A Safety Evaluation and Early Warning Method for Pressure Vessels Based on Digital Twin

Abstract

The present invention relates to the technical field of safety evaluation and early warning, and particularly relates to a method for safety evaluation and early warning of pressure vessels based on digital twins. The method includes the following steps: calculating the wall thickness difference distribution of pressure vessel design data, and dividing the structural similarity regions to obtain the data of the wall thickness region division of the structural form; calculating the resonance buckling instability probability based on the data of the wall thickness region division of the structural form to obtain the resonance buckling instability probability data; constructing a safety evaluation logic model for the resonance buckling instability probability data to obtain the safety evaluation logic model of the pressure vessel; and sending the safety evaluation logic model of the pressure vessel to the data cloud platform to execute the method for safety evaluation and early warning of the pressure vessel. The present invention makes the safety evaluation and early warning technology more perfect through the optimization of the safety evaluation and early warning technology.

Description

Technical Field

[0001] The present invention relates to the technical field of safety evaluation and early warning, and particularly to a safety evaluation and early warning method for pressure vessels based on digital twin. Background Art

[0002] Pressure vessels are widely used in fields such as petroleum, chemical industry, and energy. They are under high temperature, high pressure, and corrosive environments for a long time, and are extremely prone to fatigue, cracks, or structural failures, which may lead to equipment damage or safety accidents. Digital twin technology constructs a virtual model of a pressure vessel, simulates the working state of its physical entity under different working conditions, and combines real-time data collected by sensors to perform real-time dynamic monitoring of key parameters such as the temperature, pressure, stress, corrosion, and cracks of the vessel. This virtual model can not only reflect the current operating state of the vessel, but also predict future working conditions, and simulate the damage evolution process of the vessel based on a variety of physical and chemical models. By combining the historical data, design parameters, and real-time operating data of the pressure vessel, the digital twin model can be continuously updated and optimized to improve the simulation accuracy and achieve accurate assessment of the health status of the pressure vessel. However, there are problems in a traditional safety evaluation and early warning method for pressure vessels based on digital twin, such as inaccurate analysis of the instability probability state of the pressure vessel and large errors in the safety evaluation and early warning of the pressure vessel. Summary of the Invention

[0003] Based on this, it is necessary to provide a safety evaluation and early warning method for pressure vessels based on digital twin to solve at least one of the above technical problems.

[0004] To achieve the above object, a safety evaluation and early warning method for pressure vessels based on digital twin, the method includes the following steps:

[0005] Step S1: Obtain the design data of the pressure vessel; calculate the wall thickness difference distribution of the pressure vessel design data to obtain the structural form wall thickness difference distribution data; divide the structural similarity region according to the structural form wall thickness difference distribution data to obtain the structural form wall thickness region division data;

[0006] Step S2: Analyze the difference in the force distribution of the connection structure based on the structural form wall thickness region division data to obtain the connection structure force distribution difference data; calculate the resonance buckling instability probability according to the connection structure force distribution difference data to obtain the resonance buckling instability probability data;

[0007] Step S3: Construct a safety evaluation logic model for the resonance buckling instability probability data to obtain a safety evaluation logic model for the pressure vessel;

[0008] Step S4: Send the safety evaluation logic model of the pressure vessel to the data cloud platform to execute the safety evaluation and early warning method for the pressure vessel.

[0009] The present invention obtains the design data of a pressure vessel and conducts a detailed calculation of the wall thickness difference, which can reveal the distribution characteristics of the wall thickness under different structural forms. This process can not only clarify the stress state of each region but also help designers deeply understand the influence of the wall thickness on the overall performance of the structure. By dividing the regions with wall thickness differences, designers can more accurately identify potential weak links, providing a basis for subsequent improvement measures. In addition, the analysis of the stress distribution differences based on these wall thickness region divisions can reveal the stress characteristics of the connection structure under different working conditions and evaluate its stability. By analyzing the stress distribution differences of the connection structure, important data support can be provided for calculating the probability of resonance buckling instability. Understanding the stress state of different regions is crucial for predicting their instability risks. By comprehensively considering these data, designers can identify the key stress points of the structure and evaluate its safety under actual working conditions. This data-based analysis method enables designers to optimize the structure more targeted, thereby improving the safety and durability of the pressure vessel, reducing the failure risk, and extending the service life. Therefore, the entire process not only improves the scientificity and rationality of the design but also provides an important theoretical basis for subsequent engineering applications. By implementing steps S3 and S4, the safety evaluation ability and early warning efficiency of the pressure vessel can be significantly improved. First, in step S3, a safety evaluation logic model based on resonance buckling instability probability data is constructed, providing a scientific theoretical basis and decision-making support for the safety assessment of the pressure vessel. This logic model can not only comprehensively consider various influencing factors but also conduct a comprehensive analysis of the stability of the pressure vessel by simulating the stress state under different working conditions. This model-based safety evaluation method can effectively identify potential safety hazards, helping designers formulate corresponding preventive measures in a timely manner, thus improving the safety of the pressure vessel in actual applications. Next, in step S4, by uploading the safety evaluation logic model to the data cloud platform, the automation and intelligence of the pressure vessel safety evaluation are realized. The powerful computing power and data processing ability of the cloud platform can monitor and analyze the operating state of the pressure vessel in real time. Once potential safety risks are detected, the cloud platform can issue early warnings in a timely manner, helping relevant personnel take measures quickly to prevent accidents. This cloud computing-based safety evaluation and early warning method greatly improves the safety management level of the pressure vessel, ensuring its reliability and stability under complex working conditions. In addition, this method also provides real-time data support for subsequent safety management decisions, helping to optimize maintenance strategies and improve resource allocation efficiency, and ultimately achieving the goals of safe, economic, and sustainable engineering management.Therefore, the present invention is an optimized treatment of a traditional safety evaluation and early warning method for pressure vessels based on digital twins, solving the problems of inaccurate analysis of the instability probability state of pressure vessels and large errors in the safety evaluation and early warning of pressure vessels in the traditional method, improving the accuracy of the analysis of the instability probability state of pressure vessels, and reducing the errors in the safety evaluation and early warning of pressure vessels.

[0010] Preferably, step S1 includes the following steps:

[0011] Step S11: Obtain the design data of the pressure vessel;

[0012] Step S12: Conduct a structural form analysis on the design data of the pressure vessel to obtain the structural form data of the pressure vessel;

[0013] Step S13: Calculate the wall thickness difference distribution of the structural form data of the pressure vessel to obtain the structural form wall thickness difference distribution data;

[0014] Step S14: Divide the structural form data of the pressure vessel into structural similarity regions according to the structural form wall thickness difference distribution data to obtain the structural form wall thickness region division data.

[0015] Through the preferred implementation of step S1 of the present invention, the design accuracy and safety of pressure vessels can be systematically improved. First of all, in step S11, obtaining the design data of the pressure vessel lays a foundation for subsequent analysis. These data cover all aspects of the design and provide important information for in-depth understanding of the structural performance. In step S12, conducting a structural form analysis of the pressure vessel can help designers identify the geometric features and force characteristics of different components, thereby obtaining the structural form data of the pressure vessel. This analysis process is crucial for comprehensively understanding the response of the structure under various loads. Subsequently, in step S13, by calculating the wall thickness difference distribution of the structural form data, the wall thickness changes in each region can be revealed. This differential wall thickness distribution data not only helps to identify weak links but also provides specific basis for design optimization. In addition, the division of the structural similarity regions according to the wall thickness difference data in step S14 further subdivides the structural form data to form different wall thickness region division data. The results of this region division provide a more refined perspective for designers, enabling them to make more targeted design improvements and safety assessments. Overall, the implementation of this series of steps not only improves the design quality of pressure vessels but also provides scientific data support for subsequent safety analysis and optimization, ensuring the reliability and safety of pressure vessels during use.

[0016] Preferably, step S2 includes the following steps:

[0017] Step S21: Based on digital twins, construct a virtualized pressure vessel regional structure model from the data of the structural form wall thickness area division, obtaining the virtualized pressure vessel regional structure model;

[0018] Step S22: Conduct a regional structure fluid load simulation on the virtualized pressure vessel regional structure model to obtain regional structure fluid load data;

[0019] Step S23: Based on the data of the structural form wall thickness difference distribution and the data of the structural form wall thickness area division, analyze the difference in the force distribution of the connection structure for the regional structure fluid load data, obtaining the difference data of the connection structure force distribution;

[0020] Step S24: Calculate the resonance buckling instability probability for the regional structure fluid load data according to the difference data of the connection structure force distribution, obtaining the resonance buckling instability probability data.

[0021] The present invention constructs a virtualized pressure vessel regional structure model based on digital twin technology, laying a solid foundation for subsequent simulations and analyses. This virtualized model can accurately reflect the actual structural characteristics of the pressure vessel and provides a necessary virtual environment for in-depth fluid load analysis, helping designers intuitively understand the performance of the structure under different working conditions. Immediately afterwards, in Step S22, a regional structure fluid load simulation is performed on the virtualized model to obtain regional structure fluid load data. These data not only reveal the way the fluid acts inside the structure but also help analyze the force characteristics of each region, ensuring that designers can effectively evaluate the dynamic fluid load. In Step S23, based on the data of the structural form wall thickness difference distribution and the area division data, an analysis of the difference in the force distribution of the connection structure is carried out to further clarify the force conditions of each connection part, helping to identify potential weak connections and stress concentration areas. Finally, in Step S24, calculating the resonance buckling instability probability for the regional structure fluid load data according to the difference data of the connection structure force distribution is extremely crucial. It provides designers with the probability of the structure experiencing resonance buckling instability under actual operating conditions, helping to identify risks in advance and take appropriate preventive measures. Overall, the implementation of these steps not only improves the safety performance evaluation ability of the pressure vessel but also provides data support for optimizing the design and improving the scheme, ensuring the stability and safety of the pressure vessel under complex working conditions.

[0022] Preferably, Step S23 includes the following steps:

[0023] Step S231: Based on the data of the structural form wall thickness difference distribution and the data of the structural form wall thickness area division, conduct an analysis of the geometric characteristics of the connection structure between different regions to obtain the connection structure geometric characteristic data;

[0024] Step S232: Calculate the adjacent connection rotation angles between different regions of the geometric feature data of the connection structure to obtain the structural adjacent connection rotation angle data;

[0025] Step S233: Calculate the slope of the connection surface between different regions of the geometric feature data of the connection structure to obtain the structural connection surface slope data;

[0026] Step S234: Perform fluid force dispersion analysis on the regional structure fluid load data based on the structural adjacent connection rotation angle data and the structural connection surface slope data to obtain the regional structure force dispersion data;

[0027] Step S235: Analyze the difference in the force distribution of the connection structure for the regional structure fluid load data based on the regional structure force dispersion data to obtain the connection structure force distribution difference data.

[0028] First of all, in step S231 of the present invention, based on the structural form wall thickness difference distribution data and the regional division data, the geometric feature analysis of the connection structure is carried out. The obtained geometric feature data of the connection structure provides a basis for subsequent force analysis. This analysis can deeply understand the geometric relationship and characteristics of the connection parts in different regions, and help identify potential problems in the design. Then, in step S232, the calculation of the adjacent connection rotation angles of the geometric feature data of the connection structure can reveal the geometric shape of the connection part and its influence on the fluid load. This analysis is crucial for ensuring the structural stability, because excessive rotation angles lead to stress concentration, thus affecting the overall performance of the structure. In step S233, the calculation of the connection surface slope further provides detailed information on the relative position between the connection surfaces, helping to analyze the force state of each connection surface under the action of the fluid. In step S234, according to the structural adjacent connection rotation angle data and the connection surface slope data, the fluid force dispersion analysis of the regional structure fluid load data can effectively identify the force dispersion situation in each region. This process ensures that designers can clearly understand the distribution and action mode of the fluid inside the structure, so as to optimize the design to reduce risks. Finally, step S235 analyzes the difference in the force distribution of the connection structure based on the regional structure force dispersion data, further enhancing the understanding of the force conditions at each connection point. The implementation of this series of steps makes the design process of the pressure vessel more scientific and refined, helps to improve its safety and reliability in practical applications, and ensures its stability under various working conditions.

[0029] Preferably, step S234 includes the following steps:

[0030] Decompose the normal component of the connection surface according to the structural adjacent connection rotation angle data and the structural connection surface slope data to obtain the normal component data of the connection surface;

[0031] Perform an interface force stress dispersion analysis on the normal component data of the connection surface to obtain interface force stress dispersion data;

[0032] Calculate the fluid shear force azimuth difference between different regions of the regional structure fluid load data based on the normal component data of the connection surface and the interface force stress dispersion data to obtain fluid shear force azimuth difference data;

[0033] Perform a fluid stress dispersion analysis between different regions based on the fluid shear force azimuth difference data and the normal component data of the connection surface to obtain regional structure stress dispersion data.

[0034] Through the implementation of the detailed steps of the fluid stress dispersion analysis, the present invention can significantly improve the design safety of pressure vessels and the prediction accuracy of fluid loads. During the analysis process, first, decompose the normal component of the connection surface through the structural adjacent connection corner data and the connection surface slope data to obtain the normal component data of the connection surface. This process lays the foundation for understanding the acting direction of the fluid on the connection surface and ensures the accuracy of subsequent analysis. The clarity of the normal component of the connection surface can help designers identify which connection areas are facing greater fluid pressure, so as to make timely design adjustments. Next, perform an interface force stress dispersion analysis based on the normal component data of the connection surface to obtain interface force stress dispersion data. This analysis reveals the stress state differences between different connection surfaces, helps identify stress concentration areas caused by improper design or structural shape, and provides an important basis for optimizing the design. Then, calculate the fluid shear force azimuth difference of the regional structure fluid load data according to the normal component data of the connection surface and the interface force stress dispersion data. This calculation can clarify the acting direction and intensity change of the fluid on the connection surface, thus revealing the potential impact of fluid shear force between different regions. Finally, the regional structure stress dispersion analysis based on the fluid shear force azimuth difference data and the normal component data of the connection surface can comprehensively evaluate the stress dispersion of the fluid between different regions. Through the implementation of this series of steps, not only the understanding of the fluid stress distribution of the pressure vessel under working conditions is improved, but also detailed data support is provided for subsequent safety assessment and optimization design. This refined analysis method ensures the safety and stability of the pressure vessel in actual use and promotes the scientific and rationalization of its design process.

[0035] Preferably, step S24 includes the following steps:

[0036] Step S241: Simulate the fluid resonance frequency of the regional structure fluid load data according to the connection structure stress distribution difference data to obtain regional fluid resonance frequency data;

[0037] Step S242: Calculate the load cross-section moment of inertia between different regional structures of the regional structure fluid load data based on the regional fluid resonance frequency data to obtain structural load cross-section moment of inertia data;

[0038] Step S243: Perform inertial distortion integration on the structural load cross-sectional moment of inertia data to obtain cross-sectional inertial distortion integration data;

[0039] Step S244: Based on the cross-sectional inertial distortion integration data, perform a structural tolerance limit simulation on the regional structural fluid load data to obtain regional structural tolerance limit data;

[0040] Step S245: Calculate the resonance buckling instability probability of the regional structural fluid load data based on the cross-sectional inertial distortion integration data and the regional structural tolerance limit data to obtain resonance buckling instability probability data.

[0041] First of all, in step S241 of the present invention, based on the connection structure force distribution difference data, a fluid resonance frequency simulation is performed on the regional structural fluid load data, and the obtained regional fluid resonance frequency data provides key parameters for subsequent analysis. This step can reveal the vibration characteristics of the fluid in different regions, help identify potential resonance risk regions, and ensure that designers can optimize them specifically. Subsequently, in step S242, based on the regional fluid resonance frequency data, the load cross-sectional moment of inertia between different regional structures is calculated to obtain the structural load cross-sectional moment of inertia data. This calculation can not only help understand the force conditions of each region under different loads, but also provide an important basis for evaluating the stability of the structure. In the next step S243, by performing inertial distortion integration on the structural load cross-sectional moment of inertia data, cross-sectional inertial distortion integration data is obtained, further analyzing the structural deformation characteristics under the action of the fluid, and laying a foundation for evaluating the adaptability of the structure. In step S244, based on the cross-sectional inertial distortion integration data, a structural tolerance limit simulation is performed on the regional structural fluid load data, and regional structural tolerance limit data can be obtained. This step is very important because it helps designers clarify the bearing capacity of the structure under extreme working conditions and provides a scientific basis for safety assessment. Finally, in step S245, the resonance buckling instability probability calculation based on the cross-sectional inertial distortion integration data and the regional structural tolerance limit data, and the obtained resonance buckling instability probability data provides key decision-making basis for designers to identify and prevent potential instability risks. The implementation of this series of steps not only improves the safety assessment ability of the pressure vessel under complex working conditions, but also provides practical data support for the optimized design of the structure, ensuring its long-term stability and safety in practical applications.

[0042] Preferably, step S243 includes the following steps:

[0043] Perform discretization processing of the moment of inertia of different cross-sections on the structural load cross-sectional moment of inertia data to obtain cross-sectional moment of inertia discretization data;

[0044] Perform non - linear regression analysis on the structural load cross - section moment of inertia data for different cross - sections according to the discretized data of the cross - section moment of inertia, and obtain the non - linear regression data of the moment of inertia;

[0045] Perform piece - wise interpolation on the non - linear regression data of the moment of inertia to obtain the non - linear interpolation data of the moment of inertia;

[0046] Perform inertia distortion integration on the non - linear interpolation data of the moment of inertia by the Gauss - Legendre integration method to obtain the cross - section inertia distortion integration data.

[0047] Through the detailed steps of performing inertia distortion integration on the structural load cross - section moment of inertia data, the design accuracy and safety of pressure vessels can be greatly improved. First, in this process, through the discretization of the moment of inertia of the structural load cross - section data for different cross - sections, the discretized cross - section moment of inertia data is obtained. The implementation of this step enables designers to transform the overall complex cross - section characteristics into discrete data that is easier to analyze, facilitating subsequent non - linear regression analysis. Next, the non - linear regression analysis based on the discretized cross - section moment of inertia data can reveal the complex relationship between the cross - section moment of inertia and other variables, thus obtaining the non - linear regression data of the moment of inertia. This analysis not only helps to understand the response characteristics of each cross - section under fluid load, but also provides a necessary mathematical model for subsequent interpolation processing to ensure the accuracy and effectiveness of calculations. In the subsequent piece - wise interpolation process, by processing the non - linear regression data of the moment of inertia, the non - linear interpolation data of the moment of inertia is obtained, further improving the smoothness and continuity of the cross - section moment of inertia data for use in subsequent calculations. Finally, through the inertia distortion integration of the non - linear interpolation data of the moment of inertia using the Gauss - Legendre integration method, the cross - section inertia distortion integration data is obtained. This efficient numerical integration method can effectively calculate the distortion degree of complex structures under fluid action, providing an important basis for evaluating the stability and reliability of structures. The implementation of this series of steps not only deepens the understanding of the structural stress characteristics, but also provides strong support for the safe design and operation of pressure vessels, ensuring their safety and stability under various working conditions.

[0048] Preferably, step S244 includes the following steps:

[0049] Extract the cross - section distortion resistance extreme value according to the cross - section inertia distortion integration data to obtain the cross - section distortion resistance extreme value data;

[0050] Perform structural distortion evolution response analysis on the regional structural fluid load data based on the cross - section distortion resistance extreme value data to obtain the structural distortion evolution response data;

[0051] Perform structural fracture failure simulation on the structural distortion evolution response data to obtain the structural fracture failure data;

[0052] Based on the structural fracture failure data and the structural distortion evolution response data, perform a structural tolerance limit simulation on the regional structural fluid load data to obtain the regional structural tolerance limit data.

[0053] By implementing the steps of performing a structural tolerance limit simulation on the regional structural fluid load data, the present invention can effectively improve the safety assessment ability of pressure vessels under complex working conditions. First, extract the extreme values of cross-section distortion resistance based on the cross-section inertia distortion integral data to obtain the cross-section distortion resistance extreme value data. The acquisition of this data lays a foundation for subsequent structural analysis, enabling designers to clarify the resistance characteristics of the cross-section under different fluid loads, thereby identifying existing weak links and potential failure modes. Next, based on the cross-section distortion resistance extreme value data, conduct a structural distortion evolution response analysis to deeply explore the influence of fluid load on the structural distortion characteristics. The obtained structural distortion evolution response data provides detailed information for evaluating the performance of the structure under dynamic loads. This analysis can reveal the behavioral changes of the structure under the stress state, helping designers better understand the influence of fluid on the structural stability and overall safety. In addition, further perform a structural fracture failure simulation on the structural distortion evolution response data to identify fracture points and failure modes in advance, providing a practical basis for the optimized design of the structure. Finally, based on the structural fracture failure data and the structural distortion evolution response data, perform a regional structural tolerance limit simulation to obtain the regional structural tolerance limit data. The result of this simulation provides a scientific basis for designers to ensure that the structure can still maintain sufficient safety margins under extreme working conditions and prevent structural failures caused by fluid loads. By implementing this series of steps, not only is the understanding of the stress and failure of pressure vessels under complex working conditions strengthened, but also solid data support is provided for subsequent design optimization and safety verification, ensuring the long-term safety and stable operation of pressure vessels.

[0054] Preferably, step S3 includes the following steps:

[0055] Step S31: Normalize the resonance buckling instability probability data to obtain the normalized resonance buckling instability probability data;

[0056] Step S32: Based on the random forest algorithm, construct a safety assessment logic model for the normalized resonance buckling instability probability data to obtain the safety assessment logic model of the pressure vessel.

[0057] Through the implementation of step S3, the safety assessment ability of the pressure vessel can be effectively improved, ensuring its reliability in practical applications. First, in step S31, the resonance buckling instability probability data is normalized to obtain the normalized resonance buckling instability probability data. The main purpose of normalization is to convert data with different dimensions and ranges into a unified standard, thereby eliminating the relative differences between data. This step can ensure data consistency in subsequent analyses, facilitating comparison and analysis. The normalized data is mathematically easier to process, while enhancing the stability and reliability of the model, providing a clearer basis for subsequent safety evaluations. Next, in step S32, based on the normalized data, a safety assessment logic model of the pressure vessel is constructed using the random forest algorithm. Random forest is an ensemble learning method with the advantage of handling high-dimensional data and complex relationships, capable of effectively capturing the non-linear relationship between the resonance buckling instability probability and other relevant factors. This step not only provides an effective tool for safety assessment but also improves the prediction accuracy and robustness of the model through the combination of multiple decision trees. The constructed safety assessment logic model can help engineers quickly evaluate the safety of the pressure vessel under various working conditions during the design stage, identify potential failure risks in advance, and provide a scientific basis for optimizing the design and safety verification. Through the implementation of this series of steps, the safety assessment ability of the pressure vessel is ultimately improved, providing solid data support and decision-making basis for subsequent safety designs, ensuring its reliability and stability under extreme working conditions.

[0058] Preferably, step S32 includes the following steps:

[0059] Step S321: Conduct a logical error test on the normalized resonance buckling instability probability data to obtain the resonance buckling logical error data;

[0060] Step S322: Perform error balance iteration on the normalized resonance buckling instability probability data according to the resonance buckling logical error data to obtain the resonance buckling error balance data;

[0061] Step S323: Analyze the time effect influence characteristics of the resonance buckling error balance data to obtain the error time effect influence characteristic data;

[0062] Step S324: Based on the random forest algorithm, construct a safety assessment logic model for the resonance buckling error balance data and the error time effect influence characteristic data to obtain the safety assessment logic model of the pressure vessel.

[0063] The implementation of the present invention through step S32 can significantly enhance the safety assessment ability of pressure vessels under dynamic conditions, ensuring their reliability and stability in actual use. First, in step S321, a logical error test is performed on the normalized data of the resonance buckling instability probability to obtain the resonance buckling instability logical error data. This step is crucial because it can help identify potential error sources and inconsistencies in the model, providing data support for subsequent error correction. The results of the logical error test will provide key clues for understanding the influencing factors of the resonance buckling instability probability, ensuring that subsequent analyses are based on more reliable data. Next, in step S322, based on the resonance buckling instability logical error data, error balance iteration is performed on the normalized data of the resonance buckling instability probability to obtain the resonance buckling error balance data. Through the process of error balance iteration, the original data can be effectively corrected and optimized, reducing the influence caused by errors, thereby improving the accuracy and reliability of the data. The implementation of this step provides more accurate data for subsequent analyses of the model, enabling a better reflection of the actual situation when constructing the safety evaluation model. In step S323, an analysis of the time-effect influence characteristics of the resonance buckling error balance data is performed to obtain the time-effect influence characteristic data of the error. This analysis process can help engineers understand the influence of time factors on the resonance buckling instability probability, identify changes in the performance of pressure vessels during long-term use or under specific conditions, thereby providing a basis for maintenance and monitoring. These data will enhance the adaptability and accuracy of the model to actual working conditions. Finally, in step S324, based on the random forest algorithm, a safety evaluation logical model is constructed for the resonance buckling error balance data and the time-effect influence characteristic data of the error to obtain the safety evaluation logical model of the pressure vessel. Utilizing the advantages of the random forest, important features can be extracted from complex datasets to generate an efficient logical model. This model can not only quickly evaluate the safety of pressure vessels but also provide real-time feedback for optimizing the design, enhancing the safety and reliability of pressure vessels under various working conditions. Through the implementation of this series of steps, the ultimately constructed safety evaluation logical model of the pressure vessel will provide solid data support and decision-making basis for engineering design, operation, and maintenance.

[0064] The beneficial effects of the present invention are as follows. By obtaining the design data of the pressure vessel and calculating the wall thickness difference in detail, the distribution characteristics of the wall thickness under different structural forms can be revealed. This process can not only clarify the stress states of each region but also help designers deeply understand the influence of the wall thickness on the overall performance of the structure. Through the regional division of the wall thickness difference, designers can more accurately identify potential weak links, providing a basis for subsequent improvement measures. In addition, the analysis of the stress distribution difference based on these wall thickness regional divisions can reveal the stress characteristics of the connection structure under different working conditions and evaluate its stability. By analyzing the stress distribution difference of the connection structure, important data support can be provided for calculating the probability of resonance buckling instability. Understanding the stress states of different regions is crucial for predicting their instability risks. By comprehensively considering these data, designers can identify the key stress points of the structure and evaluate its safety under actual working conditions. This data-based analysis method enables designers to carry out structural optimization more targeted, thereby improving the safety and durability of the pressure vessel, reducing the failure risk, and extending the service life. Therefore, the entire process not only improves the scientificity and rationality of the design but also provides an important theoretical basis for subsequent engineering applications. By implementing steps S3 and S4, the safety evaluation ability and early warning efficiency of the pressure vessel can be significantly improved. First, in step S3, a safety evaluation logic model based on the resonance buckling instability probability data is constructed, providing a scientific theoretical basis and decision support for the safety assessment of the pressure vessel. This logic model can not only comprehensively consider various influencing factors but also comprehensively analyze the stability of the pressure vessel by simulating the stress states under different working conditions. This model-based safety evaluation method can effectively identify potential safety hazards, helping designers timely formulate corresponding preventive measures, thereby improving the safety of the pressure vessel in actual applications. Next, in step S4, by uploading the safety evaluation logic model to the data cloud platform, the automation and intelligence of the pressure vessel safety evaluation are realized. The powerful computing power and data processing ability of the cloud platform can monitor and analyze the operating state of the pressure vessel in real time. Once potential safety risks are detected, the cloud platform can issue early warnings in a timely manner, helping relevant personnel quickly take measures to prevent accidents. This cloud computing-based safety evaluation and early warning method greatly improves the safety management level of the pressure vessel, ensuring its reliability and stability under complex working conditions. In addition, this method also provides real-time data support for subsequent safety management decisions, helping to optimize maintenance strategies and improve resource allocation efficiency, and ultimately achieving the goals of safe, economic, and sustainable engineering management.Therefore, the present invention is an optimized treatment of a traditional pressure vessel safety evaluation and early warning method based on digital twin, which solves the problems of inaccurate analysis of the instability probability state of pressure vessels and large errors in the safety evaluation and early warning of pressure vessels in the traditional method, improves the accuracy of the analysis of the instability probability state of pressure vessels, and reduces the errors in the safety evaluation and early warning of pressure vessels. Brief Description of the Drawings

[0065] Figure 1 It is a schematic flow chart of the steps of a pressure vessel safety evaluation and early warning method based on digital twin;

[0066] Figure 2 is Figure 1 a detailed implementation step flow chart of step S2 in

[0067] The realization, functional characteristics and advantages of the object of the present invention will be further described in conjunction with the embodiments with reference to the drawings. Detailed Embodiments

[0068] The technical method of the present invention will be clearly and completely described below with reference to the drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work belong to the scope of protection of the present invention.

[0069] In addition, the drawings are only schematic diagrams of the present invention and are not necessarily drawn to scale. The same reference numerals in the drawings represent the same or similar parts, and thus the repeated description of them will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. The functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor methods and / or microcontroller methods.

[0070] It should be understood that although the terms "first", "second", etc. may be used here to describe various units, these units should not be limited by these terms. These terms are only used to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, the first unit may be referred to as the second unit, and similarly the second unit may be referred to as the first unit. The term "and / or" used here includes any and all combinations of one or more of the listed related items.

[0071] To achieve the above object, please refer to Figures 1 to 2, a safety evaluation and early warning method for pressure vessels based on digital twins, the method comprising the following steps:

[0072] Step S1: Obtain the design data of the pressure vessel; calculate the wall thickness difference distribution of the pressure vessel design data to obtain the wall thickness difference distribution data of the structural form; divide the structural similarity regions according to the wall thickness difference distribution data of the structural form to obtain the wall thickness region division data of the structural form;

[0073] Step S2: Analyze the difference in the force distribution of the connection structure based on the wall thickness region division data of the structural form to obtain the difference data of the force distribution of the connection structure; calculate the resonance buckling instability probability according to the difference data of the force distribution of the connection structure to obtain the resonance buckling instability probability data;

[0074] Step S3: Construct a safety evaluation logic model for the resonance buckling instability probability data to obtain a safety evaluation logic model for the pressure vessel;

[0075] Step S4: Send the safety evaluation logic model of the pressure vessel to the data cloud platform to execute the safety evaluation and early warning method for the pressure vessel.

[0076] In the embodiment of the present invention, refer to Figure 1 As described, it is a schematic diagram of the step flow of a safety evaluation and early warning method for pressure vessels based on digital twins in the present invention. In this example, the safety evaluation and early warning method for pressure vessels based on digital twins comprises the following steps:

[0077] Step S1: Obtain the design data of the pressure vessel; calculate the wall thickness difference distribution of the pressure vessel design data to obtain the wall thickness difference distribution data of the structural form; divide the structural similarity regions according to the wall thickness difference distribution data of the structural form to obtain the wall thickness region division data of the structural form;

[0078] In the embodiment of the present invention, the acquisition of the pressure vessel design data includes extracting key information such as structural dimensions and material properties from the manufacturer of the pressure vessel, design drawings, and engineering standard specifications. These design data are standardized to ensure that data from different sources have a consistent format and unit. In the calculation of the wall thickness difference distribution, based on the finite element analysis (FEA) technology and applying the stress analysis theory, different wall thickness regions of the pressure vessel are calculated. By refining the discrete distribution of the wall thickness data, the difference between the wall thickness fluctuation range of each region and the standard wall thickness is extracted. To ensure the calculation accuracy, the numerical integration method is used to calculate the deviation between the local wall thickness and the overall wall thickness distribution, and "wall thickness difference distribution data of the structural form" is generated. This data will be stored in matrix form and the difference degree of each wall thickness region is distinguished to support subsequent structural form analysis.

[0079] Step S2: Analyze the differences in the force distribution of the connection structure based on the data of the wall thickness area division of the structural form to obtain the data of the force distribution differences of the connection structure; calculate the probability of resonance buckling instability according to the data of the force distribution differences of the connection structure to obtain the data of the probability of resonance buckling instability;

[0080] In the embodiment of the present invention, the "data of the wall thickness area division of the structural form" generated in Step S1 is used, combined with the stress distribution theory, and the finite element method is used to analyze the force of the connection structure (such as welds, flange connections, etc.) of the pressure vessel. Using elastoplastic mechanics and structural analysis methods, a force field distribution model of the connection structure under different load conditions is established. By numerically iterating the stress distribution in the wall thickness difference area, the "data of the force distribution differences of the connection structure" is generated. In this process, it is necessary to calculate the stress concentration coefficients of different connection parts under various stress actions (such as internal pressure, external pressure, and torsion, etc.), and then evaluate the distribution differences of the forces in each area. The final data shows the force changes in different areas in the form of a three-dimensional stress field diagram. According to the buckling theory in structural mechanics, the probability of resonance buckling instability is calculated for the "data of the force distribution differences of the connection structure". The buckling instability calculation needs to consider the material nonlinear characteristics and stress hardening effect of the pressure vessel, and the energy method is used to analyze the critical stress values of different connection parts. By establishing a random vibration analysis model, the occurrence probability of structural buckling instability under external random vibration is calculated. The Monte Carlo method is used to perform multiple iterative operations on the probability of resonance buckling instability, and finally the "data of the probability of resonance buckling instability" is obtained, and this data represents the instability risk of different parts in the form of a multi-dimensional matrix.

[0081] Step S3: Construct a safety evaluation logic model for the data of the probability of resonance buckling instability to obtain a safety evaluation logic model of the pressure vessel;

[0082] In the embodiment of the present invention, after obtaining the "data of the probability of resonance buckling instability", a safety evaluation logic model of the pressure vessel is constructed. The construction of the logic model is based on the fuzzy logic theory and the analytic hierarchy process (AHP). By quantitatively and qualitatively analyzing each key risk factor, factors such as the structural buckling, force difference, wall thickness distribution, and environmental load of the pressure vessel are incorporated into the model. The safety margin evaluation method is used to weight different parameters, and the comprehensive safety factor of each structural part is obtained through logical operations. The output of the model is the safety evaluation grade of each structure, and the logical relationship is represented in the form of a decision tree. The finally generated safety evaluation logic model of the pressure vessel can automatically adapt to different load conditions and environmental conditions.

[0083] Step S4: Send the safety evaluation logic model of the pressure vessel to the data cloud platform to execute the safety evaluation and early warning method of the pressure vessel.

[0084] In the embodiments of the present invention, the operating state of the pressure vessel is monitored in real time by Internet of Things (IoT) devices, and the real-time monitoring data is combined with the safety evaluation logic model constructed in step S3. In the data cloud platform, the received data is parsed in real time to evaluate the operating safety of the current pressure vessel. The data cloud platform regularly analyzes the monitoring data and triggers a warning signal according to the risk warning rules in the safety evaluation logic model. When the safety factor in a certain area is lower than the set threshold, the platform will automatically send a safety warning message to remind the relevant maintenance personnel to perform an intervention operation. At the same time, the data cloud platform will generate a detailed safety evaluation report, including historical operating data and risk trend analysis, to ensure continuous monitoring and warning of the operating state of the pressure vessel.

[0085] Preferably, step S1 includes the following steps:

[0086] Step S11: Obtain the design data of the pressure vessel;

[0087] Step S12: Perform a structural form analysis on the design data of the pressure vessel to obtain the structural form data of the pressure vessel;

[0088] Step S13: Calculate the wall thickness difference distribution of the pressure vessel structural form data to obtain the structural form wall thickness difference distribution data;

[0089] Step S14: Divide the structural similarity regions of the pressure vessel structural form data according to the structural form wall thickness difference distribution data to obtain the structural form wall thickness region division data.

[0090] In the embodiments of the present invention, the acquisition of pressure vessel design data is carried out by extracting drawings and specification documents from pressure vessel manufacturers, which contain key structural information and parameters, such as diameter, length, material properties, weld positions, design pressure, and design temperature, etc. The data includes two-dimensional CAD drawings, three-dimensional model data, and technical requirements in engineering standard specifications. Through a standardized technical process, the design data is converted into a format that can be further processed to ensure that each value and parameter remains consistent in subsequent calculations. These data will be used for calculations and analyses in the subsequent steps. The pressure vessel structural morphology analysis is carried out using the finite element analysis (FEA) method. First, the design data of the pressure vessel is meshed to establish an accurate three-dimensional model. The meshing uses adaptive mesh generation technology to divide the key parts of the pressure vessel, such as connection points, welds, and local weak areas, into denser meshes to improve the calculation accuracy. By performing static and dynamic analyses on the structural model, the key structural areas of the pressure vessel are identified. Then, morphological analysis technology is applied to extract the geometric morphological features of the pressure vessel, including curved surface shape, corner radius, and spatial position distribution of welds. After multiple iterations and corrections, "pressure vessel structural morphology data" is generated, which is stored in a multi-dimensional space and contains detailed information about each local structure. When processing the "pressure vessel structural morphology data", first, the wall thickness of each structural area is measured and compared with the standard wall thickness in the design specification. The calculation of the wall thickness difference distribution uses the deviation analysis method in statistics to calculate the difference between the wall thickness values in different areas and the standard values. Specifically, the numerical integration method is used to calculate the area of each wall thickness area to ensure the accuracy of the data. At the same time, in order to capture subtle wall thickness changes, multi-dimensional difference calculations are used, especially in the areas around local weak points and stress concentration points, to ensure that the wall thickness changes in these areas are accurately recorded. The generated "structural morphology wall thickness difference distribution data" is stored in the form of two-dimensional and three-dimensional matrices and presented in the form of a color gradient map to show the spatial distribution of the wall thickness difference for subsequent analysis. Based on the "structural morphology wall thickness difference distribution data", a clustering algorithm is used to divide the structure of the pressure vessel into similarity classes. This step uses the K-means clustering algorithm. By calculating the similarity between the wall thickness difference values of each area and its neighboring areas, the areas with similar wall thickness differences are grouped together. First, the wall thickness difference data of each area is standardized, and then the similarity between each area is calculated through the Euclidean distance and divided into multiple structural areas according to the similarity. The divided areas are marked and stored as "structural morphology wall thickness area division data". The output data of this step is used to generate a heat map through a spatial data visualization tool to show the division results of each similar area, displaying the wall thickness change trend of the pressure vessel and the distribution of the structural difference areas.

[0091] Preferably, step S2 includes the following steps:

[0092] Step S21: Based on digital twins, construct a virtualized pressure vessel regional structure model from the data of the structural form wall thickness regional division to obtain the virtualized pressure vessel regional structure model;

[0093] Step S22: Conduct a regional structure fluid load simulation on the virtualized pressure vessel regional structure model to obtain regional structure fluid load data;

[0094] Step S23: Based on the data of the structural form wall thickness difference distribution and the data of the structural form wall thickness regional division, conduct an analysis of the difference in the force distribution of the connecting structure on the regional structure fluid load data to obtain the difference data of the force distribution of the connecting structure;

[0095] Step S24: Calculate the resonance buckling instability probability for the regional structure fluid load data based on the difference data of the force distribution of the connecting structure to obtain the resonance buckling instability probability data.

[0096] As an example of the present invention, refer to Figure 2 As shown, in this example, step S2 includes:

[0097] Step S21: Based on digital twins, construct a virtualized pressure vessel regional structure model from the data of the structural form wall thickness regional division to obtain the virtualized pressure vessel regional structure model;

[0098] In the embodiment of the present invention, based on the "data of the structural form wall thickness regional division", a virtualized pressure vessel regional structure model is constructed. Digital twin technology is used to generate a high-precision virtual model of the pressure vessel to ensure that the model can truly reproduce the physical characteristics and dynamic behavior of the pressure vessel. First, the "data of the structural form wall thickness regional division" is imported into the three-dimensional modeling environment, and the corresponding three-dimensional regional structure model is generated through multi-point grid refinement technology. The construction process of the model applies the principles of geometric topology to ensure that the spatial characteristics of each region are accurately expressed and the difference in the wall thickness distribution of each region is clearly reflected. The model also integrates information such as the material properties, temperature distribution, and pressure gradient of the container to provide a comprehensive virtualized representation.

[0099] Step S22: Conduct a regional structure fluid load simulation on the virtualized pressure vessel regional structure model to obtain regional structure fluid load data;

[0100] In the embodiments of the present invention, after the virtualized pressure vessel regional structure model is constructed, fluid load simulation is performed on the model. This process uses the computational fluid dynamics (CFD) method to simulate the flow behavior of the fluid inside the pressure vessel. First, the physical property parameters of the fluid (such as density, viscosity, etc.) and the flow boundary conditions inside the pressure vessel are set, including the inlet pressure, outlet velocity, and fluid temperature change. Then, the Navier-Stokes equation is used to numerically solve the fluid behavior, simulating the pressure distribution, velocity field, and shear stress in each region. This simulation uses the finite volume method for spatial discretization to ensure that the dynamic changes of the fluid in complex structure regions are accurately captured. The finally output "regional structure fluid load data" includes the fluid pressure borne by each region and its distribution.

[0101] Step S23: Based on the structural form wall thickness difference distribution data and the structural form wall thickness region division data, perform an analysis of the force distribution difference of the connection structure on the regional structure fluid load data to obtain the connection structure force distribution difference data;

[0102] In the embodiments of the present invention, in this step, the "structural form wall thickness difference distribution data" and the "structural form wall thickness region division data" are combined with the "regional structure fluid load data" to perform an analysis of the force distribution difference of the connection structure. First, through the superposition principle of the mechanical field, the fluid load borne by the regional structure is associated with the wall thickness difference of the structure, and the change of the mechanical stress received by each structure connection point is analyzed. Using stress analysis techniques (such as the von Mises stress criterion), calculate the stress distribution of different wall thickness regions when stressed, and pay special attention to the stress concentration regions at the joints. To ensure the accuracy of the analysis results, the differential finite element method is used to further refine the force changes in these regions to generate the "connection structure force distribution difference data", which reflects the force differences of each connection point and identifies the structural regions that cause fatigue failure or local stress overload.

[0103] Step S24: Calculate the resonance buckling instability probability of the regional structure fluid load data according to the connection structure force distribution difference data to obtain the resonance buckling instability probability data.

[0104] In the embodiments of the present invention, the calculation of the resonance buckling instability probability is based on the "data of the stress distribution difference of the connection structure" and the "data of the fluid load of the regional structure". First, through the natural frequency analysis, the vibration modes of the pressure vessel under stress are identified, and combined with the elastic modulus of the material and the geometric characteristics of the structure, the natural frequencies of the structure under different stress states are calculated. Subsequently, the vibration response of the pressure vessel under the fluid load is compared with its natural frequency to determine the regions where resonance occurs. Using the Euler buckling theory, the buckling critical loads of these regions in the resonance state are further calculated to evaluate the risk of instability. Finally, using the extreme value distribution theory in probability theory, combined with the stress distribution and buckling critical loads of each structural region, the probabilities of resonance buckling instability occurring in each region are calculated to generate the "data of resonance buckling instability probability", providing a basis for the safety evaluation of the pressure vessel.

[0105] Preferably, step S23 includes the following steps:

[0106] Step S231: Analyze the geometric characteristics of the connection structure between different regions based on the data of the wall thickness difference distribution of the structural form and the data of the wall thickness region division of the structural form to obtain the data of the geometric characteristics of the connection structure;

[0107] Step S232: Calculate the adjacent connection angles between different regions of the data of the geometric characteristics of the connection structure to obtain the data of the adjacent connection angles of the structure;

[0108] Step S233: Calculate the slopes of the connection surfaces between different regions of the data of the geometric characteristics of the connection structure to obtain the data of the slopes of the connection surfaces of the structure;

[0109] Step S234: Analyze the dispersion of the fluid forces between different regions of the data of the fluid load of the regional structure according to the data of the adjacent connection angles of the structure and the data of the slopes of the connection surfaces of the structure to obtain the data of the dispersion of the forces on the regional structure;

[0110] Step S235: Analyze the difference in the stress distribution of the connection structure of the data of the fluid load of the regional structure according to the data of the dispersion of the forces on the regional structure to obtain the data of the difference in the stress distribution of the connection structure.

[0111] In the embodiments of the present invention, by comparing the "structural form wall thickness difference distribution data" and the "structural form wall thickness region division data", the geometric characteristics of the connection structures in different regions are analyzed. First, for the wall thickness change trends in each region, combined with geometric characteristic analysis methods, three-dimensional geometric models of each region are established. By extracting the geometric information of the connection parts region by region, special attention is paid to the connection boundaries between adjacent regions and the local geometric forms of the connection parts, such as arc connections, straight connections, and transition sections. The curvature analysis method of differential geometry is used to quantitatively calculate the geometric characteristics at the connection points, and finally, "connection structure geometric characteristic data" is generated. This data contains geometric difference information between different regions and provides a basis for subsequent mechanical analysis. Using the "connection structure geometric characteristic data" generated in the previous step, the connection structure rotation angles between adjacent regions are calculated through geometric topology analysis. The specific method is to select the connection surfaces of each pair of adjacent regions, and based on the difference in normal vectors between these surfaces, use the vector dot product formula to calculate the connection rotation angle between the two regions. At the same time, considering the influence of the rotation angle change on the stress concentration region, a multi-point fitting algorithm is used to accurately calculate the average rotation angle and local rotation angle difference at each connection point. The calculation process includes point-by-point sampling of the geometric data of each region to ensure the high precision and accuracy of the rotation angle calculation results. Finally, "structural adjacent connection rotation angle data" is obtained, and this data will be used for subsequent mechanical load analysis. Based on the "connection structure geometric characteristic data", the slope of the connection surface between each region is calculated through gradient analysis. First, the connection surfaces of each region are locally planarized, and the spatial coordinate information of each point on the surface is extracted. Then, derivative and difference methods are used to calculate the local slope of each point on the connection surface. To ensure the accuracy of the slope calculation, multiple points on each connection surface are sampled multiple times, and a weighted average method is used to synthesize the local slope changes of each point. This calculation can not only quantify the inclination degree of the connection surfaces of each region but also capture the bending or mutation of the local region, generating "structural connection surface slope data". This data will help analyze the force-bearing situation of the connection structure. Combining the "structural adjacent connection rotation angle data" and the "structural connection surface slope data", a force dispersion analysis of the fluid load distribution in the regional structure is carried out. The analysis method is based on the pressure dispersion principle in fluid mechanics. By analyzing the dispersion effect of the rotation angle and slope on the fluid load at the connection, the force-bearing situation of each region is judged. The specific operations include using the Laplace equation to reconstruct the fluid load of each region, inputting the data of the rotation angle and slope as boundary conditions, and gradually calculating the pressure gradient change and the dispersion path of the fluid load in each region. The finally output "regional structure force dispersion data" details the force dispersion law of the fluid in different connection regions and lays a foundation for further force analysis. Through the "regional structure force dispersion data", an in-depth analysis of the difference in the force distribution of the connection structure of the "regional structure fluid load data" is carried out. Using the finite element method in stress analysis, the fluid load distribution of each region is combined with the force dispersion data to analyze the force difference of the fluid load in the connection structure.First, focus on analyzing the stress concentration areas at each connection point, and use the von Mises stress criterion to calculate the stress distribution of the connection structure. Secondly, based on the fluid load distribution and the structural geometric characteristics, calculate the strain gradient change in the stress concentration area. Finally, the generated "data on the differences in the force distribution of the connection structure" will reflect the force differences at each connection part under different load conditions, which helps to evaluate the stability and safety of the structure.

[0112] Preferably, step S234 includes the following steps:

[0113] Decompose the normal component of the connection surface according to the adjacent connection corner data of the structure and the slope data of the connection surface of the structure to obtain the normal component data of the connection surface;

[0114] Conduct an analysis of the dispersion of the interface force on the normal component data of the connection surface to obtain the data on the dispersion of the interface force;

[0115] Calculate the difference in the azimuth of the fluid shear force between different regions for the regional structure fluid load data according to the normal component data of the connection surface and the data on the dispersion of the interface force to obtain the data on the difference in the azimuth of the fluid shear force;

[0116] Conduct an analysis of the dispersion of the fluid force between different regions based on the data on the difference in the azimuth of the fluid shear force and the normal component data of the connection surface to obtain the data on the dispersion of the regional structure force.

[0117] In the embodiments of the present invention, based on the "structural adjacent connection corner data" and the "structural connection surface slope data", the vector decomposition method of analytic geometry is used to calculate the normal components of each connection surface. The specific operations include, first, extracting the normal vector of the connection surface and decomposing it into components parallel to each main axis. During the decomposition process, the normal components of each connection surface in three-dimensional space are calculated by the cosine of the angle method. Matrix operations are used to process a large number of connection surfaces one by one to ensure the comprehensiveness and accuracy of the calculation. Especially in the curved surface connection area, more sampling points are added to improve the accuracy. The finally generated "connection surface normal component data" is used to describe the normal distribution characteristics of each connection surface between different regions, ensuring that in subsequent mechanical analyses, the direction and magnitude of the force can accurately reflect the actual situation of the regional structure. Based on the "connection surface normal component data", the mechanical dispersion method in finite element analysis (FEM) is used to analyze the force-bearing situation of the interface force. First, for each connection surface, different external force loads are applied according to the data of its normal components. By the step-by-step loading method, the effect of fluid pressure on each connection surface is simulated, and the distribution characteristics of the normal force are focused on. During this process, the stress-strain relationship law is used, combined with the elastic modulus and structural form of the material, to analyze the distribution path of the normal force on the connection surface and the stress concentration area. After multiple rounds of calculations, the "interface force force dispersion data" is generated, which accurately describes the diffusion and dispersion of the fluid force on each connection surface and can further reveal the force-bearing law of the connection surface. Through the "connection surface normal component data" and the "interface force force dispersion data", the shear force under the action of fluid load is calculated. The specific implementation method is, first, based on the normal components of the connection surface, the direction and magnitude of the shear force are calculated, and the shear force distribution on each connection surface is evaluated through the boundary layer theory of fluid mechanics. For the connection surfaces between different regions, the angular differential method is used to calculate the azimuth difference of the shear force, that is, the change in the direction of the shear force on adjacent connection surfaces. This method can effectively capture the shear force imbalance phenomenon caused by the change in the inclination angle and slope of the connection surfaces between regions. The finally generated "fluid shear force azimuth difference data" will be used to evaluate the force change of the fluid in the pressure vessel structure, especially the stress concentration phenomenon in the high shear force area. Combining the "fluid shear force azimuth difference data" and the "connection surface normal component data", the final analysis of the fluid force dispersion situation in the regional structure is carried out. Using the principle of force decomposition and synthesis, the fluid forces in different regions are vectorially superimposed and dispersed. By constructing a force-bearing network model, the fluid force is gradually dispersed to each connection surface, and the distribution of the fluid force in the regional structure is evaluated according to the direction difference of the shear force. Especially for complex geometric structures and adjacent connection regions, the multi-dimensional stress path analysis method is used to ensure the uniformity and continuity of the fluid force. The output of this step is the "regional structure force dispersion data", which describes the dispersion path of the fluid force in different structural regions and provides key data basis for structural safety assessment and early warning.

[0118] Preferably, step S24 includes the following steps:

[0119] Step S241: Perform a fluid resonance frequency simulation on the regional structural fluid load data according to the force distribution difference data of the connection structure to obtain regional fluid resonance frequency data;

[0120] Step S242: Calculate the moment of inertia of the load cross-section between different regional structures for the regional structural fluid load data based on the regional fluid resonance frequency data to obtain structural load cross-section moment of inertia data;

[0121] Step S243: Perform an inertial distortion integration on the structural load cross-section moment of inertia data to obtain cross-section inertial distortion integration data;

[0122] Step S244: Perform a structural tolerance limit simulation on the regional structural fluid load data according to the cross-section inertial distortion integration data to obtain regional structural tolerance limit data;

[0123] Step S245: Calculate the resonance buckling instability probability for the regional structural fluid load data according to the cross-section inertial distortion integration data and the regional structural tolerance limit data to obtain resonance buckling instability probability data.

[0124] In the embodiments of the present invention, the fluid resonance frequency is simulated based on the "data of the difference in the force distribution of the connection structure". The specific operations include, first, combining the fluid load data with the structural force distribution, and determining the potential resonance regions by analyzing the non-uniformity of the force distribution. Using the natural frequency calculation method in fluid dynamics, the morphological characteristics of the regional structure are combined with the fluid load to establish a mathematical model of the resonance frequency. Applying Fourier transform to perform frequency-domain analysis on the fluid force fluctuations, identifying the peak values of the resonance frequency, and refining the resonance frequency of each region through local resonance analysis, finally generating the "regional fluid resonance frequency data". This data will be used to further evaluate the dynamic response and stability of the structure. Based on the "regional fluid resonance frequency data", the moment of inertia of the structural load of different regions is calculated. As an important parameter for measuring the torsional and bending resistance of the structure, the moment of inertia is first calculated in detail by the mechanical integration method for the stress field distribution caused by the fluid load applied to each cross-section. Using the cross-sectional shape integration formula and combining the structural geometric characteristics of different regions, the moment of inertia of each cross-section under the action of the fluid load is gradually calculated. Considering the influence of the resonance frequency on the moment of inertia, the dynamic moment equation is used to correct the load moment of inertia, and finally the "structural load cross-sectional moment of inertia data" is obtained, which lays the foundation for the subsequent inertia distortion analysis. Based on the "structural load cross-sectional moment of inertia data", the mechanical distortion integral method in mechanics is used to analyze the inertia distortion effects of different regions. In the specific operation, by the structural mechanics integration method, the moment of inertia of each cross-section in each region is integrated point by point to calculate the stress distribution of each cross-section in the distorted state. The Lagrangian integration method is used in this process to calculate the change path of the moment of inertia in segments, ensuring that the inertia distortion effects of each region can be accurately captured and described. By introducing the energy conservation equation, the total effect of the inertia distortion is analyzed, and finally the "cross-sectional inertia distortion integral data" is obtained. This data provides a key mechanical basis for the evaluation of the structural tolerance under the action of the fluid load. In this step, the tolerance limit of the regional structure is simulated using the "cross-sectional inertia distortion integral data". In the specific implementation process, the limit analysis method is used to evaluate the tolerance of each region's structure. By comparing the stress under the action of the fluid load with the physical limit value of the structure, the critical stress points of different regions are calculated. Using the yield criterion in material mechanics (such as the Von Mises criterion), the distortion effects and load limits of each region are matched and analyzed to confirm the tolerance limit of each region one by one. After multiple rounds of iteration and data correction, the "regional structure tolerance limit data" is finally generated, which defines the tolerance limit state of different regions under the action of complex fluids. Combining the "cross-sectional inertia distortion integral data" and the "regional structure tolerance limit data", the probability of resonance buckling instability under the fluid load is calculated. Using the buckling instability theory, first, the stability of the stress state of each region is analyzed, and by introducing the probability distribution model of the stochastic resonance effect, the buckling instability risk caused by the fluid resonance is calculated.This process quantifies the instability probability using the Poisson distribution function and further refines the instability risks in different regions through the critical load equation in structural buckling theory. The finally generated "resonance buckling instability probability data" is used to evaluate the buckling instability risk of the pressure vessel under dynamic loads, ensuring the accuracy and comprehensiveness of the structural safety assessment.

[0125] Preferably, step S243 includes the following steps:

[0126] Perform discretization processing of the moment of inertia of the structural load cross-section for different cross-sections to obtain discretized moment of inertia data of the cross-section;

[0127] Conduct non-linear regression analysis of the structural load cross-section moment of inertia data based on the discretized moment of inertia data of the cross-section to obtain non-linear regression data of the moment of inertia;

[0128] Perform piecewise interpolation processing on the non-linear regression data of the moment of inertia to obtain non-linear interpolation data of the moment of inertia;

[0129] Perform inertia distortion integration on the non-linear interpolation data of the moment of inertia through the Gauss-Legendre integration method to obtain cross-section inertia distortion integration data.

[0130] In the embodiments of the present invention, first, the moment of inertia data of the structural load cross-section is analyzed in segments. Based on the geometric and physical characteristics of each cross-section, the corresponding moment of inertia data is discretized. To ensure the accuracy of the discretization result, multiple sets of discrete points are selected to characterize the moment of inertia distribution of the cross-section. Each discrete point is refined by the influence of the cross-sectional area, position, and fluid load on the structure. By adopting discretization methods such as the trapezoidal method or equal-distance discretization method, the discrete values of the moment of inertia of each cross-section are determined one by one to ensure that all discrete points can completely describe the change of the cross-sectional moment of inertia. The finally obtained "discretized data of the cross-sectional moment of inertia" will provide data support for the subsequent non-linear regression analysis. Based on the discretized moment of inertia data, a non-linear regression analysis method is used to fit the moment of inertia data of each cross-section. First, a suitable non-linear function form (such as a polynomial function or an exponential function) is selected to express the change trend of the moment of inertia with the cross-sectional position. Then, the least squares method is used to fit the discretized moment of inertia data of each cross-section point, and the function parameters are adjusted step by step through iteration to achieve the best fitting effect. Through such non-linear regression analysis, the change law of the moment of inertia between different cross-sections can be accurately captured, and finally, "non-linear regression data of the moment of inertia" is obtained, which reflects the non-linear mechanical characteristics of each cross-section under the action of fluid load. To further refine the change of the moment of inertia, the piecewise interpolation method is used to interpolate the "non-linear regression data of the moment of inertia". In specific operations, first, the non-linear regression curve of each cross-section is divided into several small segments to ensure that the interpolation function can accurately fit the actual data within each small segment. The cubic spline interpolation method or Lagrange interpolation method is used to perform local interpolation on each small segment, so that the interpolated curve can not only smoothly connect each regression segment but also accurately reflect the non-linear change of the moment of inertia of each cross-section. Through precise interpolation processing, "non-linear interpolation data of the moment of inertia" is generated, which can provide a more accurate input for the next integral calculation. Finally, based on the "non-linear interpolation data of the moment of inertia", the inertial distortion integral of the moment of inertia of different cross-sections is performed by the Gauss-Legendre integral method. The Gauss-Legendre integral method is an efficient numerical integration method suitable for dealing with the integral problems of non-linear functions. This method approximates the integral value of the moment of inertia by selecting multiple integration points (weight coefficients). First, the moment of inertia interpolation data is divided into several integral intervals, and then the Gauss-Legendre integral is used to integrate each interval, and the integral results of each interval are accumulated to obtain the final inertial distortion effect value. Through precise integral processing, "cross-sectional inertial distortion integral data" is generated, which can be used to evaluate the distortion response of the structure under the action of fluid load and its tolerance limit.

[0131] Preferably, step S244 includes the following steps:

[0132] Extract the extreme value of cross-section distortion resistance according to the cross-section inertia distortion integral data to obtain the cross-section distortion resistance extreme value data;

[0133] Conduct a structural distortion evolution response analysis on the regional structure fluid load data based on the cross-section distortion resistance extreme value data to obtain the structural distortion evolution response data;

[0134] Conduct a structural fracture failure simulation on the structural distortion evolution response data to obtain the structural fracture failure data;

[0135] Conduct a structural tolerance limit simulation on the regional structure fluid load data according to the structural fracture failure data and the structural distortion evolution response data to obtain the regional structure tolerance limit data.

[0136] In the embodiments of the present invention, the extreme values of the torsional resistance of each cross-section under different fluid loads are extracted according to the "cross-sectional inertia torsional integral data". First, using the extreme value extraction algorithm, and adopting the judgment conditions based on the first derivative and the second derivative, the extreme value points in the cross-sectional torsional integral data are identified. By solving the derivative of the curve, the local maximum and minimum values are determined. This process involves using the linear interpolation method to improve the positioning accuracy of the extreme values, ensuring that the extracted extreme values of the torsional resistance can truly reflect the load-bearing capacity of the cross-section. Through rigorous analysis, the obtained "cross-sectional torsional resistance extreme value data" can effectively describe the anti-torsion ability of the structure under the action of external fluid loads. Combining the "cross-sectional torsional resistance extreme value data" with the "regional structure fluid load data", the structural torsional evolution response analysis is carried out. Using the finite element analysis method, first, the regional structure is divided into multiple small units. By establishing the mechanical model of each unit, the torsional resistance extreme values are used to weight the fluid load, and the torsional response under different conditions is simulated. During the simulation process, the dynamic analysis technology is adopted. Considering the change of the fluid load over time, the deformation and stress distribution of the structure under the action of the fluid are gradually calculated. Finally, the generated "structural torsional evolution response data" can comprehensively reflect the dynamic response characteristics of the regional structure under the influence of the fluid load. Using the "structural torsional evolution response data" for the structural fracture failure simulation. First, based on the fracture mechanics theory, by calculating the stress intensity factor of the structure, the possibility of the structure fracture under the existing fluid load is evaluated. Adopting the interaction model of the stress field and the strain field, the torsional evolution response data is converted into the stress distribution, and the stress concentration area is determined by the threshold method. Then, the step-by-step incremental method is used to simulate the fracture process, observing the failure behavior of the structure under different load conditions, and obtaining the "structural fracture failure data". This data not only reflects the critical point of the fracture but also provides important information about the failure mode. Combining the "structural fracture failure data" and the "structural torsional evolution response data", the tolerance limit simulation of the regional structure is carried out. By establishing a comprehensive mechanical model, combining the maximum load-bearing capacity and the failure mode of the structure under the fluid load, the limit analysis method and the limit equilibrium method are used to evaluate the tolerance limit of the structure. First, by calculating the limit load-bearing capacity of the structure under different fluid pressures, combined with the fracture failure mode, the tolerance limit is gradually deduced. During this process, the force and deformation states of the structure are visualized by graphical means, making the result of the tolerance limit more intuitive, and finally obtaining the "regional structure tolerance limit data". This data provides a scientific basis for the safety assessment of pressure vessels and helps to improve the effectiveness of safety warning.

[0137] Preferably, step S3 includes the following steps:

[0138] Step S31: Normalize the resonance buckling instability probability data to obtain the normalized resonance buckling instability probability data;

[0139] Step S32: Construct a safety evaluation logic model for the normalized data of resonance buckling instability probability based on the random forest algorithm to obtain a safety evaluation logic model for pressure vessels.

[0140] In the embodiment of the present invention, first, "resonance buckling instability probability data" is collected, which represents the probability of a pressure vessel buckling and becoming unstable under different working conditions. To improve the consistency and comparability of the data, this data is normalized. The specific method is to use the min-max normalization algorithm to scale the data proportionally within the range of 0 to 1. This processing ensures that data from different sources has equal weight and avoids evaluation biases caused by differences in the ranges of the original data. The finally obtained "normalized data of resonance buckling instability probability" lays the foundation for subsequent safety evaluations. A "safety evaluation logic model for pressure vessels" is constructed to more accurately evaluate the safety of pressure vessels. First, a random forest model is established using the "normalized data of resonance buckling instability probability" as input features. Random forest is an ensemble learning algorithm that classifies or regresses by constructing multiple decision trees. The normalized data is divided into a training set and a test set. Usually, 70% of the data is used for training and 30% for testing. In the training stage, several decision trees are constructed. Each tree uses randomly selected features for node splitting to ensure the diversity and anti-overfitting ability of the model. Votes are taken on the outputs of each tree to comprehensively judge the evaluation results of the safety of the pressure vessel. The hyperparameters in the random forest, such as the number of trees, maximum depth, and minimum sample split number, are adjusted through the cross-validation method to ensure the generalization ability of the model.

[0141] Preferably, step S32 includes the following steps:

[0142] Step S321: Conduct a logical error test on the normalized data of resonance buckling instability probability to obtain resonance buckling instability logical error data;

[0143] Step S322: Perform error balance iteration on the normalized data of resonance buckling instability probability according to the resonance buckling instability logical error data to obtain resonance buckling error balance data;

[0144] Step S323: Analyze the time-effect influence characteristics of the resonance buckling error balance data to obtain error time-effect influence characteristic data;

[0145] Step S324: Construct a safety evaluation logic model for the resonance buckling error balance data and the error time-effect influence characteristic data based on the random forest algorithm to obtain a safety evaluation logic model for pressure vessels.

[0146] In the embodiments of the present invention, in this step, a logical error test is performed on the "normalized data of resonance buckling instability probability" to evaluate the reliability and effectiveness of the data under different working conditions. The test is carried out by comparing the actually occurred buckling instability events with the predicted probability values. First, count the number of actually occurred buckling instability events and record the relevant working condition data. Then, using logistic regression analysis, fit the normalized data to obtain the predicted values of the model. By comparing the predicted values with the actually occurred values, calculate the logical error, and statistically analyze the error values of all data. Finally, obtain the "logical error data of resonance buckling instability", which provides a basis for subsequent error balance and model optimization. First, analyze the logical error to determine its influence degree and pattern. Use the weighted average method, combined with the magnitude and direction of the error, to adjust the normalized data. Evaluate the difference between the updated data and the original data in each iteration until the difference is less than the preset threshold to obtain the "resonance buckling error balance data". This data provides corrected basic data for subsequent analysis of the influence characteristics of aging. Analyze the influence of aging factors on the instability probability in the "resonance buckling error balance data". First, define time factors, such as operation time, service life, etc., and perform correlation analysis with the error balance data. Through time series analysis methods, construct a linear regression model to explore the relationship between time factors and errors, and evaluate the significance of time factors through analysis of variance. The finally generated "data of influence characteristics of error aging" includes the influence of time factors on the resonance buckling instability probability, providing necessary features for model construction. Focus on constructing the "logical model for safety assessment of pressure vessels". According to the "resonance buckling error balance data" and the "data of influence characteristics of error aging", use the random forest algorithm to construct the model. First, divide the data set into a training set and a test set with a ratio of 7:3 to ensure the generalization ability of the model. In the training stage, the random forest algorithm is trained by constructing multiple decision trees, and each tree uses random feature selection to enhance the robustness of the model. Subsequently, perform cross-validation to optimize model parameters, such as the number of trees and the maximum depth of each tree. After the model training is completed, use the test set to evaluate the accuracy and recall rate of the model, and evaluate the performance of the model through confusion matrix analysis. The finally generated "logical model for safety assessment of pressure vessels" will provide a scientific basis for real-time monitoring and early warning, and help ensure the safe operation of pressure vessels.

[0147] Therefore, from any perspective, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, it is intended to encompass all changes within the meaning and scope of the equivalent elements of the application documents in the present invention.

[0148] The above are only specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features invented herein.

Claims

1. A pressure vessel safety assessment and early warning method based on digital twins, characterized in that: The following steps are involved: Step S1: obtaining pressure vessel design data; performing wall thickness difference distribution calculation on the pressure vessel design data to obtain structural morphology wall thickness difference distribution data; According to the structural morphology and wall thickness difference distribution data, the structural similarity region division is performed to obtain the structural morphology and wall thickness region division data; Step S2: performing a stress distribution difference analysis of the connection structure based on the structural morphology wall thickness area division data to obtain stress distribution difference data of the connection structure; performing a resonance buckling instability probability calculation based on the stress distribution difference data of the connection structure to obtain resonance buckling instability probability data; Step S2 includes the following steps: Step S21: constructing a virtualized pressure vessel regional structure model based on the structural morphology and wall thickness regional division data based on the digital twin to obtain a virtualized pressure vessel regional structure model; Step S22: performing regional structural fluid load simulation on the virtualized pressure vessel regional structural model to obtain regional structural fluid load data; Step S23: Based on the structural form wall thickness difference distribution data and the structural form wall thickness regional division data, the regional structural fluid load data is subjected to a connection structure force distribution difference analysis to obtain the connection structure force distribution difference data; Step S24: Calculate the probability of resonant buckling instability of the regional structure fluid load data according to the force distribution difference data of the connection structure to obtain the probability data of resonant buckling instability; Step S24 includes the following steps: Step S241: performing fluid resonance frequency simulation on the regional structure fluid load data according to the force distribution difference data of the connection structure to obtain regional fluid resonance frequency data; Step S242: Calculating the load section moment of inertia between different regional structures on the regional structural fluid load data based on the regional fluid resonance frequency data to obtain structural load section moment of inertia data; Step S243: performing inertial distortion integration on the structural load section inertia moment data to obtain section inertial distortion integration data; Step S244: performing structural tolerance limit simulation on the regional structural fluid load data according to the cross-section inertial distortion integral data to obtain regional structural tolerance limit data; Step S245: Calculating the resonant buckling instability probability of the regional structure fluid load data according to the cross-section inertial distortion integral data and the regional structure tolerance limit data to obtain resonant buckling instability probability data; Step S3: constructing a safety evaluation logic model for the resonant buckling instability probability data to obtain a safety evaluation logic model for the pressure vessel; the construction of the safety evaluation logic model for the resonant buckling instability probability data includes: Performing a logical error test on the normalized data of the resonant buckling instability probability, and obtaining the resonant buckling instability logical error data; According to the resonant buckling instability logical error data, the resonant buckling instability probability normalized data is subjected to error balance iteration to obtain the resonant buckling error balance data; Perform time-dependent influence characteristic analysis on the resonant buckling error balance data to obtain error time-dependent influence characteristic data; Based on the random forest algorithm, a safety evaluation logic model is constructed for the resonant buckling error balance data and the error time-effect characteristic data, specifically: Based on the resonant buckling error balance data and error time-effect characteristic data, the model was constructed using the random forest algorithm, and the data set was divided into a training set and a test set with a ratio of 7:

3. In the training stage, the random forest algorithm was trained by constructing multiple decision trees, and each tree used random feature selection. Subsequently, cross-validation was performed to optimize the model parameters, specifically the number of trees and the maximum depth of each tree. After the model training was completed, the accuracy and recall rate of the model were evaluated using the test set, and the performance of the model was evaluated through confusion matrix analysis to generate a pressure vessel safety evaluation logic model. Step S4: Send the pressure vessel safety assessment logic model to the data cloud platform to execute the pressure vessel safety assessment early warning method.

2. The pressure vessel safety evaluation and early warning method based on digital twin according to claim 1 is characterized in that: Step S1 includes the following steps: Step S11: obtaining pressure vessel design data; Step S12: performing structural morphology analysis on the pressure vessel design data to obtain structural morphology data of the pressure vessel; Step S13: performing wall thickness difference distribution calculation on the pressure vessel structure morphology data to obtain structure morphology wall thickness difference distribution data; Step S14: dividing the pressure vessel structure data into structural similarity regions according to the structure-form wall thickness difference distribution data to obtain structure-form wall thickness region division data.

3. The pressure vessel safety evaluation and early warning method based on digital twin according to claim 1 is characterized in that: Step S23 includes the following steps: Step S231: performing geometric characteristic analysis of connection structures between different regions based on the structural form wall thickness difference distribution data and the structural form wall thickness region division data to obtain geometric characteristic data of the connection structure; Step S232: Calculating adjacent connection angles between different regions of the connection structure geometric feature data to obtain structure adjacent connection angle data; Step S233: calculating the connection surface slopes between different regions of the connection structure geometric feature data to obtain structure connection surface slope data; Step S234: performing fluid force dispersion analysis between different regions on the regional structural fluid load data according to the structural adjacent connection angle data and the structural connection surface slope data, to obtain regional structural force dispersion data; Step S235: performing connection structure force distribution difference analysis on the regional structure fluid load data according to the regional structure force dispersion data to obtain connection structure force distribution difference data.

4. The pressure vessel safety evaluation and early warning method based on digital twin according to claim 3 is characterized in that: Step S234 includes the following steps: Decomposing the connection surface normal component according to the structural adjacent connection angle data and the structural connection surface slope data to obtain the connection surface normal component data; Conducting interface force dispersion analysis on the connection surface normal component data to obtain interface force dispersion data; According to the connection surface normal component data and the interface force dispersion data, the fluid shear force orientation difference between different regions is calculated for the regional structural fluid load data to obtain the fluid shear force orientation difference data; Based on the fluid shear force azimuth difference data and the connection surface normal component data, the fluid force dispersion between different regions is analyzed to obtain the regional structural force dispersion data.

5. The pressure vessel safety evaluation and early warning method based on digital twin according to claim 1 is characterized in that: Step S243 includes the following steps: Discretize the moment of inertia of different sections of the structural load section moment of inertia data to obtain the discretized data of the section moment of inertia; According to the discretized data of section inertia moment, nonlinear regression analysis of the structure load section inertia moment data of different sections is performed to obtain the nonlinear regression data of the moment of inertia; Performing piecewise interpolation processing on the nonlinear regression data of the moment of inertia to obtain the nonlinear interpolation data of the moment of inertia; The inertia distortion integral is performed on the nonlinear interpolation data of the moment of inertia using the Gauss-Legendre integration method to obtain the section inertia distortion integral data.

6. The pressure vessel safety evaluation and early warning method based on digital twin according to claim 1 is characterized in that: Step S244 includes the following steps: Extract the extreme value of section distortion resistance according to the section inertial distortion integral data to obtain the extreme value data of section distortion resistance; Based on the extreme value data of cross-section distortion resistance, the structural distortion evolution response analysis is performed on the regional structural fluid load data to obtain the structural distortion evolution response data; Perform structural fracture failure simulation on the structural distortion evolution response data to obtain structural fracture failure data; According to the structural fracture failure data and the structural distortion evolution response data, the structural tolerance limit of the regional structural fluid load data is simulated to obtain the regional structural tolerance limit data.

7. The pressure vessel safety evaluation and early warning method based on digital twin according to claim 1 is characterized in that: Step S3 includes the following steps: Step S31: normalizing the resonant buckling instability probability data to obtain resonant buckling instability probability normalized data; Step S32: constructing a safety evaluation logic model for the normalized data of the resonant buckling instability probability based on the random forest algorithm to obtain a safety evaluation logic model for the pressure vessel.

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