the current learning result achieves a good learning effect.

##### 3.2. Prediction of Graphene Defect Modification

###### 3.2.1. BPNN Predictive Control Principle

When organic molecules are introduced into the surface of graphene, the charge transport or channel doping of charge can be adjusted, which leads to the adjustment of the concentration and mobility of charge carriers on the surface of graphene, and the remarkable change of graphene, which changes the conductivity of graphene. Especially, because of its three-dimensional porous space structure, foamed graphene can greatly increase the contact area between graphene and target detection molecules, so graphene has good detection sensitivity.

The pattern recognition algorithm-based intelligent sensor can classify and identify various detected objects, as well as repeat the measurement and classification process many times, extending the sensor’s life. At the same time, the sensor has a lot of potential for application research. Furthermore, the new biochemical sensor system, when combined with a pattern recognition algorithm in artificial intelligence technology, challenges people’s perceptions of traditional sensor specificity, expands sensor specificity research ideas, and has significant implications for future intelligent sensor research. In this study, a complex neural network predictive control method is designed. On the basis of generalized predictive control, the BPNN model is used as the predictive model to make the predictive control strategy suitable for the control of complex nonlinear systems. The controlled system is described by the nonlinear autoregressive average sliding discretization model as follows:

The three-layer forward network shown in Figure 2 is used as the prediction model.

In the graph, IL has nodes, HL has nodes, and OL is a single node. are the orders of output and input, respectively and are the output and input of the system at time *k*, respectively. HL output of neural network is as follows: where is the HL output vector. OL output is as follows: In the formula, is the output of the OL node, is the connection weight vector between the HL and the output node, and is the OL transfer function. If the module fails during the application of the graphene defect correction prediction model, then the output node has only one output information, thus obtaining only one output value. In practise, the research of graphene defect modification prediction model based on the BPNN algorithm must determine whether the output value indicates an error in the node. That is, there is no error if the calculation result is close to 0, but there is an error if the calculation result is close to 1. The sigmoid logarithm, tangent function, and linear function are all common BPNN transfer functions. This model uses an asymmetric sigmoid function, which is a continuously differentiable sigmoid function with certain threshold properties, such as excitation of functional neurons and the gradient descent learning method [10, 11]. Type function is as follows:

In addition, the BPNN algorithm needs to use derivatives in the process of inverse weight adjustment. The function can be easily derived, and the inverse of the function can be accurately mapped to the input value of the function . The gradient learning method includes processing using the reciprocal of function . The inverse function of is shown in the following formula:

In the formula, can be quickly obtained by the input calculation result, thus realizing the convenient calculation of its reciprocal.

The modified prediction model of graphene defects based on the BPNN algorithm takes the related data of graphene defect model as the learning sample of BPNN algorithm and uses this BPNN to learn the data, so as to predict the unknown graphene defect data to obtain better prediction effect.

###### 3.2.2. CNN Defect Modification Prediction Model

Graphene has great potential application value in many fields because of its excellent performance, but its inherent zero bandgap characteristics limit its application in semiconductor electronic devices. Pores of porous graphene were previously arranged in a regular and uniform pattern. Because the degree of freedom of the pore distribution is too high and the design space is too large to find the optimal distribution using a simple searching method, it is unclear how to optimize and control the thermal conductivity of porous graphene by designing the pore distribution. Machine learning is a technique for learning and processing large amounts of data that has recently been applied to material and structure design with great success. The influence of pore position on thermal conductivity in porous graphene will be studied using a machine learning method. We will start by building a CNN to learn and predict the thermal conductivity of porous graphene and then use CNN reverse design to find the porous graphene structure with the best thermal resistance.

CNN is a deep neural network with convolution computation and multilayer structure, which is a widely used structure in deep learning and widely used in visual image analysis. CNN has the characteristics of sharing weights, pooling, and translation invariance, which greatly reduces the complexity of network parameters and enhances the generalization ability and robustness of the model. In the CNN model, we use “*c*” to represent the convolution layer and “*f*” to represent the fully connected layer, so the CNN composed of three convolution layers and one fully connected layer can be expressed as CNN_c18c64c128f128.

In our CNN, in order to reduce the amount of computation, IL selects the gray-scale image of the perforated area of graphene. Specifically, the convolution kernel size in the convolution layer is fixed at 3 × 3, and the moving step of the convolution kernel is 1. As a regression problem, there will be no incentive function in the last layer of CNN. In this section, RMSE (root mean square error) is defined as follows:

Among them, is the number of samples involved in learning or prediction, is the real value of the sample obtained from the molecular dynamics calculation, and is the predicted value of the CNN model.

For the performance evaluation of machine learning model, besides RMSE on the test set, we also introduce the determination coefficient to measure the predictive ability of the model. The determination coefficient is defined as follows:

For each model, the decision coefficient in the training set is slightly larger than that in the verification set or the test set, which indicates that there is no fitting problem in the training process.

We randomly selected 200 drilling configurations from the total sample set and calculated their thermal conductivity by molecular dynamics method. Based on these 200 images and thermal conductivity data, the CNN model is trained and the first generation CNN model is established. The complete flow of CNN search algorithm is shown in Figure 3.

The whole search algorithm will complete the iteration after finding the target structure. In the search algorithm, the training set of CNN model increases with the number of iterations; that is, the actual thermal conductivity of top 200 configurations predicted by each generation of CNN model will be added to the training.

###### 3.2.3. Optimized GA BPNN

BPNN is used to create a public opinion prediction model, but it has some flaws, which this study addresses. GA (genetic algorithm) is used to optimize the BPNN network structure, which cannot be unified and the number of HL layers is uncertain. To make BPNN more efficient, the network parameters are optimized. GA is created by replicating natural genetic mechanisms and applying biological evolution theory. The “survival of the fittest” principle of biological evolution is applied to the coded sequence population created by parameter optimization. Individuals with good fitness values are retained, while those with poor fitness values are eliminated, according to the fitness selection function and the algorithm’s selection, crossover, and mutation operations.

The four parts of BPNN, including IL and HL connection weight, HL threshold, HL and OL connection weight, and OL threshold, are integrated into a real number string individual. Selection roulette method, that is, the selection strategy based on fitness ratio, the selection probability of each individual is as follows:where is the fitness value of individual , because the smaller the fitness value, the better is the fitness, so calculate the reciprocal of the fitness value before individual selection; is the coefficient; is the number of individuals in the population.

Considering the actual situation, this study chooses the single-point crossing method. That is, the crossover operation of chromosome and chromosome at point are as follows:where is the random number in [0, 1].

Selecting the gene of the th individual for mutation, the mutation operation method is as follows:where is the upper bound of gene , is the lower bound of gene , , is a random number, is the current iteration number, is the maximum number of evolutions, and is a random number in [0, 1].

The flow chart for optimizing the GABP network is shown in Figure 4.(1)Set the HL number of BPNN and the range of the number of neurons in each layer, and encode N chromosomes into corresponding neural networks.(2)Set different initial connection weights to learn and train the network.(3)Calculate the fitness of each individual in the initial state, and the fitness function is the error function of neural network.(4)Select individuals with large fitness value as parents, and carry out the genetic operation.(5)The crossover and mutation operations in GA are used to deal with the contemporary population, and a new population is generated.(6)Repeat Steps (2) to (5) until an individual in the group can meet the end condition, and the individual obtained at this time is approximately the optimal solution of BPNN network structure.

#### 4. Experiment and Results

##### 4.1. Experimental Environment

In the prediction process of experimental graphene defect modification based on the BPNN algorithm, the input parameters of BPNN algorithm are set according to the number of parameters of experimental data itself. For better learning efficiency, the learning rate is set to 0.01, the training times are set to 1000, and the allowable error value is set to 0.002. The experimental environment adopts Windows 7 operating system, and the hardware is equipped with a 4 GB memory. The programming environment adopts the combination of Java and Eclipse. BPNN algorithm and BP-based graphene defect correction prediction are realized by Java programming. In the final programming implementation, the input parameters of BPNN algorithm are set in an adjustable and configurable way to obtain better experimental efficiency.

##### 4.2. Experimental Result Analysis

The experimental results of graphene defect modification prediction model algorithm based on the BPNN algorithm are shown in Figure 5.

The S9 sample set employs the BPNN algorithm to learn graphene defect information, and the graphene defect prediction effect is good, with an accuracy rate of 88.86%. Other data can also be used to predict graphene defect modification with an accuracy of more than 75%. This demonstrates that graphene defect modification prediction based on BP can predict graphene defects based on sample information and can obtain a certain prediction effect, which is feasible in practise. However, it should be noted that the training sample selection will have some impact on the final prediction results. The graphene defect modification prediction model based on the BPNN algorithm cannot accurately predict bad results if the selected samples do not contain bad samples. As a result, the BPNN algorithm must consider how to give the algorithm a good chance of avoiding the local optimal solution during the improvement process.

In fact, the prediction effect is closely related to the number of learning samples. From Table 1, it can be seen there are more learning samples, richer learning samples, and better learning effects.

It can be seen from the experiment that the selection of learning samples will directly affect the learning effect. If only the samples with more modulus defects are selected, the experimental results will mainly predict the results of modulus defects, and the correct modulus cannot be predicted correctly. The number of study samples is guaranteed, and the number of study samples cannot be too small.

In the process of determining the hyperparameter optimization of the model, we respectively investigated the influence of the depth of the network and the number of neurons in the full connection layer on the performance of the model. The comparison results are shown in Figures 6 and 7.

A deeper network will perform better than a wider network. According to the performance of different models, we choose the CNN model with the best comprehensive performance, which shows that the CNN model we trained can predict the thermal conductivity of porous graphene more accurately. The calculation accuracy of molecular dynamics is to calculate five different random numbers for five randomly selected configurations and finally get the mean root mean square error of these five configurations. In order to test the effectiveness of the algorithm, we averaged the actual thermal conductivity values of 200 configurations with the highest thermal resistance in each generation of training set to judge the convergence of the algorithm. In addition, for comparison, we introduce the random search algorithm to find the structure with the highest thermal resistance, and the result is shown in Figure 8.

It can be seen that the convergence speed of the random search algorithm is slow, and all configurations need to be calculated to get the 200 structures with the highest thermal resistance. In the 5th generation, 200 structures with the highest practical thermal resistance were found. This result proves that we use the CNN model to find the optimal structure of reverse design. The GA BPNN graphene defect modification prediction model is optimized, and the weight threshold of the established six modified BPNN graphene defect modification prediction submodels is optimized. The change of the optimal individual fitness value in the optimization process is shown in Figure 9.

From Figure 9, it can be seen that the optimal fitness values obtained by the four BPNN graphene defect modification prediction submodels after training are equivalent to the test mean square error of each BPNN graphene defect modification prediction submodels before optimization, which shows that the optimization results are in line with the actual situation. Table 2 lists the predicted RMSE comparison data of four BPNN graphene defect modification prediction submodels before and after optimization by the GA algorithm.

From Table 2, it can be seen that the predicted RMSE of each submodel optimized by the GA algorithm is reduced to a certain extent, and the predicted RMSE of submodels 1–4 is reduced by 13.26%, 3.86%, 11.71%, and 19.63%, respectively. Generally speaking, the genetic optimization BPNN graphene defect modification prediction model has achieved the expected goal.

#### 5. Conclusions

Although the research on functional modification of graphene has achieved remarkable results, how to apply the research results to real life and realize large-scale production are problems that need to be considered and solved. In this study, BPNN is selected as the basic model of graphene defect modification prediction. According to the current experiments and research, the following conclusions can be drawn: BPNN algorithm can be applied to the prediction model of graphene defect modification, but it is easy to fall into local minimum and the calculation efficiency is poor. We tested the CNN model search algorithm on a system with a small sample space. The results show that the structure with the highest thermal resistance of porous graphene can be found with only a small amount of data. GA is used to optimize the BPNN graphene defect modification prediction model, and the optimization object is the initial network weight threshold of four submodels. After optimizing the initial value of BPNN graphene defect modification prediction model, the network training and prediction errors were further reduced, and the RMSE predicted by submodels 1–4 decreased by 13.26%, 3.86%, 11.71%, and 19.63%, respectively. GA basically achieves the purpose of optimizing the prediction model of BPNN graphene defect modification.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This study was supported by Colleges and Universities Natural Science Research General Project of Jiangsu Province (grant no. 18KJB210008) and Scientific Research Foundation of Nanjing Polytechnic Institute (grant no. NHKY-2019-17).