Continuous Model Research Articles

Continuous patient state attention model for addressing irregularity in electronic health records

BackgroundIrregular time series (ITS) are common in healthcare as patient data is recorded in an electronic health record (EHR) system as per clinical guidelines/requirements but not for research and depends on a patient’s health status. Due to irregularity, it is challenging to develop machine learning techniques to uncover vast intelligence hidden in EHR big data, without losing performance on downstream patient outcome prediction tasks.MethodsIn this paper, we propose Perceiver, a cross-attention-based transformer variant that is computationally efficient and can handle long sequences of time series in healthcare. We further develop continuous patient state attention models, using Perceiver and transformer to deal with ITS in EHR. The continuous patient state models utilise neural ordinary differential equations to learn patient health dynamics, i.e., patient health trajectory from observed irregular time steps, which enables them to sample patient state at any time.ResultsThe proposed models’ performance on in-hospital mortality prediction task on PhysioNet-2012 challenge and MIMIC-III datasets is examined. Perceiver model either outperforms or performs at par with baselines, and reduces computations by about nine times when compared to the transformer model, with no significant loss of performance. Experiments to examine irregularity in healthcare reveal that continuous patient state models outperform baselines. Moreover, the predictive uncertainty of the model is used to refer extremely uncertain cases to clinicians, which enhances the model’s performance. Code is publicly available and verified at https://codeocean.com/capsule/4587224.ConclusionsPerceiver presents a computationally efficient potential alternative for processing long sequences of time series in healthcare, and the continuous patient state attention models outperform the traditional and advanced techniques to handle irregularity in the time series. Moreover, the predictive uncertainty of the model helps in the development of transparent and trustworthy systems, which can be utilised as per the availability of clinicians.

Statistical design and analysis of controlled human malaria infection trials

BackgroundMalaria is a potentially life-threatening disease caused by Plasmodium protozoa transmitted by infected Anopheles mosquitoes. Controlled human malaria infection (CHMI) trials are used to assess the efficacy of interventions for malaria elimination. The operating characteristics of statistical methods for assessing the ability of interventions to protect individuals from malaria is uncertain in small CHMI studies. This paper presents simulation studies comparing the performance of a variety of statistical methods for assessing efficacy of intervention in CHMI trials.MethodsTwo types of CHMI designs were investigated: the commonly used single high-dose design (SHD) and the repeated low-dose design (RLD), motivated by simian immunodeficiency virus (SIV) challenge studies. In the context of SHD, the primary efficacy endpoint is typically time to infection. Using a continuous time survival model, five statistical tests for assessing the extent to which an intervention confers partial or full protection under single dose CHMI designs were evaluated. For RLD, the primary efficacy endpoint is typically the binary infection status after a specific number of challenges. A discrete time survival model was used to study the characteristics of RLD versus SHD challenge studies.ResultsIn a SHD study with the continuous time survival model, log-rank test and t-test are the most powerful and provide more interpretable results than Wilcoxon rank-sum tests and Lachenbruch tests, while the likelihood ratio test is uniformly most powerful but requires knowledge of the underlying probability model. In the discrete time survival model setting, SHDs are more powerful for assessing the efficacy of an intervention to prevent infection than RLDs. However, additional information can be inferred from RLD challenge designs, particularly using a likelihood ratio test.ConclusionsDifferent statistical methods can be used to analyze controlled human malaria infection (CHMI) experiments, and the choice of method depends on the specific characteristics of the experiment, such as the sample size allocation between the control and intervention groups, and the nature of the intervention. The simulation results provide guidance for the trade off in statistical power when choosing between different statistical methods and study designs.

Optical snake states in a photonic graphene

We propose an optical analog of electron snake states based on an artificial gauge magnetic field in a photonic graphene implemented by varying distances between cavity pillars. We develop an intuitive and exhaustive continuous model based on tight-binding approximation and compare it with numerical simulations of a realistic photonic structure. The allowed lateral propagation direction is shown to be strongly coupled to the valley degree of freedom, and the proposed photonic structure may be used as a valley filter.

Abstract PO5-24-09: Optimizing the Therapeutic Treatment of Breast Cancer Through a Dual Data-driven Theoretical Model

Abstract Despite rapid advancements in treatments and technology, breast cancer remains the second leading cause of cancer related morbidity in women in the US. As a heterogeneous disease, the unique genetic and phenotypic profile of each tumor complicates the prediction of treatment responses and optimized treatment strategies. One primary manifestation of phenotypic plasticity and concomitant intra-tumoral heterogeneity is the Epithelial-Mesenchymal Transition (EMT). The acquisition of migratory and invasive properties through EMT facilitates tumor metastasis and results in worse patient outcomes. As a result, the EMT and its reverse process (MET) often influence treatment response. However, the different mechanisms through which these therapeutic drugs affect the EMT-related phenotypic switching rates as well as each phenotype’s replication rates are unclear, and further investigation is required for better understanding their precise effect for directing optimal treatment strategies and improved patient outcomes. Here, we compile an atlas of publicly available metastatic and non-metastatic RNA sequencing data of breast cancer cell lines treated with therapeutic and chemotherapeutic drugs and propose a dual data-driven theoretical framework for understanding the effects of each drug on breast cancer treatment response. We infer the cell fractions, EMT phenotypic transition rates and phenotypic replication rates of each case through an extension of our previously developed hybrid data-driven and theoretical model, COMET. We infer single-cell RNA sequencing-derived EMT-related trajectories and apply a continuous time Markov chain model to infer inter-state transition rates. By analyzing the atlas of RNA sequencing data and integration with our framework, we gain novel insights into the context-specific mechanisms by which therapeutic drugs affect the phenotypic transition rates. This comprehensive understanding will contribute to optimizing breast cancer therapy and ultimately improving patient outcomes. Citation Format: A. Najafi. Optimizing the Therapeutic Treatment of Breast Cancer Through a Dual Data-driven Theoretical Model [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO5-24-09.

Fourier-Based Vibration Model of Electrical Machines Considering Nonideal Orthogonality Between Electromagnetic Forces and Structural Modes

This paper proposes a Fourier-based model of vibration synthesis, improving both precision and speed. For the first time, the nonideal orthogonality between electromagnetic (EM) forces and structural modes is theoretically proposed and modelled by spatial harmonics. Different from the discrete vectors used in previous literature, the proposed method achieves a one-dimension (1-D) continuous model of EM forces and modes. On the basis, the vectors of modes and forces on tooth surfaces are decomposed by fast Fourier transform (FFT), so that the vibration response is synthesized based on Fourier coefficients. Further, the proposed model is applied to a 12-slot/10-pole (12s/10p) interior permanent-magnet (IPM) machine. The spatial harmonics of mode vectors are elaborated to identify the key orders of EM forces before the vibration response is completed. Then, the proposed model is compared with the coupled-field finite element analysis (FEA). The advantages are verified in terms of computational accuracy, speed, and sensitivity to mesh quality. Finally, the feasibility of the proposed model is verified by both coupled-field finite element analysis (FEA) and experiment.

Fake Currency Detection System

Abstract: This project aims to develop a robust fake currency detection system leveraging image processing and machine learning techniques. Data cleaning involves image quality enhancement and handling of torn or dirty notes. The experimental setup includes a digital camera in a controlled lighting environment to capture currency images. MATLAB is used for software setup due to its extensive libraries. The algorithm involves pre-processing, feature extraction, and classification using machine learning algorithmslike decision trees or SVM. Continual model learning ensures adaptation to emerging counterfeit techniques. This system promises effective counterfeit detection with ongoing refinement, enhancing financial security.

Relationship between effective blood flow rate and clinical outcomes in maintenance hemodialysis patients: a single-center study

The association between blood flow rate (BFR) and clinical outcomes in patients undergoing maintenance hemodialysis (MHD) is inconclusive. This retrospective study included 175 patients undergoing MHD treatment between July 2015 and March 2022, divided into two groups based on time-averaged effective blood flow rate (eBFR) median value. We investigated arteriovenous fistula (AVF) outcomes and the association of eBFR with all-cause mortality and new major adverse cardiovascular events (MACE). Mean ± SD and median time-averaged eBFR values were 276 ± 24 and 275 mL/min, respectively. After adjusting for relevant factors including age, sex, vintage, diabetes, CVD, receiving hemodiafiltration (HDF) treatment and spKt/V, Cox models indicated a low time-averaged eBFR (≤ 275 ml/min) was associated with increased risks of all-cause mortality (hazard ratio [HR] 14.18; 95% confidence interval [CI], 3.14–64.1) and new MACE (HR 3.76; 95% CI, 1.91–7.40) in MHD patients. Continuous Cox models demonstrated each 20 ml/min increase in eBFR linked to a 63% decrease in the risk of all-cause mortality (HR: 0.37, 95% CI: 0.23–0.59) and a 38% decrease in the occurrence of new MACE (HR: 0.62, 95% CI: 0.46–0.84). There was no significant difference in AVF outcomes between the two groups. Our study noted higher eBFR (>275 mL/min) is associated with lower risks of both all-cause mortality and new MACE compared with low eBFR (≤275 mL/min). Increased eBFR is not associated with a higher risk of AVF failure.

Grid Cells in Cognition: Mechanisms and Function.

The activity patterns of grid cells form distinctively regular triangular lattices over the explored spatial environment and are largely invariant to visual stimuli, animal movement, and environment geometry. These neurons present numerous fascinating challenges to the curious (neuro)scientist: What are the circuit mechanisms responsible for creating spatially periodic activity patterns from the monotonic input-output responses of single neurons? How and why does the brain encode a local, nonperiodic variable-the allocentric position of the animal-with a periodic, nonlocal code? And, are grid cells truly specialized for spatial computations? Otherwise, what is their role in general cognition more broadly? We review efforts in uncovering the mechanisms and functional properties of grid cells, highlighting recent progress in the experimental validation of mechanistic grid cell models, and discuss the coding properties and functional advantages of the grid code as suggested by continuous attractor network models of grid cells.

The chemostat reactor: A stability analysis and model predictive control

This contribution develops the model predictive control for an unstable chemostat reactor. Initially, we analyze the system’s model — a nonlinear first-order hyperbolic partial integro-differential equation (PIDE) — and carry the model linearization around an unstable operating condition. Employing the structure-preserving Cayley–Tustin transformation, we obtain a discrete-time model representation of the continuous model. Subsequently, we solve the operator Ricatti equations in the discrete-time setting to derive a full state feedback controller that stabilizes the closed-loop and design a Luenberger observer for state reconstruction given the system output measures. Finally, we formulate a dual-mode MPC ensuring constraint satisfaction and optimality, integrating the gain-based unconstrained full-state feedback optimal control obtained from the Ricatti equation. This dual-mode strategy describes an optimization problem where the predictive controller acts only if constraints become active within the control horizon. Simulation studies validate the controller performance, where the MPC only takes action if the constraints are predicted to be active within the control horizon while also guaranteeing closed-loop stabilization under only output feedback. This type of controller can be easily implemented with other control strategies and significantly decreases the computational costs of solving the optimal control problems when compared to other MPC approaches.

Experimental Research on the Floating Amount of Shield Tunnel Based on the Innovative Cumulative Floating Amount Calculation Method

The study of shield tunnel segment flotation is crucial for controlling the precision of underground excavation projects. Based on Winkler’s beam foundation theory, the load structure method, and the equivalent continuous beam model, and by considering the mechanical and spatial conditions that cause segment flotation, a novel theoretical calculation method for cumulative flotation is proposed using a simplified equivalent stiffness model of the tunnel. Additionally, a new concept of “equivalent flotation force” is introduced. The rationality and applicability of this theoretical calculation method are verified by comparing it with on-site construction data from the Yuanjiang River Crossing Tunnel Project in Changde, Hunan Province, China. The experimental results demonstrate that the theoretical calculation closely approximates the surface deformation monitoring data of the tunnel alignment in the eastern section of the project, and their deformation patterns are similar. Near the starting shaft, there is significant settlement influenced by stratum loss due to smaller tunnel flotation, with greater settlement occurring in the upper part. However, at approximately 45 m into both sections, they enter a deformation stability zone showing significant correlation in longitudinal deformation. Through comparison and verification of on-site experiments and theoretical model analysis, we preliminarily elucidate the feasibility of this innovative cumulative flotation theoretical calculation method which provides an important theoretical basis for assessing segment flotation issues in subsequent tunnel shield construction evaluations.

Association between visceral adiposity index and risk of diabetes and prediabetes: Results from the NHANES (1999-2018).

To investigate the association between the visceral adiposity index and the prevalence of diabetes and prediabetes in the US adult population. We conducted a cross-sectional study using data from the National Health and Nutrition Examination Survey (NHANES) from 1999 to 2018 for ten consecutive years, including 18745 eligible participants. The weighted multivariate logistic model and fitting curve were used to explore the correlation and dose-response relationship between visceral adiposity index (VAI) and diabetes (DM) and prediabetes in the general population and the prevalence of different subgroups. In the fully adjusted continuous model, the risk of diabetes and prediabetes in the general population increased 0.15 times [1.15 (1.10,1.20), p<0.0001] with every increase of 1 unit of VAI. In the fully adjusted classification model, with the lowest quartile array Q1 of VAI as the reference group, Q2 of the second Quantile group, Q3 of the third Quantile group, and Q4 of the Quartile group increased 0.26 times [1.26 (1.10,1.44), p<0.001], 0.65 times [1.65 (1.43,1.89), p<0.0001], 1.60 times [2.60 (2.28,2.97), p<0.0001] respectively with the risk of diabetes and prediabetes. The above results showed that VAI was positively associated with the prevalence of diabetes and prediabetes, and the fitted curves showed a non-linear trend. (P for non-linear = 0<0.05). The results of the subgroup population were consistent with the total population and a significant interaction was found in gender (P for interaction<0.0001). In conclusion, we found a non-linear positive association between VAI and the risk of diabetes and prediabetes in the US adult population and found that women have a higher risk of diabetes and prediabetes than men; therefore, we should focus on the female population, and we call for the use of VAI to manage the development of diabetes and prediabetes in the clinical setting.

Quantitative analysis and stochastic modeling of osteophyte formation and growth process on human vertebrae based on radiographs: a follow-up study

Osteophytes are frequently observed in elderly people and most commonly appear at the anterior edge of the cervical and lumbar vertebrae body. The anterior osteophytes keep developing and will lead to neck/back pain over time. In clinical practice, the accurate measurement of the anterior osteophyte length and the understanding of the temporal progression of anterior osteophyte growth are of vital importance to clinicians for effective treatment planning. This study proposes a new measuring method using the osteophyte ratio index to quantify anterior osteophyte length based on lateral radiographs. Moreover, we develop a continuous stochastic degradation model with time-related functions to characterize the anterior osteophyte formation and growth process on cervical and lumbar vertebrae over time. Follow-up data of anterior osteophytes up to 9 years are obtained for measurement and model validation. The agreement test indicates excellent reproducibility for our measuring method. The proposed model accurately fits the osteophyte growth paths. The model predicts the mean time to onset of pain and obtained survival function of the degenerative vertebrae. This research opens the door to future quantification and mathematical modeling of the anterior osteophyte growth on human cervical and lumbar vertebrae. The measured follow-up data is shared for future studies.

Non-smooth dynamics of impacting viscoelastic pipes conveying pulsatile fluid

This paper aims to investigate the stability and nonlinear dynamics of an initially curved viscoelastic clamped–clamped pipe conveying pulsatile fluid, with special attention to the non-smooth dynamics of this gyroscopic system under the influence of initial curvature and gravity. In this study, the impacting contact is modeled as a trilinear repulsive force. Based on the Euler–Bernoulli beam theory, the nonlinear governing equations, which take into account geometric, curvature, and damping nonlinearities, are developed using Hamilton’s principle. The continuous model is discretized using the Galerkin method and then solved using the arc-length technique and a time integration method. A linear analysis of the natural frequency and complex mode shape shows the unexpected frequency intersection and modal asymmetry. The qualitative changes in the nonlinear dynamics of the impacting pipe in both sub- and super-critical regions are examined and presented in the form of bifurcation diagrams, frequency–amplitude curves, force–amplitude curves, time histories, and phase portraits. Numerical results show that some complex dynamical behaviors can occur in different impact constraint cases, including a grazing bifurcation, sticking, period doubling, and chaos at the impact location, may occur. The initial curvature and gravity result in different behaviors, such as the asymmetry change of the equilibrium configuration and the occurrence of the flutter instability. The current analysis is significant to understand the non-smooth dynamic mechanisms and also provide design and technology guidance for the pipe system with motion-limiting constraints.

Service-aware real-time slicing for virtualized beyond 5G networks

Edge Intelligence is expected to play a vital role in the evolution of 5G networks, empowering them with the capability to make real-time decisions regarding various allocations related to their management and service provisioning to end-users. This shift facilitates the transition from a network-aware approach, where applications are developed to manage network quality fluctuations, to a service-aware network that self-adjusts based on the hosted applications. In this paper, we design and implement a service-aware network managed from the network edge. We utilize and assess various Machine Learning models to classify cellular network traffic flows in the backhaul, aiming to predict their future impact on network load. Leveraging these predictions, the network can proactively and autonomously reallocate slices in the Radio Access Network via programmable APIs, ensuring the demands of the traffic-generating applications are met. The approach integrates innovative MLOps methodologies for distributed and online training, enabling continuous model refinement and adaptation to evolving network dynamics. Our framework was tested in a real-world environment with realistic traffic scenarios, and the results were evaluated in real-time, down to a granularity of 10ms. Our findings indicate that the network can swiftly adjust to traffic, providing users with slices tailored to their application needs. Notably, our experiments show that under the studied settings, the users experienced up to 4 times lower latency (jitter) and nearly 4 times higher throughput when interacting with various applications, compared to the standard non-AI/ML unit. Furthermore, our dynamic scheme significantly optimizes resource allocation, ensuring energy efficiency by avoiding over- and under-provisioning of resources.

Effect of discretization choices when modeling the thermo-chemical history of the accreting core

Different discretizations methods applied to models of core/mantle segregations are tested (single stage, multistage accretion, results of N-body simulations) in order to test the sensitivity of the thermo-chemical coupling to the type of discretization used. We found that while single stage and large discretization of segregation steps yield very different core temperature, multistage models of accretion and core mantle segregation, at least for the model presented in this paper, tend to yield similar results, whether it is for the light element concentrations or the final temperature of the core. As long as a magma ocean existence throughout the entire process of core/mantle segregation is posited, and that only the impactor's masses of metal and silicate are re-equilibrated at each step, the degree of discretization of continuous model does not matter as long as it encompasses more than 10 steps of calculations.

Cholinergic neuromodulation of prefrontal attractor dynamics controls performance in spatial working memory.

The behavioral and neural effects of the endogenous release of acetylcholine following stimulation of the Nucleus Basalis of Meynert (NB) have been recently examined in two male monkeys (Qi et al. 2021). Counterintuitively, NB stimulation enhanced behavioral performance while broadening neural tuning in the prefrontal cortex (PFC). The mechanism by which a weaker mnemonic neural code could lead to better performance remains unclear. Here, we show that increased neural excitability in a simple continuous bump attractor model can induce broader neural tuning and decrease bump diffusion, provided neural rates are saturated. Increased memory precision in the model overrides memory accuracy, improving overall task performance. Moreover, we show that bump attractor dynamics can account for the nonuniform impact of neuromodulation on distractibility, depending on distractor distance from the target. Finally, we delve into the conditions under which bump attractor tuning and diffusion balance in biologically plausible heterogeneous network models. In these discrete bump attractor networks, we show that reducing spatial correlations or enhancing excitatory transmission can improve memory precision. Altogether, we provide a mechanistic understanding of how cholinergic neuromodulation controls spatial working memory through perturbed attractor dynamics in PFC.Significance statement Acetylcholine has been thought to improve cognitive performance by sharpening neuronal tuning in prefrontal cortex. Recent work has shown that electrical stimulation of the cholinergic forebrain in awake-behaving monkeys induces a reduction in prefrontal neural tuning under stimulation conditions that improve performance. To reconcile these divergent observations, we provide network simulations showing that these derive consistently from specific conditions in prefrontal attractor dynamics: firing rate saturation leads to increased storage precision and reduced neural tuning upon cholinergic activation via an increase in neural excitability, a reduction in neural correlations, and an increase in excitatory transmission. Our study integrates previously reported data into a consistent mechanistic view of how acetylcholine controls spatial working memory via attractor network dynamics in prefrontal cortex.

Developing a continuous SIR epidemic model and its discrete version using Euler method: Analyzing dynamics with analytical and numerical methods

Developing a continuous SIR epidemic model and its discrete version using Euler method: Analyzing dynamics with analytical and numerical methods

Multibody dynamics in robotics with focus on contact events

Abstract Multibody dynamics methodologies have been fundamental tools utilized to model and simulate robotic systems that experience contact conditions with the surrounding environment, such as in the case of feet and ground interactions. In addressing such problems, it is of paramount importance to accurately and efficiently handle the large body displacement associated with locomotion of robots, as well as the dynamic response related to contact-impact events. Thus, a generic computational approach, based on the Newton–Euler formulation, to represent the gross motion of robotic systems, is revisited in this work. The main kinematic and dynamic features, necessary to obtain the equations of motion, are discussed. A numerical procedure suitable to solve the equations of motion is also presented. The problem of modeling contacts in dynamical systems involves two main tasks, namely, the contact detection and the contact resolution, which take into account for the kinematics and dynamics of the contacting bodies, constituting the general framework for the process of modeling and simulating complex contact scenarios. In order to properly model the contact interactions, the contact kinematic properties are established based on the geometry of contacting bodies, which allow to perform the contact detection task. The contact dynamics is represented by continuous contact force models, both in terms of normal and tangential contact directions. Finally, the presented formulations are demonstrated by the application to several robotics systems that involve contact and impact events with surrounding environment. Special emphasis is put on the systems’ dynamic behavior, in terms of performance and stability.

Simulation of Solidification Structure in the Vacuum Arc Remelting Process of Titanium Alloy TC4 Based on 3D CAFE Method

Vacuum arc remelting is the main production method of titanium alloy ingots at present. In order to obtain good quality ingots, it is of great significance to study the formation of the solidification structure of ingots via vacuum arc remelting. In order to select and optimize the nucleation parameters for the solidification microstructure simulation of an ingot, a 3D CAFE model for microstructure evolution during vacuum arc remelting was established, taking into account heat transfer, flow, and solute diffusion. The Gaussian distribution continuous nucleation model and extended KGT model were used to describe the grain nucleation and dendrite tip growth rates, respectively. The multi-point mass source and moving boundary method were used to simulate the ingot growth. The results show that there are three typical crystal regions in the solidification structure of vacuum arc remelting titanium alloy ingots, namely the surface fine crystal region, columnar crystal region, and central equiaxed crystal region. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with the increase in the undercooling of the maximum bulk nucleation. With an increase in the maximum bulk nucleation density, the equiaxed grain zone gradually increases, and the grain size gradually decreases. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with an increase in the undercooling of the maximum bulk nucleation. The maximum volume nucleation variance has no obvious effect on the change in the solidification structure. When the maximum volume nucleation undercooling is 5.5 K, the maximum volume nucleation standard deviation is 4 K, and the maximum volume nucleation density is 5 × 108. The solidification structure simulation results are in good agreement with the experimental results.

The Development of a Continuous Constitutive Model for Thin-Shell Components with A Sharp Change in the Property at Welded Joints.

Large-dimension complex integral thin-shell components are widely used in advanced transportation equipment. However, with the dimensional limitations of raw blanks and the manufacturing process, there are inhomogeneous geometric and mechanical properties at welded joints after welding, which have a significant effect on the subsequent forming process. Therefore, in this paper, the microstructure of welded joints with a sharp property change was accurately characterized by the proposed isothermal treatment method using the BR1500HS welded tube as an example. In addition, an accurate constitutive model of welded tubes was established to predict the deformation behavior. Firstly, the heat-treated specimens were subjected to uniaxial tensile tests and the stress-strain curves under different heat treatment conditions were obtained. Then, the continuous change in flow stress in the direction of the base metal zone, the heat-affected zone and the weld zone was described by the relationship between the microhardness, flow stress and center angle of the welded tube. Using such a method, a continuous constitutive model of welded tubes has been established. Finally, the constitutive model was compiled into finite-element software as a user material subroutine (VUHARD). The reliability of the established constitutive model was verified by simulating the free hydro-bulging process of welded tubes. The results indicated that the continuous constitutive model can well describe the deformation response during the free hydro-bulging process, and accurately predicted the equivalent strain distribution and thickness thinning rate. This study provides guidance in accurately predicting the plastic deformation behavior of welded tubes and its application in practice in hydroforming industries.