The increasing popularity of portable smart devices has led to the emergence of vehicular crowdsensing as a novel approach for real-time sensing and environmental data collection, garnering significant attention across various domains. Within vehicular crowdsensing, task assignment stands as a fundamental research challenge. As the number of vehicle users and perceived tasks grows, the design of efficient task assignment schemes becomes crucial. However, existing research solely focuses on task deadlines, neglecting the importance of task duration. Additionally, the majority of privacy protection mechanisms in the current task assignment process emphasize safeguarding user location information but overlook the protection of user-perceived duration. This lack of protection exposes users to potential time-aware inference attacks, enabling attackers to deduce user schedules and device information. To address these issues in opportunistic task assignment for vehicular crowdsensing, this paper presents the minimum number of participants required under the constraint of probability coverage and proposes the User-Based Task Assignment (UBTA) mechanism, which selects the smallest set of participants to minimize the payment cost while measuring the probability of accomplishing perceived tasks by user combinations. To ensure privacy protection during opportunistic task assignment, a privacy protection method based on differential privacy is introduced. This method fuzzifies the sensing duration of vehicle users and calculates the probability of vehicle users completing sensing tasks, thus avoiding the exposure of users’ sensitive data while effectively assigning tasks. The efficacy of the proposed algorithm is demonstrated through theoretical analysis and a comprehensive set of simulation experiments. In recent years, the widespread adoption of portable smart IoT devices has become an integral part of people’s lives ,2. TheseTask assignment stands as a critical research aspect in the realm of vehicular crowdsensing ,13,14,15Most of the existing research ,21,22 taPrivacy protection concerns in task assignment also hold significant importance ,26,27. VRecently, researchers have proposed several methods to address user privacy protection in vehicular crowdsensing. To et al.  introducTo sum up, this paper focuses on the space–time characteristics of vehicular crowdsensing and conducts research on task allocation in this context. Additionally, it designs a privacy protection mechanism to safeguard vehicle users’ sensitive data while ensuring efficient task allocation. The research encompasses two main areas: probabilistic task assignment with a probabilistic coverage constraint in vehicular crowdsensing, and privacy protection in the task assignment process. By addressing these aspects, this study successfully resolves the issues of ineffective task assignment caused by neglecting the spatio-temporal characteristics of users and tasks. Moreover, it tackles the problem of user-sensitive data leakage, resulting from the oversight of privacy protection concerning users’ perceptual time in the task assignment process of spatio-temporal-related vehicular crowdsensing.Task assignment stands as a crucial research aspect in vehicular crowdsensing. It involves the rational allocation of perceived tasks to vehicle users by servers, considering system optimization objectives and real-world constraints. And the research delves into the trade-off between cost and benefit, representing two opposing factors. Li et al.  considerHowever, the majority of existing research only focuses on the deadline of the perceptual task, disregarding the working time of the vehicle user during task execution. Furthermore, few studies take into account both the space–time constraints of vehicle users and perceived tasks. In a cluster-aware system, vehicle users typically possess different route budgets and time budgets. Additionally, sensory tasks are linked to specific locations and sensing duration. As the complexity and scale of perception systems increase, the corresponding optimization problems for task assignment is NP-hard, making it challenging to find effective optimal algorithms. In such cases, suboptimal algorithms need to be considered. Hence, given the unique characteristics of task perception duration and the space–time constraints of users and tasks in spatio-temporal correlated vehicular crowdsensing, there is a critical need to thoroughly investigate the spatio-temporal-related task assignment problem. The objective is to achieve optimal task assignment while considering the intricate real-world space–time constraints. In addition, none of the above works take into account the protection of user privacy, which will affect the effectiveness of task assignment.In the task assignment process of vehicular crowdsensing, vehicle users often share data with the platform through wireless access points or cellular infrastructure, which involves many sensitive data . These sensitive data may leak users’ daily travel or real identity, resulting in a significant reduction in users’ motivation to participate in perceived tasks. In recent years, some research work has focused on the issue of privacy protection in the process of task assignment for vehicular crowdsensing. Zhang et al.  assumed The current research on privacy protection during the task assignment process for vehicular crowdsensing is still in its early stages. While some mechanisms have been proposed, they suffer from issues like high computational costs, vulnerability, or reliance on trusted third-party platforms. Moreover, the existing privacy mechanisms in task assignment predominantly focus on safeguarding user location information, overlooking the protection of user perceived time. However, it is crucial to consider the privacy of user-perceived time in space–time-related cluster awareness systems since attackers can potentially infer user schedules and device information through these data. Therefore, there is a pressing need to delve deeper into privacy protection issues in the task assignment process for space–time-related vehicular crowdsensing. This research aims to achieve optimal task assignment while ensuring the fulfillment of users’ privacy protection requirements.In this paper, we mainly focus on the spatio-temporal-related vehicular crowdsensing, in which the perception task is not only located in a specific spatial region, but also needs a certain amount of sensing time to complete. In this model, vehicular crowdsensing aims to recruit vehicle users who can dedicate a specific duration to perform tasks effectively. For instance, in application scenarios like crowd monitoring, air quality assessment, and noise level detection, the perception tasks necessitate vehicle users to collect data  within a certain time frame to obtain sufficient and meaningful information.The environmental department of the municipal government has planned an air quality monitoring project to update the air quality index every hour throughout the day. However, due to the high costs associated with deploying, maintaining, and consuming energy for basic monitoring equipment, the municipal government decided to leverage vehicular crowdsensing to accomplish the task. The project aims to recruit vehicle users equipped with smartphones, who will install a specific application to perceive air quality. To execute the project effectively, the sensing area is divided into 45 regions based on signal tower coverage. Each day is further divided into 10 sensing cycles, spanning from 8:00 to 18:00, with each cycle lasting for 1 h. About 1000 smartphone users have agreed to participate in the two-week air quality sensing project. Each selected vehicle user is responsible for sensing air quality in a specific area and transmitting the collected data through the designated signal tower. The project’s objective is to ensure that the tasks performed by the recruited users cover at least 90% of the 45 areas in all sensing cycles. Consequently, in each sensing cycle, no fewer than 41 air quality monitoring tasks should be completed. To minimize the total project cost while ensuring the perceived quality, the municipal government intends to select the minimum number of users from the pool of 1000 candidates. For this purpose, the municipal government obtained the two-week call records of the 1000 candidates  with the assistance of telecom operators, after obtaining the consent of users.As shown in i and the sensing area a, it is said that the area a is covered in the cycle i. If a vehicle user goes to multiple sensing areas and completes the sensing tasks in these areas in the sensing cycle i, it is said that these sensing areas are covered in the sensing cycle i. Therefore, the goal of this study is to give a group of call records and confused residence time data of vehicle users, select the minimum number of users, and meet the space–time coverage constraint of the specified proportion, that is, in all sensing cycles, the proportion of the covered sensing area should be equal to or greater than the set coverage threshold.As can be seen from the above examples, the goal of this research work is to select the smallest set of participants for the perception task, and ensure that in each sensing cycle, there is a sensing area that is not lower than the predefined coverage. We propose a vehicular crowdsensing opportunistic task allocation problem. The main goal is to minimize the total incentive cost while satisfying the predefined coverage constraints. In the described model, the project can exist for a period of time , including multiple sensing cycles, such as 10 cycles per day, from 8:00 to 18:00, each cycle of 1 h. We set that, if a vehicle user completes the sensing task in the sensing period A, the call records , and dwell time data of all vehicle users, we define R is the preset coverage threshold and N is the number of sensing cycles. Due to the fact that we cannot know in advance when vehicle users will appear and in which sensing area to perform sensing tasks  Calculate the probability that each user makes at least one call in a specific sensing cycle and sensing area. First, map the historical call record of each user to u in the sensing cycle i and sensing area a is not less than the sensing duration required by the task. Finally, the probability (2) Calculate the probability that each user’s residence time in a specific sensing cycle and sensing area is equal to or greater than the sensing duration required by the task. What the vehicle user uploads is the residence time after confusion, and the sensing tasks concerned in this paper are all time-dependent tasks . Therefore, it is necessary to calculate the probability According to the user mobility data obtained in the first stage, we propose a user utility-based task assignment mechanism (UBTA), which iteratively selects participants by calculating the utility of the user portfolio, which is divided into three steps:(1) Select the most effective user among all candidate vehicle users, and add the user to the recruited user set.(2) Among the remaining non-recruited vehicle users, select the user who has the greatest utility after combining with the recruited vehicle users, and add this user to the recruited user set.(3) Continue to select and add new vehicle users until the recruited user set can cover the sensing area of the preset threshold in each sensing cycle.u makes n calls in the sensing area u in sensing area a in sensing period i. For example, in order to estimate i from 08:00 to 09:00, we will calculate the average number of calls made by vehicle user u in sensing area a from 08:00 to 09:00 in historical call records. Therefore, the probability that the vehicle user u makes at least one call in the sensing area a during the sensing period i can be calculated as follows:In this section, users utilize the Laplacian mechanism to add noise to their own residence time, and then upload the confusing residence time instead of the real residence time to the platform to protect their privacy. In this process, only the platform and the users are aware of the privacy protection mechanism, so the attackers cannot infer from the residence time which user completed the task. At the same time, based on the fact that the platform is not interfered with by confusing data, the User6Based Task Allocation (UBTA) algorithm that we propose selects the smallest set of participants to minimize the payoff cost while measuring the probability of performing the tasks perceived by the user combinations. Moreover, the Poisson distribution, commonly used in queuing theory, is employed in this research. In real-life scenarios, numerous situations adhere to the Poisson distribution, such as passengers arriving at an airport or calls received by a customer service desk. Similarly, the Poisson distribution finds relevance in the domain of cellular networks. For this study, we assume that the call sequence adheres to a non-homogeneous Poisson process. Consequently, we model the probability of each vehicle user completing each sensing task based on the Poisson distribution. In the sensing period u in the perception area a during the sensing period i, and In this paper, the sensing time of vehicle users plays a crucial role in determining whether a task can be successfully completed. The sensing task is considered effectively completed only when the vehicle users reach a specific perception area and remain there for a duration equal to or exceeding the required perception time. To facilitate accurate and efficient task assignment, vehicle users can submit their stay time in the sensing period and area to the platform. However, privacy concerns arise due to potential malicious attackers who may infer daily habits, tracks, and other sensitive information from the real stay time, leading to privacy risks. To address this issue, this paper employs the Laplacian mechanism, which locally confuses the residence time. Subsequently, vehicle users upload the fuzzy residence time instead of the actual residence time to the platform, thereby safeguarding their privacy. We use Considering the noise added to the residence time, we transform the problem into the probability that the fuzzy residence time is greater than the perceived duration. When the sensing duration required to define the perception task is u in perception cycle i and perception region a not less than the sensing duration required by the task according to the fuzzy residence time As a result, the platform can calculate the probability i and sensing area a, that is, the probability that sensing area a is covered by vehicle user u in sensing cycle i. In addition, Based on the above calculation process, we can obtain the probability Next, we calculate the utility of users. Given all candidate mobile user set The task assignment mechanism based on user utility calculates the utility of each combination set, selects the combination set with the maximum utility, and continues the next iteration until the stop criterion is met. After obtaining the set of combinations with maximum utility After obtaining the probability vector calculated based on the aggregation of the maximum utility user group, the algorithm identifies the minimum probability value within the vector. It then compares this minimum probability value with the given stop threshold. If the minimum probability is greater than or equal to the stop threshold, the combination set returned will be considered as the final user set selected by the algorithm. On the other hand, if the minimum probability falls below the stop threshold, the algorithm will use the combination set as the selected participant and initiate the next iteration. To summarize, the algorithm iteratively repeats the process until it finds a combination set with a minimum probability value greater than or equal to the stop threshold. This set will then be used as the final selected user set.Given the number of users In this section, we evaluate the proposed UBTA algorithm, first design the greedy algorithm for comparison, then introduce the experimental settings, and finally give the detailed experimental results between the UBTA algorithm and the comparison method.For the task assignment problem in this chapter, we designed a greedy algorithm (GA), whose basic idea is to select from all unselected vehicle users in each iteration the user that covers the most perceived area in the history of call records until the set probability threshold is reached and the cycle stops. We will compare the UBTA algorithm with the GA algorithm in subsequent experiments.This paper conducts an analysis and study of passenger flow patterns at various passenger hotspots during different time periods by mining GPS historical data from taxis. The dataset used comprises GPS historical data from 4000 taxis in Shanghai, collected over the course of one month. To account for the distinct travel patterns of residents on working days and weekends, the dataset is divided into two subsets: one for working days and the other for weekends. With the massive GPS historical data available in these subsets, this study quantifies the number of passenger-carrying events occurring at different time periods within the passenger hot spot areas. To predict passenger flow in various regions, the Gaussian process regression algorithm is employed. Ultimately, these predictions aim to enhance the efficiency of taxi passenger transportation.The setup for our study is as follows: we set the number of perception areas, denoted as It is worth noting that, when the coverage default is 50%, there is little difference between the number of vehicle users recruited by the UBTA algorithm and the GA algorithm. Therefore, we compared the vehicle users selected by the two algorithms when the coverage preset was 95%, 85%, and 50%, respectively, and calculated the proportion of common users recruited by the two algorithms . As shown in First, Next, we set the coverage default to 95% and compared the process of selecting vehicle users by UBTA and GA. Finally, we test the effectiveness of the two algorithms, that is, test data are used to test whether the participants recruited by the algorithm can reach the pre-set coverage. In this paper, we address the task allocation challenge in vehicular crowdsensing through an opportunistic approach based on the real-world scenario. We propose a user utility-based task allocation algorithm that involves several key steps. Firstly, we predict the mobility of users to understand their movement patterns. Next, we calculate the utility of various user combinations to assess their effectiveness in completing tasks. Additionally, we measure the probability of sensing task coverage for each user combination. Based on these calculations, we determine the set of participants with the minimum number of users required for optimal task allocation. To protect user privacy, we employ differential privacy technology. Users upload their residence time data with Laplace noise, ensuring that their sensitive information remains secure. The platform then analyzes user mobility by solving the probability problem of continuous random variables, utilizing the fuzzy residence time. The proposed algorithm is further analyzed theoretically, including time complexity and efforts to reduce the computational complexity of the coverage probability vector. Finally, we conduct experimental evaluations to demonstrate the effectiveness of the proposed algorithm.


Prestressed girders reduce cracking and allow for long spans, but their construction requires complex equipment and strict quality control. Their accurate design depends on a precise knowledge of tensioning force and stresses, as well as monitoring the tendon force to prevent excessive creep. Estimating tendon stress is challenging due to limited access to prestressing tendons. This study utilizes a strain-based machine learning method to estimate real-time applied tendon stress. A dataset was generated using finite element method (FEM) analysis, varying the tendon stress in a 45 m girder. Network models were trained and tested on various tendon force scenarios, with prediction errors of less than 10%. The model with the lowest RMSE was chosen for stress prediction, accurately estimating the tendon stress, and providing real-time tensioning force adjustment. The research offers insights into optimizing girder locations and strain numbers. The results demonstrate the feasibility of using machine learning with strain data for instant tendon force estimation. The monitoring of precast construction is gaining attention nowadays . Among pPrestressed concrete structures have had a significant impact on infrastructure networks. However, the prestressing process can be challenging to implement due to the need for specialized equipment, skilled labor, and strict quality control measures . The lacMonitoring the tendon force is essential to assessing the health and quality of prestressed concrete (PSC). Over time, the prestressing force in tendons may be reduced due to the long-term effects on prestressing steel. Variations in prestressing stress compared to design strength can result in cracks, creep, or shrinkage in the structure . If thisIn addition to quality control, the prestressing technique is often used to achieve the desired camber for girders by applying the required tendon force . Camber The accurate estimation of deflection and strain values is essential for evaluating the serviceability of prestressed bridges. Several methods have been used to estimate prestressing force and observe its effects on various parameters ,19. J. HIn general, two approaches are commonly used for monitoring prestressed structures: the direct onsite monitoring of prestressing tendons and using FEM. The onsite monitoring of prestressed girders can be carried out using strain-based methods ,23,24,25A more advanced approach to estimating structural stresses in real-time is to use machine learning (ML) models, also known as surrogate models, to replace computationally expensive nonlinear numerical simulations . A surroThe current study presents a novel framework that employs machine learning techniques to the enable immediate estimation of tendon stress based on strain data. The novelty of the research is the use of strain data from girders with bonded tendons to predict tendon stress in real time. The bridge girder’s finite FE model was created based on field observations. Three ML models, namely random forest (RF), support vector regression (SVR), and artificial neural network (ANN), were trained using the dataset obtained from the FE model, which was validated using analytical calculations. The proposed model demonstrated the most exceptional performance, and hence it was utilized to make accurate predictions of tendon stresses, affirming the effectiveness of the proposed tendon stress estimator. The ANN-based calculator enabled real-time stress estimation on new data and provided insights into the significance of various sensor permutations for optimizing the sensor number and location.The proposed tendon stress estimation model comprises two main components: FEM and machine learning (ML). The proposed framework is illustrated in In some cases, the most critical areas of a structure or material may experience high deformation or stress. It is essential that the sensors are placed in these locations to capture accurate measurements. The high-stress regions of symmetrical structures can be assumed; however, the stress distribution differs for unsymmetrical members, and the assumption cannot be made easily. Therefore, the surrogate model framework also provides information regarding the best location and number of strain gauges to be installed, based on identifying the essential features in the ML model.The selection of the girder was based on two factors. Firstly, the research required using a bonded tendon girder, which was a prestressed concrete beam with bonded tendons running along its length. Secondly, the girder was selected from available girders on the field to validate the accuracy of the FEM model by comparing the results with the analytical solutions that the field experts performed.The specific girder chosen for the study was a 45 m long I-beam girder, as illustrated in The I-beam girder featured four parabolic bonded tendons anchored at both ends. These tendons allowed the prestressed force to create a camber at the midspan of the girder. This means that the girder had a slight upward curve in the center, which helps to counteract the sag that would otherwise occur due to the weight of the girder itself and any additional loads it may be supporting.The provided CAD drawings were used to develop a three-dimensional FEM model  of an I-The main parts of the model consist of the concrete I-beam, steel rebars and tendons. The girder was modeled as C3D8R, an eight-node linear brick element that has six faces and four integration points per face. In terms of deformation capabilities, the C3D8R element can undergo plastic deformation, exhibit large strains, and can handle material nonlinearity. It can also model crack propagation, contact behavior, and damage evolution. Meanwhile, a T3D2, a three-dimensional, two-node truss element, was used to model the reinforcement of steel bars and pre-tensioned tendons. The interaction between the steel and concrete was modeled as surface-to-surface contact, with embedded constraint properties. The girder was modeled as a simply supported beam with one end hinged and the other end set as roller support. The diameter of the steel bars was kept at around 16 mm. The four bonded tendons were designed using a truss element following a parabolic curve and represented by embedded constraints. Prestressing was applied to each tendon using a predefined field, with the tendon stress involved in the x-direction specified as sigma11 in Abaqus FEM, along the length of the girder. A fine meshing of 50 mm in size was assigned to the structure. An implicit scheme was utilized by performing a static linear analysis under gravity load, allowing the model to deform in all directions. The details for process of girder analysis are presented in the The FEM model of the bridge girder was validated using analytical solutions obtained from the field. The formulas used to compute the tendon force fpt≤0Based on the analytical solutions, a tendon stress of approximately 1109 MPa was applied as initial prestressing, less than the tendon stress limit of 1488 MPa provided by Equation (4). The stress in concrete immediately after the introduction of prestress to the girder and the resulting deflected shape is shown in The analytical solutions were compared with those obtained from the finite element model, and the differences were negligible. This demonstrates the validity of the finite element model. The comparison results are summarized in An investigation of the statistical properties of the material strength of the concrete, rebar, and tendon strand commonly used in domestic construction sites was performed by Paik et al.  in orderThe Abaqus script was used to generate a total of 5000 data points, with the elastic modulus (EM) and tendon stress (TS) serving as input parameters, resulting in strain values at the locations S1, S2, S3, S4, S5, S6, and S7, as shown in The data generation process involved varying the tendon stress within a range of 100 to 5000 MPa and the elastic modulus within a range of 20,000 to 50,000 MPa. Using the concept of reverse engineering, the generated data were split into input and output features for the ML models. The eight input features were the strains at locations S1, S2, S3, S4, S5, S6, and S7, as well as the elastic modulus, while the tendon stress was taken as the output label.Past research has shown that the accuracy of ML models that consist of decision trees is better than those that use artificial neural networks . TherefoSupervised ML models that rely on decision tree ensembles, such as RFR, are commonly employed for regression analysis. In contrast, SVR is a supervised ML model that utilizes a hyperplane instead of a line to make predictions. In contrast, RFR does not require feature scaling .This study used a grid search method to determine the optimal parameters for the ML models, including RFR and SVR. The grid search was conducted using the sci-kit-learn Python library, and the models were evaluated based on their mean square error or accuracy for each combination of hyperparameters. In addition to these models, an artificial neural network (ANN) model was also trained to compare the performance of each model in terms of percentage errors. The flow chart of the framework is shown in In this study, the ANN model’s hyperparameters were tuned to obtain a minimum mean square error score. The ANN architecture comprises a single input layer, two hidden layers, and one output layer. The number of hidden layers was determined based on the model performance and overall comparison of the model with other ML models. A total of 128 neurons for the first hidden layer and 512 neurons for the second hidden layer were finalized; refer to The architecture of the ANN utilizes Relu and linear activation functions. The optimization process utilized the Adam optimizer with a learning rate of 0.001, a batch size of 256, and early stopping at the lowest validation score at epoch 606. The advantage of using the ML model is its ability to make predictions very quickly compared to the FEM model, making it ideal for applications in which real-time predictions are required, such as structural health monitoring.In order to train the ML models, the dataset was divided into training and testing subsets, where 80% of the data was allocated for training the model, and the rest was reserved for assessing its performance in the current study. The present study utilized the programming language Python and its commonly used libraries for code execution. By utilizing CPU and GPU resources, the conducted research effectively trained and evaluated the performance of the proposed ML models.In this section, the outcomes of the ML models for anticipating the tensile stress of bridge tendons are presented. The predicted values of the different ML models were in good agreement with the observed values. The RFR model, on the other hand, showed a better fit curve of the predicted versus actual values compared to the RFR model for both the training and testing datasets, as shown in In contrast, the artificial neural network model showed a better centered fit line than the other models in both the testing and training datasets c,f. The The reliability of the ANN model for the prediction can be attributed to its ability to generalize well. In addition, a good fit model is often characterized by residual plots, where the distance of the points from the zero line is small. Thus, the normal distribution of the residual plot displayed in Further, the performance evaluation of ML models is performed by utilizing the mean squared error (MSE) as the loss function , and it R2), RMSE, and mean absolute error (MAE) are some of the popular evaluation matrices used in this study (see Equations (6)–(8)). The R2 acts as a goodness-of-fit tool by describing how well a regression line fits the data points.The coefficient of determination  MSE increases the weight on large errors and is, therefore, more appropriate for the dataset used in this research. Additionally, the measurements obtained from RMSE are in the same units as the response variable, making it preferred for comparing the performance of ML models.The ML models utilized the three-fold cross-validation method to evaluate their ability to make predictions on new data, providing a more comprehensive understanding of the model’s performance.R2, RMSE, and MAE for the different ML models are summarized in R2 value of 0.9984, followed by the SVR model (R2 = 0.9971) and RFR model (R2 = 0.9717). The RMSE values for the training and testing data were similar, with a slightly low RMSE value for the training data, indicating that all the ML models were optimal. None of the models in this study were under-fit or over-fit, as the models were selected after hyperparameter tuning. However, when considering the RMSE values in R2 score. Therefore, the ANN model was selected to predict the tendon stresses in the stress calculator.The results of The performance of the ML models was compared with that of the finite element method model used for predicting the tensile stress of bridge tendons. The ML models were preprocessed and optimized to achieve high accuracy. All the models performed efficiently, with the ANN model showing the highest accuracy. The ANN model was then used to validate the prediction results using out-of-sample data as input values and was compared to the FEM results, which require more computation time for execution. The validation results are mentioned in The most important factor while observing any civil engineering structure under various loading conditions is its response in the form of strains or deflection. The strain values that show the most fluctuation in response to external loading can result in critical strain values, and the location of such critical strain values on a structure is of great importance. To observe the change in the girder strain values at different girder locations while changing the tendon stress, a graph is generated from FEM data for a particular elastic modulus value, as shown in In the present research, the inputs are mostly strain values, which are assumed to be obtained from the strain gauges attached at different locations to the bridge girder. To determine the most relevant features for evaluating the structure, the impact of each feature on the predictions of the trained model was estimated and ranked using the feature permutation importance method. This method involves randomly shuffling the values of a single feature and measuring how much the RMSE score increases as a result. Feature importance assigns a score to each feature in the provided data. The score reflects the degree of importance or relevance of the feature with respect to the output variable. The higher the score, the more significant the feature is to the output variable. As depicted in Based on the observations, the optimal sensor location can be predicted. For instance, the inputs S7 and S5 represent the strain values located at the mid-bottom and mid-top, respectively, of the girder , it is noteworthy to analyze the change in the tendon stress along the length of the girder caused by the loss resulting from the elastic shortening (ES), creep in concrete (CR), shrinkage in concrete (SH) and steel relaxation (RE) under the self-weight of the pre-tensioned prestressed girder during the initial stage, which has a duration of 30 days. The percentage loss for ES was 8%, and CR (7.5%), SH (3.2%) and RE (1.5%) were computed as per the ACI-ASCE committee 432 method . The totUpon cutting tendons, the initial loss of prestress in pre-tensioned concrete members occurs, and the prestressing force is transferred to the member. This transfer causes the simultaneous shortening of both the concrete and tendon, which is termed elastic shortening. The reflection of the losses during the initial stage of prestressing can be observed in the FEM analysis results, which clearly showed the reductions in the tendon stress caused by ES across the length of the girder due to the bond defined as embedded property between the prestressing steel and concrete. The average tendon stress at the anchorage location (support) and at the midspan were 1075 MPa and 1014 MPa; the significant loss of stress at the midspan was due to bending movements, since concrete and steel are treated as a single section once bonded, leading to a loss of 8.5%, which is close to the calculated loss of ES. Out of TL, the rest of the loss of 11.4% (127 MPa), due to other factors, was compensated by adding it to the initial prestressing and modifying the limit mentioned in Equation (4) to an Equation (9).The reduction in prestressing across the length after the FEM analysis and after the addition of TL is depicted in One of the promising outcomes of the developed framework is its ability to monitor the initial tendon stress so that it is within the limits, as per ACI 318-19 . EnsurinTo provide a more accessible method for estimating the stress in tendons during application, a more user-friendly approach is required. Therefore, for real-time tendon stress estimation, the stress estimator is proposed. The stress estimator takes, as input, the elastic modulus and strain values that are monitored in the field from the sensor and returns the tendon stress applied on the girder in real time. For safety purposes, the stress calculator considers the initial tendon stress limit provided in Equation (9). The predicted tendon stress is then compared to the stress limit to determine whether it is within the limit or not. If stress exceeds the provided limit, the user can issue a warning to check the design tendon stress during the prestressing process, ensuring quality control.In addition, the ANN tendon stress calculator displays the sequence of strain variations from high to low for strain gauges at different locations of the girder, and an optimum number of strain gauges is suggested. The strain at S7, located at the midspan of the girder, showed the highest strain fluctuation when the tendon stress was applied. Therefore, it is convenient to place the strain gauges at locations in which the strain varies the most. The user-friendly calculator can be used prior to sensor placement to best optimize the sensor location and number.This exploratory study presents some limitations based on simplifying a numerical model. The impact of environmental factors, such as humidity and temperature fluctuations, can influence stress and strains, which is one of the limitations of this study. The present study suggests the use of more real-world data in order to create accurate models that represent actual prestress losses.Further, the type of girder used can differ; therefore, for each girder type, there is a requirement for an updated FE model to provide a training dataset. Once the model is trained, the tendon stress is easily estimated using the proposed framework.The ANN-based tendon stress calculator can be modified for future use as an application that receives sensor data from the cloud, predicts the stress values, and suggests critical strain values to give a warning for safety assessment, and can propose optimal gauge number and locations.The present research demonstrates the feasibility of using an ANN-based surrogate model framework to predict the stress in the tendons of a bridge girder. The research implemented a novel approach involving machine learning-based tendon stress estimation and strain gauge optimization in real time using the strain data from the FE model as inputs to a ML model.R2 values of 0.998 and 0.997 for the training and testing datasets, respectively. The average prediction error or MAE was less than 10% for the ANN and SVR depicting the sound prediction of the models. However, the ANN model with the lowest RMSE values demonstrated the best performance; therefore, it was selected for the surrogate model framework.Among other models, the ANN has the most accurately generated The proposed surrogate model framework using ANN estimated the tendon stress in real time, with only a 0.4% difference between it and the FEM model, where mostly strains at different girder locations were specified as inputs. The ANN-based tendon stress calculator showed a practical benefit of using the proposed framework, via the addition of the computed prestress loss (11.4%) to the predicted results. The added loss compensated for the losses expected on the field, and the estimated stress was compared with the standard limits for quality assurance and structure safety. The present framework can be utilized in situations where only strain data are available to monitor the tendon stress for the purposes of structural health monitoring.Further, the proposed model utilizes permutation importance to select appropriate locations and the number of strain gauge to be installed. The sensor with the most strain variation was found to be located at the midspan (S7), as expected from the behavior of a simply supported girder bridge. Therefore, the sensors can be placed at locations where there is more strain variation. In the present research, three strain gauges were suggested at locations S7, S5 of the midspan, and S2 at the support, thereby providing the advantage of improved structural health monitoring and reducing unnecessary gauge installment.The proposed surrogate model is a feasible and quick means of tendon stress estimation. The framework can be utilized for issuing warnings during the prestressing process to keep tendon stress within specified limits. In the present scenario, during the prestressing process, it is crucial to monitor the tendon stress in real time to check whether it is within the standard limits or not to avoid any consequences due to over or under-prestressing. Apart from the adaptability, the ML models are easy to use, making them accessible to a wide range of users. The research focuses on the efficient use of the ML model to replace FEM models for the tendon stress estimation of bridge girders. Tendon stress estimation benefits the industry by enhancing the safety and reliability of prestressed structures.An application that utilizes the Internet of Things (IoT) to monitor girders during prestressing in real time is recommended as future work.


As deep learning is widely used in the radiology field, the explainability of Artificial Intelligence (AI) models is becoming increasingly essential to gain clinicians’ trust when using the models for diagnosis. In this research, three experiment sets were conducted with a U-Net architecture to improve the disease classification performance while enhancing the heatmaps corresponding to the model's focus through incorporating heatmap generators during training. All experiments used the dataset that contained chest radiographs, associated labels from one of the three conditions , and numerical information regarding a radiologist's eye-gaze coordinates on the images. The paper that introduced this dataset developed a U-Net model, which was treated as the baseline model for this research, to show how the eye-gaze data can be used in multi-modal training for explainability improvement and disease classification. To compare the classification performances among this research's three experiment sets and the baseline model, the 95% confidence intervals (CI) of the area under the receiver operating characteristic curve (AUC) were measured. The best method achieved an AUC of 0.913 with a 95% CI of . “Pneumonia” and “CHF” classes, which the baseline model struggled the most to classify, had the greatest improvements, resulting in AUCs of 0.859 with a 95% CI of  and 0.962 with a 95% CI of , respectively. The decoder of the U-Net for the best-performing proposed method generated heatmaps that highlight the determining image parts in model classifications. These predicted heatmaps, which can be used for the explainability of the model, also improved to align well with the radiologist's eye-gaze data. Hence, this work showed that incorporating heatmap generators and eye-gaze information into training can simultaneously improve disease classification and provide explainable visuals that align well with how the radiologist viewed the chest radiographs when making diagnosis. Complex deep learning models have been more recently incorporated into clinical radiology practices and have given promising results to assist radiologists in identifying and classifying various diseases and abnormalities, such as pneumonia and congestive heart failure (CHF) . NeverthHence, the explainability of Artificial Intelligence (AI) models that shows the part of the model's inputs or the kind of information the models focused on when making predictions is crucial for the radiology field to gain and increase radiologists', patients', and regulators' trust in the use of the models for diagnosis , 5. The The methods to establish the explainability of the models can involve different data types, such as mathematical computations, texts, or visualization with heatmaps or saliency maps . In the Currently, there are several studies on using deep learning models for disease classification that also involve heatmap generation to visualize where the model's focus was on the given input CXR image , 11. NonTo increase the classification performance and the explainability of AI models while mitigating such dataset and labeling limitations, this work proposes and tests three different methods that use a U-Net-based  model. TAlthough the proposed models, mostly had similar overall average classification performances as the baseline model that did not use heatmap generators in the training process, there were greater improvements in classifying the “CHF” and “pneumonia” classes, which were the classes the baseline model struggled to correctly classify. Moreover, one of the proposed models had a superior improvement in both the overall average classification performance and the performances on “CHF” and “pneumonia” classes.- This research introduces three experiment sets that uniquely use gradient-based heatmap generators, such as deconvNet, and a radiologist's eye-gaze data during models' training.- This study shows the experiment sets improved the classification performance of the AI model, especially for “pneumonia” and “CHF” classes. Hence, the proposed model was able to decrease the number of false negatives with the use of heatmap generators and eye-gaze data.- This research conveys that the use of the heatmap generators and eye-gaze data can further enhance the explainability of the model by training the model to observe the input images in a similar manner to how the radiologist views them. Such enhanced explainability for the improved classifier can increase trust in the use of these AI models among clinicians and patients.The followings are the key contributions of this research:This section reviews the notion of the “explainability of AI” used in this study. Furthermore, two prominent paths of incorporating explainability into AI for radiology are specified, which include visualizing with saliency maps and training deep learning models to directly generate attention maps as one of their outputs. In this research we only consider spatial explainability because it is correlated with the eye-tracking data available. Thus, the literature review is focused on the spatial explainability of AI models.The concept of “explainability of AI” is often defined as the ability of someone to understand and see which extracted features of the input data used by an AI model contributed to the model's predictions , 2, 5. IThere are two major key methods to showcase the explainability aspects of AI models for the radiology field when using chest radiographs as a part of a model's training. Firstly, various saliency maps  generation methods can be incorporated within or after training a deep learning model to highlight the areas of the input chest radiographs the model's parameters focused on when making predictions. Secondly, there are deep learning models that were developed to simultaneously operate disease classification and heatmap generation using image segmentation.Saliency maps show the parts of the input image that contributed most to the model's output predictions . Some ofProcedures for deconvNets and GBP are quite similar where the difference between them is the way each backpropagates through ReLU non-linearity. DeconvNets run the usual back-propagation by using transpose convolution and undoing pooling operations, and they back-propagate only the positive error signals for the ReLU activation .GBP maps are produced through the combination of the deconvolution and back-propagation methods. The deconvolution part shows which pixels contributed positively to the model's output through selectively back-propagating the positive component of the gradients between the input and the output of the models; meanwhile the back-propagation part restricts the model to consider only the positive inputs, which can result in GBP maps having more zeros in the outputs than DeconvNets , and henCAM  is anothThere are several modifications and improvements made on CAM for image analysis and computer vision tasks. For example, Pyramid Localization Network, also known as PYLON,  was deveBecause CAM can only be produced using a specific set of CNN models, such as those without fully connected layers, Grad-CAM  was propThere are multiple variations of grad-CAM, including guided grad-CAM  and GradSmoothGrad  is a metDeepLIFT (Deep Learning Important FeaTures)  also useUnlike the use of gradient-methods and back-propagation related methods for explainability, LIME   creates Although there is much debate about the true effectiveness of saliency map generation, the output maps give insights into how a model arrives at its prediction output, and the maps are often used post-training to visualize the model's attention on test data.As opposed to the above heatmap generating methods that can be inserted during or after training AI models, there are several studies involving constructing deep learning models or pipelines that focus on generating heatmaps as part of the model's outputs and on operating localization tasks. One of the more widely used model architecture for image segmentation tasks is U-Net , as it cTo tackle the localization problem in the case where the annotated datasets are not large, the use of the combinations of different techniques, such as a classifier and a localizer that produces bounding boxes and probability heatmaps, is shown to be effective . Some noFor example, a proposed weakly supervised learning method in  consistsAs another example, a self-transfer learning framework introduced in  consistsAlthough saliency maps are often produced and analyzed post-training, there are several architectures that incorporate attention maps and map-generating mechanisms in model training to improve explainaibility and classification or segmentation performance, such as those introduced in –36.Kazemimoghadam et al.  incorporUnlike how  focuses Wang et al. , on the Li et al.  also devOverall, there is no one single architecture that outperforms others in terms of multi-task classification and segmentation especially for medical domain, but prior work shows that ensemble learning or multi-stage training performs better in general for the multi-tasking . AdditioThis section first gives an overview of the dataset  used forTo incorporate the heatmap generators and radiologist's eye-gaze data on CXR images when training deep learning models, this work used a dataset that contains 1,083 chest radiographs, which preserve the high image quality as DICOM files. The images were reviewed and reported by one radiologist . The datThe eye-tracking data was used to teach the model about how radiologists observed the CXR images. Thus, the eye-gaze coordinates and fixation data were utilized to generate temporal and static eye-gaze heatmaps   in addition to the average AUC values were measured for each of the three class labels over 55–60 samples with resampling for 30 iterations using the test set.For the first proposed model set, the segmentation loss was computed using heatmaps generated from the different generators (which included GBP and deconvNet) during the training time against the static eye-gaze heatmaps obtained from the dataset, which were treated as ground truth, as can be seen in The second proposed model set was run with another modification to the network training when computing the segmentation loss. In contrast to the previous proposed model that computed the segmentation loss using the heatmaps generated from either GBP or deconvNet and the static eye-gaze heatmaps, the segmentation loss for this proposed model was computed using the differences between the outputs of the U-Net's decoder and heatmaps generated from either GBP or deconvNets, as can be seen in Since the previous two proposed model sets did not focus on training the model's decoder to generate predicted heatmaps that appear similar to the gound-truth static eye-gaze heatmaps, the third proposed model set used a weighted average of two segmentation losses, where one of which was computed using the differences between the U-Net's generated masks and the dataset's static eye-gaze heatmaps, while the other loss was computed using the differences between the heatmaps derived based on GBP or deconvNet and the dataset's static eye-gaze heatmaps as shown in For the first experiment set, the use of GBP as the heatmap generator when computing the segmentation loss resulted in the highest average AUC values compared to the AUC values obtained using deconvNet and the baseline AUC values as can be seen in As can be seen in Similarly to the first proposed model set, the GBP method performed the best compared to the baseline and the deconvNet method for the proposed model set 2. Furthermore, the outcome of using GBP for this had a slight improvement in the average AUC value compared to the first one. The greatest improvement occurred for the “pneumonia” class AUC, with 6.9% increase in AUC, which contributed to the 2.5% increase in the average AUC values when using GBP compared to the baseline AUC values.For this experiment, the U-Net was trained so that the decoder would attempt to mimic the heatmaps derived from the GBP or deconvNet when outputting its predicted heatmap, which can be observed in the rightmost images Although the U-Net's predicted heatmaps appeared to not mimic the heatmaps derived using GBP or deconvNet, there seems to be a correlation among the heatmaps' intensity differences and the differences in the U-Net's predicted heatmaps' intensity and in the locations of focus when using different heatmap generators. Additionally, there was a correlation between the greater intensity of the calculated heatmaps from GBP or deconvNet and the predicted heatmaps and the higher average AUC values when comparing the use of GBP and deconvNet, which can be seen in This experiment with the combination of two segmentation losses incorporated the heatmap generators in training time to guide the model's parameters to focus on similar areas as how the radiologist viewed, while guiding the model to produce predicted heatmaps that look similar to the static eye-gaze heatmaps for explainability purposes.As can be seen in On the contrary, the use of GBP for this segmentation loss computation had improvements in most of the AUC values, and the model's decoder was also able to generate the predicted heatmap that highlighted similar areas as the static eye-gaze heatmaps as shown in the top row of Overall, the vividness of the heatmaps derived using GBP or deconvNet and the similarity between the U-Net's predicted heatmaps and the dataset's static eye-gaze heatmaps seemed to be correlated with how well the average AUC values improved for the experiments. This further confirms that the radiologist's eye-gaze information is valuable in improving the classification performance when used with the heatmap generators during model training for multitasking.AI models for radiology are improving dramatically for disease classification or localization tasks, but there is often a trade-off between performance and explainability, as higher performing models tend to be deeper and more complex. Hence, explainability for AI in medical domain is gaining more attention to give insight into how the models arrived at their predictions and to increase trust in the use of such models. Additionally, from the legal point of view, although explainability is currently not a strict requirement for the AI use in clinical situations, food and drug administration states that some level of transparency, which can include open communication regarding inputs and outputs of the AI model and its algorithm, is required to ensure transparency to the patients and the physicians . FurtherThere exist several AI studies that together classify diseases and generate heatmaps. Nonetheless, they have several issues. For example, the publicly available datasets that such research uses sometimes contain incorrect labels obtained from NLP, and the research oftentimes use only the CXR images and class labels without incorporating the other methods or data the radiologists usually use when making diagnoses.Thus, this research proposed three model sets that take a U-Net architecture with distinct loss function computations using a dataset that contains eye-gaze information from a radiologist. This study showed that using a radiologist's eye-gaze data and derived heatmap  in model training can improve disease classification AUC, especially for “CHF” and “pneumonia” classes that help reduce false negatives. Moreover, by guiding the model's gradients to align to the radiologist's eye-gaze heatmaps, the model is able to produce enhanced heatmaps that can be used for explainability purposes. Furthermore, this study confirms that using different types of data other than just the CXR images and disease class labels and following radiologists' methods for diagnosis when establishing and training AI models can boost the classification performance.The heatmap visualization outputs of the three proposed model sets highlight areas of CXR images that the model focused on when making predictions. The outputs of the first proposed model set for both GBP and deconvNet show that each generator appeared to focus on similar areas as the static eye-gaze heatmaps did, but the U-Net's predicted heatmaps seemed to not focus well, which is understandable due to the way the segmentation loss was calculated for this model set.The outputs of the second proposed model set using deconvNet as the heatmap generator (shown in the bottom row of Finally, the visualization outputs of the third proposed model set clearly showcased that the use of GBP method as the heatmap generator for this training method performed superior compared to others. Both the U-Net's predicted heatmaps and the heatmaps created from GBP focused on similar areas as the eye-gaze heatmaps, suggesting that the model is learning to produce explainable heatmaps while predicting the disease class.Viewing the results from the three experiment sets, particularly focusing on the AUC values in The major limitation of this research is the small size of the dataset and the potential bias the dataset may have because the eye-gaze data was collected from, and the diagnosis was done by one radiologist . Thus, oTo further validate the classification decisions this study's models made and to increase trust in the model's predictions, DOCTOR's Totally Black Box scenario  can be uIn this research, three proposed model sets that use heatmap generators in the U-Net model's training time were investigated for the radiology field to simultaneously improve the disease classification performance and better highlight the model's attention spots by generating explainable heatmaps. The experiments used a dataset that contain chest radiographs, eye-gaze coordinates from one radiologist, and the corresponding images' class labels. The confidence intervals of the AUC values for each experiment that incorporated the static eye-gaze information and the heatmap generators during the model's training time were computed. The proposed model in


In high energy heavy-ion collisions, the high speed valence charges will produce intense electromagnetic fields within the resulting quark-gluon plasma. Utilizing the AMPT model, this paper presents a comprehensive analysis of the magnetic field distribution generated from non-central collisions between  Recent experimental measurements and numerical simulations suggest that collisions between 3. Furthermore, 5. These fields are significantly stronger than the squared mass of electrons and light quarks 7. In particular, one important aspect of these magnetic fields is their ability to cause anomalous transport phenomena in heavy ion collisions, such as the chiral magnetic effect (CME)10, the chrial separation effect (CSE)12, and the chiral magnetic wave (CWM)14. The non-trivial topological fluctuations of gluons in the QCD vacuum can break the parity and charge conjugation parity symmetry in the strong interaction. When a strong external magnetic field is present, fermions with different chirality separate along the direction of the magnetic field to produce a vector current, which is called CME. Experimental studies on anomalous transport have been carried out in RHIC and LHC, and the measured results provide signals consistent with CME predictions18. The study of these phenomena has important implications for understanding of the properties of QGP under extreme conditions and the research for new physics.Relativistic heavy-ion collisions can produce high-speed charged particles that generate immense electromagnetic fields19. Additionally, some investigations explore the space-time evolution of electromagnetic fields and azimuthal angle fluctuations of these fields and their correlation with the initial matter geometry21. Previous studies also suggest that the magnetic field originates from the spectators of the collision nucleus, appears only at the preliminary time of collision, and then decays and disappears quickly within 25. But the QGP generated in the collision contains abundant conductive sea quarks that can respond to the magnetic field. Since the QGP behaves like a nearly ideal fluid, its response to the magnetic field can be measured through transport coefficients such as the electric conductivity and the chiral conductivity. Therefore, the calculations involving the magnetic field must take these coefficients into account. Research on the magnetofluid equation of ideal fluids under strong electromagnetic fields has shown that the electromagnetic field can affect both the ideal flow and the transport coefficients of plasma28, therefore, it is necessary to verify that the kinetic coefficients do not heavily depend on the magnetic field.To accurately understand how the magnetic field interacts with the quark-gluon plasma produced in high-energy collisions, it is essential to study the evolution of the magnetic field existing in the thermally expanded nuclear medium. The spatial distributions of the electromagnetic fields and the electromagnetic anomaly 22. As time progresses, more quarks and anti-quarks are excited and produced, leading to the QGP approaching thermal equilibrium. Despite the lack of a quantitative theory to fully comprehend the thermalization problem, phenomenological studies have demonstrated that the completion time for thermalization is relatively brief compared to the overall lifetime of QGP, and the evolution of the thermalized QGP can be well described by ideal fluid mechanics at this stage. According to the lattice QCD theory, the QGP is a good conductor, with an important transport coefficient known as the electic conductivity 29. Recently, lattice QCD calculations with 31 for temperature T and 9.At the early stages of heavy-ion collisions, gluons primarily make up the produced partonic matter, which exists in a state far from equilibrium. The QGP can be approximated as an insulator, during this particular period, which includes the time before the collision, the magnetic field in space can be determined by Lienard-Wiechert potentialsIn our work, the diffusion process of the quark-gluon plasma is treated as a perturbation to estimate its contribution to the magnetic field. This approach allows for a better understanding of the complex interactions between the magnetic field and the QGP medium produced in high-energy collisions. We employ the AMPT model to simulate the collision with impact parameter 36 can well characterizes complicated dynamic transport processes in heavy-ion collisions, which effectively supports our the magnetic field distribution calculations. To accurately describe the cases when the QGP is produced, we choose the string melting version37 which encompasses important evolution stages of collisions, including initial state, parton cascade, hadronization, and hadron rescatterings. At the initial stage, two z axis in the center of mass system. After the collision, the AMPT model tracks the trajectory of each nucleon to determine whether there was a collision and what type of collision occurred. Nucleons experiencing the inelastic collision subsequently participate in the parton cascade and contribute to the formation of quark-gluon plasma, as well as those that do not experience any collision will fly away from the center region of collision, constantly radiating magnetic field. The initial distribution of nucleons in the nucleus before the collision is given by the Woods-Saxon distribution:The AMPT model22: The Maxwell equations that describe the evolution of electromagnetic fields in a conductive plasma in diffusive thermal equilibrium can be written as22 and CME, respectively. N is the number of unwounded protons, and consider the current produced by a point charge e moving along the z-axis with velocity v in cylindrical coordinate 38, which imposes a condition for the diffusion of these particles: the velocity of the diffusive plasma Where entclass1pt{minima39, which includes a dissipation term in the medium. An analytical solution for this equation can be obtained as follows: The first of these equations describes the field created by the external currents in the stationary plasma, while the other two equations consider the plasma flow and the CME, respectively. We obtain three equations with a uniform form, and they share the same retarded Green’s function:the variables Like the retarded Green’s function is expressed as a sum of two terms, we set t, whereas For 40. Subsequently, the initial magnetic field that persists within the medium after the collision is:Furthermore, it is important to recognize that before the emergence of the quark-gluon plasma, a magnetic field was already present in space due to the movement of the colliding nuclei through the vacuum. At the moment of collision n to Eq.  takes fo41, which involves assuming that the initial entropy density profile in the transverse plane follows a Gaussian distribution:By using Eqs.  and 11)11), we cinto Eq. , we can z axis corresponds to the direction of nuclear motion, and the x axis corresponds to the collision parameter direction. We simulate For the convenience of analysis and comparison with other studies, we convert our results to the cartesian coordinate system through the coordinate transformation x direction. Figures 2. However, the time scale of the transition of magnetic field Due to the geometric symmetry of the collision, the magnetic field in the center of the overlapp region is perpendicular to the reaction plane. However, in an actual collision event, the distribution of nucleons in the two colliding nuclei may not be the same, which could destroy this geometric symmetry and cause fluctuations of the magnetic field in the As previously mentioned, the contributions to the magnetic field come from charged particles in spectators, internal currents induced by Ohm’s law and CME. Thus, it is necessary to explore how each effect affects the evolution of the magnetic field. Figure y direction. However, when the parameter b exceeds the nuclear radius, most of the nucleons are distant from the collision regione, causing a decrease in the magnetic field intensity. The dependence of field intensity on impact parameter suggest that semi-symmetric collisions are the best way to test the effects related to magnetic fields in RHIC and HLC experiments. Additionally, the magnetic field’s dependence on collision energy is evident. As the energy increases, the nucleus’s valence charge moves faster, resulting in a stronger generated magnetic field.In high energy heavy-ion collisions, the intensity of the magnetic field can be significantly dominated by impact parameters and the collision energy. In Fig. x, z component of y direction and fluctuations in the x direction, with no electromagnetic background in the z direction of the beam. However, when considering the diffusion effect and chiral conductivity, the situation changes. These two effects lead to the generation of new magnetic fields in the x and z directions, especially in the z direction, where there was previously no electromagnetic field background. Nevertheless, these two effects are relatively weak compared to the magnetic field in the y direction. The magnetic field resulting from the diffusion effect of the quark-gluon plasma accounts for around 42.The temporal evolution of the x and z directions. Nonetheless, the overall effects remain weak relative to the maximum magnetic field value devoted by spectators, and their total contributions are less than In summary, we utilize the AMPT model to simulate the non-central collision of