Bridge steel structures are widely used in bridge construction with the advantages of light self-weight, convenient use, and good bridge span. Steel bridges are subjected to cyclic loading for a long time during their service period, and cyclic loading has a certain influence on their fatigue resistance performance. Fatigue is a phenomenon in which the structure is subjected to cyclic loading that generates cracks, expands continuously, and eventually leads to fracture of the member. The bridge steel structure under the repeated action of vehicle load and cyclic load is caused by microcracks and will expand with time, and the bridge deck system structure is prone to fatigue damage, so fatigue fracture detection has a great impact on the safe service life of steel bridges. In this paper, the fatigue design guidelines in the relevant codes and the bridge steel structure detection model are compared and analyzed, and a neural network-based fatigue fracture detection model for bridge steel structures under cyclic loading is proposed for the study of fatigue and corrosion interactions and fatigue and fracture of steel bridges under complex stress conditions. For this purpose, in the relevant experiments, experiments are designed to detect the fatigue fracture of bridge steel structures under different cyclic loads, and the experimental results prove the effectiveness of the proposed method. As an important part of the national transportation trunk line, most of the steel structure bridges hold the throat of highway and railroad transportation, and it is crucial to ensure their smooth and high-quality safe service. In recent years, China's economy has continued to develop at a high speed, and the traffic load on bridges has the important characteristics of heavy load, high speed, and high traffic volume –3. To imSteel bridges are an important development direction for bridge engineering because of their outstanding advantages such as light weight and high strength, large spanning capacity, easy factory manufacturing, and convenient assembly construction. However, engineering practice shows that fatigue and fracture are the key factors leading to the reduction of structural service performance and even catastrophic accidents, which seriously restrict the development and application of steel bridges . At presThis paper presents an in-depth and systematic study of fatigue fracture of bridge steel structures under cyclic loading, now focusing on the main aspects of fatigue failure mechanism and resistance assessment methods, anti-fatigue design and construction techniques, environmental factors and their fatigue resistance effect mechanisms, fatigue crack identification and monitoring detection, and fatigue crack disposal and performance strengthening. The fatigue problem of steel bridges under cyclic loading is a research hotspot in the academic and engineering circles. Based on research on fatigue performance analysis and assessment theoretical methods, fatigue-resistant design and long-life structures, fatigue-resistant construction techniques, fatigue damage monitoring and fatigue micro-crack detection and identification, remaining fatigue life prediction, and fatigue performance strengthening, the construction of steel bridge whole-life cycle anti-fatigue technology is the future research –11.S-N curve (stress-fatigue life curve) reflects the relationship between fatigue strength and fatigue life of the specimen under cyclic loading, according to the bridge design after knowing the stress amplitude S, according to the stress-fatigue. Based on the S-N curve, some scholars have proposed a safe life design to ensure that the member or connection can be used normally within the safe service life: damage tolerance design based on fracture mechanics to ensure that the damage will not be caused by crack expansion during the trial period by estimating its remaining life [The fatigue problem of steel bridges under cyclic loading is also gradually becoming serious. Bridge designers have a full understanding of the structural load carrying capacity, but do not have a full understanding of the fatigue load action leading to member or connection failure. As bridge collapse due to environmental erosion, excessive traffic flow, and vehicle overloading occurs, fatigue damage of bridges is increasingly receiving high attention from relevant departments and researchers. At present, there are three main fatigue design methods, the first is the infinite life design, which is a simplified design method, which requires the design stress of the structure lower than its fatigue limit stress value; ing life .Current fatigue design codes around the world are mostly based on the latter two methods, and the codes of the UK, the USA, Japan, and Europe have the same safety determination guidelines and the classification of fatigue strength, while China's code for fatigue design provisions is relatively simple. In some cases, crack development will automatically stop at a certain level, and the crack will not continue to expand despite the continued action of cyclic loading. Calculating the size of the ultimate crack and the conditions of crack termination is the problem that fracture mechanics has been trying to solve in recent years –15. The Fatigue damage of steel bridges under cyclic loading usually occurs at local hidden locations and is difficult to detect when the crack is small, but once it expands into a long crack, the structural safety risk and maintenance costs are significantly increased. At present, the traditional manual inspection and contact inspection are still the main means of steel bridge damage detection and monitoring, with low detection efficiency, high cost, easy to miss concealed cracks, and difficult to detect micro-cracks. To solve this problem, it is urgent to establish a real-time monitoring and evaluation system for fatigue damage of steel bridges under cyclic loading based on the properties of fatigue problems and the actual demand of its detection and monitoring, integrating the latest research results of nondestructive testing, and providing a scientific basis for the safety assessment and operation and maintenance decisions of steel bridges. Scholars have conducted a series of studies on the application of ultrasonic, acoustic emission, infrared thermography, image recognition, and other detection methods in the fatigue damage detection of steel bridges under cyclic loading .The use of ultrasound and acoustic emission detection of internal defects and cracks is essentially the use of internal defects and cracks on the wave conduction of obscuration and reflection effect. Accurate identification of internal defects in longitudinal rib butt full fusion fillet welds of steel bridge panels was achieved by using ultrasonic phased array detection and identification method. An ultrasonic double probe penetration detection method was proposed for longitudinal cracks at the longitudinal rib weld of the top plate, and the detection method was tested and verified using prefabricated crack specimens. Piezoelectric ceramics (PZT) were embedded inside the steel UHPC composite structure, excitation was applied to them to generate ultrasonic waves, and the identification of local damage in the composite structure was achieved by ultrasonic signals. The key issues of nonlinear ultrasonic waves in weld detection were studied, and the fatigue damage characteristics of the weld in the acoustic signal were accurately extracted by combining Fourier transform and Hilbert–Huang transform. The expansion process of cracks in steel bridge panels was monitored by a combination of American Physical Acoustics (PAC), acoustic emission (AE) sensors, and PZT sensors, and the results showed that the technique can capture rich dynamic information of fatigue cracks in real time –19.As a new technology in the ultrasonic inspection family, guided wave technology has the advantage of detecting all defects within the scan area in a single scan, while enabling defect quantification and localization. The array signal processing method based on singular value decomposition (SVD) extracts the damage dispersion signal in the guided wave, and the measured analysis of steel bridge panels shows that the proposed method can successfully extract the crack information from the measured signal with low signal-to-noise ratio and weak intensity. However, the multimodal characteristics of the guided wave and the complexity of the steel bridge panel structure will lead to a more cluttered guided wave signal, so the excitation and reception of the guided wave and the reasonable choice of signal processing methods are the keys to achieve accurate defect identification.Steel bridges have been used more and more extensively in recent years, and the fatigue problem under cyclic loading has become more and more serious. However, bridge designers in China are not sufficiently aware of the failure of members or connections due to fatigue loading under cyclic loading. This paper first summarizes the fatigue design of steel bridges under cyclic loading, then compares and analyzes the fatigue design guidelines and methods under cyclic loading in the relevant codes, and finally proposes a neural network-based simulation for fatigue fracture detection of bridge steel structures under cyclic loading, which is used to analyze the fatigue fracture of steel bridges under cyclic loading in complex force cases. The comparison of test results shows that the model is simple and easy to implement, and the research results provide reference for the design application of steel bridges in practical engineering in China.Since the damage of steel bridges caused by fatigue and fracture under cyclic loading is brittle, there is no ductile deformation process and obvious signs before the damage, and failure to detect fatigue cracking under cyclic loading in critical parts and dispose of them scientifically is the direct cause of serious diseases and catastrophic structural safety accidents of steel bridges. Scientific prediction of fatigue damage state and remaining life under cyclic loading is the basic premise to ensure high-quality service of steel bridges in service and to effectively avoid structural safety risks. However, for most of the steel bridges in China, especially those built in the early years, the fatigue load information under cyclic load and the actual fatigue damage degree and fatigue resistance under cyclic load of key structural details are missing during the service process; therefore, one of the main challenges in the study of fatigue under cyclic load of steel bridges in service is how to reconstruct the fatigue resistance of key structural details under the missing information –23.The fatigue damage state under cyclic loading of structural details: The fatigue damage process under cyclic loading of structural details and the fatigue damage process under cyclic loading are cross-scale processes from microscopic to macroscopic, while the reconstruction process of the fatigue damage state under cyclic loading in the absence of information is a typical cross-scale inverse process –25. The In the whole fatigue life under cyclic loading action, microcrack sprouting extension life accounts for more than 50%; once the fatigue microcrack under cyclic loading action expands to macroscopic crack visible to the naked eye, it will rapidly expand to penetrating type grown-up crack. This leads to both problems of leakage detection prognosis and disposal timing. Due to the short time from stable expansion of macroscopic cracks to destabilization expansion, for some structures, the node or rod fracture caused by the missed detection of fatigue cracking under cyclic loading will directly trigger the catastrophic accident of brittle damage without aura in the structure; for fatigue tough structures under high resistance to cyclic loading, even if fatigue cracking under cyclic loading only reduces the service quality of the structure, the direct cost of reinforcement maintenance, the indirect cost due to the direct cost of reinforcement maintenance, and the indirect cost due to interference with traffic also increase exponentially with the increase of crack length. Due to the above characteristics, early identification of damage and timely disposal of fatigue cracking under cyclic loading are essential.However, the identification of the early extension stage of fatigue cracking under cyclic loading is highly difficult and challenging, mainly because fatigue cracking under fine cyclic loading usually does not cause significant changes in the static and dynamic response of the structure, which is difficult to be accurately identified by traditional damage identification methods: the influence of significant deteriorating structural details such as initial manufacturing defects and corrosion and the fatigue resistance of the stressed member under cyclic loading. The distribution of these factors on the structure is strongly random, and the traditional manual inspection method has low efficiency, high cost, poor working conditions, and hidden cracks that are easy to miss, which makes it difficult to meet the actual demand of full-field inspection of the whole bridge; the fatigue problem of steel bridges under cyclic load has multiple structural details and multi-mode characteristics, and a considerable proportion of fatigue cracking under cyclic load is located in hidden parts, which is difficult to detect .Based on the understanding of the basic properties of fatigue problems under cyclic loading, it is extremely necessary to construct an intelligent monitoring and identification system for fatigue damage under cyclic loading of steel bridges by introducing the latest advances in fatigue damage mechanisms under cyclic loading, fatigue resistance assessment methods under cyclic loading, testing and detection techniques, artificial intelligence, big data, and other fields. The system has already been explored and applied in the laboratory and in some steel bridge engineering practices. The related research will integrate the core research results of fatigue research under cyclic loading of steel bridges, directly support the goal of long life and high-quality service of steel bridges, and strongly promote the innovative research on fatigue problems under cyclic loading of steel bridges to a new stage of development.This area is the key development direction for future steel bridges, and the main research contents in the next phase include fatigue damage characterization, and in-situ monitoring and identification methods for new structural systems and structural details under cyclic loading; real-time assessment and prediction systems for fatigue damage and cracking probability under cyclic loading based on multi-source information; real-time monitoring and measurement techniques for fatigue crack expansion under cyclic loading; micro-new technology of high precision nondestructive testing of fatigue cracks under cyclic loading; intelligent sensing technology and intelligent sensing system of fatigue damage under cyclic loading; theory and method of structural integrity assessment of steel bridges, etc. Infrared thermographic inspection technology is a technique to determine the damage on or near the surface of a structure by the difference between the target and the background temperature of the measurement point, which has the advantages of fast measurement speed, intuitive measurement results, and large detection area compared with ultrasonic inspection methods. Infrared thermal imaging NDT techniques can be classified as passive or active according to whether they depend on external heat source excitation. The results show that passive infrared thermography can detect fatigue cracks under cyclic load in steel structures under natural environmental conditions for the blocking effect of external heat transfer. With the development progress of computer vision technology, the apparent damage identification method based on computer vision has become a current research hotspot in the field of steel structure bridge damage identification.The image acquisition device uses VGGNet-13 and VGG-FCN to classify the crack target sub-blocks. The crack geometry features of the real bridges are extracted by defining the crack pixel semantics. Various image segmentation techniques are used to locate and identify steel surfaces, and to convert steel structure rust images into HSV color space. The network input is a planar grayscale image of a CT specimen with scattered spots. The identification method of loose steel bridge bolts is proposed based on various machine vision techniques such as Fast-RCNN and perspective transformation –29. The This paper combines the latest development of intelligent detection technology and the basic properties of fatigue problems under cyclic loading of steel bridges, and initially summarizes the intelligent monitoring and identification methods of fatigue cracks under cyclic loading of steel bridges: (1) a systematic numerical simulation and experimental study of the application of ultrasonic guided wave in fatigue crack detection under cyclic loading of steel structures, and the results show the ultrasonic guided wave has good applicability in the detection of cracks in key-stressed members of steel bridges; (2) a smart sensor for fatigue crack nano-coating under cyclic loading was developed, theoretical research, numerical simulation, and experimental research were conducted on it, and the results show that the sensor has high sensitivity for small cracks; (3) a research was conducted on the fatigue crack recognition method based on computer vision under cyclic loading and the actual; the results show that the computer vision technology has high reliability in fatigue crack recognition under cyclic loading; (4) the deep learning theory is introduced into the pattern recognition of fatigue damage state under cyclic loading of the structure, which is used to mine and recognize the damage information in the time domain signal and image signal. The results show that the neural network system based on monitoring data and targeting damage pattern recognition has a broad application prospect in practical engineering.Visual defect detection aims to locate and identify defects in images, which is one of the classical tasks in computer vision, is the premise and foundation of many computer vision tasks, has important application value in the fields of automatic driving and video surveillance, and has received wide attention from researchers. With the rapid development of deep learning technology, defect detection has made great progress. The training phase includes data preprocessing, detection network, label assignment, and loss function calculation, and the testing phase uses the trained detector to generate detection results and postprocess the results , 31.Monocular visual defect detection is the basis of visual defect detection, which aims to predict the location and class information of defects present in a single image. Since the success of deep convolutional neural networks for image classification tasks in 2012, researchers have started to experiment with deep convolutional neural networks for defect detection. Since then, deep learning-based defect detection has started to dominate the development of defect detection. The defect detection methods are divided into three categories: anchor box-based defect detection methods, anchor box-free defect detection methods, and end-to-end prediction defect detection methods. It should be noted that the end-to-end predictive defect detection method belongs to the defect detection method without anchor frames. Since the end-to-end predictive defect detection method does not require postprocessing operations and mostly uses a converter model to directly predict a detection result for each defect, it is a more concise detection architecture and will be introduced in detail as a separate category.k candidate detection windows of nonspecific categories and then further classifies and regresses these candidate detection windows to generate the final detection results. Unlike the two-stage method, the single-stage method directly classifies and regresses the anchor frames. In general, the two-stage method has higher detection accuracy, while the single-stage method has faster inference speed.Anchor box-based defect detection method sets multiple rectangular boxes for each location in space to cover all defects present in the image as much as possible. Defect detection based on anchor boxes can be divided into two categories: two-stage defect detection methods and single-stage defect detection methods. The two-stage method first extracts The two-stage defect detection method regional convolutional neural network series work is the most representative work of the two-stage defect detection method. R-CNN first uses selective search method to generate 2000 most likely defective candidate detection frames, then uses deep convolutional neural network to extract the depth features of these candidate detection frames, and finally uses support vector machine for classification and regression. This method was a great success at that time and substantially improved the accuracy of defect detection. Since the R-CNN extracts the depth features of each candidate frame separately, there is a problem of slow inference speed. To address this problem, the features of the whole image are extracted by feature sharing, and then the features corresponding to each candidate frame are converted into fixed-length features for subsequent SVM classification and regression using spatial pyramid pooling operation, which is referred to as SPP-Net. R-CNN and SPP-Net feature extraction and prediction (classification and regression) is a multi-stage process, which limits the performance of deep neural networks, and an improved work Fast R-CNN is proposed for R-CNN. Fast R-CNN first extracts the depth features of the whole image, then scales the features of the candidate detection frames to a fixed size using the region of interest pooling operation, and finally uses the fully connected layer for classification and regression.The Fast R-CNN further unifies the generation of candidate windows with the classification and regression of candidate windows into a single network for joint learning. The RoI pooling operation can extract contextual information, and PS RoI can capture local information of defects. The features extracted by RoI pooling operation and PS RoI pooling operation are fused and used for subsequent classification and regression. The deformable RoI pooling operation can better characterize the deformation of defects, and the RoI align pooling operation can solve the feature mismatch problem caused by the quantization error of RoI pooling operation. Cascade R-CNN, a cascading defect detection architecture, cascades multiple Fast R-CNN head networks to further classify and regress the classification and regression results of the previous level in the current level. The cascade idea is used for candidate window generation. To cope with the variation of defect scales, the researchers proposed an image pyramid-based approach and a feature pyramid-based approach. The image pyramid-based approach uses images of different scales to detect defects at different scales, such as small-scale images to detect large-scale defects and large-scale images to detect small-scale defects. The image pyramid-based method requires the use of detection networks to detect multiple images of different scales, and the computational effort is relatively large. The feature pyramid-based method uses different layers within a single detection network to detect defects at different scales, which is relatively less computationally intensive.It is very important for fatigue fracture detection of bridge steel structures under cyclic loading. To improve the detection efficiency, using a convolutional neural network model based on deep learning to evaluate the corrosion level of the corrosion layer helps to avoid misjudgment due to human fatigue and inattentiveness. Using its efficient and automated feature extraction, this chapter proposes to establish a fatigue fracture detection model for bridge steel structures based on convolutional neural networks, as shown in Sij is the stress bias tensor, eijρ is the plastic strain bias tensor, and ZD is the skewed internal time scale.ξ is the internal time metric, ρ(Z) is the core function, f(ξ) is the hardening function, and ||−|| denotes the parametric number in Euclidean space. For isotropic incompressible materials under hydrostatic pressure, there are elastic relations.In this paper, the intra-temporal intrinsic structure theory is used. The cyclic intra-temporal intrinsic structure relationship can be expressed asThe total strain bias consists of both elastic and plastic components.The relationship between strain tensor and strain bias and stress tensor and stress bias isSubstituting the differential equations into the incremental equation,This is the tensor representation of the intrinsic structure relationship within the incremental form applied to the model in this paper.In this paper, the core function is taken as follows:Rr has the dimension of stress, and βr is a dimensionless quantity. The reinforcement function is taken as f(ξ) = 1, while Rr and βr are obtained by curve fitting based on the material test curve.The constant 𝒲 denotes the weight tensor of all layers and τ(𝒲) denotes the actual inference delay of the network, which depends on the structure of the network model's weights 𝒲. Compressing the network model affects the model's weights W and thus the model's inference delay τ(𝒲). ℓ is the loss function for a particular learning task. In deep learning, ℓ is usually a highly nonconvex function. The compression of the model is achieved by pruning, and as mentioned before, there are two different types of pruning techniques: structured and unstructured. Unstructured fine-grained pruning removes individual elements, while structured coarse-grained pruning deletes the regular structure of the DNN, such as the channels of the convolutional layer or even the whole convolutional layer. While both approaches are applicable here, this paper focuses specifically on the coarse-grained approach, which prunes channels or layers, because channel pruning is more effective on off-the-shelf DNN hardware platforms  and more likely to achieve the goal of inference latency reduction, while the fine-grained approach requires specialized hardware architectures to be effective. Using a coarse-grained structured pruning approach, the optimization problem becomes finding the sparsity of each layer, i.e., the number of channels retained in each layer, such that the total inference latency of the model satisfies a given budget, i.e.,su)( corresponds to the sparsity bound of layer u. The inference delay r of the DNN can now be expressed as a function of s. wu)( output channels and cu)( × cu)( × rhu)( × rwu) of the model by the sparsity s of each layer of the model to determine whether it still satisfies the constraint, i.e., modeling the inference delay of the DNN model as a function of the sparsity of each layer. This step is particularly important because it provides an analytical form to characterize the delay. Existing DNN latency models are dedicated to specific hardware platforms, which requires a deep understanding of the hardware and cannot be ported across different hardware architectures. Latency prediction models can be constructed directly from measurements and computations on the hardware, while treating the hardware platform as a black box. This idea is like Net-Adapt, which builds latency models from hardware measurements. However, these models are like a huge nonminiature lookup table, which greatly reduces the efficiency. Therefore, the goal of this chapter is to construct a microscopic model to solve optimization problems using traditional gradient-based algorithms. The main idea of this paper is that the time delay model can be obtained by a data-driven approach. Let r be a differentiable function to approximate τ.f is the space consisting of all potential sparse models and their corresponding inferred time delays, and Es is the expectation. To find a differentiable delay model, our intuition is that the time consumption of a layer in a DNN is influenced by the number of channels in its input and output feature mapping, which in turn corresponds to the sparsity of the current layer and the next layer, respectively. Thus, the time consumption of layer j can be obtained by modeling a function of the interaction between sj and sj+1, where s denotes the sparsity of layer j. Based on this intuition, we use the following bilinear model to approximate the total network model time delay.s is defined as the network output dimension, e.g., the number of classes in the classification task. The coefficients a0, a1,…, aℜ1 are the variables that define this space. The rationale for using a bilinear structure is that the total number of arithmetic operations (multiplication and addition) during DNN inference for the layers defined by s is roughly in bilinear form. While other more complex models are possible, the bilinear model is simple and compact, and easy to train, and effectively avoids overfitting. For some specific DNN architectures, what happens if the time delay function cannot be essentially modeled in bilinear form. In this case, a neural network can be used to approximate the delay function, since a three-layer neural network can theoretically approximate any function. The constrained optimization in the equation only requires the delay model to be differentiable, so it still applies. To obtain τ, s is sampled from a uniform distribution and the actual inference latency on the target hardware platform is measured to obtain τ(𝒲). The stochastic gradient descent method is then used to solve the equation and obtain τ. For a given combination of network and hardware, the procedure is performed only once.To evaluate the inference delay of the initial model as well as the model after compression, if the model is executed once completely each time to obtain the inference delay of the model, this will undoubtedly be very time-consuming during the experiment and greatly reduce the efficiency of the experiment. The key aspect of solving the equation is to obtain the inference delay S-1 and S-2, respectively. D, structural height h1, stiffening mother plate thickness t, transverse spacer thickness td, stiffening rib thickness ts, stiffening rib height hs, transverse spacer spacing a, longitudinal stiffening rib spacing a′, and section width and length directions divided by longitudinal stiffening ribs as nx and ny, respectively. The stiffening ribs are connected to the stiffening mother plate by fillet welds, and the adjacent mother plate and the mother plate are connected to the base plate by full penetration welds. The basic mechanical properties of steel bridge steel Q345qC are shown in E, Poisson's ratio μ, yield strength oy, ultimate strength ou, and strain at break cy and elongation A. The values of these parameters were obtained from the material property test results of Q345qC steel.The software and hardware configurations used in this study are shown in A∼D, and the displacement sensors are numbered 1∼5, where displacement sensors 1 and 2 are used to measure the horizontal displacement of the top of the structure and the base, respectively, and displacement sensors 3∼5 are used to monitor the loaded bridge for fatigue and fracture. The data detected by the sensors are analyzed and processed using the algorithm proposed in the text. The training process loss convergence and performance enhancement are shown in Figures In this study, a large multifunctional electro-hydraulic servo structural test system of 10,000 kN was used to load the steel bridge for the proposed cyclic load test. The bottom plate of the structure is connected to the base through high-strength bolts, which is cemented to the floor, and the top of the structure is connected to the two actuators through the loading beam. The vertical actuator applies axial load to the structure, the horizontal actuator applies forced displacement to the structure in the horizontal direction, and the vertical actuator follows the top of the pier to move to prevent eccentricity. The four mother plates of the structure are The fatigue data under cyclic loading of the bridge steel structure experiments were obtained by using the above settings and preparations, and the fatigue curves under cyclic loading were used to complete the display of the results, considering the differences between the specimen and the time bridge, as shown in To verify the fatigue effect of the bridge steel structure under cyclic loading, the effect of simulated multiple transverse loads on the test points was analyzed, and the experimental results with the test points at level 2 loading are shown in The experimental load double output is set to the limit value in the parameter, and the experimental results are obtained in the three-stage load parameter, and the experimental data are shown in As can be seen from Steel bridges have been widely used in modern bridge engineering for their outstanding advantages such as light weight and high strength, large spanning capacity, easy factory fabrication, and convenient assembly construction, but the development and application of steel bridges in China have long lagged developed countries such as Europe, America, and Japan. In the current context, it is important to stand on the shoulders of giants, grasp the historical opportunity of the strategy of a strong transportation country and the vigorous promotion of steel bridges in China, introduce the latest achievements in mathematics, mechanics, theoretical analysis, test and inspection technology, processing and manufacturing technology, and artificial intelligence, and continue to make efforts in both basic theory and major engineering applications to further deepen the understanding of fatigue failure mechanisms of steel bridges under cyclic loading, and develop new methods of fatigue failure. This paper expands the understanding of fatigue failure mechanisms of steel bridges under cyclic loading and develops new theories and methods.In this paper, we expand the research field of steel bridges according to the practical needs, propose a fatigue fracture detection model based on artificial intelligence algorithm for the fatigue fracture detection of steel bridges under cyclic loading, and establish a more complete guaranteed system for the sustainable development of fatigue fracture detection of steel bridges under cyclic loading through innovative results. In the future, we plan to start using cyclic neural networks for fatigue fracture detection of bridge steel structures under cyclic loading.


Evolutionary dynamics is well captured by the replicator equations when the population is infinite and well-mixed. However, the extinction dynamics is modified with finite and structured populations. Experiments on the non-transitive ecosystem containing three populations of bacteria found that the ecological stability sensitively depends on the spatial structure of the populations. Based on the Reference–Gamble–Birth algorithm, we use agent-based Monte Carlo simulations to investigate the extinction dynamics in the rock-paper-scissors ecosystem with finite and structured populations. On the fully-connected network, the extinction time in stable and unstable regimes falls into two universal functions when plotted with the rescaled variables. On the two dimensional grid, the spatial structure changes the transition boundary between stable and unstable regimes but doesn’t change its extinction trend. The finding of universal scaling in extinction dynamics is unexpected, and may provide a powerful method to classify different evolutionary dynamics into universal classes. The opposite side of the same question is about extinction mechanism. Derived from the evolutionary game theory, replicator equations11 deliver a deterministic description for population dynamics with frequency-dependent selection. The competitions between individuals of different species are described by the payoff matrix13 in the game theory and the resultant replicative dynamics has been rather successful in many ecosystems11. Despite of the general applicability with success, it is important to keep in mind that the replicative dynamics is limited to the well-mixed configurations in the infinite population limit.The paramount question in evolution is how to maintain robust biodiversity in an ecosystem hosting mutually competing species31 show that ecosystems with finite populations and/or on structured networks reveal significant deviations from the replicative dynamics. For instance, in a recent study32 on the non-transitive rock-paper-scissors ecosystem containing three populations of Escherichia coli. They found that diversity is rapidly lost in the ecosystem when dispersal and interaction occur over relatively large spatial scales, while all species coexist when ecological competitions are localized. That is to say, the ecological stability seems to be weakened in the well-mixed populations. Their findings inspire us to explore the role of spatial structure in evolutionary dynamics.What happens if the populations are finite and/or competitions between individuals occur on a network with specific spatial structure? Many studies33 shows that a critical population size 34claims that the extinction time is always finite and the ecological stability needs to be defined by the trend of the extinction dynamics. The ecological stability of an ecosystem with finite population means that the extinction time grows exponentially with the population size, In addition, there has been controversy over the effect of finite population in the rock-paper-scissors ecosystem. Some study56, known as a paradigm to illustrate the species biodiversity. Recent empirical investigations have identified several ecological systems as the rock-paper-scissors system including the coral reef invertebrates57, the mating strategies of lizards in California58, the bacterial game in vitro and in vivo60, the vertebrate community in the high-Arctic tundra in Greenland61 and the plant communities63. These findings in nature make rock-paper-scissors game not only a theoretically interesting model but also a practical system to study.To put the discussions on firm ground, we concentrate on the non-transitive rock-paper-scissors game65 and its generalized versions67 may not be appropriate. One shall turn to the evolutionary theory on graphs70 to include the local mutual competitions. Following the same spirit, we introduce a local three-party Reference–Gamble–Birth (RGB) algorithm and perform the agent-based Monte Carlo simulations for the evolutionary dynamics. The RGB algorithm only requires local information in the stochastic processes and captures the network structure into account. And, it correctly reproduces the replicator dynamics when the populations are infinite and well-mixed.In this Report, we use agent-based Monte Carlo simulations to investigate the extinction dynamics in the rock-paper-scissors ecosystem with finite and structured populations. Making use of numerical simulations, one can extract the extinction time in different regimes. However, for the finite and structured populations, the usual Moran algorithm34 but also suggest a potential tool to classify different evolutionary dynamics by universal scaling.Two major results are found in our numerical simulations. The first one is the universal scaling: the extinction time is always finite and falls onto the universal function when plotted with the rescaled variables. On the fully-connected network, two universal functions for stable and unstable regimes are found and the phase transition between them corresponds to neutral  dynamics where the extinction time shows power-law behavior. The unexpected universal scaling may provide a powerful method to classify ecosystems with different dynamical behaviors into universal classes. The second major result is the notion of global payoff versus local payoff. On the two dimensional grid, the spatial structure changes the transition boundary between stable and unstable regimes but the universal function remains the same. This observation motivates us to introduce the notion of global payoff which turns out to be consistent with our numerical simulations. Our numerical simulations not only resolve the conflicting results in the previous studiesA, B and C described by the payoff matrixg denotes the gain in the cyclic competitions. The replicative dynamics of the ecosystem with populations A, B, C is captured by the following differential equations,A in the total population  Here we consider the symmetric cyclic competitions between species 34 host a non-trivial fixed point g is tuned through the critical point The symmetric replicator equations The above scenario is well known for the rock-paper-scissors game when the population is infinite and well-mixed. But, what happens when the population is finite and the competitions among different species occur on the network with specific spatial structure? To investigate these important issues, we utilized the agent-based Monte Carlo simulations. To incorporate the locality of mutual competitions on the reasonable ground, we introduce a local three-party Reference–Gamble–Birth (RGB) algorithm. For each RGB update, it consists four steps as shown in Fig. D plays a central role in RGB algorithm. Similar to payoff matrix, its matrix elements D for RGB algorithm from an arbitrary negative payoff matrix P; (iii) extracting the extinction time  k Gamble when contacting with a Reference of species j and the random replacement of a Birth of species i, where i Gamble dies during the interaction between a species-j Reference and a Birth of species-k is randomly chosen to fill the empty site, where N24, i.e. i. Defining i and In a single update, there are two possible ways to change the population size 11. Based on the gauge redundancy, we consider a negative payoff matrix P with negative values for all matrix elements (i.e. i and j) without loss of generality. Because s, which has a lower bound s,s. Thus, the extinction time obtained by the numerical simulations should also be rescaled by the same factor, i.e. Now, we can derive the relation between the death matrix in RGB algorithm and the payoff matrix in replicator equations when frequency-dependent selection is taken into account. The gauge redundancy of the payoff matrix indicates the replicator equations remain invariant when adding a arbitrary constant to all elements in the payoff matrixThe RGB algorithm has several advantages over the Moran process. First of all, only local information is involved in the stochastic process, more realistic than the need of global information for the Moran process. Secondly, the RGB algorithm reproduces the dynamics of frequency-dependent selection described by the replicator equations in infinite and well-mixed populations when the rescaling of time is restored properly. Finally, the the RGB algorithm takes the network structure into account, capturing the sensitive dependence of evolutionary dynamics in structured populations.N and the gain g defined in the payoff matrix, is computed by taking ensemble average of 10,000 runs in numerical simulations. We first focus on the well-mixed population, i.e. the fully connected network where every individual is connected to each other. It is rather remarkable that all numerical data can be collapsed onto the universal functions,N and g. In the following paragraphs, we would like to show that these scaling variables can be understood within the framework of the renormalization group (RG)71. But, it is worth mentioning that the scaling variable 72 that the extinction time in finite populations will scale as the product of population size and selection strength. We perform agent-based Monte Carlo simulations to extract the mean extinction time. For each run, when one of the species goes extinct, we stop the simulated evolution and mark the time of extinction. The mean extinction time entclass1pt{minima71 by RG analysis. Assuming the scaling dimensions for N and Let us derive the scaling form of the extinction timet in Eq. . Note thp to go extinct. Suppose the typical size of the cluster is N and the asymptotic form of A is some positive constant and 34 and agree with the numerical simulations presented in Fig. The emergent universal scaling is highly non-trivial. For instance, extinction time of different population sizes at the critical point all collapse onto just one point  give different results. Because the fully-connected network looks the same either locally or globally, it is invariant under renormalization-group transformation and serves as a good reference. In RG analysis, the partition function is kept invariant to extract the renormalized coupling constants71. Here we adopt the same method and introduce the global gain G on an arbitrary network via the relationg on the considered network is set equal to that for the global gain G on the fully-connected network. According to the definition, G and g on the 2D grid is carried out numerically  and equals C. To explore the different dynamics arisen from the network structure, it is helpful to study the spatial and temporal correlation functions,g is not found in the numerics. Thus, the temporal oscillation must come from a different origin.The spatial and temporal dependences of the correlation function is shown in Fig. 73 where the correlation in one direction  is stronger than the other . One can picture the whole system is roughly divided into many spiraling units of linear size p. The interactions among the units ignite or suppress the neighboring ones. Thus, the probability for the complete extinction The situation is close to the nematic phase74 on the cooperation in social games also found that the rescaled extinction time follows universal scaling. However, their emphasis is in the neutral regime  where the power law reigns. But, in the rock-paper-scissors game we studied here, we find the phase transition can be collapsed onto two universal curves when plotted in terms of the rescaled variables. This is quite unexpected and shows that the universal scaling works not just in the neutral regimes . Thus, our conclusions are stronger and can serve as an important method to classify different dynamical trends for ecosystems with finite populations.Two major results are found in the agent-based Monte Carlo simulations. The first one is the emergence of universal scaling. The second one is the renormalized global payoff due to spatial structure of the network. While our numerical results clearly support the above conclusions, a rigorous proof remain open at the point of writing. In fact, some other numerical studyOne can try to understand the extinction trends qualitatively by the dynamics of the biodiversity indicator 34. The exponential trend for Now consider the effect of finite population. At the critical point G to collapse all data onto the same scaling function is encouraging for further studies along the route of renormalization-group techniques. This shall provides an independent check on the relation between G and g, which is obtained numerically in our study here. The plausible coarse-graining in the time domain is further supported from the prolonged correlation time in the temporal correlation. The renormalization group may also provide more information about the exponents and the scaling functions.The 2D grid posts even more challenging puzzles. The success of applying global gain


In a harsh environment, function aggregation of air–ground integrated network service function chaining (SFC) deployment can easily cause network load imbalance, which affects the network security and reliability. In this study, a task-similarity-based virtual network function (VNF) aggregation scheme was proposed. It considered air–ground network resource consumption and load balance before SFC mapping. A model for selecting VNFs to be aggregated based on task similarity was built. The tasks were classified based on their similarity. Furthermore, the VNFs to be aggregated were selected within the class under the constraints of the underlying physical resources. Load balancing was achieved by adjusting the similarity threshold. Moreover, an SFC mapping selection scheme based on network resource awareness was used to obtain the most suitable physical nodes for single-chain and multi-chain mapping according to various attributes of physical network nodes. The simulation results indicated that the proposed scheme with a better load balance design outperformed existing works on VNF aggregation. We also demonstrated that the task-similarity-based scheme was resource-consumption efficient and effective. The air–ground integrated network makes up for the shortcomings of the independent ground network and the air network composed of drones. Network integration provides seamless global connections and highspeed computing capabilities  to satisIn the NFV network, the required functional requirements are fulfilled by instantiating the virtual network function (VNF). To improve resource utilization, different studies adopted different function aggregation methods. For example, in , the VNFHowever, due to the difference between the arrival time and the life cycle of the SFC request in the NFV network, such a functional aggregation will cause some physical nodes to deploy a large number of VNFs. When the resource occupancy rate reaches the bottleneck, the quality of service (QoS) will drop sharply . At the So far, there have been related works on the network load balancing problem of a single network under NFV technology, but there are few studies on load balancing in an air–ground integrated network. In , load baDue to the apparent similar characteristics of task types in the air–ground integrated network, this study proposed a VNF aggregation method based on task similarity and network resource awareness that considered network load balancing before SFC mapping. First, a model for selecting the VNFs to be aggregated based on task similarity was proposed. The tasks were classified based on their similarity, the functions to be aggregated were selected within the class under the constraints of the underlying physical resources and the load balance was achieved by adjusting the similarity threshold. Second, a resource awareness SFC mapping node selection algorithm was used to obtain the most suitable physical node for single-chain and multi-chain mapping according to the various attributes of physical network nodes. It can make full use of the underlying physical resources to reduce resource consumption and load imbalance.Since the air–ground integrated network and the service function chaining have node attribution and link attribution that are remarkably similar to those of graphs in the mathematical model, they are modeled as different types of graphs according to their characteristics. Due to the diversity and heterogeneity of air–ground network resources, it is necessary to distinguish them according to their attribution when modeling.Air–ground physical network: We regarded the air–ground physical network as a strongly connected directed graph, which is represented by tuples Service request definition: We treated the service request as a directed acyclic graph, assuming that a batch of requests is processed with an interval Consumption model: To visually express the SFC mapping and to make calculations more convenient, the model variables were defined in matrix form. The mapping of unknown vertices We defined a virtual network function mapping binary matrix Similarly, we defined a binary matrix For each successfully deployed SFC, the following constraints must be met:Uniqueness constraint: a virtual network function of a task can only be embedded on one physical node, and a virtual link of a task can only be mapped to a unique physical link.Bandwidth constraint: each path in the routing path must have enough bandwidth to meet the requirements of the virtual link.Computing power constraint: the physical node needs to have enough computing resources to handle the data traffic carried by the SFC.Compatibility constraints: Each virtual network function can only be mapped to a physical node capable of processing this function, and a virtual link can only be mapped to a physical link with sufficient bandwidth resources, that is, the bandwidth resources of the physical link must meet the bandwidth resources required by the service request.The function We used the load-balancing index Since the computational consumption of the processing VNF is fixed, the resource consumption requested by the task in this article includes instantiation consumption and bandwidth consumption. However, air–ground integrated network nodes are different in terms of coverage and computing power. Therefore, their instantiation overhead and bandwidth consumption are different.If each VNF is instantiated for each SFC, it will cause a huge instantiation overhead and waste of resources when deploying the service function chain. VNF aggregation effectively solves this problem. However, the existing function aggregation methods only focus on reducing the instantiation overhead and ignoring the load balancing problem caused by VNF aggregation. To solve the problem of load balance, Refs. ,10,12,13As shown in In response to the above problems, this study proposed a VNF selection method to aggregate tasks based on task similarity.(1)For tasks that arrive in time interval T, the virtual network functions required by the task and the access to task resources that are more similar are placed into the same category. Tasks within the same class share the same type of physical node.(2)In the same category, the same VNF is selected for functional aggregation under the condition of satisfying bandwidth and computing constraints.(3)By adjusting the similarity threshold, there is a trade-off between resource consumption and load balancing.The core idea of the method is as follows:The specific implementation is as follows:Task similarity is divided into functional similarity and resource similarity. Task similarity within the time interval T is considered in order to divide similar tasks into the same class to share physical network nodes with the same functionality. On the one hand, this can reduce the instantiation overhead of the same virtual network function for similar tasks, reduce the global waiting time and maintain network stability. On the other hand, it can reduce the uneven load caused by all tasks sharing the same physical node for the same virtual network function. However, the task similarity division according to the time interval T cannot completely solve the problem of an uneven load, and thus, the task similarity threshold can be adjusted to balance the resource consumption and load balancing to meet the task requirements in different scenarios.The definition of task similarity in the time interval T is given here, which includes virtual network function similarity and resource similarity.Virtual network function similarity refers to the similarity of VNFs by different tasks.When When Resource similarity refers to the similarity of the actual demand for the same virtual network function resources.When The task similarity isAfter classification according to task similarity, the system judges whether the aggregation can be performed by whether the bandwidth and computing resources meet the physical network constraints. The aggregation can be performed when the constraints are met; otherwise, it is achieved by adjusting the similarity. Each time, the network resource status is updated after a division by task similarity. For load balancing, this study took an approach to determine task classification by presetting similarity thresholds. While ensuring that the resource consumption is reduced, load balancing is achieved by adjusting the similarity threshold to avoid too many tasks waiting for the same physical node to meet the requirements of the tasks.In order to complete the user’s service request, after the task that arrives in time T is classified by task similarity, the task is deployed on the appropriate physical node through the SFC mapping algorithm. The algorithm we proposed was based on the awareness of network resources, which includes the remaining resources of the link bandwidth and the usage of computing resources of nodes. We adopt an improved genetic algorithm to select the mapped physical network node through the awareness of network resources. Different SFC construction schemes will cause different mapping results of the service function chain, and different mapping results will also be obtained by selecting different physical nodes for mapping. Compared with searching for a single VNF separately or mapping using graph theory, the feature of genetic algorithm exploring from a string set reduces the complexity of the algorithm. At the same time, a genetic algorithm can easily realize parallelization. It can handle multiple individuals in the group and simultaneously deal with different construction schemes of SFC. However, the efficiency of a single genetic algorithm is low, and it can easily converge prematurely. A particle swarm has the advantages of fast calculation speed and solid global searchability; therefore, this study proposed a genetic-particle swarm optimization (GA-PSO) algorithm.(1)Chromosome codingThe particle swarm algorithm is added to the genetic algorithm as the genetic parent chromosome. The speed and position update of the particle swarm is replaced by the crossover and mutation of the genetic algorithm. For single-chain and multi-chain deployments, different coding, crossover and mutation methods are used to implement the deployment of service function chains.Single-chain individual mapping coding: When performing single-chain mapping, SFCs in the same category are deployed one after the other in the order of arrival. That is, within the same category, for the VNF that has been instantiated, the same VNF of the subsequent SFC is deployed on the same physical node, as shown in Multi-chain and multi-encoding: In the case of multi-chain mapping, SFCs in the same class are deployed simultaneously, multiple service function chains are coded as a chromosome and multiple SFC mapping schemes in the class are multi-encoded. The same VNF in the same category is mapped on the same physical node, as shown in (2)Fitness functionSingle-chain: When performing single-chain mapping, SFCs in the same category are deployed one after the other in the reference order. After each service function chain is deployed, the subsequent service function chains realize function sharing for the same VNF. Therefore, when deploying a single chain, the resource consumption needs to remove the overhead saved after aggregation. It includes the reduced instantiation overhead of the air nodes and ground nodes.Multi-chain: In multi-chain deployment, SFCs in the same category are deployed simultaneously. First, we select the optimal deployment location of the aggregated VNF and then find the deployment location of other VNFs. Therefore, when multiple chains are deployed simultaneously, the changes in bandwidth resources after aggregation should be considered. At the same time, the resource consumption needs to be subtracted from the overhead saved after aggregation, which includes the reduced instantiation overhead of the air nodes and ground nodes.(3)Chromosome crossover and mutationThe chromosome crossover was divided into two parts, namely, optimal crossover and free crossover. The optimal crossover is the crossover between the optimal chromosome and the common chromosome. It includes not only the crossover between the individual optimal chromosome and the common chromosome but also the crossover between the group optimal chromosome and the common chromosome. Free crossover avoids the fast convergence of the algorithm and crossovers the chromosomes obtained by the optimal crossover with common chromosomes. When the crossover is performed, the crossover bit is randomly selected for replacement. In the crossover operation, it is necessary to satisfy the conflict detection, that is, to satisfy the uniqueness constraint and the compatibility constraint.When a chromosome is mutated, the mutation position is randomly selected. Then, a node is randomly selected from the set of physical nodes carrying the same VNF and is replaced at the mutated location.When performing the crossover and mutation operations, it is necessary to satisfy the conflict detection, that is, to satisfy the uniqueness constraint and the compatibility constraint.To verify the performance of the algorithm, we used MATLAB 2018a software to simulate it on a computer, which was configured with an 8 GB Intel Core i5-4210U CPU. The simulation used the network topology on SNDlib , includiFirst, in order to verify the effectiveness and convergence of the GA-PSO algorithm proposed in this study, we randomly selected the task request and set the task request bandwidth to 20 M/s, the population number to 20, the number of iterations to 100 and an average of 200 experimental times. The results are shown in It can be seen from This study mainly investigated the load imbalance caused by the use of function aggregation in the deployment of SFC in the air–ground network under the network function virtualization technology. A virtual network function (VNF) aggregation scheme based on task similarity was proposed. Before SFC mapping, the air–ground network resource consumption and load imbalance were considered. A model for selecting VNFs to be aggregated based on task similarity was established. The tasks were classified according to the similarity, and the functions to be aggregated were selected within the class under the constraints of the underlying physical resources, and the load balance was achieved by adjusting the similarity threshold. We adopted the SFC mapping selection scheme based on network resource awareness and obtained the most suitable physical nodes for single-chain and multi-chain mapping according to the various attributes of physical network nodes to make full use of the underlying physical resources to reduce the resource consumption and load imbalance. It was shown that the proposed algorithm solved the load imbalance problem caused by the aggregation of functions, and the similarity threshold was adjusted to meet the demand for load balancing in different scenarios. However, the method of task classification still needs to be improved. In the future, task classification will be expanded in combination with machine learning methods to better achieve functional aggregation.


Target detection and tracking algorithms are one of the key technologies in the field of autonomous driving in intelligent transportation, providing important sensing capabilities for vehicle localization and path planning. Siamese network-based trackers formulate the visual tracking mission as an image-matching process by regression and classification branches, which simplifies the network structure and improves the tracking accuracy. However, there remain many problems, as described below. (1) The lightweight neural networks decrease the feature representation ability. It is easy for the tracker to fail under the disturbing distractors  or large changes in the viewing angle. (2) The tracker cannot adapt to variations of the object. (3) The tracker cannot reposition the object that has failed to track. To address these issues, we first propose a novel match filter arbiter based on the Euclidean distance histogram between the centers of multiple candidate objects to automatically determine whether the tracker fails. Secondly, the Hopcroft–Karp algorithm is introduced to select the winners from the dynamic template set through the backtracking process, and object relocation is achieved by comparing the Gradient Magnitude Similarity Deviation between the template and the winners. The experiments show that our method obtains better performance on several tracking benchmarks, i.e., OTB100, VOT2018, GOT-10k, and LaSOT, compared with state-of-the-art methods. In recent years, autonomous driving has been considered one of the most promising areas of automotive research for research and development. Vision tracking technology has a significant role to play in the field of autonomous driving. Vision sensors are used to dynamically track the target vehicle during the vehicle’s driving process to achieve information interaction between vehicles such as location and driving status, as well as the vehicle’s road condition perception of the environment.Although vision tracking technology has made significant progress in recent years, factors such as interference targets, appearance deformation, and motion blur can seriously affect the performance and robustness of tracking algorithms in practical application scenarios.Traditional trackers, such as the correlation filter tracker represented by the correlation filter KCF  and CSK Early visual tracking methods can be divided into two categories according to the tracking mode, namely, the generative model and the discriminative model. With the development of deep learning, visual tracking methods based on deep learning have gradually become mainstream.Visual tracking is focused on the research of the generative model, such as the optical flow method , particlConsidering the object and background information at the same time, the discriminative model regards the tracking process as a classification or regression problem, and the purpose is to find a discriminant function to separate the object from the background, so as to realize the tracking of the object. The evaluation of the algorithm  found thThe introduction of deep features enhances the feature representation capability of the tracker. HCF  utilizedRecently, Siamese networks based on trackers have received significant attention for their balance between high speed and accuracy ,19. SINTIn addition, the development of adversarial training  has imprTo overcome the above problems, we proposed a SiamFC++-based object relocation tracker. The main contributions of the work are as follows.We designed a matching filter arbiter with a hierarchical architecture based on the distance histogram of the candidate objects, which can accurately and quickly find the failure.We propose an efficient corrector that generates a template set by backtracking. The corrector relocates the object by Gradient Magnitude Similarity Deviation (GMSD) and the assignment algorithm measurement to increase the tracker’s resistibility to interference.Experiments on several challenging benchmarks including VOT-18, GOT-10k, OTB-100, and LaSOT have shown that our proposed tracker is superior to many state-of-the-art trackers.The remainder of this paper is organized as follows. The section Materials and Methods introduces the related work of visual tracking and describes the principle and implementation of our tracker. The Results section evaluates and analyzes the experimental results. Finally, we summarize our work in the Conclusion section.As shown in SiamFC++ introduces four principles for designing trackers and the anchor-free structure to reduce the prior knowledge, and combines classification and regression branches to increase the tracking accuracy. SiamFC++ extracts the deep feature map of the search regions and the template regions, respectively, through backbone network, and inputs the feature maps into the regression head and classification head, respectively, to obtain the similarity map, where the highest scoring position represents the object position. The similarity map is the degree of similarity between different positions of the search image and the template. As shown in Herein, the purpose of the arbiter is to determine whether the tracker fails. We need to reposition the object once the tracking fails. The main matching filter arbiter based on the candidate object histogram determines whether distractors exist. The transfer arbiter determines whether the object is transferred based on the change of the object in relative position, and finally, both together determine whether the tracker is not working.Considering the observation that the similarity map shows two highlighted areas corresponding to the distractor and the object, respectively, when the distractor is presented, we attempt to arbitrate the existence of the distractor using the histogram of the distance between the region centroids. Let The matching filter arbiter could determine whether the distractor exists, but it could not determine whether the object is displaced by the distractor. As shown in The framework of the transfer arbiter is shown in The object needs to be relocated once the tracker fails. We propose a corrector consisting of dynamic template update, assignment algorithm, and GMSD. Updated by the similarity backtracking, the template set is to find the previous tracking results. The assignment algorithm is used for selecting the winner set, which is similar to the object. Finally, the object is relocated by computing the GMSD between the template set and winner set.In long-term tracking, a single template cannot handle the changes of object appearance, such as: (1) when the object appearance changes gradually, the error accumulates and finally the object cannot match the template well, and (2) when the object appearance changes suddenly and drastically, the object is very different from the template. Therefore, we propose a template update procedure that automatically adds the result different from the template into the template set, so that the diversity of the template set can be enriched. The template update mechanism is to find the target with the lowest similarity score when the target is lost by retracing the tracking failure process, i.e., the image with the largest change in appearance during the tracking process, and add this target to the template set.The process of generating the template set is shown in (1)M from Take an initial match (2)P from M and add non-matching edges of While there exists an augmenting path (3)Return Since there are lots of candidate objects, the corrector utilizes the Hopcroft–Karp algorithm  to selecWe obtained a complete match of Since the backbone of SiamFC++ has difficulty in distinguishing the distractor from the object, it is essential to choose another efficient algorithm to restart the tracker. We introduce the gradient magnitude similarity deviation (GMSD) to relocate the object. GMSD can distinguish the object by its appearance and structure, and only uses the gradient magnitude as a feature to generate a highly accurate score. It can precisely locate the objects that are similar to the template in the case of similar semantic information. The calculation of GMSD is shown in the following Equations.We used GoogLeNet as the backbone network of SiamFC++. The number of candidate objects In our experiments, OTB2015, VOT, LaSOT, and GOT-10k are adopted as our training dataset. OTB2015 Benchmark OTB2015 includes 100 videos, and VOT Benchmark VOT2018 consists of 60 videos with challenging factors such as deformation and occlusion. LaSOT is a long-term tracking dataset with 1400 video sequences, which can be divided into 70 categories. The training set of the GOT-10K dataset consists of 10,000 video sequences, which is generally a single-target tracking algorithm evaluation dataset. We followed the protocol of GOT-10k and only trained our tracker on the training subset.To demonstrate the effectiveness of the arbiter, the tracking invalid accuracy ratio (TIAR) on each dataset was calculated, which is the percentage of all tracking failure scenarios that were judged correctly. Moreover, in the verification experiment, the tracking valid accuracy ratio (TVAR) on each dataset was calculated, which is the percentage of all successful tracking scenarios that were judged correctly.As shown in We compared our proposed tracker with some of the state-of-the-art trackers on four tracking benchmarks, as shown in OTB2015 Benchmark OTB2015 provides a standard evaluation benchmark for trackers. A comparison with state-of-the art trackers is shown in LaSOT Benchmark LaSOT contains 1400 videos, which is a high-quality, large-scale dataset for long-term tracking. By relocating the lost objects, the tracker reached the top performance with a success score of 0.575, which shows that our tracker also has a good performance in difficult scenarios.GOT-10k Benchmark GOT-10k contains a lot of small objects and they become smaller as the objects move and the viewpoint changes. It causes our tracker to fail to capture the real object when the tracker fails, which keeps the tracker from achieving a better performance.In this paper, we proposed a Siamese network based on trackers with a generic arbiter-corrector module. It could resolve the tracking failure problem caused by the appearance changes of objects and distractors. The arbiter proposed an efficient architecture based on the match filter that determines whether the tracker has lost the object. The template is updated to increase the tracker’s resistance to interference. The corrector repositions the object by GMSD and dynamic template set. The generic arbiter-corrector module can be easily integrated into other trackers. The associated experiments show that the proposed arbiter-corrector mechanism is effective in improving the accuracy of the tracker. The next step of this study will introduce a self-supervised contrast learning method to construct an efficient online learning tracking corrector to further improve the tracking accuracy and real-time performance.