Predicting construction accidents on sites: An improved atomic search optimization algorithm approach

Construction accidents in the construction industry cause a large amount of property damage and human casualties. Therefore, avoiding construction accidents as much as possible is a problem that engineers have been working on for a long time. Currently, few construction managers use artificial intelligence methods for construction safety management. The purpose of this article is to propose a new artificial neural network (ANN) prediction model to provide early warning for future construction and to provide reference for construction organization decision‐makers. In the proposed method, atomic search optimization algorithm is used to optimize the weights and thresholds of back propagation neural network, and the Tent chaotic mapping is used to initialize the population to increase the diversity of the population. The statistical data of production safety accidents of housing and municipal engineering in China from 2015 to 2019 are used as an example, and the prediction results of the proposed model are compared with back‐propagation neural network (BPNN) and wavelet neural network (WNN). The mean absolute error (MAE) of predicting construction accidents is 0.2225, with small fluctuations in the predicted results. The mean absolute percentage error (MAPE) of the predictions is 0.6048%. The research results indicate that IASO‐BPNN has higher prediction accuracy than standard BPNN and WNN, providing judgment methods for ensuring construction progress and decision support for construction organization decision‐makers.

the accuracy of predicting the likelihood of future injuries has become a research focus in the field of construction engineering in recent years.
Through the risk assessment of engineering construction projects, professionals can supervise construction projects and implement intervention measures in a timely manner. 7It would be beneficial for construction practitioners to be able to accurately predict fatal accidents due to potential injuries. 8Statistics of past safety accidents can be used to prevent future incidents. 9In recent years, many studies have carried out accident analysis in the construction industry from the perspective of risk assessment, 10,11 factor analysis, 12 regulations, and management. 5For example, fault trees are used for quantitative risk analysis in the construction industry, 13 which can consider both objective and subjective uncertainties; based on the data of 15 large construction sites, risk assessment is carried out to improve construction safety performance, a research idea aimed at finding the key factors that influence the impact of safety accidents. 14The analysis and integration of risk assessment, leading indicators, precursor analysis, and safety climate are used to synergize construction safety prediction models. 15rtificial neural networks (ANN) and other machine learning (ML) have been used to estimate the consequences of accidents.This is because machine learning-based methods can process large amounts of data and are able to predict and interpret outcomes. 16ANN can have the same simple decision-making ability and simple judgment ability as humans, and has potential in predicting construction accidents. 17Random forest and stochastic gradient tree boosting are used to provide reliable probabilistic predictions of possible outcomes in the event of an accident. 18In another study, ANN and decision trees are identified as suitable techniques for assessing safety cognitive factors in working at heights. 19Latent class clustering analysis is used together with ANN to predict construction accidents, and has achieved good results in the prediction of fatal events. 20,21Whereby, ANNs show many unique advantages in solving large samples, nonlinear and complex problems.3][24] However, the artificial neural network is easy to fall into the local optimum, and the convergence effect is not good.In this article, the latest meta-heuristic optimization algorithm (atomic search optimization [ASO]) is used to improve the weight and threshold value of ANN, and the Tent chaotic map is used to improve the global search ability of the model.Backpropagation neural network (BPNN), as the most classic ANN, can fit any nonlinear function with multiple inputs and multiple outputs, so they are used in this article to predict construction accidents.
To sum up, in this article, a BPNN prediction model based on Tent chaotic mapping and ASO is proposed to reduce the risk of construction accidents.And the proposed model is verified by the data of China's housing construction and municipal engineering production safety accident statistics from 2015 to 2019.The proposed TentASO-BPNN prediction model can provide decision support for departments concerned and take specific preventive measures to reduce risks.The article structure is as follows: Literature is reviewed in Section 1; the construction method of the model is given in Section 3. Section 4 is the prediction result of the proposed model; in Section 5, the proposed model is compared with BPNN and wavelet neural network (WNN); and finally, the conclusions are given.

Data collection and processing
All data used in this article are from the official website of the Ministry of Housing and Urban-Rural Development of the People's Republic of China, with the website address being https://www.mohurd.gov.cn/.The data summary of safety accidents from 2015 to 2019 is shown in Table 1.After collecting annual data on production safety accidents in China's housing and municipal engineering projects from 2015 to 2019, the data were normalized.The purpose of normalization is to eliminate the impact of data dimensionality and make the data comparable.In view of the law of data distribution, Equation ( 1) is used to linearly transform the data.
where max() means taking the maximum value; min() means taking the minimum value.

Back propagation neural network
As the most widely used ANN, BPNN has a complete theoretical system and learning mechanism. 25In the learning process of BPNN, it is divided into two phases: the forward propagation of the signal and the back propagation of the error.In the forward propagation phase, the input values are passed from the input layer to the hidden layer and then to the output layer.During the forward transmission of the signal, the weights of BPNN remain unchanged, and the neuron value of each layer affects the state of the neurons in the next layer.If the mean output cannot be obtained in the output layer, then it is transferred to error back propagation.In the back propagation stage, the error signal that cannot meet the accuracy requirements starts to propagate forward layer by layer from the output end, and the error is apportioned to all units of each layer, and the connection weight of each unit layer is adjusted in real time according to the error signal.Continuously modifying the weights among neurons is adopted to meet the error accuracy requirements of the output values.
A typical three-layer BPNN is shown in Figure 1.Input signal, output of hidden layer, and output of output layer are represented by x i , y i , and z i , respectively.The connection weight from the input node "i" to the hidden layer node "j" is denoted by  ij , and the connection weight from the node in the hidden layer k to the node in the output layer j is denoted by  jk .It is the essence of BPNN to find the mapping function that can reflect the input variables to the output variables, and mathematical theory has proved that BPNN can realize any nonlinear mapping process. 26It is worth noting that the trained BPNN only needs to use forward propagation.Therefore, the source inversion method based on BPNN greatly saves time compared with other inversion methods, and is very suitable for construction safety accident prediction.In addition, BPNN has been widely used in various industries, and the BPNN algorithm process is not described and derived here.

ASO algorithm
ASO is an algorithm model established according to the laws of physical motion of atoms in molecular dynamics. 27Suppose a molecular system is a d-dimensional space consisting of s atoms.Xd i(t) is the position of the ith atom at the tth iteration, which can be expressed as follows: where T is the total number of iterations.Newton's second law stipulates that F i is the interaction force acting on the ith atom, G i is the binding force acting on the ith atom, and the mass of the atom is m i , then the acceleration of the ith atom can be obtained: The sum of the forces of surrounding atoms on the current atom i can be expressed as Fd i, and its solution formula is where t and d are the current iteration number and the dimension of the atom, respectively.rand j is a random number on [0,1]; K best is the set of atoms that exert a force on atom i; Fd ij(t) is the Leonard Jones potential force of the jth atom on atom i in the tth iteration. 28And K best is usually defined as follows: where N is the total number of atoms.
In the ASO algorithm, in order to strengthen the global exploration ability at the early stage of iteration, each atom needs to interact with more adjacent atoms with better fitness.In the later stage of iteration, in order to enhance local development and promote algorithm convergence, each atom needs to interact with fewer neighboring atoms with better fitness.(The force of the atomic group is shown in Figure 2).The number of neighboring atoms with good fitness is denoted by K With the adaptive reduction of iterations, it not only ensures the ability of the algorithm to jump out of the local optimum for global search in the early stage of the iteration, but also ensures the local development ability of the algorithm in the later stage and ensures the convergence of the algorithm.K best in Equation ( 5) is also a set of k atoms with better fitness function values.According to Equations ( 4) and ( 5), Fd i(t) can be rewritten as follows: where (t) is a function that adjusts the depth of the repulsive or attractive region, and is related to the depth weight .
As iterations increases, (t) decreases adaptively, so that the scope of global search and local development is gradually reduced to the optimal value.This guarantees the convergence of the algorithm.Its expression is where hi j(t) is the distance between two atoms, and different h values correspond to different force properties.When h ∈ (0.9, 1.1), it is repulsive force, and it increases with the increase of h value; when h is 1.12, it is a state of equilibrium, and the acting force is 0; and when h ∈ (1.12, 1.24), it is attractive and increases with the increase of h; it is worth noting that when h ∈ (1.24, 2), it is still attractive, but the force decreases to 0 as h increases. 29So hi j(t) can be expressed as follows: where h min =  0 + (t) is the lower bound of h, and (t) is the drift factor that changes with iterations, making the algorithm switch between global search and local development; h max is the upper bound of h; , it represents the distance range between the atom and the ith atom in the K best set.
Geometric constraints in molecular dynamics also play an important role in atomic motion.There is a covalent bond between each atom and the optimal atom, so the binding force is created by the optimal atom.In Equation ( 3), the geometric constraint effect of G i in the d-dimensional space at the tth iteration can be written as Gd i(t), which is expressed as follows: where  is the multiplier weight.
In Equation (3), m i is the mass of the atom, and the atomic mass m i in the d-dimensional space at the t-th iteration can be expressed as follows: The mass mi(t) of the i-th atom in the t-th iteration is determined by the fitness of the current population: where f i (t) represents the fitness value of the ith atom; f max (t) and f min (t) represent the maximum fitness and the minimum fitness in the atomic population, respectively.Substituting Equations ( 4)- (11) into Equation ( 3), the acceleration of the i-th atom in the d-th dimension at time t can be obtained: In the iterative process, the acceleration changes the speed and displacement of the atom, and the speed and position of the atom i are updated according to the obtained acceleration.The update formula is where vd i is the velocity of the atom; Xd i is the position of the atom; randd i is a random number between [0,1].Equation ( 13) is the core process of the position update of the ASO.The flow of the ASO algorithm is shown in Figure 3.

F I G U R E 4
Tent chaotic mapping change curve.

Tent chaotic mapping improved atomic search algorithm
The random initialization method is used in the ASO algorithm to determine the initial position of the atom.Although the randomness of the initial position is guaranteed, the convergence speed and solution accuracy of the ASO are reduced.The chaotic sequence is random and sensitive to the initial value of the ergodic character, which can effectively make up for the deficiency of the initialization method in the ASO algorithm.The commonly used chaotic mapping methods include Tent mapping and logistic mapping. 30The traversal of Tent mapping is uniform and random, and has greater advantages in iteration speed.Moreover, Tent chaotic mapping can make the algorithm easily escape from the local optimal solution, so that the diversity of the population can be maintained, and the global search ability can be improved at the same time. 31he expression of Tent chaotic mapping is where n represents the number of mappings; x n represents the function value of the nth mapping; a is the parameter set to 0.7.It can be seen from Equation ( 14) that the Tent chaotic mapping involves fewer parameters and the operation process is relatively simple.Figure 4 shows the distribution of initial positions in the [0, 1] interval when the number of iterations of the Tent chaotic mapping is 200.It can be seen from Figure 4 that the distribution of Tent chaotic mapping is relatively uniform.

RESULTS
In Figure 5, the statistical data on the production safety accidents of housing and municipal engineering in China from 2015 to 2019 are given, from the Ministry of Housing and Urban-Rural Development of People's Republic of China.It can be seen from Figure 5 that the overall safety accidents reflect regular changes.Every year from June to September is the peak period for construction accidents, which has a certain relationship with the high summer temperature in China.
In this article, the population size of the ASO algorithm is set to 20, and the maximum number of iterations is set to 200.In the BPNN structure, the number of nodes in the input layer is 2, the number of nodes in the hidden layer is 10, and the number of nodes in the output layer is 1.The upper and lower bounds of the weight threshold are −5 and 5, respectively.The upper and lower bounds of the weight threshold are −5 and 5, respectively.The display frequency is set to every 50 times according to the scale of the data, the training times are 200, the training minimum error is 0.01, and the

F I G U R E 6 Iterative curve.
learning rate is 0.01.In the statistics of production safety accidents of housing and municipal engineering in China from 2015 to 2019, the statistical data of the first 48 months was used as the training set, and the data of the last 12 months was used as the test set.After the model parameters are determined, the atomic positions in the ASO are initialized through the Tent chaotic mapping.After the ASO atomic positions are initialized, the fitness function value of each individual is calculated according to the objective function, and is retained as the current optimal value and optimal solution.Then, the acceleration of the atomic motion, the speed of the atomic motion, and the individual position of the atom are updated in turn.After the above steps are completed, the fitness function value of the individual population is calculated again, and the optimal solution and optimal value are updated according to the fitness value, and the operation is terminated when the maximum number of iterations is reached.
The iterative curve of TentASO in this article is given in Figure 6, which gradually converges after more than 120 iterations.It can be seen from Figure 7 that the TentASO-BPNN is very close to the statistical data.Moreover, the prediction results also shows obvious seasonal effects.In order to reflect the difference between the prediction results of TentASO-BPNN and the true value, mean-square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) were selected for error analysis.MSE, RMSE, MAE, and MAPE are calculated by The error of IASO-BPNN is given in Figure 8. Overall, the prediction results of IASO-BPNN on construction accidents are not much different from the statistical results.The maximum error is only 0.3159, and the average error is 0.2225.The error metrics calculated by Equations ( 15)-( 18) are given in Table 2. MSE, RMSE, and MAE were 0.6753, 0.8218, 0.5781, and 0.8059, respectively.MSE, RMSE, and MAE all do not exceed 1, which meets the requirements for solving practical problems for regression prediction models.Another evaluation indicator of the regression model, MAPE, is 0.8059, which is close to 0. It can be seen that the IASO-BPNN prediction model has achieved very good prediction performance.

DISCUSSION
Predicting construction safety accidents plays an important role in reducing construction safety management.Many construction safety accident prediction models have been proposed.In this article, the TentASO-BPNN method is described in detail and applied to the prediction of production safety accidents in China's housing and municipal engineering.In order to verify the accuracy and prediction performance of the method proposed in this article, the method proposed in this article is compared with the standard BPNN and WNN.BPNN is the most widely used neural network model, which has been applied in the prediction of construction accidents. 24WNN is a feedforward neural network constructed based on the wavelet transform theory.Wavelet function instead of sigmoid activation function is used in wavelet neural network (WNN). 32The mathematical formula of the Morlet mother wavelet basis function is: The output layer of WNN is calculated by the following formula: where  ij is the weight from the hidden layer to the output layer; h(i) is the output of the i-th hidden layer node; l is the number of hidden layer nodes; and m is the number of output layer nodes.The output error energy function of WNN is The training set and test set are kept the same among the three prediction models.In the standard BPNN structure, the number of nodes in the input layer is 4, the number of nodes in the hidden layer is 6, and the number of nodes in the output layer is 1.The display frequency is set to be displayed every 100 times, the training times are 100 times, the training minimum error is 0.01, and the learning rate is 0.01.In the WNN structure, the input layer is set with 4 corner points, the output layer is set with 1 corner point, the learning rate is 0.01, the learning probability is 0.001, and the maximum number of iterations is 100.In Figure 9, the prediction results of the three prediction models for the production safety accidents of housing and municipal engineering in China in 2019 are, respectively, given.The errors and error metrics of the three models are given in Figure 10 and Table 2. F I G U R E 10 Errors of three prediction models.
In Figure 9, it can be seen that the IASO-BPNN prediction model proposed in this article is the closest to the actual statistical data.As can be seen from Figure 10 and Table 2, the IASO-BPNN prediction model has the smallest error, with an error of −3.7%only in results of February.The result error of the standard BPNN prediction model is high, and the maximum error reaches −8.8%.The prediction performance of WNN is better than that of BPNN, with MSE, RMSE, MAE, and MAPE being 0.4561, 0.6753, 0.5830, and 1.0116, respectively, but still higher than IASO-BPNN.The error-index of IASO-BPNN calculated by Equations ( 15)-( 18) is given in Table 2. Table 3 shows that the proposed method has small MSE and RMSE, indicating that the prediction error is relatively small.Both MAE and MAPE are less than 1, indicating that the prediction model has acceptable performance and good accuracy.It can be seen that the IASO-BPNN prediction model proposed in this article has achieved excellent prediction performance in the prediction of construction accidents.On the basis of historical data, it can provide scientific and technical support for safety management decision makers when formulating corresponding policies and management regulations, as well as timely early warning for engineering construction.

STUDY IMPLICATIONS AND CONTRIBUTIONS
This article proposes a construction accident prediction model based on artificial neural networks.With regard to the theoretical part, the method proposed in this article is an improved model based on BPNNs.BPNN has the defects of slow convergence speed and being easy to fall into local optimum, while ASO, as the latest physics-inspired meta-heuristic optimization algorithm, has fast convergence speed and has the ability of local and global search at the same time.Therefore, in the article, ASO is used to improve the neuron weights and thresholds in BPNN, while Tent chaotic mapping is used to increase population diversity and accelerate the convergence process.
In practical engineering, the method proposed in this article has achieved good results in annual data on production safety accidents in China's housing and municipal engineering projects from 2015 to 2019 prediction.The prediction model proposed in this article can provide early warning for construction accidents, and provide decision-making support for construction organization and management based on time series during the high accident season or time period.

CONCLUSIONS
In order to avoid construction accidents many possible, a neural network construction accident prediction model based on ASO algorithm is proposed in this article.At the same time, Tent chaotic mapping is used to improve the initialization method of atomic position.The accuracy of this method is verified by the statistical data validation of production safety accidents in China's housing and municipal engineering from 2015 to 2019.The error evaluation indicators MSE, RMSE, MAE, and MAPE are 0.0736, 0.2714, 0.2225, and 0.6048%, respectively.The error indicators MSE, RMSE, MAE, and MAPE are all smaller than those of the standard BPNN and WNN prediction models.The prediction accuracy of IASO-BPNN is higher than that of BPNN and WNN, and the prediction results are more stable.The proposed method has better robustness and faster convergence speed compared to standard BPNN and WNN.Although witnessing the benefits, the study has limitations.Due to limitations in statistical data, this article did not classify and predict different types of construction accidents, which may affect the lack of targeted training for professionals.The improvement strategy adopted by this model is only an attempt, and in this article, we only compare the proposed method with traditional models, without comparing the advantages and disadvantages of different improvement strategies.Therefore, in future research work, relevant data will be collected as much as possible to conduct research on different types of construction accident prediction models.

F I G U R E 2
Schematic diagram of the interaction of atomic groups.

StartF I G U R E 3
The flow of the atomic search algorithm.

F I G U R E 5
Production safety accidents of construction and municipal engineering in China from 2015 to 2019.

F I G U R E 7
Prediction of production safety accidents in China's housing and municipal engineering in 2019.

F I G U R E 8
TentASO-BPNN prediction error.TA B L E 2Error metrics for TentASO-BPNN prediction model.

F I G U R E 9
Comparison of the results of the three prediction models with statistics.

TA B L E 1
The data summary of safety accidents in China's housing and municipal engineering projects from 2015 to 2019.

time period Construction accidents Deaths Statistical time period Construction accidents Deaths Statistical time period Construction accidents Deaths
Error analysis of IASO-BPNN, BPNN, and WNN.