A Method for Constructing Multi-Scale and Multi-Domain Digital Twin Models of Complex Equipment

Abstract

This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment, belonging to the field of intelligent manufacturing and engineering technology. The method involves: considering the multi-scale and multi-disciplinary nature of machine tool equipment, the Modelica modeling language is used. Through non-causal modeling and connector modeling, a unified modeling approach is adopted to represent the multi-scale and multi-disciplinary nature of the physical equipment, overcoming the limitations of the complex coupling characteristics of the equipment; with the optimization objective of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, a correction and optimization problem model for the machine tool digital twin model is constructed, considering spindle stiffness, spindle dimensions, machining temperature, thermal conductivity, and coefficient of thermal expansion; an improved particle swarm optimization algorithm with a "role model-elite" learning strategy is employed to find the optimal parameter combination, thereby correcting the machine tool digital twin model, improving the consistency between the twin model and the physical equipment, and ensuring the accuracy of the machine tool equipment digital twin model.

Description

Technical Field

[0001] This invention relates to a method for constructing multi-scale and multi-domain digital twin models of complex equipment, belonging to the field of intelligent manufacturing and engineering technology. Background Technology

[0002] With the development of next-generation network information technology, integrating related information technologies into physical equipment to achieve intelligent control and optimization has become a focus of attention worldwide. Digital twins (DT) can effectively realize the interaction, integration, and fusion between physical and information spaces, and are considered a key technology for realizing cyber-physical systems (CPS). Models, as the core and crucial prerequisite for realizing digital twin technology, play a vital role in constructing comprehensive, accurate, and autonomously optimizable models for digital twin systems, thus significantly impacting the development of related fields.

[0003] With the development of technology, physical equipment is becoming increasingly complex, encompassing multiple scales and disciplines, and possessing extremely complex coupling characteristics, making it difficult to construct complete and comprehensive digital twin models. Current methods for constructing digital twin models only focus on certain features of the equipment, neglecting its multi-scale and multi-disciplinary characteristics, and failing to comprehensively and holistically display both static and dynamic operational information. Furthermore, during the implementation of digital twin models, due to the influence of various actual operating conditions on the physical equipment, the currently constructed idealized digital twin models deviate significantly from the actual equipment outputs. Moreover, there is a lack of methods for real-time correction of digital twin models, which cannot effectively support the reliable implementation of intelligent services related to digital twin systems and cannot meet the needs of intelligent manufacturing development. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing multi-scale and multi-domain digital twin models of complex equipment. Using the Modelica modeling language, it presents the multi-scale levels and multi-disciplinary fields of the physical equipment through a unified modeling approach, overcoming the limitations of the complex coupling characteristics of the equipment. With the optimization objective of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, it considers correction variables such as spindle stiffness, spindle size, machining temperature, thermal conductivity, and coefficient of thermal expansion to construct a model for the correction and optimization of the machine tool digital twin model. An improved particle swarm optimization algorithm with a "role model-elite" learning strategy is employed to find an optimal combination of parameters to achieve the correction of the machine tool digital twin model, improving the consistency between the twin model and the physical equipment, and enhancing the accuracy of the machine tool equipment model.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment. Targeting machine tool equipment, which encompasses multiple scale levels (unit level, subsystem level, system level) and multiple disciplines (electrical, control, mechanical), the method employs the Modelica modeling language and utilizes non-causal modeling and connector modeling to construct multi-scale and multi-domain digital twin models of the machine tool equipment, uniformly displaying the multi-scale and multi-disciplinary information of the physical entity equipment. Based on the aforementioned multi-scale and multi-domain digital twin model of the machine tool equipment, with the optimization objective of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, an improved particle swarm optimization algorithm with a "role model-elite" learning strategy is used to iteratively correct parameters such as spindle stiffness, spindle dimensions, machining temperature, thermal conductivity, and coefficient of thermal expansion, seeking an optimal parameter combination to correct the digital twin model, improve the consistency between the twin model and the physical equipment, and ensure the accuracy of the machine tool equipment digital twin model.

[0007] This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment, comprising the following steps:

[0008] Step 1: Considering the multi-scale and multi-domain characteristics of machine tool equipment, divide the equipment into hierarchical structures and disciplinary fields. Divide the physical equipment into subsystems of different domains, including control subsystems, electrical subsystems, and mechanical subsystems, and further divide each subsystem into minimum components and parts. The control subsystem includes PLC control systems, PWM control systems, and servo control systems, which regulate the position, speed, and current of the machine tool. The electrical subsystem includes motors, contactors, and relays, responsible for starting, stopping, and speed regulation of the machine tool and motors. The mechanical subsystem includes drive mechanisms, transmission mechanisms, and actuators, coordinating the completion of the machine tool's machining tasks.

[0009] Step 2: Analyze and determine the physical modeling elements of different disciplines, use physical model relationships to describe the physical phenomena and processes in different fields, and analyze the interaction relationships between parameters of different disciplines in machine tool equipment.

[0010] An electrical subsystem has three basic components: inductor, resistor, and capacitor. If the electrical subsystem contains only inductive loads, the relationship between the load current and voltage is expressed as:

[0011] U(t)=Ldi(t) / dt (1)

[0012] Where U is voltage and L is inductance.

[0013] If the circuit contains only a resistive load, the relationship between the load current and the drive voltage is expressed as:

[0014] U(t)=Ri(t) (2)

[0015] Where R is the load resistance.

[0016] If the subsystem contains only capacitive loads, the relationship between the load current and the drive voltage is expressed as:

[0017]

[0018] Where C is the capacitance.

[0019] The control subsystem includes a position controller and a speed controller. The position controller uses PID control to ensure the motor spindle can move precisely according to commands, reducing deviations.

[0020] w(t) = K p (θ-θ * (4)

[0021] Where Kp is the PID proportional control factor and θ is the rotation angle.

[0022] The speed controller uses PID regulation to enable precise control of the motor speed according to instructions, reducing deviations.

[0023]

[0024] Where Ksp is the proportional-integral (PID) control factor, and w is the rotational angular velocity.

[0025] A mechanical subsystem consists of mechanical components, mainly classified into three categories: elastic components, inertial components, and damping components. If the subsystem has only one elastic load and one end of the system is fixed, then the relationship between the displacement (rotation angle) of the transmission mechanism and the driving force (driving torque) can be expressed as:

[0026] F(t)=Kx(t)(T(t)=Gθ(t)) (6)

[0027] Where K is the elastic stiffness coefficient of the transmission component, G is the torsional stiffness coefficient of the transmission mechanism, x is the load displacement, θ is the load rotation angle, F is the driving force, and T is the driving torque.

[0028] If the subsystem has only viscous friction damping load, the relationship between displacement and driving force of the transmission mechanism is expressed as:

[0029] F(t)=Bdx(t) / dt(T(t)=Bdθ(t) / dt) (7)

[0030] Where B is the viscous damping coefficient of the transmission mechanism, and x is the load displacement.

[0031] When the subsystem has only inertial load, the relationship between displacement and driving force of the transmission mechanism is expressed as:

[0032] F(t) = md 2 x(t) / dt 2 (T(t=Jd) 2 θ(t) / dt 2 (8)

[0033] Where m is the mass of the load, J is the moment of inertia of the load, x is the displacement of the load, and θ is the rotation angle of the load.

[0034] The control system sends control signals to the power system, modifying electrical parameters such as voltage and current, causing the power system equipment to output different dynamic parameters to the mechanical system, thus controlling the machine tool's machining tasks. Furthermore, the mechanical and power systems output feedback signals to the control system, adjusting its control parameters. These dynamic parameters include rotational angular velocity and rotational torque.

[0035] Step 3: Leveraging the non-causal modeling capabilities of the Modelica language, the behavior and performance of the system or components are described through physical model relationships. Based on physical laws and the constitutive formulas of components and parts, the Modelica language is used to describe the physical model relationship equations of components and parts, constructing a physical model relationship model of components and parts. Instances of the Connector class are used to represent component interfaces, defining shared information between components and the structure and attributes of the interfaces. The shared information includes flow variables and potential variables. Components are connected through connectors, enabling the flow of parameters from different disciplines between different component models. From an energy perspective, by simultaneously solving the constitutive equations of the components (Ohm's law) and using connectors based on conservation equations (energy balance, momentum balance, and mass balance) and generalized Kirchhoff's laws, the models of various disciplines (electrical, control, and mechanical) are seamlessly integrated to obtain the equation set of the entire system. The models of various disciplines include electrical, control, and mechanical models. By assembling and integrating models, the external coupling interfaces between unit models are connected sequentially to complete the construction of subsystem models in various domains. The external coupling interfaces between subsystem models in various domains are connected sequentially to complete the construction of multi-domain system models of machine tools. Multi-scale and multi-domain machine tool models are constructed in a unified modeling method.

[0036] Step 4: With the goal of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, and considering the optimization design variables and their upper and lower boundary constraints, the parameters of the twin model are iteratively modified to find an optimal combination of parameters to correct the digital twin model.

[0037] The optimization and correction variables include spindle stiffness, spindle dimensions, machining temperature, thermal conductivity, and coefficient of thermal expansion.

[0038] Based on the upper and lower boundary constraints of the design variables, the objective function is to minimize the error between the output of the machine tool digital twin model and the test on the machine tool test bench. The objective function consists of multiple error or residual functions, each relatively independent. By weighted summing of these objective functions to minimize the overall trend of the objective function, the multi-objective optimization problem is transformed into a single-objective optimization problem. The machine tool correction optimization problem model is constructed as follows:

[0039]

[0040] Where k represents spindle stiffness, l represents spindle dimension, t represents machining temperature, r represents thermal conductivity, Δq represents coefficient of thermal expansion; wi represents the correction weights for different parameters, Psim represents the twin model output, and Preal represents the actual equipment output; x L and x U These represent the lower and upper bounds of the design variable, respectively.

[0041] Step 5: Adopt an improved particle swarm optimization algorithm based on the "role model-elite" learning strategy to overcome the shortcomings of traditional particle swarm optimization algorithms that are prone to premature convergence to local optima. Effectively solve the optimization and correction problem of the machine tool digital twin model constructed in Step 4, find an optimal set of parameters to correct the digital twin model, improve the consistency between the twin model and the physical equipment, and ensure the accuracy of the machine tool equipment digital twin model.

[0042] Step 5.1: In x L ≤x≤x U Within the design interval, N sets of model correction parameters are randomly selected. Each combination vector x = [k,l,t,r,Δq] is treated as a particle, generating an initial population of size N.

[0043] Step 5.2: Import each particle into the machine tool digital twin model, calculate the fitness value of each particle according to equation (10), and record the historical best position pbest of each particle and the historical best position best of the entire particle population.

[0044]

[0045] Where wi represents the correction weights for different parameters, Psim represents the output of the twin model, and Preal represents the actual output of the equipment.

[0046] Step 5.3: Add a Gaussian perturbation term to the self-learning strategy part of the algorithm for each particle. At the same time, set an elite center or role model center for each particle in the swarm with a certain probability as the swarm learning strategy corresponding to that particle. Calculate the speed Vi of the next particle swarm movement and the position Xi+1 after taking one step forward.

[0047] V i =ω×V i +C1×rand()×(pbest i +ζ1ζ2Gaussian(μ,σ 2 )-X i )+C2×rand()×(Ecenter i -X i ) (11) X i+1 =X i +V i

[0048] Where w is called the inertia factor, C1 and C2 are called the learning factors, and rand() and ζ represent random numbers with values ​​between (0,1). Gaussian(μ,σ) 2 ) represents the mean being μ and the variance being σ. 2 The Gaussian perturbation factor. Ecenter represents the particle swarm learning strategy, which is set as either the elite center ELcenter or the role model center EXcenter with a certain probability.

[0049]

[0050]

[0051] Step 5.4: Re-input the new generation of particles x = [k,l,t,r,Δq] into the machine tool digital twin model, modify the model parameters and simulate, calculate the fitness value of each particle, and determine whether the stopping criterion is met. If not, return to step 5.3 and iteratively optimize to generate a new population; if yes, an optimal combination of correction variables is found to correct the digital twin model, improve the consistency between the twin model and the physical equipment, and improve the accuracy of the machine tool equipment model.

[0052] Beneficial effects:

[0053] 1. This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment. Based on the non-causal modeling characteristics of the Modelica language, it describes the behavior and performance of systems or components through physical model relationships, constructing component and part models. Instances of the connector class are used to represent component interfaces, defining shared information (flow variables, potential variables) between components, as well as the structure and attributes of the interfaces. Components are connected through connectors, enabling the flow of parameters from different disciplines between different component models. Through coupling connections between interfaces based on generalized Kirchhoff's laws, the assembly and integration of models are completed, constructing models at different levels (unit level, subsystem level, system level), achieving the construction of multi-scale and multi-domain digital twin models of machine tool equipment in a unified modeling manner.

[0054] 2. This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment. Considering the error between the machine tool digital twin model and the machine tool equipment, the optimization objective is to minimize the error between the output of the machine tool digital twin model and the test on the machine tool test bench. An improved particle swarm intelligent optimization algorithm with a "role model-elite" learning strategy is adopted. By iteratively modifying the parameters of the twin model, an optimal set of parameters is found to correct the digital twin model, improve the consistency between the twin model and the physical equipment, and improve the accuracy of the machine tool equipment model.

[0055] 3. This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment. It models the multi-scale dimensions and multi-disciplinary characteristics of machine tool equipment in a unified manner, overcoming the limitations of the complex coupling characteristics of the equipment and constructing a complete digital twin model to display comprehensive information about the machine tool equipment. By improving the iterative correction of the particle swarm optimization algorithm, the consistency between the twin model and the physical equipment is enhanced. This invention can construct a comprehensive and real-time correctable digital twin model for complex equipment, thereby providing effective support for various intelligent functions and services in the operation, management, and maintenance of complex equipment.

[0056] 4. This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment. Using the Modelica modeling language, the physical and mathematical equations between parameters (electrical, control, and mechanical) of machine tool equipment across different disciplines are modeled through its non-causal modeling characteristics. This enables the interaction and transformation between parameters from different disciplines. Then, the interfaces of each component model are modeled. Through coupling connections between interfaces based on generalized Kirchhoff's laws, the models are assembled and integrated, constructing models at different levels (unit level, subsystem level, and system level). Ultimately, a multi-scale and multi-domain digital twin model of the machine tool equipment is constructed. This unified modeling method displays the multi-scale levels and multi-disciplinary domains of the physical equipment, overcoming the limitations of the complex coupling characteristics of the equipment and constructing a complete digital twin model to display comprehensive information about the equipment. With the optimization objective of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, and considering correction variables such as spindle stiffness, spindle size, machining temperature, thermal conductivity, and coefficient of thermal expansion, a correction and optimization problem model for the machine tool digital twin model is constructed. An improved particle swarm optimization (PSO) algorithm employing a "role model-elite" learning strategy overcomes the shortcomings of traditional PSO algorithms, which are prone to premature convergence to local optima, and provides an efficient solution to this optimization problem. Ultimately, the improved PSO algorithm finds an optimal set of parameters to correct the machine tool digital twin model, ensuring consistency between the twin model and the physical equipment, and improving the accuracy of the machine tool digital twin model. Attached Figure Description

[0057] Figure 1 This is an overall flowchart of an embodiment of a method for constructing multi-scale and multi-domain digital twin models of complex equipment disclosed in this invention.

[0058] Figure 2 This is a schematic diagram of the multi-scale composition of a machine tool digital twin model.

[0059] Figure 3 This is a schematic diagram showing the multi-domain composition of a machine tool digital twin model.

[0060] Figure 4 Flowchart for constructing multi-scale, multi-domain digital twin models of machine tools.

[0061] Figure 5 Flowchart for improving the particle swarm optimization algorithm.

[0062] Figure 6 Flowchart for iterative correction and optimization of machine tool digital twin model. Detailed Implementation

[0063] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0064] To make the objectives, technical solutions, and advantages of this invention clearer, the design process of this invention will be described in detail below with reference to the accompanying drawings. Throughout the description, the same or similar symbols represent the same or similar functions.

[0065] Example 1:

[0066] like Figure 1 As shown in the figure, this embodiment discloses a method for constructing a multi-scale and multi-domain digital twin model of complex equipment. The specific implementation steps are as follows:

[0067] Step 1: Considering the multi-scale and multi-domain characteristics of machine tool equipment, divide the equipment into hierarchical structures and disciplinary fields. Divide the physical equipment into subsystems of different domains, including control subsystems, electrical subsystems, and mechanical subsystems. Then, divide each subsystem into the smallest components and modules, such as... Figure 2 As shown. The control subsystem includes a PLC control system, a PWM control system, and a servo control system, which regulate the machine tool's position, speed, and current. The electrical subsystem includes motors, contactors, and relays, responsible for starting, stopping, and speed regulation of the machine tool and motors. The mechanical subsystem includes drive mechanisms, transmission mechanisms, and actuators, coordinating the completion of the machine tool's machining tasks.

[0068] Step 2: Summarize the physical modeling elements of different disciplines, use mathematical formulas to describe the physical phenomena and processes in different fields, and analyze the interaction relationships between parameters of different disciplines in machine tool equipment.

[0069] An electrical subsystem has three basic components: inductor, resistor, and capacitor. If the electrical subsystem contains only inductive loads, the relationship between the load current and voltage can be expressed as:

[0070] U(t)=Ldi(t) / dt (14)

[0071] Where U is voltage and L is inductance.

[0072] If the circuit contains only a resistive load, the relationship between the load current and the driving voltage can be expressed as:

[0073] U(t)=Ri(t) (15)

[0074] Where R is the load resistance.

[0075] If the subsystem contains only capacitive loads, the relationship between the load current and the drive voltage can be expressed as:

[0076]

[0077] Where C is the capacitance.

[0078] The control subsystem includes a position controller and a speed controller. The position controller uses PID control to ensure the motor spindle can move precisely according to commands, minimizing deviations.

[0079] w(t) = K p (θ-θ * (17)

[0080] Where Kp is the PID proportional control factor and θ is the rotation angle.

[0081] The speed controller uses PID regulation to enable precise control of the motor speed according to instructions, reducing deviations.

[0082]

[0083] Where Ksp is the proportional-integral (PID) control factor, and w is the rotational angular velocity.

[0084] A mechanical subsystem consists of mechanical components, mainly classified into three categories: elastic components, inertial components, and damped components. Assuming the subsystem has only one elastic load and one end of the system is fixed, the relationship between the displacement (rotation angle) and driving force (driving torque) of the transmission mechanism can be expressed as:

[0085] F(t)=Kx(t)(T(t)=Gθ(t)) (19)

[0086] Where K is the elastic stiffness coefficient of the transmission component, G is the torsional stiffness coefficient of the transmission mechanism, x is the load displacement, θ is the load rotation angle, F is the driving force, and T is the driving torque.

[0087] If the subsystem has only viscous friction damping load, the relationship between displacement and driving force of the transmission mechanism can be expressed as:

[0088] F(t)=Bdx(t) / dt(T(t)=Bdθ(t) / dt) (20)

[0089] Where B is the viscous damping coefficient of the transmission mechanism, and x is the load displacement.

[0090] When the subsystem has only inertial load, the relationship between displacement and driving force of the transmission mechanism can be expressed as:

[0091] F(t) = md 2 x(t) / dt 2 (T(t=Jd) 2 θ(t) / dt 2 ) (twenty one)

[0092] Where m is the mass of the load, J is the moment of inertia of the load, x is the displacement of the load, and θ is the rotation angle of the load.

[0093] The control system sends control signals to the power system, modifying electrical parameters such as voltage and current. This causes power system equipment, such as motors, to output different dynamic parameters to the mechanical system, such as rotational angular velocity and rotational torque, thereby controlling the machine tool's machining tasks. Furthermore, both the mechanical and power systems output feedback signals to the control system, adjusting its control parameters, such as... Figure 3 As shown.

[0094] Step 3: Leveraging the non-causal modeling capabilities of the Modelica language, the behavior and performance of systems or components are described using physical mathematical equations. Based on physical laws and the constitutive formulas of components and parts, the Modelica language is used to describe the components and parts mathematically, constructing component and part models. Instances of the Connector class are used to represent component interfaces, defining shared information (flow variables, potential variables) between components and the structure and attributes of the interfaces. Components are connected through connectors, enabling the flow of parameters from different disciplines between different component models. From an energy perspective, by simultaneously solving the constitutive equations of components (Ohm's law) and using connectors based on conservation equations (energy balance, momentum balance, and mass balance) and generalized Kirchhoff's laws, models from various disciplines (electrical, control, and mechanical) are seamlessly integrated to obtain the equation set of the entire system. Through model assembly and model integration, the external coupling interfaces between unit models are connected sequentially to complete the construction of subsystem models in each domain. The external coupling interfaces between subsystems in each domain are then connected sequentially to complete the construction of a multi-domain machine tool system model. Finally, a unified modeling approach is used to construct multi-scale, multi-domain machine tool models. The modeling process is as follows: Figure 4 As shown.

[0095] Step 4: With the goal of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, and considering the optimization design variables and their upper and lower boundary constraints, the parameters of the simulation model are iteratively modified to find an optimal combination of parameters to correct the digital twin model.

[0096] The optimization and correction variables include spindle stiffness, spindle dimensions, machining temperature, thermal conductivity, and coefficient of thermal expansion.

[0097] Based on the upper and lower boundary constraints of the design variables, the objective function is to minimize the error between the output of the machine tool digital twin model and the test on the machine tool test bench. The objective function typically consists of multiple error or residual functions, and these functions are generally relatively independent. By weighted summing of these objective functions to minimize their overall trend, the multi-objective optimization problem is transformed into a single-objective optimization problem. The mathematical model for the machine tool correction optimization problem is constructed as follows:

[0098]

[0099] Where k represents spindle stiffness, l represents spindle dimension, t represents machining temperature, r represents thermal conductivity, Δq represents coefficient of thermal expansion; wi represents the correction weights for different parameters, Psim represents the twin model output, and Preal represents the actual equipment output; x L and x U These represent the lower and upper bounds of the design variable, respectively.

[0100] Step 5: An improved particle swarm optimization algorithm using a "role model-elite" learning strategy is adopted to overcome the shortcomings of traditional particle swarm optimization algorithms, which are prone to premature convergence to local optima. This algorithm effectively solves the optimization and correction problem of the machine tool digital twin model constructed in Step 4, finding an optimal set of parameters to correct the digital twin model, ensuring consistency between the twin model and the physical equipment, improving the accuracy of the machine tool equipment model, and improving the implementation process of the particle swarm optimization algorithm as follows: Figure 5 The specific implementation steps are as follows:

[0101] Step 5.1: In x L ≤x≤x U Within the design interval, N=50 combinations of model correction parameters are randomly selected. Each combination vector x=[k,l,t,r,Δq] is treated as a particle, generating an initial population of size N=50.

[0102] Step 5.2: Import each particle into the machine tool digital twin model, calculate the fitness value of each particle according to equation (10), and record the historical best position pbest of each particle and the historical best position best of the entire particle population.

[0103]

[0104] Where wi represents the correction weights for different parameters, Psim represents the output of the twin model, and Preal represents the actual output of the equipment.

[0105] Step 5.3: Add a Gaussian perturbation term to the self-learning strategy part of the algorithm for each particle. At the same time, set an elite center or role model center for each particle in the swarm with a certain probability as the swarm learning strategy corresponding to that particle. Calculate the speed Vi of the next particle swarm movement and the position Xi+1 after taking one step forward.

[0106] V i =ω×V i +C1×rand()×(pbest i +ζ1ζ2Gaussian(μ,σ 2 )-X i )+C2×rand()×(Ecenter i -X i ) (24) X i+1 =X i +V i

[0107] Where w is called the inertia factor, C1 and C2 are called the learning factors, and rand() and ζ represent random numbers with values ​​between (0,1). Gaussian(μ,σ) 2 ) represents the mean being μ and the variance being σ. 2 The Gaussian perturbation factor. Ecenter represents the particle swarm learning strategy, which is set as either the elite center ELcenter or the role model center EXcenter with a certain probability.

[0108]

[0109] Step 5.4: Re-input the new generation of particles x = [k, l, t, r, Δq] into the machine tool digital twin model, modify the model parameters and simulate, calculate the fitness value of each particle, and determine whether the stopping criterion is met. If not, repeat step 5.3 to iteratively optimize and generate a new population; if yes, an optimal combination of correction variables is found to correct the digital twin model, ensuring consistency between the twin model and the physical equipment, and improving the accuracy of the machine tool equipment model. The iterative correction and optimization process of the machine tool digital twin model is as follows: Figure 6 As shown.

[0110] This invention discloses a method for constructing multi-scale and multi-domain digital twin models of complex equipment. It can model the multi-scale dimensions and multi-disciplinary characteristics of machine tool equipment in a unified manner, overcoming the limitations of the complex coupling characteristics of the equipment and constructing a complete digital twin model to display comprehensive information about the equipment. By improving the iterative correction of the particle swarm optimization algorithm, the consistency between the twin model and the physical equipment is enhanced. This invention can construct a comprehensive and real-time corrected digital twin model for complex equipment, facilitating the realization of various intelligent functions and services in the operation, management, and maintenance of complex equipment.

[0111] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing multi-scale and multi-domain digital twin models of complex equipment, characterized in that: Includes the following steps, Step 1: Considering the multi-scale and multi-domain characteristics of machine tool equipment, divide the equipment into hierarchical structures and disciplinary fields; divide the physical equipment into subsystems of different fields, including control subsystem, power subsystem, and mechanical subsystem, and further divide each subsystem into the smallest components and parts; the control subsystem includes PLC control system, PWM control system, and servo control system, which performs position, speed, and current regulation control of the machine tool; the power subsystem includes motors, contactors, and relays, which are responsible for starting, stopping, and speed regulation of the machine tool and motors; the mechanical subsystem includes drive mechanism, transmission mechanism, and actuator, which coordinate the completion of the machine tool's processing tasks; Step 2: Analyze and determine the physical modeling elements of different disciplines, use physical model relationships to describe the physical phenomena and processes of different disciplines, and analyze the interaction relationships between parameters of different disciplines in machine tool equipment; Step 3: Based on the non-causal modeling characteristics of the Modelica language, the behavior and performance of the system or components are described through physical model relationships. Based on the laws of physics and the constitutive formulas of components and parts, the physical model relationship equations of components and parts are described using the Modelica language to construct the physical model relationship model of components and parts. Instances of the connector class are used to represent component interfaces, defining the shared information between components and the structure and attributes of the interfaces. The shared information includes flow variables and potential variables. Components are connected to each other through connectors to realize the flow of parameters from different disciplines between different component models. From the perspective of energy analysis, by combining the constitutive equations of components and the connectors based on conservation equations and generalized Kirchhoff's laws, the models of various disciplines are seamlessly integrated to obtain the equation set of the entire system. The models of various disciplines include electrical models, control models, and mechanical models. Through model assembly and model integration, the external coupling interfaces between unit models are connected in sequence to complete the construction of subsystem models in various fields. The external coupling interfaces between subsystems in various fields are connected in sequence to complete the construction of multi-domain system models of machine tools. Multi-scale and multi-domain machine tool models are constructed in a unified modeling method. Step 4: With the goal of minimizing the error between the output of the machine tool digital twin model and the test on the machine tool test bench, and considering the optimization design variables and their upper and lower boundary constraints, the parameters of the twin model are iteratively modified to find an optimal combination of parameters to correct the digital twin model. The optimized design variables include spindle stiffness, spindle dimensions, machining temperature, thermal conductivity, and coefficient of thermal expansion. Step 5: An improved particle swarm optimization algorithm based on the "role model-elite" learning strategy is used to effectively solve the optimization and correction problem of the machine tool digital twin model constructed in Step 4. An optimal set of parameters is found to correct the digital twin model, improve the consistency between the twin model and the physical equipment, and improve the accuracy of the machine tool equipment model.

2. The method for constructing a multi-scale and multi-domain digital twin model of complex equipment as described in claim 1, characterized in that: The second step is implemented as follows: An electrical subsystem has three basic components: inductor, resistor, and capacitor. If the electrical subsystem contains only inductive loads, the relationship between the load current and voltage is expressed as: U(t)=Ldi(t) / dt (1) Where U is voltage and L is inductance; If the circuit contains only a resistive load, the relationship between the load current and the drive voltage is expressed as: U(t)=Ri(t) (2) Where R is the load resistance; If the subsystem contains only capacitive loads, the relationship between the load current and the drive voltage is expressed as: Where C is the capacitance; The control subsystem includes a position controller and a speed controller; the position controller uses PID control to enable the motor spindle to make precise displacements according to commands, reducing deviations. w(t)=K p (θ-θ * ) (4) Where Kp is the PID proportional control factor and θ is the rotation angle; The speed controller uses PID regulation to enable precise control of the motor speed according to instructions, reducing deviations. Where Ksp is the PID proportional-integral control factor, and w is the rotational angular velocity; A mechanical subsystem consists of mechanical components, mainly classified into three categories: elastic components, inertial components, and damping components. If the subsystem has only one elastic load and one end of the system is fixed, then the relationship between the displacement of the transmission mechanism and the driving force can be expressed as: Where K is the elastic stiffness coefficient of the transmission component, G is the torsional stiffness coefficient of the transmission mechanism; x is the load displacement, θ is the load rotation angle, F is the driving force, and T is the driving torque. If the subsystem has only viscous friction damping load, the relationship between displacement and driving force of the transmission mechanism is expressed as: F(t) = Bdx(t) / dt T(t)=Bdθ(t) / dt (7) Where B is the viscous damping coefficient of the transmission mechanism, and x is the load displacement; When the subsystem has only inertial load, the relationship between displacement and driving force of the transmission mechanism is expressed as: Where m is the mass of the load, J is the moment of inertia of the load, x is the displacement of the load, and θ is the rotation angle of the load. The control system sends control signals to the power system to modify the electrical parameters voltage and current, causing the power system equipment to output different dynamic parameters to the mechanical system, thereby controlling the machine tool's machining tasks. In addition, the mechanical system and the power system will output feedback signals to the control system to adjust the control parameters of the control system. The dynamic parameters include rotational angular velocity and rotational torque.

3. The method for constructing a multi-scale and multi-domain digital twin model of complex equipment as described in claim 2, characterized in that: In step four, Based on the upper and lower boundary constraints of the design variables, the objective function is to minimize the error between the output of the machine tool digital twin model and the test on the machine tool test bench. The objective function consists of multiple error or residual functions, and each function is relatively independent. By weighting and summing the objective functions, the overall trend of the objective function is minimized, thus transforming the multi-objective optimization problem into a single-objective optimization problem. The machine tool correction optimization problem model is constructed as follows: Where k represents spindle stiffness, l represents spindle dimension, t represents machining temperature, r represents thermal conductivity, Δq represents coefficient of thermal expansion; wi represents the correction weights for different parameters, Psim represents the twin model output, and Preal represents the actual equipment output; x L and x U These represent the lower and upper bounds of the design variable, respectively.

4. The method for constructing a multi-scale and multi-domain digital twin model of complex equipment as described in claim 3, characterized in that: Step five is implemented as follows: Step 5.1: In x L ≤x≤x U Within the design interval, N sets of model correction parameters are randomly selected. Each combination vector x = [k,l,t,r,Δq] is treated as a particle to generate an initial population of size N. Step 5.2: Import each particle into the machine tool digital twin model, calculate the fitness value of each particle according to equation (10), and record the historical best position pbest of each particle and the historical best position best of the entire particle population. Where wi represents the correction weights for different parameters, Psim represents the output of the twin model, and Preal represents the actual output of the equipment; Step 5.3: Add a Gaussian perturbation term to the self-learning strategy part of the algorithm for each particle, and set an elite center or role model center for each particle in the swarm with a certain probability as the swarm learning strategy corresponding to that particle. Calculate the speed Vi of the particle swarm moving forward in the next step, and the position Xi+1 after taking one step forward. Where w is called the inertia factor, C1 and C2 are called the learning factors, and rand() and ζ represent random numbers with values ​​between (0,1); Gaussian(μ,σ) 2 ) represents the mean being μ and the variance being σ. 2 The Gaussian perturbation factor; Ecenter represents the particle swarm learning strategy, which is set as either the elite center ELcenter or the role model center EXcenter with a certain probability; Step 5.4: Re-input the new generation of particles x = [k,l,t,r,Δq] into the machine tool digital twin model, modify the model parameters and simulate, calculate the fitness value of each particle, and determine whether the stopping criterion is met; if not, return to step 5.3, iteratively optimize to generate a new population; if it is met, then find a set of optimal combination of correction variables to realize the correction of the digital twin model, improve the consistency between the twin model and the physical equipment, and ensure the accuracy of the machine tool equipment digital twin model.

Images