Digital twin service optimization method based on information age driving

Abstract

The invention discloses a digital twinning service optimization method based on information age driving, which adopts information age to represent the data freshness provided by digital twinning service, and on the basis, the utility gain of an edge computing network compared with a cloud architecture is used as the service quality, and the maximization of the utility gain is used as the target. The digital twinning model is deployed on an edge server and a digital twinning model is selected for the interaction request. According to the digital twinning service optimization method based on distributed robust optimization, the influence of the freshness of digital twinning data and the uncertainty of interaction requests on the service quality is comprehensively considered, and the deployment and selection strategy of digital twinning is jointly optimized. According to the method, based on the Wollaston distance, an algorithm for converting and solving a distributed robust optimization problem by applying multi-level dual transformation provides high-quality digital twinning service under the condition of an unpredictable extreme interaction request.

Description

Technical Field

[0001] The present invention belongs to the field of network service optimization, and specifically relates to a solution for model deployment and selection in an edge network, and particularly to a method for optimizing digital twin services driven by the age of information. Background Art

[0002] Digital twin, as an advanced technology, aims to create a high-precision and dynamic digital twin model for a physical entity to reflect the real-time state of the corresponding entity, and is widely used in fields such as intelligent manufacturing, autonomous driving, and personalized healthcare. This progress has led to the emergence of digital twin as a service, enabling users to interact with digital twin models. The quality of digital twin services provided depends on the freshness of the digital twin service response data to ensure that users obtain an accurate and timely interaction experience, and its freshness can be quantified by the age of information. However, deploying digital twin models on cloud servers results in long communication delays, further causing high age of information and a decline in system service quality, unable to meet the requirements of latency-sensitive applications. Edge computing, as a more flexible mode, deploys digital twin models on edge servers and is an alternative solution for providing real-time digital twin services.

[0003] Although some research has focused on optimizing digital twin service provision on edge networks, there are still some key issues that have not been well studied. On the one hand, the problem of updating digital twin models to maintain their accuracy has been ignored, resulting in outdated service response data and seriously affecting the quality of service provision. On the other hand, existing research usually relies on the assumption that all digital twin interaction information is completely known in advance, which is unrealistic. However, due to the following reasons, it is challenging to solve these problems. First, the quality of digital twin service provision is affected by model fidelity and service latency, but since these two factors have significant heterogeneity, it is not easy to design an index that integrates these two elements. In addition, the uncertainty of future digital twin interaction request initiation exacerbates the complexity of seamlessly configuring digital twin services in system optimization. Therefore, it is necessary to ensure the quality of service provision while fully considering digital twin model updates and the uncertainty of digital twin interaction requests. Summary of the Invention

[0004] Object of the Invention: Aiming at the low service quality faced by the existing digital twin service provision and the difficulty in coping with the uncertainty of service requests, the present invention provides a method for optimizing digital twin services driven by the age of information.

[0005] Technical solution: An information age-driven digital twin service optimization method, the method includes quantifying the freshness of digital twin data with information age, and facing the unforeseen request distribution in the edge network, based on distributionally robust optimization, maximizing the quality of digital twin services in extreme cases, and realizing the deployment of digital twin models and the selection of different digital twin service requests;

[0006] The method includes the following steps:

[0007] (1) Combine the digital twin model to provide a service scenario, build a digital twin service model based on edge computing, including physical entities, edge servers, and digital twin models, and realize the transmission of data between cellular units based on the communication network;

[0008] (2) Design the utility gain based on the difference in information age on the edge server as an index to evaluate the quality of digital twin services, and accordingly improve the quality of digital twin services;

[0009] The utility gain of the digital twin interaction request r is:

[0010]

[0011] In the formula, and respectively represent the information age of the user's digital twin interaction request obtaining digital twin services from the cloud server and the edge server, represents the set of servers g that the digital twin interaction request can get a response from;

[0012] (3) Optimize the digital twin services provided under the edge computing network, and the mathematical representation of this optimization process:

[0013]

[0014] Constraint: ∑ m∈M c m ·x m,v ≤Φ v

[0015]

[0016] y r,g ,x m,v ∈{0,1}

[0017] R represents the set of digital twin interaction requests, x m,v ∈{0,1} represents the digital twin model deployment strategy, y r,g ∈{0,1} represents the model selection strategy of digital twin interaction requests; the constraint ∑ m∈M c m ·xm,v ≤Φ v Indicates that the data volume of the digital twin model deployed by the edge server cannot exceed the maximum storage space Φ v ,c m Indicates the storage space required for the digital twin model corresponding to the physical entity m∈M, m represents the digital twin model, M represents the set of digital twin models, and the constraint condition Indicates that each digital twin interaction request r∈R can only be served by one digital twin model Provide services;

[0018] (4) Transform the joint optimization of digital twin model deployment and selection in digital twin service provision in step (3) into a problem based on distributionally robust optimization to ensure the robustness of digital twin service provision:

[0019]

[0020] Constraint condition: ∑ m∈M c m ·x m,v ≤Φ v

[0021]

[0022] y r,g ,x m,v ∈{0,1}

[0023]

[0024] where D is the confidence set of the fuzzy distribution, and the true interaction request distribution exists in this set with a certain confidence level, represents the reference distribution, P represents the fuzzy distribution, and θ is the maximum distance between the fuzzy distribution and the reference distribution; considering risk aversion, focus on the worst-case distribution in the confidence set D to ensure the robustness of service provision, and formulate the problem in min-max form;

[0025] (5) Solve the min-max form problem, transform the internal maximization problem into a convex problem through multiple dual transformations, and combine it with the external minimization problem; use the Gurobi optimization solver to solve the mixed-integer nonlinear problem.

[0026] Furthermore, the digital twin model corresponding to the physical entity deployed based on the edge server provides digital twin interaction services for users; users initiate interaction requests to the digital twin model through the edge server, and then receive digital twin service responses from the edge server or the cloud server.

[0027] In the above solution, the digital twin model on the edge server needs to be regularly updated with data from the physical entity to maintain the synchronization between the digital twin model and the physical entity. The process is as follows:

[0028] The information age of the digital twin interaction request response The information age of the data in the digital twin model that responds to the request at time t is expressed as:

[0029]

[0030] i) Update period: The number of cycles n for the physical entity to update the digital twin model, τ m represents the time interval between two consecutive updates;

[0031] ii) Transmission delay: The transmission delay of data between the physical entity and the digital twin model When both are in the same cell in the cellular network a m represents the size of the updated data, I upload represents the delay of transmitting unit data to the local edge server; When both are in different cells in the cellular network represents the transmission delay of unit data between two edge servers through the core network;

[0032] iii) Update the digital twin model on the cloud server: The information age of the digital twin model on the cloud server:

[0033]

[0034] In the above solution, the digital twin interaction request is represented as a tuple t r is the request initiation time, loc r is the request initiation location, m r represents the digital twin model for request interaction, is the data size of the obtained digital twin service response;

[0035] The information age of obtaining the digital twin interaction request response from the edge server in step (3)

[0036]

[0037] where represents the delay of obtaining the digital twin service response from the edge server;

[0038] The information age of obtaining the digital twin interaction request response from the cloud server in step (3)

[0039]

[0040] wherein represents the latency of obtaining the digital twin service response from the cloud server.

[0041] Furthermore, in the tuple r of each uncertain digital twin interaction request in step (3), the calculation of the utility gain is as follows:

[0042]

[0043] Based on this formula, the uncertainty of the digital twin interaction request initiation time can be eliminated, and the uncertain data size of the digital twin service response is determined by the target digital twin model type m r Therefore, the initiation location of the interaction request and the type of digital twin model for the requested interaction are uncertain. Based on this, a sample space Ω = {e1, e2, …, e k , …, e K} is formed, and each sample point corresponds to a class of interaction requests for initiating an interaction request for a specific type of digital twin model at a specific location.

[0044] In the above solution, in step (4), a confidence set for establishing a fuzzy distribution is based on distributionally robust optimization Since the specific distribution information of the interaction request is unknown, the true distribution exists in the confidence set with a certain confidence level through the confidence set. θ is the maximum distance between the fuzzy distribution and the reference distribution, which determines the size of the confidence set and is affected by the historical digital twin interaction request volume |R'| and the confidence level β ∈ [0, 1]. The calculation formula is

[0045]

[0046] The reference distribution of the confidence set is constructed using a step function:

[0047]

[0048] where when the historical data sample matches the elementary event e k ∈ Ω, δ j (k) = 1; if not, δ j (k) = 0.

[0049] In the above solution, in step (5), the optimization problem based on distributionally robust optimization is specifically transformed through multi-level dual transformation as follows:

[0050] Aggregate the digital twin model decisions for the interaction requests before conversion. The digital twin interaction requests are classified according to the initiation location and the type of digital twin model for which interaction is requested, and the same digital twin model selection strategy is formulated for the digital twin interaction requests of the same category;

[0051] The original optimization problem is transformed into:

[0052]

[0053] When solving the inner maximization problem, assume that the outer decision variables X and Y are known, perform a dual transformation at the problem level, and use the Wasserstein distance to define the distance between two distributions. The inner maximization problem is expressed as: Constraints:

[0054]

[0055] The objective is a linear combination of π, and the constraints are linear inequalities or equations of variables. This is a convex linear programming problem. Therefore, the dual transformation is:

[0056] Constraints: where λ and h j are the introduced dual variables, ||ξ k -ξ j || represents the distance between two sample points e k and e j ;

[0057] Perform a dual transformation at the norm level, use the continuous set Ξ = {ξ|c·ξ ≤ d} to partially discretize the problem, and convert the original constraint conditions to:

[0058]

[0059] According to the transformation principle with max as the minuend, re-express the right side of the constraint and exchange the solution order of max and min to perform a dual transformation at the constraint condition level. After the constraint conversion of the confidence set in problem P2 in step (4), problem P3 is formed:

[0060]

[0061] Constraints: ∑ m∈M c m ·x m,v ≤ Φ v ;

[0062] y r,g ,x m,v ∈ {0,1},

[0063]

[0064] Problem P3 is a mixed-integer non-linear programming problem, and the Gurobi optimization solver is used to solve it.

[0065] Beneficial effects: Compared with the prior art, the remarkable features and substantial progress of the present invention include the following three points:

[0066] First, the digital twin service provision optimization method based on distributionally robust optimization proposed by the present invention comprehensively considers the impact of digital twin data freshness and the uncertainty of interaction requests on service quality, and jointly optimizes the deployment and selection of digital twins to maximize the total benefit gain.

[0067] Second, the present invention comprehensively considers the update of the digital twin model and calculates the age of information in the service interaction process. Under the condition of fully considering the characteristics of digital twin service provision, it comprehensively characterizes the data freshness of interaction requests to obtain services.

[0068] Third, the algorithm proposed by the present invention based on the Wasserstein distance, which applies multi-level dual transformation to transform and solve the distributionally robust optimization problem, solves the problem of infinite distribution in the permutation set of the optimization problem, provides a robust optimization solution for the optimization problem, and provides high-quality digital twin services in the case of unforeseen extreme interaction requests. Description of the Drawings

[0069] Figure 1 is the system model structure diagram of digital twin service provision in the edge computing network of the present invention;

[0070] Figure 2 is the evolution diagram of the age of information of data in the digital twin model of the present invention;

[0071] Figure 3 is the line chart of the total utility gain of different methods in different network scales in the example;

[0072] Figure 4 is the line chart of the total utility gain of different methods with different numbers of physical entities in the example;

[0073] Figure 5 is the bar chart of the total utility gain of different methods with different storage capacities of edge servers in the example. Detailed Embodiments

[0074] In order to elaborate in detail the technical solutions disclosed by the present invention, the present invention will be further described below in conjunction with the drawings and specific embodiments.

[0075] First, the key problem solved by the method of the present invention is how to deploy and select digital twin models under uncertain interactive service requests to maximize the utility gain of service quality in the case of unforeseen extreme interactive requests. The overall system model structure provided by this method is as Figure 1 shown.

[0076] The main idea of the present invention is based on distributionally robust optimization to cope with the uncertainty of digital twin interactive requests. Among them, considering the update and service provision of digital twin models, the age-of-information utility gain compared with the services provided by the cloud is used as an index to quantify the interactive service quality, and the deployment and selection strategies of digital twins in the edge computing network are jointly optimized. The Wasserstein distance is used to measure the distance between distributions, and the multi-level dual transformation is applied to solve the robust optimization scheme.

[0077] Specifically, an optimization method for digital twin service provision based on distributionally robust optimization driven by age-of-information includes the following steps:

[0078] Step 1: Establish a system model for digital twin service provision

[0079] First, construct a system model, as Figure 1 shows the data transmission for providing digital twin services in the edge computing network. Each edge server maintains multiple digital twin models to support different types of interactive requests. The physical entity interacts with the edge server in the base station to maintain the data freshness of the digital twin model in the edge server, enabling it to represent the state of its corresponding physical entity with high fidelity, including the update of the digital twin model in the edge server and the update of the digital twin model in the cloud, to ensure the synchronization and data consistency of the digital twin models.

[0080] When a user initiates a digital twin interactive request, the request can be directly responded to by the digital twin model in the local edge server, thus achieving low-latency service provision. If the local edge digital twin cannot meet the request, the request will be forwarded through the core network to other servers, and processed and returned by the digital twin in other regional edge servers or the cloud.

[0081] Age-of-information of digital twin interactive request response includes the age-of-information of the data in the digital twin model and the transmission delay of the service response from the edge server to the user. Among them, the age-of-information of the data in the digital twin model for responding to the request at time t is expressed as:

[0082]

[0083] which includes: i) the number of cycles n of the physical entity in updating the data twin model, and the time interval τ between two consecutive updates; ii) the transmission delay of data between the physical entity and the digital twin model When both are in the same cell of a cellular network m represents the size of the update data, I upload Indicates the latency of transmitting a unit of data to the local edge server; when the two are in different cells in the cellular network Represents the transmission delay of unit data between two edge servers through the core network; iii) Information age of the digital twin model on the cloud server:

[0084] The user initiates an interaction request to the digital twin model through the local edge server, and then receives a digital twin service response from the edge server or cloud server.

[0085] Digital twin interaction requests are tuples t r is the time when the request was initiated, loc r is the location where the request is initiated, m r A digital twin model representing the request interaction, is the data size of the digital twin service response obtained. The information age of the digital twin interaction request response obtained from the edge server in Delay in getting digital twin service response from edge server; Information age of getting digital twin interaction request response from cloud server in Indicates the latency of getting a response from the digital twin service from the cloud server.

[0086] The utility gain is used as an indicator to evaluate the quality of digital twin services achieved through edge computing. The utility gain of a digital twin interaction request r is:

[0087] When building an edge computing network, the digital twin service provides an optimization problem, which can be expressed mathematically as follows:

[0088]

[0089] Constraints: m∈M c m ·x m,v ≤Φ v

[0090]

[0091] y r,g , x m,v ∈{0,1}

[0092] Among them, and respectively represent the age of information for the digital twin service obtained by the user digital twin interaction request from the cloud server and the edge server. denotes the set of servers \(g\) for which the digital twin interaction request can receive a response; \(R\) represents the set of digital twin interaction requests \(r\in R\); \(x\) m,v \(\in\{0,1\}\) represents the digital twin model deployment strategy, and \(y\) r,g \(\in\{0,1\}\) represents the model selection strategy for the digital twin interaction request; the constraint \(\sum\) m∈M \(c\) m \(\cdot x\) m,v \(\leq\varPhi\) v means that the data volume of the digital twin model deployed on the edge server cannot exceed the maximum storage space \(\varPhi\). v where \(c\) m represents the storage space required for the digital twin model corresponding to the physical entity \(m\in M\), \(m\) represents the digital twin model, and \(M\) represents the set of digital twin models. The constraint means that each digital twin interaction request \(r\in R\) can only be served by one digital twin model .

[0093] Step 2. Uncertainty modeling of digital twin interaction requests

[0094] The joint optimization of digital twin model deployment and selection for digital twin service provision requires prior knowledge of digital twin interaction requests. However, due to the uncertainty of future digital twin interaction requests, such prior knowledge is not available. Based on distributionally robust optimization, a confidence set of fuzzy distributions is established to characterize the uncertainty of interaction requests. The true distribution exists in the confidence set with a certain confidence level. The interaction request where due to the calculation of utility gain:

[0095]

[0096] the uncertainty of the initiation time can be eliminated. And the uncertain data size of the digital twin service response is determined by the type \(m\) of the target digital twin model r . Therefore, the initiation location of the interaction request and the type of digital twin model for which the interaction is requested are uncertain. Based on this, a sample space \(\Omega=\{e_1,e_2,\ldots,e\) k ,\ldots,e\) K}, each sample point corresponds to a type of interaction request that initiates an interaction request for a specific type of digital twin model at a specific location. θ is the maximum distance between the fuzzy distribution and the reference distribution, which determines the size of the confidence set and is affected by the historical digital twin interaction request volume |R'| and the confidence level β ∈ [0, 1]. The calculation formula is: The reference distribution of the confidence set is constructed using a step function: where when the historical data sample and the basic event e k ∈Ω match, δ j (k) = 1; if not, δ j (k) = 0.

[0097] Therefore, this optimization problem is transformed into a problem based on distributionally robust optimization to ensure the robustness of digital twin services:

[0098]

[0099] Constraint: ∑ m∈M c m ·x m,v ≤Φ v

[0100]

[0101] y r,g , x m,v ∈{0, 1}

[0102]

[0103] Considering risk aversion and focusing on the worst-case distribution in the confidence set to ensure the robustness of service provision, the problem is formulated in a min-max form.

[0104] Step 3, Aggregation of Digital Twin Interaction Request Decisions

[0105] Design an algorithm to solve the above min-max form problem. Convert the internal maximization problem into a convex problem through multiple dual transformations and combine it with the external minimization problem; use the Gurobi optimization solver to solve the mixed-integer nonlinear problem.

[0106] Before the transformation, aggregate the decisions of digital twin model selection for interaction requests. Digital twin interaction requests can be classified according to the initiation location and the type of digital twin model requested for interaction, and the same digital twin model selection strategy is formulated for digital twin interaction requests of the same category. Divide the digital twin interaction requests into subsets R k according to the initiation location and the type of digital twin model requested for interaction, and transform the original optimization problem:

[0107]

[0108] where r k represents any digital twin interaction request within R k , and p k is the ratio of the size of subset R k to the size of set R.

[0109] Step 4, Dual transformation at the problem level

[0110] To solve the inner maximization problem, assuming that the outer decision variables X and Y are known, perform a dual transformation at the problem level and use the Wasserstein distance to define the distance between two distributions. The inner maximization problem can be expressed as: Constraints:

[0111]

[0112] π k,j represents the cost of transmitting from ξ j to ξ k . Replace p with the equality constraint k to completely eliminate p k , and the transformed problem expression is obtained as:

[0113]

[0114] Constraints:

[0115]

[0116] where ||ξ k - ξ j || represents the distance between two sample points e k and e j .

[0117] The objective is a linear combination of π, and the constraints are linear inequalities or equations of variables. This is a convex linear programming problem and can be dual-transformed into: Constraints: where λ and h j are the introduced dual variables.

[0118] Step 5, Dual transformation at the norm level

[0119] Perform a dual transformation at the norm level. Use the continuous set Ξ = {ξ|c·ξ ≤ d} to partially discretize the problem and convert the original constraint conditions into:

[0120]

[0121] Express the norm in the formula as the dual of the dual norm, and further transform the constraint condition into:

[0122]

[0123] Step 6: Dual transformation at the constraint condition level

[0124] According to the transformation principle with max as the subtrahend, re - express the right - hand side of the constraint and exchange the solution order of max and min for the dual transformation at the constraint condition level. After the constraint transformation of the confidence set in problem P2 in step (4), problem P3 is formed: Constraint condition: ∑ m∈M c m ·x m,v ≤Φ v ;

[0125] y r,g ,x m,v ∈{0,1},

[0126]

[0127] Problem P3 is a mixed - integer non - linear programming problem, which is characterized by the existence of dual norm, continuous variables and binary variables, so it belongs to the NP - hard problem. To effectively handle the mixed - integer programming and non - linear components in the objective function and constraints, the Gurobi optimization solver is used to solve it.

[0128] To comprehensively illustrate the proposed hybrid - flow scheduling strategy of the present invention, the following respectively compares the performance of different algorithms under the changes of the following three parameters to evaluate the performance:

[0129] (1) Total utility gain under different network scales;

[0130] (2) Total utility gain under different numbers of physical entities;

[0131] (3) Total utility gain under different maximum storage capacities.

[0132] In this embodiment, all algorithms and simulation experiments written in Python 3.9 were completed on a PC with a 2.9 GHZ CPU and 8G of memory. Using the service request dataset in the real-world edge computing network, it was divided into historical data for establishing the reference distribution and future service requests. After multiple rounds of experiments, the average total utility benefit value was selected. Among them, the algorithm proposed in the present invention is called WDRO, the algorithm that preferentially deploys the digital twin model to the local edge server is called Near-PT; the algorithm that preferentially deploys the corresponding type of digital twin model to high-demand areas according to historical data is called Near-RQ; compared with WDRO, the distributionally robust optimization algorithm that directly uses the average distribution for the reference distribution is called DRO-AVG.

[0133] As Figure 3 shown, the applicability of WDRO in large-scale networks is significantly better than other algorithms, and as the network scale increases, the utility gain shows an obvious upward trend. Compared with DRO-AVG, WDRO grows more significantly because it considers the similarity between historical interaction information and upcoming digital twin interaction requests, while Near-RQ and Near-PT grow slower because they only focus on digital twin model updates or service responses. As Figure 4 shown, as the number of physical entities increases, the utility gain decreases, but the decrease rate of WDRO is significantly slower than other algorithms because its robustness can better mitigate the negative impact brought by storage limitations. As Figure 5 shown, as the maximum storage capacity of the edge server increases, for the utility gain of digital twin model updates and service response delays, WDRO performs excellently in both aspects. The utility gain increases with the increase of the storage capacity and tends to be stable, indicating its effectiveness in meeting digital twin interaction requests and maintaining high-fidelity digital twin models.

[0134] The present invention can be applied to scenarios where users request digital twin services and user interaction requests are highly uncertain. In the autonomous driving scenario, connected vehicles may need to interact with different types of digital twin models, such as obtaining real-time road conditions, querying traffic light status, or requesting digital twin data of road infrastructure. However, the dynamic nature of the vehicle driving path means that the system cannot accurately predict in advance when and where a vehicle will request a specific digital twin service. If traditional methods optimize service deployment based on a fixed request pattern, it may lead to ineffective responses to requests in some areas, thus affecting driving decisions. Through distributionally robust optimization, the present invention enables the system to still optimize the deployment of digital twin models and the model selection for different digital twin service requests in the face of highly uncertain vehicle request patterns, ensuring that vehicles obtain as fresh environmental data as possible, thereby improving the safety and adaptability of autonomous driving.

Claims

1. A digital twin service optimization method driven by age of information, characterized in that: The method includes quantifying the freshness of digital twin data with age of information, aiming at the unforeseen request distribution in the edge network, and maximizing the quality of digital twin services in extreme cases based on distributionally robust optimization, and realizing the deployment of digital twin models and the selection of different digital twin service requests; The method includes the following steps: (1) Combining the service scenario, constructing a digital twin service model based on edge computing, including physical entities, edge servers, and digital twin models, and realizing the transmission of data between cellular units based on the communication network; (2) Designing a utility gain based on the age of information difference on the edge server as an index to evaluate the quality of digital twin services, thereby improving the quality of digital twin services; The utility gain of the digital twin interaction request r is: In the formula, and respectively represent the information ages of obtaining digital twin services for the user digital twin interaction requests from the cloud server and the edge server, represents the set of servers g for which the digital twin interaction request r can get a response; (3) Optimizing the digital twin services provided under the edge computing network, and the mathematical representation of the optimization process is: [P1]: Constraint: ∑ m∈M c m ·x m,v ≤ Φ v y r,g ,x m,v ∈ {0, 1} R represents the set of digital twin interaction requests, x m,v ∈{0,1} represents the digital twin model deployment strategy, y r,g ∈{0,1} represents the model selection strategy for digital twin interaction requests. The constraint ∑ m∈M c m ·x m,v ≤Φ v means that the amount of data for deploying the digital twin model on the edge server cannot exceed the maximum storage space Φ of the edge server v ,c m represents the storage space required for the digital twin model corresponding to the physical entity m∈M. m represents the digital twin model, and M represents the set of digital twin models. The constraint means that each digital twin interaction request r∈R can only be served by one digital twin model ; (4) Transforming the joint optimization of the digital twin model deployment and selection in the digital twin service supply in step (3) into a problem based on distributionally robust optimization to ensure the robustness of digital twin service provision: [P2]: Constraint: ∑ m∈M c m ·x m,v ≤ Φ v y r,g ,x m,v ∈ {0, 1} where D is the confidence set of the fuzzy distribution, within which the true interactive request distribution exists with a certain confidence level. represents the reference distribution, P represents the fuzzy distribution, and θ is the maximum distance between the fuzzy distribution and the reference distribution. Considering risk aversion, focusing on the worst-case distribution in the confidence set D to ensure the robustness of service provision, and formulating the problem in the min-max form; (5) Solving the min-max form problem, transforming the internal maximization problem into a convex problem through multiple dual transformations, and combining it with the external minimization problem; using the Gurobi optimization solver to solve the mixed-integer non-linear problem.

2. The method for optimizing digital twin services driven by information age according to claim 1, wherein: The digital twin model corresponding to the physical entity is deployed on the edge server to provide digital twin interaction services for users; users initiate interaction requests to the digital twin model through the edge server and receive digital twin service responses from the edge server or the cloud server.

3. The method for optimizing digital twin services driven by information age according to claim 1 or 2, characterized in that: The digital twin model on the edge server is regularly updated according to the data of the physical entity to maintain the synchronization between the digital twin model and the physical entity. The specific approach for this process is: The information age of the digital twin interaction request response In the digital twin model that responds to the request, the information age of the data at time t is expressed as: i) Update period: the number of cycles n for a physical entity to update its digital twin model, τ m which represents the time interval between two consecutive updates; ii) Transmission delay: The transmission delay of data between the physical entity and the digital twin model When both are in the same cell in the cellular network a m represents the size of the updated data, I upload represents the delay of transmitting unit data to the local edge server; When both are in different cells in the cellular network represents the transmission delay of unit data between two edge servers through the core network, loc m represents the edge server corresponding to the area where the physical entity m is located; iii) Updating the digital twin model on the cloud server: The age of information of the digital twin model on the cloud server:

4. The information age-driven digital twin service optimization method according to claim 1, characterized in that: Represent the digital twin interaction request as a tuple t r is the request initiation time, loc r is the request initiation location, m r represents the digital twin model for request interaction, is the data size of the obtained digital twin service response; The information age of obtaining the digital twin interaction request response from the edge server in step (3) Among them represents the latency of obtaining the digital twin service response from the edge server; In step (3), obtain the information age of the digital twin interaction request response from the cloud server Among them represents the latency of obtaining the digital twin service response from the cloud server.

5. The method for optimizing digital twin services driven by information age according to claim 1 or 4, characterized in that: In each tuple r of the uncertain digital twin interaction requests in step (3), the calculation of the utility gain is: Based on this formula, the uncertainty of the digital twin interaction request initiation time can be eliminated, and the digital twin service responds to uncertain data sizes determined by the target digital twin model type m r Therefore, the initiation location of the interaction request and the digital twin model type for which the interaction is requested are uncertain. Based on this, a sample space Ω = {e1, e2, …, e k , …, e K} is formed, and each sample point corresponds to a type of interaction request that initiates an interaction request for a specific type of digital twin model at a specific location.

6. The method for optimizing digital twin services driven by information age according to claim 1, wherein: In step (4), a confidence set for the fuzzy distribution is established based on distributionally robust optimization Since the specific distribution information of the interaction requests is unknown, the true distribution exists in the confidence set with a certain confidence level through the confidence set. θ is the maximum distance between the fuzzy distribution and the reference distribution, which determines the size of the confidence set and is affected by the historical digital twin interaction request volume |R'| and the confidence level β ∈ [0, 1]. The calculation formula is The reference distribution of the confidence set is constructed using a step function: where when the historical data sample and the basic event e k ∈Ω match, δ j (k) = 1; if not, δ j (k) = 0.

7. The method for optimizing digital twin services driven by information age according to claim 1, characterized in that: Specifically, how the optimization problem based on distributionally robust optimization in step (5) is transformed through multi-level dual transformations is: Before the transformation, aggregate the digital twin model decision-making for interaction request selection. The digital twin interaction requests are classified according to the initiation location and the type of digital twin model for which the interaction is requested, and the same digital twin model selection strategy is formulated for digital twin interaction requests of the same category; The original optimization problem is transformed into: When solving the inner maximization problem, it is assumed that the outer decision variables X and Y are known. A problem-level dual transformation is performed, and the Wasserstein distance is used to define the distance between two distributions. The inner maximization problem is formulated as: Constraints: The objective is a linear combination of π, and the constraints are linear inequalities or equations of variables. This is a convex linear programming problem, so the dual transformation is as follows: Constraints: where γ and h j are the introduced dual variables, ||ξ k - ξ j || represents the distance between two sample points e k and e j ; Perform a dual transformation at the norm level, and use the continuous set Ξ = {ξ|c·ξ ≤ d} to partially discretize the problem, and transform the original constraint conditions into: According to the transformation principle with max as the subtrahend, re-express the expression on the right side of the constraint and exchange the solution order of max and min to perform a dual transformation at the constraint condition level. After the constraint conversion of the confidence set in problem P2 in step (4), problem P3 is formed: [P3] Constraints: y r,g ,x m,v ∈ {0, 1}, The problem P3 is a mixed-integer non-linear programming problem, and the Gurobi optimization solver is used to solve it.

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