Unified design method of comprehensive performance and reliability of electromagnetic equipment under service conditions

Abstract

The application provides a unified design method for comprehensive performance and reliability of electromagnetic equipment under service conditions, comprising the following steps: S1, measuring service characteristic parameters of electromagnetic energy materials in the electromagnetic equipment, and establishing a material characteristic database; S2, using the material characteristic database to establish a multi-physical field full-coupling model of the electromagnetic equipment under service conditions; S3, determining key parameters of comprehensive performance of the electromagnetic equipment and performance failure criteria, and establishing a reliability model of the comprehensive performance of the electromagnetic equipment; S4, using a modern optimization algorithm to incorporate reliability influence parameters into the multi-physical field full-coupling model, associating the full-coupling model with the reliability model, and forming a unified design for the comprehensive performance and reliability of the electromagnetic equipment under service conditions. The application realizes the long-service goal of the equipment by combining high-precision modeling of electromagnetic thermal force under service conditions of the electromagnetic equipment with reliability design, and lays a foundation for independent innovation of intelligent industrial design software for the electromagnetic equipment under service conditions.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic equipment design technology, and in particular relates to a unified design method for the comprehensive performance and reliability of electromagnetic equipment under service conditions. Background Technology

[0002] With the expansion of applications for electromagnetic equipment, the simulation of its comprehensive electromagnetic performance and the design of its reliability have become increasingly important. Electromagnetic equipment is based on electromagnetic field theory, but a product with normal comprehensive electromagnetic performance is not necessarily safe and reliable. How to integrate electromagnetic performance and reliability in the design process is a crucial and critical issue that the electromagnetic equipment manufacturing industry must address. In the current context of the continuous convergence of the energy and information revolutions, electromagnetic equipment needs to not only fulfill its normal functions but also operate more safely, reliably, stably, and efficiently. Therefore, a unified design of the comprehensive electromagnetic performance and reliability of electromagnetic equipment is necessary to better serve the construction of the future energy internet. Summary of the Invention

[0003] In view of this, the present invention aims to propose a unified design method for the comprehensive performance and reliability of electromagnetic equipment under service conditions, so as to realize the integrated design of electromagnetic comprehensive performance and reliability, provide important technical support for the design of high-reliability electromagnetic equipment, and realize the maximum application of equipment in service.

[0004] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0005] The unified design method for the comprehensive performance and reliability of electromagnetic equipment under service conditions includes the following steps: S1, measuring the service characteristic parameters of electromagnetic energy materials in the electromagnetic equipment and establishing a material characteristic database; S2, using the material characteristic database, establishing a full-fledged multi-physics coupling model of the electromagnetic equipment under service conditions; S3, determining the key parameters of the comprehensive performance of the electromagnetic equipment and performance failure criteria, and establishing a reliability model of the comprehensive performance of the electromagnetic equipment; S4, using modern optimization algorithms to incorporate reliability-influencing parameters into the full-fledged multi-physics coupling model, linking the full-fledged coupling model and the reliability model, and forming a unified design for the comprehensive performance and reliability of the electromagnetic equipment under service conditions.

[0006] Furthermore, the measurement of material service characteristic parameters in step S1 includes temperature characteristic measurement, stress characteristic measurement, and electromagnetic characteristic measurement; the temperature characteristic measurement is the magnetic characteristic measurement of soft magnetic materials in the range of 20℃-150℃, the stress characteristic measurement is the triaxial stress vector magnetic characteristic measurement, and the electromagnetic characteristic measurement is the magnetic characteristic measurement under pulsed current excitation.

[0007] Furthermore, step S2, establishing a full-fledged multiphysics coupling model of the electromagnetic equipment under service conditions, includes:

[0008] S21. Establish the multi-physics coupling relationship of electromagnetic equipment, and establish a unified Helmholtz free energy expression ψ(B,ε,T) for electromagnetic field, stress field and temperature field through energy theory. Then, obtain the multi-physics constitutive equation through differential relations:

[0009]

[0010] Where σ is the stress vector, ε is the strain vector, M is the magnetization, B is the magnetic flux density, and T is the temperature;

[0011] S22. Based on the material's magnetic field and stress constitutive equations, the coupling relationship equation between magnetic field strength H and stress σ is obtained:

[0012]

[0013] Among them, H prev σ represents the magnetic field strength in the previous step. prev Let represent the strain vector of the previous step, and o(ΔB,Δε,ΔT) represent a higher-order infinitesimal;

[0014] S23. Establish the constitutive equations for the quasi-static electromagnetic field, stress field, and temperature field that do not include displacement current:

[0015]

[0016] Among them, J ext It is the vector of applied excitation current density, J eddy It is the eddy vector, F ext It is applied stress, F mag It is electromagnetic force, q mag It is the heat per unit volume generated by the electromagnetic field, k is the thermal conductivity, and q is the heat generated per unit volume. F It is the heat generated by mechanical force per unit volume, including the heat generated by the high-speed frictional motion of electromagnetic energy equipment;

[0017] S24. Let the test function of the finite element variable (B,ε,T) be (w,v,T0). Use this test function to perform variational analysis on equation (3), and then substitute equation (2), ignoring higher-order terms, into the variational relation to obtain the final multiphysics coupled finite element variational result:

[0018]

[0019] Where A represents magnetic vector potential, u represents vector displacement, T represents temperature, Ω represents the multiphysics solution geometry, ρ represents density, and C represents the magnetic vector potential. p Represents the specific heat capacity of the material, operator L is the projection operator from vector displacement u to strain, and A prev ,u prev ,T prevThese are the calculated values ​​from the previous iteration; the variational form is discretized and the system of algebraic equations required by the Newton-Raphson method is constructed, and (δA, δu, δT) is solved.

[0020] Furthermore, step S3 involves determining the key parameters of the overall performance of the electromagnetic equipment and the performance failure criteria, and establishing a reliability model for the overall performance of the electromagnetic equipment, including:

[0021] S31. Based on the multi-temporal-scale multi-physics field finite element model and experiments, establish a correlation database between working stress and electromagnetic equipment performance degradation data under service conditions, obtain performance degradation characteristics, and determine the parameters affecting the comprehensive performance degradation of electromagnetic equipment and reliability impact parameters.

[0022] S32. Based on data augmentation technology, establish a proxy model for lifetime prediction of characteristic parameters and degradation data; using statistical data-driven methods, estimate degradation model parameters based on degradation trajectory to establish a probabilistic model for lifetime prediction.

[0023] S33. Based on multivariate correlation analysis, reliability allocation is achieved, the reliability function is determined, and the reliability is analyzed using surrogate model and probability model respectively. The inconsistency analysis results of the two types of models are analyzed, the performance characteristics of the two models are given, and the performance boundaries and applicable scope of surrogate model and probability model are determined.

[0024] Furthermore, step S4 includes: taking the key parameters affecting the overall performance of electromagnetic equipment under service conditions as optimization variables, taking the electromagnetic overall performance fault criteria and reliability impact parameters as constraints, taking the optimal electromagnetic overall performance and reliability as optimization objectives, and using modern optimization algorithms for uncertain problems to establish a unified design for the overall performance and reliability of electromagnetic equipment.

[0025] The modern optimization algorithms for uncertain problems include:

[0026] (1) Guided optimization algorithm based on physical distribution characteristics: predict the comprehensive performance cloud map of electromagnetic equipment; determine the distribution characteristics and structured expression of the field based on the standard deviation and variance of the overall and local physical fields of electromagnetic equipment, and obtain the optimal solution of physical field distribution through calculation and comparison; compare and study multiple population hybrid algorithms and improved non-dominated sorting genetic algorithms, and combine the obtained optimal solution to guide the optimization process to achieve the optimization of the optimization variables; continuously iterate and update until the optimal solution set is obtained.

[0027] (2) Uncertainty-based interval optimization algorithm: In the outer layer, multiple design vector individuals are generated by a multi-objective optimization algorithm. For each design individual, the upper and lower bounds of the objective function and constraints are calculated using the interval analysis method, thereby calculating the midpoint value of the objective function and the interval probability of the constraints. Then, the transformed deterministic multi-objective optimization problem is calculated to obtain the required non-dominated solution set.

[0028] Furthermore, the present invention also includes: step S5, using cloud computing and artificial intelligence to achieve a unified design of the comprehensive performance and reliability of electromagnetic equipment under service conditions.

[0029] Compared with existing technologies, the unified design method for the comprehensive performance and reliability of electromagnetic equipment under service conditions described in this invention has the following advantages:

[0030] (1) This invention measures the temperature, electromagnetic, and stress characteristics of materials under service conditions, and establishes a full-fledged multi-physics coupling model for electromagnetic equipment under service conditions; it also establishes a comprehensive performance reliability model for electromagnetic equipment, and introduces the constraint functions and uncertainties of reliability theory into the full-fledged coupling model, and constructs a unified design method for electromagnetic comprehensive performance and reliability through modern optimization methods.

[0031] (2) This invention utilizes cloud computing and artificial intelligence to achieve a unified design of the comprehensive performance and reliability of electromagnetic equipment under service conditions, and can realize precise simulation of the design method and rapid and effective calculation. Attached Figure Description

[0032] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0033] Figure 1 This is a flowchart of the unified design method for the comprehensive performance and reliability of electromagnetic equipment under service conditions as described in an embodiment of the present invention.

[0034] Figure 2 Flowchart for establishing a full-fledged coupling model of multiphysics field electromagnetic equipment under service conditions as described in the embodiments of the present invention;

[0035] Figure 3 This is a flowchart illustrating the reliability model for establishing the overall performance of electromagnetic equipment as described in an embodiment of the present invention.

[0036] Figure 4 This is a schematic diagram of the guided optimization algorithm based on physical distribution characteristics as described in an embodiment of the present invention;

[0037] Figure 5 This is a schematic diagram of the uncertainty-based interval optimization algorithm described in an embodiment of the present invention. Detailed Implementation

[0038] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0039] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0040] refer to Figure 1 This invention provides a unified design method for the comprehensive performance and reliability of electromagnetic equipment under service conditions, comprising the following steps:

[0041] S1. Measure the service characteristic parameters of the electromagnetic energy materials in the electromagnetic equipment and establish a material characteristic database.

[0042] The production and manufacturing of electromagnetic equipment, especially those operating under service conditions, must begin with materials. Accurate modeling requires first measuring the service characteristics of the materials. In this embodiment, the measured material service characteristic parameters include temperature characteristic measurement, stress characteristic measurement, and electromagnetic characteristic measurement; the temperature characteristic measurement is the magnetic characteristic measurement of soft magnetic materials within the range of 20℃-150℃, the stress characteristic measurement is the triaxial stress vector magnetic characteristic measurement, and the electromagnetic characteristic measurement is the magnetic characteristic measurement under pulsed current excitation.

[0043] For example, experiments and database construction of magnetic properties under triaxial stress under extreme conditions, design of magnetic property measurement system for orthogonal triaxial spatial stress loading, horizontal stress loading device driven by electric cylinder, vertical stress by hydraulic method, sample is cross-shaped with adjacent ends fixed, stress acquisition system consists of strain gauge, stress sensor and professional stress acquisition card.

[0044] Establishing a materials property database includes: establishing a materials property database for standard / non-standard excitation conditions of advanced electromagnetic materials; exploring methods for evaluating physicochemical parameters that can characterize the entire life cycle of advanced electromagnetic materials; and obtaining reliability data under the premise of standardization.

[0045] S2. Using the aforementioned material property database, establish a full-fledged coupling model of multi-physics fields for electromagnetic equipment under service conditions.

[0046] When a magnet operates dynamically, under the influence of a changing electromagnetic field, the conductor components within the electromagnetic equipment system experience heat loss. The armature, under the influence of the electromagnetic field, undergoes strain due to electromagnetic force. During the extremely short ejection process, there are significant temperature changes, resulting in changes in the state of matter and mechanical problems within the magnet. These temperature changes also cause variations in electrical parameters (conductivity, critical current, etc.), magnetic parameters (permeability, etc.), mechanical parameters (elastic modulus, yield strength, etc.), and thermal parameters (thermal conductivity, specific heat capacity, etc.). (Reference) Figure 2In this embodiment, establishing a full-fledged multi-physics coupling model of electromagnetic equipment under service conditions includes the following steps:

[0047] S21. Establish the multi-physics coupling relationship of electromagnetic equipment, and establish a unified Helmholtz free energy expression ψ(B,ε,T) for electromagnetic field, stress field and temperature field through energy theory. Then, obtain the multi-physics constitutive equation through differential relations:

[0048]

[0049] Where σ is the stress vector, ε is the strain vector, M is the magnetization, B is the magnetic flux density, and T is the temperature;

[0050] S22. Based on the material's magnetic field and stress constitutive equations, the coupling relationship equation between magnetic field strength H and stress σ is obtained:

[0051]

[0052] Among them, H prev σ represents the magnetic field strength in the previous step. prev Let represent the strain vector of the previous step, and o(ΔB,Δε,ΔT) represent a higher-order infinitesimal;

[0053] S23. Establish the constitutive equations for the quasi-static electromagnetic field, stress field, and temperature field that do not include displacement current:

[0054]

[0055] Among them, J ext It is the vector of applied excitation current density, J eddy It is the eddy vector, F ext It is applied stress, F mag It is electromagnetic force, q mag It is the heat per unit volume generated by the electromagnetic field, k is the thermal conductivity, and q is the heat generated per unit volume. F It is the heat generated by mechanical force per unit volume, including the heat generated by the high-speed frictional motion of electromagnetic energy equipment;

[0056] S24. Let the test function of the finite element variable (B,ε,T) be (w,v,T0). Use this test function to perform variational analysis on equation (3), and then substitute equation (2), ignoring higher-order terms, into the variational relation to obtain the final multiphysics coupled finite element variational result:

[0057]

[0058] Where A represents magnetic vector potential, u represents vector displacement, T represents temperature, Ω represents the multiphysics solution geometry, ρ represents density, and C represents the magnetic vector potential. p Represents the specific heat capacity of the material, operator L is the projection operator from vector displacement u to strain, and Aprev ,u prev ,T prev These are the calculated values ​​from the previous iteration; the variational form is discretized and the system of algebraic equations required by the Newton-Raphson method is constructed, and (δA, δu, δT) is solved.

[0059] S3. Determine the key parameters of the overall performance of the electromagnetic equipment and the performance failure criteria, and establish a reliability model of the overall performance of the electromagnetic equipment.

[0060] Starting from the causes of failures in electromagnetic energy equipment, this paper clarifies the key parameters of the equipment's overall electromagnetic performance, determines performance failure criteria, and establishes a reliability model for the equipment's overall electromagnetic performance, considering factors such as operating temperature, structure, and environment. (Reference) Figure 3 In this embodiment, determining the key parameters of the overall performance of the electromagnetic equipment and the performance failure criteria, and establishing a reliability model of the overall performance of the electromagnetic equipment includes the following steps:

[0061] S31. Based on the multi-temporal and spatial scale multi-physics field finite element model and experiments, establish a correlation database between working stress and electromagnetic equipment performance degradation data under service conditions, obtain performance degradation characteristics, and determine the parameters affecting the comprehensive performance degradation of electromagnetic equipment (such as electromagnetic thrust, wear degree, vibration, etc.) and reliability impact parameters (such as temperature rise, wear, number of launches, etc.).

[0062] S32. Based on data augmentation technology, establish a machine learning proxy model for lifetime prediction of characteristic parameters and degradation data; use statistical data-driven methods to estimate degradation model parameters based on degradation trajectory and establish a probabilistic model for lifetime prediction (such as Markov, Wiener process method and Bayesian estimation model).

[0063] S33. Based on multivariate correlation analysis, implement reliability allocation, determine the reliability function (such as the probability of successful launch of the system under specified launch conditions), analyze the reliability using surrogate model and probability model respectively, analyze the inconsistency analysis results of the two types of models, give the performance characteristics of the two models, and determine the performance boundaries and applicable scope of surrogate model and probability model.

[0064] S4. Utilize modern optimization algorithms to incorporate reliability-influencing parameters into a multi-physics field full-fidelity coupling model, link the full-fidelity coupling model with the reliability model, and form a unified design for the comprehensive performance and reliability of electromagnetic equipment under service conditions.

[0065] By taking the key parameters affecting the overall performance of electromagnetic equipment under service conditions as optimization variables, the electromagnetic overall performance fault criteria and reliability impact parameters as constraints, and the optimal electromagnetic overall performance and reliability as optimization objectives, a unified design of electromagnetic equipment overall performance and reliability is established using modern optimization algorithms for uncertain problems.

[0066] Among them, modern optimization algorithms for uncertain problems include guided optimization algorithms based on physical distribution characteristics and interval optimization algorithms based on uncertainty.

[0067] refer to Figure 4 The guided optimization algorithm based on physical distribution characteristics includes predicting the comprehensive performance cloud map of electromagnetic equipment; determining the distribution characteristics and structured expression of the field based on the standard deviation and variance of the overall and local physical fields of the electromagnetic equipment; obtaining a better solution for the physical field distribution through calculation and comparison; comparing and studying multiple population hybrid algorithms and improved non-dominated sorting genetic algorithms, and combining the obtained better solution to guide the optimization process to achieve optimization of the optimization variables; and continuously iterating and updating until the optimal solution set is obtained.

[0068] refer to Figure 5 The interval optimization algorithm based on uncertainty involves generating multiple individual design vectors from a multi-objective optimization algorithm at the outer layer. For each individual design vector, the upper and lower bounds of the objective function and constraints are calculated using the interval analysis method, thereby calculating the midpoint value of the objective function and the interval probability of the constraints. Then, the transformed deterministic multi-objective optimization problem is calculated to obtain the required non-dominated solution set.

[0069] In this embodiment, considering the safety requirements of electromagnetic equipment, it also includes establishing a blockchain-based encryption technology to achieve end-to-end encryption of the storage and transmission of programs, instructions, and data; secondly, a dynamic access control strategy based on user permission control to achieve controlled access to system resources and services by users; and finally, mutual isolation of resource pools based on user hierarchy.

[0070] The computational burden of high-precision numerical simulation of electromagnetic equipment under service conditions, involving multi-temporal and spatiotemporal scales and multi-physics coupling, increases significantly, making traditional computational methods insufficient. Electromagnetic equipment under service conditions needs to consider various constraints, including extreme operating conditions, material nonlinearity, multi-temporal and spatiotemporal scales, manufacturing process constraints, and service characteristics. The data to be optimized exhibits high-dimensional characteristics, and the robustness, feasibility, and operability of traditional artificial intelligence methods are also unsatisfactory. In this embodiment, the unified design of the comprehensive performance and reliability of electromagnetic equipment under service conditions is achieved using cloud computing and artificial intelligence. Cloud computing and artificial intelligence can provide support for the detailed simulation and rapid, efficient calculation of the unified design of the comprehensive performance and reliability of electromagnetic equipment under service conditions.

[0071] The above embodiments illustrate only one implementation of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. Those skilled in the art can make various modifications, substitutions, and improvements without departing from the concept of the present invention, and these should all be covered within the protection scope of the present invention.

Claims

1. A method for unified design of comprehensive performance and reliability of electromagnetic equipment under service conditions, characterized in that: It comprises the following steps: S1, measuring the service characteristic parameters of electromagnetic energy materials in the electromagnetic equipment, and establishing a material characteristic database; S2, using the material characteristic database to establish a multi-physical field full-coupling model of the electromagnetic equipment under service conditions; S3, determining the key parameters of the comprehensive performance of the electromagnetic equipment and the performance failure criterion, and establishing a reliability model of the comprehensive performance of the electromagnetic equipment; S4, using modern optimization algorithms to incorporate reliability influence parameters into the multi-physical field full-coupling model, correlating the full-coupling model with the reliability model, and forming a unified design of the comprehensive performance and reliability of the electromagnetic equipment under service conditions; The measurement of material service characteristic parameters in step S1 includes temperature characteristic measurement, stress characteristic measurement, and electromagnetic characteristic measurement; In step S3, the determination of the key parameters of the comprehensive performance of the electromagnetic equipment and the performance failure criterion, and the establishment of the reliability model of the comprehensive performance of the electromagnetic equipment include: S31, based on multi-time and space scale multi-physical field finite element model and experiment, establishing the correlation database between working stress and electromagnetic equipment performance degradation data under service conditions, obtaining performance degradation characteristics, determining parameters affecting the comprehensive performance degradation of the electromagnetic equipment and reliability influence parameters; S32, based on data enhancement technology, establishing a proxy model for life prediction of characteristic parameters and degradation data; using statistical data-driven method, estimating degradation model parameters according to degradation trajectory to establish a probability model for life prediction; S33, based on multi-element correlation analysis, realize reliability allocation, determine reliability function, respectively use proxy model and probability model to analyze reliability, analyze inconsistent analysis results of two kinds of models, give performance characteristics of two kinds of models, determine performance boundary and application scope of proxy model and probability model; Step S4 includes: taking the key parameters affecting the comprehensive performance of the electromagnetic equipment under service conditions as optimization variables, taking the electromagnetic comprehensive performance failure criterion and reliability influence parameters as constraint conditions, and taking the best electromagnetic comprehensive performance and reliability as optimization objectives.

2. The method of claim 1, wherein the method is characterized by: It also includes: Step S5, using cloud computing and artificial intelligence to realize the unified design of the comprehensive performance and reliability of the electromagnetic equipment under service conditions.

3. The method of claim 1, wherein the method is characterized by: The temperature characteristic measurement is the measurement of soft magnetic material magnetic properties in the range of 20-150℃, the stress characteristic measurement is the measurement of three-axis stress vector magnetic properties, and the electromagnetic characteristic measurement is the measurement of magnetic properties under pulse current excitation.

4. The method of claim 1, wherein the method is characterized by: In step S2, the establishment of the multi-physical field full-coupling model of the electromagnetic equipment under service conditions includes: S21, establishing the multi-physical field coupling relationship of the electromagnetic equipment, establishing the unified Helmholtz free energy expression of electromagnetic field, stress field and temperature field through energy theory, and obtaining the multi-physical field constitutive equation through differential relationship: （1） Where σ is the stress vector, ε is the strain vector, M is the magnetization, B is the magnetic flux density, and T is the temperature; S22, according to the material magnetic field and stress constitutive equation, the coupling relationship equation of magnetic field intensity H and stress σ is obtained: （2） where H prev represents the magnetic field strength of the previous step, σ prev represents the strain vector of the previous step, represents a higher order infinitesimal; S23, establishing the constitutive equation of quasi-static electromagnetic field, stress field and temperature field without displacement current: （3） where J ext is the impressed current density vector, J eddy is the vortex vector, F ext is the impressed stress, F mag is the electromagnetic force, q mag is the heat per unit volume generated by the electromagnetic field, k is the thermal conductivity, q F is the heat per unit volume generated by mechanical forces, including heat generated by high-speed frictional motion of the electromagnetic energy equipment; S24, let finite element variable The test function is (w, v, T0), and the variational is carried out on formula (3) by using the test function. Then, formula (2) ignoring high order terms is brought into the variational relationship, and the final multi-physical field coupling finite element variational is obtained as follows: （4） where A denotes the magnetic vector potential, u denotes the vector displacement, T denotes the temperature, Ω denotes the multi-physics solution geometry, p denotes the density, C p denotes the material specific heat capacity, L is the projection operator of the vector displacement u to the strain, A prev , u prev , T prev are the computed values of the last iteration; the variational form is discretized and the algebraic equations required for the Newton-Raphson method are constructed to solve for (δA, δu, δT).

5. The method of claim 1, wherein: The modern optimization algorithm for uncertain problems includes: (1) Guided optimization algorithm based on physical distribution characteristics: predicting the comprehensive performance of electromagnetic equipment cloud map; based on the standard deviation and variance of the overall and local physical field of electromagnetic equipment, determining the distribution characteristics and structured expression of the field, and obtaining the optimal solution of the physical field distribution through calculation and comparison; comparative study of multi-population hybrid algorithm and improved non-dominated sorting genetic algorithm, and combined with the obtained optimal solution to guide the optimization process, the optimization of optimization variables is realized; through continuous iteration and update until the optimal solution set is obtained; (2) Interval optimization algorithm based on uncertainty: in the outer layer, multiple design vector individuals are generated by multi-objective optimization algorithm, for each design individual, the upper and lower bounds of the objective function and the constraints are calculated by interval analysis method, so as to calculate the midpoint value of the objective function and the interval possibility of the constraints, and then the transformed deterministic multi-objective optimization problem is calculated to obtain the required non-inferior solution set.

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