Application of BP Neural Network Improved by Fireworks Algorithm on Suspender Damage Prediction of Long-Span Half-Through Arch Bridge

Guo, Jian; Guo, Wu

doi:https://doi.org/10.1155/2023/6590979

Shock and Vibration

On this page

Abstract Introduction Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 6590979 | https://doi.org/10.1155/2023/6590979

Application of BP Neural Network Improved by Fireworks Algorithm on Suspender Damage Prediction of Long-Span Half-Through Arch Bridge

Jian Guo¹and Wu Guo²

Academic Editor: Denise-Penelope Kontoni

Received28 Mar 2023

Revised30 May 2023

Accepted28 Jun 2023

Published05 Jul 2023

Abstract

In recent decades, with the large-scale construction and rapid development of half-through arch bridges, as well as the increase of bridge service time, the suspender damage of arch bridge has become increasingly prominent. Therefore, real-time monitoring and regular detection of the health of arch bridge suspenders and timely detection and accurate judgment of the damage location and extent of suspenders are of great engineering significance for evaluating the reliability and residual life of arch bridge structures. By analyzing the main difficulties and existing problems of suspender damage identification, this paper takes the change rate of modal curvature as the damage index, introduces fireworks algorithm into the neural network model, optimizes the optimization process of neural network weight and threshold, and proposes a prediction model based on improved BP neural network by fireworks algorithm. According to the measured data of the damage degree of a long-span arch bridge in daily monitoring and on-site inspection, the proposed prediction method is applied to verify the effectiveness and accuracy in engineering health detection. On this basis, the improved BP neural network by fireworks algorithm is used to predict the suspender damage of a certain long-span half-through arch bridge, which provides an important basis for the actual bridge safety assessment.

1. Introduction

With the development of smart cities and the progress of science and technology, countries all over the world have increased their investment in infrastructure construction. A large number of complex structural forms have emerged, such as super-high-rise buildings, long-span spatial structures, super-large bridges, large dams, nuclear power plants, and large marine structures [1, 2]. These structural forms have brought great convenience to economic development and people’s lives, but once damaged, they will do great harm to our cities. Large scale and complexity are the development direction of the structure, and its service life is often decades or even hundreds of years. In this service process, the structure will be damaged to varying degrees due to congenital defects such as design and construction, catastrophic factors such as external load, environmental factors, material aging, corrosion effect, fatigue effect, and other uncertain factors [3]. After the damage, the bearing capacity and durability of the structure will be affected, the ability to resist external forces will be significantly reduced, and then accidents will occur. This will lead to heavy casualties and economic losses and cause adverse social impact [4]. Taking the bridge structure as an example, the data statistics show that various deterioration phenomena occur on the bridge decks of about 253000 concrete bridges in the United States. Some of the bridges have been damaged in different forms and degrees in less than 20 years of service. Moreover, 35000 bridges will be added every year, and the average number of partially or completely collapsed bridges is about 200 every year. The construction cost of 11 concrete viaducts located on the ring expressway in the middle of England Island is 28 million pounds. However, the maintenance cost reached over 120 million pounds, which will be close to six times the original cost. According to the Yangcheng Evening News in China, the Department of Communications of Guangdong Province organizes a large number of personnel to conduct a general survey on the technical status of existing and under-construction roads and bridges in the province. The results showed that of the 18700 bridges in Guangdong Province, 4244 were in category III and IV poor conditions and had insufficient bearing capacity, accounting for 22.7% of the total census, with a cumulative length of 109616 linear meters. For example, arch bridges have been widely used due to their beautiful appearance, simple construction methods, and strong spanning capacity. The suspenders of arch bridges in service commonly suffer from diseases, which directly affect the safety and durability of bridge structures. The suspender can be damaged or even broken due to corrosion, fatigue, and other reasons, which can greatly shorten the service life of the bridge and increase the risk of bridge collapse, as shown in Figure 1. Therefore, it is particularly important to identify the damage of bridge suspenders [5].

It can detect and predict the performance of the structure in real time, find and judge the damage location and degree of the structure in time, and then predict the performance change and remaining life of the structure to obtain the maintenance decision and the evacuation of local residents, which is of great significance to improve the service efficiency of engineering structures and ensure the safety of people’s lives and property [6]. As the core of structural health monitoring, the successful research of damage identification has essential guiding significance for how to establish the health monitoring system of engineering structures. Therefore, the research on structural damage identification has become a hot issue in the field of structural health detection [7]. Structural damage detection technology and its identification methods have made great progress in academic or practical application research in recent years, but there are still many problems to be further studied and solved in the damage detection of complex civil engineering structures such as high-rise buildings and bridges [8]. A considerable part of the existing damage detection technologies and methods for civil engineering structures are copied from aerospace, aerospace, and mechanical structures. When the same technology and method are introduced into another discipline, we should pay attention to its applicability and the characteristics of this discipline.

At present, there are also some technical difficulties in the field of engineering structure damage detection [9]. Firstly, civil engineering structures are different from aviation, aerospace, and mechanical structures. Relatively large model error is allowed in design, analysis, and calculation. However, if a large error exists in the model used for detection, it will lead to a great difference between the calculated and actual dynamic characteristics of the damaged structure, so the error of the detection results based on the dynamic characteristics will be very large. Secondly, noise is unavoidable due to the influence of many factors of the engineering structure. In the process of long-term health detection, noise may be introduced at every step and link from data acquisition to transmission. Therefore, a good ability to filter noise is what the identification method used should have. At present, damage identification in engineering structures is a nonunique problem, and if it cannot be well distinguished, it will result in unpredictable results of damage location and degree.

Because of the existence of these factors, many damage identification methods become invalid, which makes the research of damage identification face bottleneck. Therefore, a new method to overcome the above difficulties has become an urgent need [10–12]. The dynamic characteristics and response of the structure will change with the damage of the structure. In other words, there is a complex nonlinear relationship between the dynamic characteristics and response changes before and after the damage and the damage location and degree of the structure. The traditional acoustic emission method, ultrasonic method, infrared method, and other nondestructive testing techniques are not only time-consuming and expensive but also cannot detect some parts of large structures [13–15]. However, the dynamic characteristics and response of structures can be obtained through various detection methods and modal analysis. The artificial neural network (ANN) can take the damage index related to the dynamic characteristics and a certain response of the structure in various states as the input vector and take the damage diagnosis results (whether the damage exists, the damage location, damage degree, etc.) in various states as the output vector [16]. By learning to form a mapping, the neural network weights containing this mapping relationship can be saved, and there is no need to call the analysis model in the back analysis process. Through the effective and fast forward operation of the weight obtained by learning and the damage index obtained by detection, the damage diagnosis results can be obtained during the online diagnosis [17]. In a word, the achievements and research of artificial neural network in this field are still in the basic exploration stage, and it still needs the continuous efforts and exploration of relevant personnel to make the structural health monitoring technology and damage identification method better serve the field of engineering structures [18]. Since the performance of the neural network-based prediction model largely depends on the network structure and the weights and thresholds of each node of the network, the neural network structure, initial weights, and thresholds of the network will greatly restrict the prediction accuracy and convergence of the neural network-based prediction model.

To sum up, aiming at the problem that the single neural network model has slow convergence speed and is easy to fall into local optimization, the existing research mainly focuses on the optimization and improvement of the neural network using intelligent optimization algorithms such as particle swarm optimization (PSO) and genetic algorithm (GA), which solves the problem of low prediction accuracy of the single neural network prediction model to a certain extent [19–23]. However, with the deepening of research, scholars found that the above algorithm itself also has aspects to be improved [24]. Improper setting of genetic operator will affect the search performance of the algorithm and make the algorithm easy to fall into local optimal solution [25], and too large initial population in PSO algorithm will lead to the problem of slow search speed of the algorithm, which will restrict the performance of optimizing BP neural network prediction model based on swarm intelligence algorithm [26]. For example, the BP neural network prediction model optimized based on GA algorithm is limited to the large sample data model, while the prediction ability of the sample model with small samples and uneven distribution is not significantly improved [27]. At the same time, the diversity of particles will be lost due to the too fast particle optimization speed, which restricts the accuracy of the prediction results of BP neural network model optimized based on PSO algorithm.

Fireworks algorithm (FWA) is a new swarm intelligence optimization algorithm proposed by Tan et al., which works by simulating the mechanism of simultaneous explosion and diffusion of firework at multiple points in the air [28]. It shows high optimization performance in solving optimization problems and has attracted the attention of scholars at home and abroad. Compared with GA and PSO algorithms, FWA simulates the mechanism of simultaneous explosion and diffusion of firework explosion operators and ensures the diversity of firework population; at the same time, the fireworks algorithm has stronger global search ability by introducing the idea of immune concentration and the distributed information sharing mechanism. Therefore, this paper introduces the fireworks algorithm (FWA) into the BP neural network model to optimize the weight and threshold of BP neural network, proposes a prediction model based on the fireworks algorithm to improve BP neural network (FWA-BPNN), to solve the problem that the traditional BP neural network prediction model has slow convergence speed and is easy to fall into the local optimal solution in the training process, and applies it to the damage prediction of long-span arch bridges.

2. Classical Model of BP Neural Network

BP neural network shows good self-learning and self-adjusting ability in solving nonlinear problems and is widely used to solve complex system prediction problems with many factors interlaced. The essence of the BP neural network prediction model is to train the model through a large number of data in the finite solution space and then find the weight and threshold between network neurons θ_i and other parameters to establish the mapping relationship between input and output and minimize the network error, as follows:①Initialize the network weights and thresholds: the initial weights and thresholds of the network are initialized randomly in the interval [1, 1].②Feed forward calculation: assuming that the weight value of the network in the kth iteration process, the threshold value of the ith neuron, and the expected output of the ith neuron node in the lth layer are known, then where is the input of the ith neuron in the lth layer of the neural network; is the output of the lth layer; l is the layer number of the network and l = 1, 2, … L; ; and .③Error backpropagation: calculate the error of the lth layer in the kth iteration of the neural network through equations (2) and (3). where is the expected output value of the ith neuron node, and . Based on this, can be calculated by recursion formula (2) and l = , , …, 1.④Update network weights and thresholds: use equation (4) to update the weights and thresholds of the neural network. where and are the weights and thresholds of the network in the iteration process, respectively; α is the momentum factor; ; ; and .

3. Suspender Damage Prediction Model Based on Improved BP Neural Network with Fireworks Algorithm

3.1. Fireworks Algorithm

Fireworks algorithm is a new swarm intelligence optimization algorithm. For the optimization problem min , , to be solved, fireworks algorithm is used to solve the optimization problem. The specific steps are as follows:①Initialize the population: Some fireworks are randomly generated in a specific solution space. Each firework individual x_i represents a solution in the solution space, that is, .②Calculate the fitness value: for each firework individual x_i in the initial population, calculate the fitness value f(x_i) according to the fitness function f(x) and calculate the number of fireworks produced by each firework explosion S_i and the explosion radius A_i according to the following equations: where y_max = max(f(x_i)) (i = 1, 2, …, n) is the fitness value of the individual with the worst fitness value of all fireworks in the current population; y_min = min (f(x_i)) (i = 1, 2, …, n) is the fitness value of the best individual in the current population; c and d are constants, which are, respectively, used to limit the total number of sparks and represent the maximum explosion radius; and ε is a constant used to avoid the denominator being zero.③Generate sparks: Randomly select z dimensions to form a set Z, where z = rand (1, d × rand (0, R_i)), and rand (0, R_i) is a random number generated within the explosion radius A_i. In set Z, for each dimension k, use equations (7) and (8) to perform explosion mutation on fireworks, map sparks beyond the boundary through the Gaussian mutation mapping rules in equation (9), and save them in the spark population. where A_i is the explosion radius of the ith firework; h is the position offset; x_ik is the kth dimension of the ith firework in the population; ex_ik is the spark generated by the explosion of the ith firework; cx_ik is the Gaussian variation spark of x_ik after Gaussian variation; and r follows the Gaussian distribution.④Select the next generation group: The next generation firework population is selected by using the selection strategy, that is, N firework individuals are selected from the firework explosion sparks and Gaussian variation spark populations to form the next generation candidate firework population. For the candidate firework population K, the selection strategy is as follows: select the individual x_k with the minimum fitness value min (f(x_i)) as the next generation of firework population individuals directly, and the remaining firework individuals adopt the roulette gambling method. For the candidate individual x_i, the probability formula (10) is adopted for its selection. where R(x_i) is the sum of the distances between firework individual x_i and other individuals, which is calculated by the following formula:⑤Determine termination conditions: if the termination conditions are met, stop the iteration; otherwise, continue with step ②.

3.2. Improved BP Neural Network Prediction Model Using Fireworks Algorithm for Suspender Damage

The weight and threshold of BP neural network are the key factors, which affect the prediction performance of the BP neural network model. Therefore, the fireworks algorithm is introduced into the neural network model, and the position x_ik of firework individuals in the firework population is used to represent the weight coefficient of network nodes and the threshold of network neurons. Based on the above rules, the specific improvement strategies are as follows:①Key parameter code: because the weights, thresholds, and firework individuals in the neural network are composed of a series of vectors, the real vector coding strategy is selected to code the key parameters in the model. Note that X = [x₁, x₂, …, x_D] represents a set of parameters to be optimized, in which each dimension is composed of network weights and thresholds. In the neural network, note n_IW(1,1) as the number of weight values between the input layer and the hidden layer, n_b(1,1) as the number of neuron thresholds in the hidden layer, n_IW(2,1) as the number of weights between the hidden layer and the output layer, and n_b(2,1) as the number of neuron thresholds in the output layer; then, D = n_IW(1,1) + n_b(1,1) + n_IW(2,1) + n_b(2,1).②Calculate the fitness value: Initialize weight coefficient and threshold. Initialize the weight coefficient and threshold between nodes in the neural network in the interval [−1, 1], i.e., x_i∼U[−1, 1], and use the position of firework individual x_i in the fireworks algorithm to represent the weight coefficient of network nodes and the threshold of neurons, and then each firework individual represents a neuron in the neural network model.③Select the fitness function: The goal of algorithm model training is to make the network output layer result as close as possible to the expected result through continuous iterative calculation, to obtain the weight parameter and threshold value θ_i between nodes when the network output result is optimal. In the FWA-BP neural network, the square error function is introduced to calculate the fitness value of individual fireworks. where t is the expected output of the network; P is the number of layers of the network; S is the number of network output units; and y is the actual output value of the network. The actual output value of the network is specifically expressed in the following equation: where x_j is the input of the network; is the weight of network nodes; θ_i is the threshold value of the ith neuron in the network; and . The fitness function f_i(x) is given in the following equation:④Optimize firework population: For each firework individual x, calculate its fitness value f(x_i) with equation (14), and calculate the number of explosive fireworks S_i and explosion radius A_i with equations (5) and (6). At the same time, based on equations (7)–(9), each firework individual is operated with explosion, displacement, and mutation, and the selection strategy of equations (10) and (11) is used to select the best firework individual to form the next generation of firework population.⑤Determine termination conditions: According to equations (11) and (14), calculate the fitness value f(x_i) of the firework individuals in the firework population and the Euclidean distance R(x_i) between the firework individuals and judge whether the termination condition of the maximum number of iterations is satisfied. If it is satisfied, the new firework population is composed of the firework individuals with the minimum fitness value min (f(x_i)) and the firework individuals with the maximum distance max (R(x_i)) in the current firework population, and take the current firework population as the optimal firework population X_best; otherwise, continue with step ⑤.⑥Update network weights and thresholds: Use the optimal firework population X_best obtained in step ⑤ to initialize and update the weight and threshold vector X in the network model. Based on the above steps, the flowchart of the whole FWA-BP algorithm can be obtained, as shown in Figure 2.

4. Health Inspection Analysis of Long-Span Arch Bridge

4.1. Health Inspection of the Long-Span Arch Bridge

To verify the validity of the prediction model based on FWA-BP neural network, the damage detection and experimental data of a long-span arch bridge are selected, and the prediction model based on FWA-BP neural network is experimentally verified and compared. The research object of the arch bridge used in this paper is shown in Figure 3. The bridge site of this bridge has a water surface width of about 230 m, a deep water flow, a minimum elevation of −36.57 m at the trough bottom, and a maximum navigable water level of 5.9 m. The rock on the bank is exposed, and the elevation of the north south small mountain top is about 27.00 m. The elevation of the foot of the mountain is about 6.00 m, and the surface of the mountain is covered by the Quaternary eluvial layer, with the surface rock mass in a gravel shape. The main bridge is a through steel tube concrete ribbed arch bridge with a main span of 245 m. The arch axis is a quadratic parabola, with a rise span ratio of 1/5, a rise height of 49 m, and a bridge deck width of 22.5 m. Among them, the carriageway is 15 m wide, the sidewalk is 2 1.5 m wide, and the design load is Grade 20 for automobiles, the trailer weighs 100 tons. The distance between suspenders is 5.9 m, and double suspenders are used. The main arch of the steel pipe arch hoisting bridge weighs from 53 to 61 tons per section, and the entire bridge has 27 installation sections, with a total weight of 1220 tons.

The arch ribs are concrete filled steel tubular trusses of equal height and width, and the upper and lower chords are of flat dumbbell shaped sections. Paired vertical web members and diagonal members are set between the upper and lower chords, which are, respectively, directly connected to the circular tubes of the chords. The total height of the arch rib section is 4.4 m, and the total width is 1.9 m. Within the range of 16.766 m above the arch springing line of the arch foot, the truss structure is wrapped with No. 50 reinforced concrete to form a reinforced concrete box rib section with a height of 4.8 m and a width of 2.3 m. Shear keys are added to the wrapped section and reinforcement is adjusted. The main pipes, batten plates, web members, and transverse joints of the upper and lower chords of the arch rib are made of 16 Mn steel, the main pipes are made of spiral welded pipes, and the web members are made of seamless steel pipes. The main pipe and batten plate cavities of the upper and lower chords are filled with C50 micro-expansive concrete. A total of 7 spatial steel pipe cross braces are provided for the entire bridge, including 5 above the bridge deck and 2 below the bridge deck. The cross bracing of the arch crown adopts a meter shaped lattice structure, and the rest adopts a straight shaped lattice structure.

The bridge deck system consists of 41 cast-in-situ sections and 38 prefabricated beams, and continuous bridge decks are formed between adjacent beams through cast-in-situ flange joints. Prefabricated beams are divided into upper column beams and suspender beams, both of which are prestressed concrete open box girders. The bridge deck of the column beam and suspender beam on the arch is a simply supported structure, which releases the temperature change and shrinkage and creep displacement of the entire continuous bridge deck system structure through the expansion joints at the simply supported ends. A box shaped steel beam is provided at the intersection of the bridge deck system and the arch ribs, with a total of two sets for the entire bridge. The bridge deck is paved with 9 cm thick steel fiber concrete and 4 cm thick asphalt concrete. The bridge deck adopts a 3% two-way longitudinal slope and a 1.5% two-way transverse slope. The longitudinal slope of the bridge deck is adjusted by the inclination of the beam flange plate, and the transverse slope is adjusted by the height change of the beam.

In order to improve stability, column top tie beams have been added to No. 1 and No. 2 columns with column heights exceeding 8 m above the arch. Each suspender beam is equipped with double suspenders with a spacing of 1.5 m, and the suspension rod is composed of 55 galvanized high-strength steel wires with a diameter of 5mm, and the outer layer is protected by hot extruded polyethylene. Both ends are cold casting heading anchorage. To avoid direct exposure to the atmosphere, the upper and lower anchor heads are protected by protective covers. To protect the exposed steel wire (approximately 50 cm long) near the anchor head under the suspender, cement mortar is poured into the conduit under the suspender. At the same time, the suspender is wrapped with stainless steel within 3 m above the bridge deck to avoid man-made damage.

The vertical web, diagonal web, and lateral connection systems of this bridge adopt hollow steel tube structures that are not filled with concrete. The inner surface of the empty pipe structure is required to be sealed and coated with two layers of rust-resistant paint. The anti-corrosion treatment of the outer surface of the steel structure adopts the GCM polymer material protection system. There are two forms of anti-corrosion for the outer surface of the arch foot outer covering section structure: the surface in contact with the concrete (including the batten plate) is not subject to anti-corrosion treatment, the shear key is welded, and rust removal treatment is conducted to ensure a good combination with the concrete. The surface of the exposed part also adopts a GCM polymer material protection system.

4.2. Suspender Damage Experimental Analysis of the Long-Span Arch Bridge

The bridge is a key transportation hub connecting the north and south sides, with an average of more than 12000 vehicles passing through it every day. Since its completion and opening to traffic, it has been operating for a long time, so long-term and comprehensive health testing and related scientific experiments have been conducted on the bridge.

The outer surface of the arch rib steel structure adopts a GCM polymer material protection system. Upon inspection, it was found that the anti-corrosion coating surface of the steel pipe arch rib has anti-rust phenomenon, with severe peeling and peeling in some parts and cracks in some parts. There are cracks on the concrete surface wrapped around the arch rib, mainly along the arch axis and perpendicular to the arch axis. In addition, there are a small number of oblique cracks, and a small number of cracks are accompanied by bleeding phenomenon.

There are 120 suspenders in the whole bridge, all of which are high-strength steel wire bundles. Except for the eight suspenders whose upper anchor heads are anchored in the upper chord batten concrete, the remaining suspenders’ upper anchor heads are all anchored in the lower chord batten concrete, and the anchor heads are all cold casting heading anchorage. Upon inspection of the protective cover, it was found that the anti-corrosion coating of the anchor head protective cover had pitting and spot corrosion, and in severe cases, there were peeling and peeling phenomena, as well as the lack of fixing bolts. The statistical results of the diseases of the upper anchor head protective cover are shown in Table 1.

For the inspection of anchor heads, 16 anchor heads are selected from both upstream and downstream sides at the upper end for inspection, while the first anchor head from both upstream and downstream sides and the midspan anchor head are selected for inspection at the lower end. Upon inspection, it was found that there was condensed water on the inner wall of the protective cover and the top of the anchor cup cover, there was rust on the outer side of the anchor cup, the butter in the anchor cup had dried and evaporated, and the steel wire pier head was exposed and corroded. The inspection results of anchor head corrosion are shown in Table 2. For ease of expression, the anchor heads are numbered sequentially from south to north. The upstream, downstream, and upper and lower ends are distinguished by UT, UB, DT, and DB. For example, UB2 represents the second lower anchor head on the upstream side, and so on.

As can be seen from Table 2, most of the upper and lower anchor head protective covers have condensed water. When there is no or a small amount of accumulated water inside the anchor cup of the upper anchor head, the steel wire pier head may experience whitening. When there is a large amount of accumulated water, the steel wire pier head will produce slight rust. The corrosion condition of the suspender was inspected, and some suspenders were selected to inspect the cable body under the protection of the intermediate PE pipe. It was found that the suspender cable body was not corroded. After the inspection, the cable body is sealed with cellophane and epoxy resin.

The surface of the precast beam concrete for the bridge deck system is uniform in color, and there are no cracks, peeling, and exposed reinforcement. However, there are alkalization and whitening phenomena on the local concrete surface. The cast-in-place concrete has cracks, mainly longitudinal cracks. Some cracks exceed the limit in width, with a maximum of 0.41 mm. In addition, there are a few oblique cracks. The bridge deck pavement shall be free of looseness, oil spillage, cracking, waves, ruts, pits, and subsidence. Most expansion joints are blocked by foreign objects and lose their expansion function. The measurement of bridge geometry includes the measurement of bridge deck geometry and arch axis geometry, which is arranged during the period when the structural temperature tends to stabilize.

The bridge deck alignment measurement is conducted using a precision electronic level combined with an indium steel ruler. Under the condition of closing all traffic on the bridge deck, it is divided into two zones, upstream and downstream, for round-trip closed leveling. The measuring points are arranged at the eighth point of the bridge deck. The permanent measurement is arranged inside the collision barrier of the upstream and downstream side traffic lanes. Comparing the design value and the measured value of the bridge deck alignment, it is found that the overall bridge deck alignment has decreased, with the difference between the measured value and the design value being between −0.095 m and 0.069 m.

The arch axis is measured using a tunnel section detector. Due to site conditions, only the arch axis elevation within 68.6 m from the midspan was tested and compared with the design value. It was found that the measured arch rib alignment slightly changed compared to the design alignment, with a difference between −0.015 m and 0.094 m. According to the theory of string vibration, the cable force of the suspension rod of the entire bridge is measured using a dynamic cable force tester.

When measuring the natural vibration frequency of the suspension rod of the bridge using the vibration frequency method, two sets of equipment, a dynamic signal collector and a cable force tester, are used together. When using a dynamic signal collector, fix the acceleration sensor with black electrical tape at half of the suspension rod, connect the dynamic signal collector through the sensor cable, and synchronize the collector with the computer acquisition system. Then, collect the natural frequency of the suspension rod under both environmental and manual excitation. For the bridge site during the operation period, environmental random vibration is selected, and the suspension rod is directly excited by using vehicle loads and wind loads in the environment as the vibration sources of the suspension rod. During measurement, if the suspension rod is stationary and there is no natural vibration or the measured natural vibration frequency is unclear, a certain amount of artificial excitation is required for the suspension rod. A small wooden mallet is used to strike the suspension rod as artificial excitation, which can compensate for the unstable and weak environmental vibration source.

The random vibration of the environment is tested using a cable force dynamic tester. The cable force dynamic tester is a portable single or dual-channel vibration detection analyzer for micro-vibration signals. The accelerometer is fixed on the suspension rod to measure its lateral vibration. The cable force dynamic tester can collect the multi-harmonic vibration curve of the suspension rod and obtain the lateral vibration frequency of the suspension rod through spectral analysis. The characteristic of the corresponding relationship between the cable force and the vibration frequency of the cable is utilized. When the length of the cable, the constraint conditions at both ends, and the distribution mass are known, the cable force of the suspension rod of the bridge can be obtained by measuring the vibration frequency of the cable.

In order to reduce measurement errors, the test points of the same suspension rod will be selected at different heights for multiple measurements under time constraints, and the measured natural frequencies will be compared to avoid significant errors in the data. In Table 3, the comparison between the tested cable force results and the cable force at completion acceptance. For ease of expression, the suspenders are numbered sequentially from south to north, and the upstream and downstream are distinguished by U and D. The first upstream suspender on the south side is U1, the first downstream suspender is D1, the first upstream suspender on the north side is U60, the first downstream suspender is D60, and so on.

In Table 3, the difference value = the measured value of regular inspection − the measured value of handover acceptance. The difference value is positive when the cable force increases and negative when the cable force decreases. From Table 3, it can be seen that the cable force of the suspender tested this time is generally deviated from the cable force at the completion acceptance, with most of the difference between 10 kN and 40 kN, with a maximum difference of 106.2 kN.

5. Damage Prediction Calculation Based on FWA-BP Neural Network Prediction Model

5.1. Suspender Damage Prediction Modeling of Arch Bridge

Using the FWA-BP neural network prediction model and taking the damage prediction of long-span arch bridge suspenders as an example, the damage prediction model based on FWA-BP neural network is established. The steps are as follows:①Select the input and output indicators: ten indexes, such as modal curvature change rate, elastic modulus, frequency, vibration mode, boom damage location, noise level, instantaneous bearing weight, lateral bending vibration displacement, beam linear mass, and bending stiffness, are selected as the input indexes of the network prediction model, and the boom damage degree is selected as the output index of the network prediction model.②Standardize the data: To eliminate the impact of different dimensions on the accuracy of the prediction model, standardize the data for each indicator to the same order of magnitude, to improve the comparability between the data. This model adopts 0-1 standardization method to standardize the experimental data. where max (X) is the maximum value in the dataset and min (X) is the minimum value in the dataset. After the data are standardized, the training data are mapped to the interval [0, 1] for comparative analysis.③Set key parameters: on the basis of the input and output indexes of the prediction model, the main parameters based on FWA-BP neural network are set as follows—the number of nodes in the input layer m = 10, the number of nodes in the output layer n = 1, the number of hidden layers e = 1, and the number of neurons in the hidden layer s of the neural network, and then empirical formula (16) is used to calculate s ≈ 6.

For the selection of activation function, tansig and purelin activation functions are selected in the input layer and output layer, respectively, and trainlm function is selected as the training function of the network model. In the process of network training, set the learning rate as 0.01, the momentum factor as 0.9, the maximum number of iterations as 20000, and the minimum training error as 0.001. For the weight value and threshold between network nodes θ, the optimal firework population obtained by iterative selection of fireworks algorithm is used to initialize the network weight and threshold.

At the same time, according to the network weight value and threshold to be optimized θ, the key parameters in the fireworks algorithm are set as follows: population size n = 70, firework explosion radius adjustment constant d = 5, firework explosion spark number adjustment constant c = 40, upper limit of firework explosion spark number ub = 0.8, lower limit of firework explosion spark number lb = 0.04, Gaussian variation spark number , and maximum iteration times T = 1000.

5.2. Experimental Results and Performance Analysis of Prediction Model

The internal force and deformation of the arch rib control section under dead load calculated by the model in this paper are shown in Table 4.

In Table 4, Calculation I is the calculation result of the testing agency, and Calculation II is the calculation result of the model in this article; the axial force in the table is positive with pressure; the side tension below the bending moment is positive; the deflection is positive downward.

The comparison between the cable force calculated by the model in this article and the detection mechanism and the measured cable force is shown in Table 5, taking the cable force of the upstream suspender as an example.

In Table 5, Calculation I is the calculation result of the testing agency, and Calculation II is the calculation result of the model in this article. Difference ① = Calculate the mean value of II − Calculate I, with an increase in the difference being positive and a decrease being negative, and a percentage of difference ① = Difference ①/Calculate I. Difference ② = calculated II mean − measured mean, if the calculated II mean is greater than the measured mean, it is positive, and if it is less than the measured mean, it is negative, and a percentage of difference ② = difference ②/measured mean.

From Tables 4 and 5, it can be seen that the axial force calculation results of the model and the detection mechanism in this paper are very similar under the dead load, the bending moment calculation results of each section are basically consistent, and the deflection calculation results are also basically similar. The maximum deviation between the upstream suspender cable force calculated by this model and the cable force calculated by the detection mechanism is 5.5%, and the maximum deviation from the measured cable force is 5.6%. Therefore, the calculation results of this model are reliable and can be used as the basis for further analysis and research.

5.3. Suspender Damage Calculation Prediction

Arch ribs, transverse connections, and suspension structures are the general components of the span structure of half-through arch bridge and through arch bridges. The suspender is composed of load-bearing steel wire and steel pipe sheathed outside it, which plays a key role in hanging the bridge deck. The waterproof system of its upper and lower anchor heads is easy to age. Among the components of the arch bridge, the suspender is the most easily damaged component, so the research on damage identification of this kind of arch bridge should focus on the suspender health detection. Taking No. 30 suspender in the middle as an example, some training samples are listed in Tables 6 and 7.

Firstly, the 0-1 standardization strategy according to equation (15) in Section 4.2 is used to standardize the experimental data, and then the experimental dataset is established with the standardized data to train and test the FWA-BP neural network prediction model. The first 80% of the data in the experimental dataset is selected as the training data set, and the last 20% of the data in the dataset is selected as the test dataset. The prediction model based on FWA-BP neural network proposed in this paper is tested and verified.

Secondly, to further verify the prediction performance based on FWA-BP neural network, the same datasets are used to train the traditional BP neural network, genetic algorithm-improved BP neural network (GA-BPNN), and particle swarm optimization algorithm-improved BP neural network (PSO-BPNN). The parameter setting of the GA is as follows: population size popu = 30, genetic algebra gen = 100, crossover probability pcross = 0.8, and mutation probability pmutation = 0.05. For PSO algorithm, the parameters are as follows: speed update parameter c₁ = c₂ = 1.49445, evolution times maxgen = 150, population size sizepop = 30, individual maximum pop_max = 7, individual minimum pop_min = −7, individual maximum speed , and individual minimum speed . The parameters of BP neural network in BP neural network prediction model optimized by different algorithms are the same as those in FWA-BP neural network model described in Section 4.2.

Thirdly, to reduce the accidental factors in the experimental process, the same algorithm model is trained and tested for 3 times with the same data, and the average value of the prediction error and iteration time of 3 times are taken as the prediction error and iteration times of the algorithm. Specifically, under the same experimental conditions, the GA-BP neural network and PSO-BP neural network models are simulated, and the prediction results of the neural network prediction models optimized by different algorithms are obtained. The results are shown in Tables 8 and 9.

It can be seen from Tables 8 and 9 that in the three rounds of tests, the average relative error AE, maximum relative error AE_max, similarity R, and single round cumulative time T are predicted by each model, and the prediction results of BP neural network optimized by different algorithms fluctuate in different test samples. However, on the whole, the error rate of the prediction model based on FWA-BP neural network is lower than that of the existing prediction models based on PSO-BP neural network and GA-BP neural network, and its results are closer to target values than the other models.

6. Conclusions

In view of the weak generalization ability and low prediction accuracy of the prediction model based on the traditional BP neural network, the fireworks algorithm is introduced into the BP neural network, and the weights and thresholds of the BP neural network are optimized and improved with the help of the fireworks algorithm. A prediction model based on the fireworks algorithm-improved BP neural network (FWA-BP) is proposed, and the algorithm of the prediction model based on FWA-BP neural network is implemented. Then, taking the damage prediction of long-span arch bridge as an example, the damage prediction model based on FWA-BP neural network is established, and the performance of damage prediction is simulated and tested. Compared with the prediction methods based on BP neural network, GA-BP neural network, and PSO-BP neural network, the results show that under the given training target value, the prediction method based on FWA-BP neural network proposed in this paper has smaller prediction error rate and fewer iterations, which can effectively improve the prediction performance of BP neural network. Therefore, the damage degree prediction method of long-span arch bridge proposed in this paper is feasible and provides a theoretical basis for related engineering research.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The authors appreciate the financial support from the Heilongjiang Province Government of China and acknowledge the technical support from the bridge design and construction enterprises for this work. This research was supported by the Special Research Project of Basic Business in Colleges and Universities (grant nos. 135509212 and 145209147) and Provincial Platform Opening Project of Heilongjiang Province of China (grant no. WNCGQJKF202101).

References

J. P. Shu, Z. Y. Zhang, I. Gonzalez, and R. Karoumi, “The application of a damage detection method using Artificial Neural Network and train-induced vibrations on a simplified railway bridge model,” Engineering Structures, vol. 52, pp. 408–421, 2013.
View at: Publisher Site | Google Scholar
Y. S. Ma, Y. F. Wang, L. Su, and S. Q. Mei, “Influence of creep on dynamic behavior of concrete filled steel tube arch bridges,” Steel and Composite Structures, vol. 21, no. 1, pp. 109–122, 2016.
View at: Publisher Site | Google Scholar
X. L. Xu, K. W. Shi, X. H. Li, Z. J. Li, R. G. Wang, and Y. W. Chen, “Optimization analysis method of new orthotropic steel deck based on backpropagation neural network-simulated annealing algorithm,” Advances in Civil Engineering, vol. 2021, Article ID 8888168, 16 pages, 2021.
View at: Publisher Site | Google Scholar
Z. Y. Xia, S. T. Quek, A. Q. Li et al., “Sensitivity analysis in seismic reliability of an urban self-anchored suspension bridge,” Mechanical Systems and Signal Processing, vol. 164, Article ID 108231, 2022.
View at: Publisher Site | Google Scholar
J. Yuan, S. T. Lv, X. H. Peng, L. Y. You, and M. Borges Cabrera, “Investigation of strength and fatigue life of rubber asphalt mixture,” Materials, vol. 13, no. 15, p. 3325, 2020.
View at: Publisher Site | Google Scholar
C. X. Li and J. H. Li, “Support vector machines approach to conditional simulation of non-Gaussian stochastic process,” Journal of Computing in Civil Engineering, vol. 26, no. 1, pp. 131–140, 2012.
View at: Publisher Site | Google Scholar
H. B. Hwarng, “Insights into neural-network forecasting of time series corresponding to ARMA structures,” Omega, vol. 29, no. 3, pp. 273–289, 2001.
View at: Publisher Site | Google Scholar
H. Q. Mu, Z. J. Zheng, X. H. Wu, and C. Su, “Bayesian network-based modal frequency-multiple environmental factors pattern recognition for the Xinguang Bridge using long-term monitoring data,” Journal of Low Frequency Noise, Vibration and Active Control, vol. 39, no. 3, pp. 545–559, 2020.
View at: Publisher Site | Google Scholar
P. Zhang, H. N. Wu, R. P. Chen, and T. H. T. Chan, “Hybrid meta-heuristic and machine learning algorithms for tunneling-induced settlement prediction: a comparative study,” Tunnelling and Underground Space Technology, vol. 99, Article ID 103383, 2020.
View at: Publisher Site | Google Scholar
M. Lu, S. M. AbouRizk, and U. H. Hermann, “Sensitivity analysis of neural networks in spool fabrication productivity studies,” Journal of Computing in Civil Engineering, vol. 15, no. 4, pp. 299–308, 2001.
View at: Publisher Site | Google Scholar
Y. Sun, Q. H. Jiang, T. Yin, and C. B. Zhou, “A back-analysis method using an intelligent multi objective optimization for predicting slope deformation induced by excavation,” Engineering Geology, vol. 239, pp. 214–228, 2018.
View at: Publisher Site | Google Scholar
Y. Cao, Y. Zandi, A. S. Agdas et al., “A review study of application of artificial intelligence in construction management and composite beams,” Steel and Composite Structures, vol. 39, no. 6, pp. 685–700, 2021.
View at: Google Scholar
X. Fang, H. Luo, and J. Tang, “Structural damage detection using neural network with learning rate improvement,” Computers and Structures, vol. 83, no. 25-26, pp. 2150–2161, 2005.
View at: Publisher Site | Google Scholar
G. B. Zhang, C. F. Chen, Y. H. Zhang, H. C. Zhang, Y. F. Wang, and X. Y. Wang, “Optimised neural network prediction of interface bond strength for GFRP tendon reinforced cemented soil,” Geomechanics And Engineering, vol. 28, no. 6, pp. 599–611, 2022.
View at: Google Scholar
M. Su, H. Peng, and S. F. Li, “Application of an interpretable artificial neural network to predict the interface strength of a near-surface mounted fiber-reinforced polymer to concrete joint,” Journal of Zhejiang University Science, vol. 22, no. 6, pp. 427–440, 2021.
View at: Publisher Site | Google Scholar
M. A. Mashrei, R. Seracino, and M. S. Rahman, “Application of artificial neural networks to predict the bond strength of FRP-to-concrete joints,” Construction and Building Materials, vol. 40, pp. 812–821, 2013.
View at: Publisher Site | Google Scholar
J. A. Abdalla, A. Elsanosi, and A. Abdelwahab, “Modeling and simulation of shear resistance of R/C beams using artificial neural network,” Journal of the Franklin Institute, vol. 344, no. 5, pp. 741–756, 2007.
View at: Publisher Site | Google Scholar
Z. Waszczyszyn and L. Ziemianski, “Neural networks in mechanics of structures and materials new results and prospects of applications,” Computers and Structures, vol. 79, no. 22-25, pp. 2261–2276, 2001.
View at: Publisher Site | Google Scholar
L. Wang, Y. Zeng, and T. Chen, “Back propagation neural network with adaptive differential evolution algorithm for time series forecasting,” Expert Systems with Applications, vol. 42, no. 2, pp. 855–863, 2015.
View at: Publisher Site | Google Scholar
B. Han, F. Geng, S. Dai, G. Y. Gan, S. L. Liu, and L. H. Yao, “Statistically optimized back-propagation neural-network model and its application for deformation monitoring and prediction of concrete-face rockfill dams,” Journal of Performance of Constructed Facilities, vol. 34, no. 4, 2020.
View at: Publisher Site | Google Scholar
Z. J. Li, G. Y. Kan, C. Yao, Z. Y. Liu, Q. L. Li, and S. Yu, “Improved neural network model and its application in hydrological simulation,” Journal of Hydrologic Engineering, vol. 19, no. 10, 2014.
View at: Publisher Site | Google Scholar
H. Dongmei, H. Shiqing, H. Xuhui, and Z. Xue, “Prediction of wind loads on high-rise building using a BP neural network combined with POD,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 170, pp. 1–17, 2017.
View at: Publisher Site | Google Scholar
Z. X. Yue, Y. L. Ding, H. W. Zhao, and Z. W. Wang, “Case study of deep learning model of temperature-induced deflection of a cable-stayed bridge driven by data knowledge,” Symmetry, vol. 13, no. 12, p. 2293, 2021.
View at: Publisher Site | Google Scholar
F. L. Kuang, Z. L. Long, D. M. Kuang, X. W. Liu, and R. Q. Guo, “Application of back propagation neural network to the modeling of slump and compressive strength of composite geopolymers,” Computational Materials Science, vol. 206, Article ID 111241, 2022.
View at: Publisher Site | Google Scholar
G. W. Chen, W. C. Tang, S. Chen, S. Y. Wang, and H. Z. Cui, “Prediction of self-healing of engineered cementitious composite using machine learning approaches,” Applied Sciences, vol. 12, no. 7, p. 3605, 2022.
View at: Publisher Site | Google Scholar
J. Luo, R. Ren, and K. D. Guo, “The deformation monitoring of foundation pit by back propagation neural network and genetic algorithm and its application in geotechnical engineering,” PLoS One, vol. 15, no. 7, Article ID e0233398, 2020.
View at: Publisher Site | Google Scholar
C. Hou and X. G. Zhou, “Strength prediction of circular CFST columns through advanced machine learning methods,” Journal of Building Engineering, vol. 51, Article ID 104289, 2022.
View at: Publisher Site | Google Scholar
Y. Tan and Y. C. Zhu, “Fireworks Algorithm for Optimization Lecture Notes in Computer Science,” in Proceedings of the International Conference on Swarm Intelligence ICSI 2010, pp. 355–364, Springer, Beijing, China, June 2010.
View at: Google Scholar

Copyright

Copyright © 2023 Jian Guo and Wu Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

173

Downloads

222

Citations