Opportunistic mobile crowdsensing(MCS)non-intrusively exploits human mobility trajectories,and the participants’smart devices as sensors have become promising paradigms for various urban data acquisition tasks.Howeve...Opportunistic mobile crowdsensing(MCS)non-intrusively exploits human mobility trajectories,and the participants’smart devices as sensors have become promising paradigms for various urban data acquisition tasks.However,in practice,opportunistic MCS has several challenges from both the perspectives of MCS participants and the data platform.On the one hand,participants face uncertainties in conducting MCS tasks,including their mobility and implicit interactions among participants,and participants’economic returns given by the MCS data platform are determined by not only their own actions but also other participants’strategic actions.On the other hand,the platform can only observe the participants’uploaded sensing data that depends on the unknown effort/action exerted by participants to the platform,while,for optimizing its overall objective,the platform needs to properly reward certain participants for incentivizing them to provide high-quality data.To address the challenge of balancing individual incentives and platform objectives in MCS,this paper proposes MARCS,an online sensing policy based on multi-agent deep reinforcement learning(MADRL)with centralized training and decentralized execution(CTDE).Specifically,the interactions between MCS participants and the data platform are modeled as a partially observable Markov game,where participants,acting as agents,use DRL-based policies to make decisions based on local observations,such as task trajectories and platform payments.To align individual and platform goals effectively,the platform leverages Shapley value to estimate the contribution of each participant’s sensed data,using these estimates as immediate rewards to guide agent training.The experimental results on real mobility trajectory datasets indicate that the revenue of MARCS reaches almost 35%,53%,and 100%higher than DDPG,Actor-Critic,and model predictive control(MPC)respectively on the participant side and similar results on the platform side,which show superior performance compared to baselines.展开更多
Under the current long-term electricity market mechanism,new energy and thermal power face issues such as deviation assessment and compression of generation space.The profitability of market players is limited.Simulta...Under the current long-term electricity market mechanism,new energy and thermal power face issues such as deviation assessment and compression of generation space.The profitability of market players is limited.Simultaneously,the cooperation model among various energy sources will have a direct impact on the alliance’s revenue and the equity of income distribution within the alliance.Therefore,integrating new energy with thermal power units into an integrated multi-energy complementary system to participate in the long-term electricity market holds significant potential.To simulate and evaluate the benefits and internal distribution methods of a multi-energy complementary system participating in long-term market transactions,this paper first constructs a multi-energy complementary system integrated with new energy and thermal power generation units at the same connection point,and participates in the annual bilateral game as a unified market entity to obtain the revenue value under the annual bilateral market.Secondly,based on the entropy weight method,improvements are made to the traditional Shapley value distribution model,and an internal distribution model for multi-energy complementary systems with multiple participants is constructed.Finally,a Markov Decision Process(MDP)evaluation system is constructed for practical case verification.The research results show that the improved Shapley value distribution model achieves higher satisfaction,providing a reasonable allocation scheme for multi-energy complementary cooperation models.展开更多
The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and...The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.展开更多
Shapley value is one of the most fundamental concepts in cooperative games.This paper investigates the calculation of the Shapley value for cooperative games and establishes a new formula via carrier.Firstly,a necessa...Shapley value is one of the most fundamental concepts in cooperative games.This paper investigates the calculation of the Shapley value for cooperative games and establishes a new formula via carrier.Firstly,a necessary and sufficient condition is presented for the verification of carrier,based on which an algorithm is worked out to find the unique minimum carrier.Secondly,by virtue of the properties of minimum carrier,it is proved that the profit allocated to dummy players(players which do not belong to the minimum carrier)is zero,and the profit allocated to players in minimum carrier is only determined by the minimum carrier.Then,a new formula of the Shapley value is presented,which greatly reduces the computational complexity of the original formula,and shows that the Shapley value only depends on the minimum carrier.Finally,based on the semi-tensor product(STP)of matrices,the obtained new formula is converted into an equivalent algebraic form,which makes the new formula convenient for calculation via MATLAB.展开更多
Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with ...Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with fuzzy payoffs by using fuzzy sets theory. Fuzzy Shapley function is defined based on these extended axioms. From the viewpoint the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, a crisp allocation scheme based on fuzzy Shapley values is proposed.展开更多
Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable t...Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.展开更多
Under green supply chain mode, how to Carry out the distribution of profits between subjects is an important problem. Through the comparison of the green supply chain benefit allocation of non-cooperative game and coo...Under green supply chain mode, how to Carry out the distribution of profits between subjects is an important problem. Through the comparison of the green supply chain benefit allocation of non-cooperative game and cooperative game the payoffmatrix, it is clearly that the necessity of interest distribution cooperative game. Put general manufacturing enterprises of green supply chain as the research object, using Shapley value method for theory analysis and example verification, vertifys that enterprise synergy gains more than their own separate management, and puts forward a feasible path of supply chain collaboration through the construction of the distribution of interests coordination model.展开更多
Rural sewage treatment is in need of more capital investment,in which the financing model of PPP(public-private partnership)is able to encourage the investment of social capital in this sector.Risk sharing is one of t...Rural sewage treatment is in need of more capital investment,in which the financing model of PPP(public-private partnership)is able to encourage the investment of social capital in this sector.Risk sharing is one of the core features in the PPP model.In view that the risk loss of projects cannot be accurately estimated,this article describes the uncertainty of risk loss with fuzzy numbers and allocates the distribution of risk loss among the participants of rural sewage treatment PPP projects with interval fuzzy Shapley value to ensure a more reasonable and effective risk distribution.展开更多
Tree models have made an impressive progress during the past years,while an important problem is to understand how these models predict,in particular for critical applications such as finance and medicine.For this iss...Tree models have made an impressive progress during the past years,while an important problem is to understand how these models predict,in particular for critical applications such as finance and medicine.For this issue,most previous works measured the importance of individual features.In this work,we consider the interpretation of feature groups,which is more effective to capture intrinsic structures and correlations of multiple features.We propose the Baseline Group Shapley value(short for BGShapvalue)to calculate the importance of a feature group for tree models.We further develop a polynomial algorithm,BGShapTree,to deal with the sum of exponential terms in the BGShapvalue.The basic idea is to decompose the BGShapvalue into leaves’weights and exploit the relationships between features and leaves.Based on this idea,we could greedily search salient feature groups with large BGShapvalues.Extensive experiments have validated the effectiveness of our approach,in comparison with state-of-theart methods on the interpretation of tree models.展开更多
An iterative method based on Shapley Value Cooperative Game Theory is proposed for the calculation of local marginal price (LMP) for each Distributed Generator (DG) bus on a network. The LMP value is determined for ea...An iterative method based on Shapley Value Cooperative Game Theory is proposed for the calculation of local marginal price (LMP) for each Distributed Generator (DG) bus on a network. The LMP value is determined for each DG on the basis of its contribution to reduce loss and emission reduction, which is assessed using the Shapley Value approach. The proposed approach enables the Distribution Company (DISCO) decision-maker to operate the network optimally in terms of loss and emission. The proposed method is implemented in the Taiwan Power Company distribution network 7 warnings consisting of 84 buses and 11 feeders in the MATLAB environment. The results show that the proposed approach allows DISCO to operate the network on the basis of its priority between the reduction of active power loss and emission in the network.展开更多
With the tremendous success of machine learning(ML),concerns about their black-box nature have grown.The issue of interpretability affects trust in ML systems and raises ethical concerns such as algorithmic bias.In re...With the tremendous success of machine learning(ML),concerns about their black-box nature have grown.The issue of interpretability affects trust in ML systems and raises ethical concerns such as algorithmic bias.In recent years,the feature attribution explanation method based on Shapley value has become the mainstream explainable artificial intelligence approach for explaining ML models.This paper provides a comprehensive overview of Shapley value-based attribution methods.We begin by outlining the foundational theory of Shapley value rooted in cooperative game theory and discussing its desirable properties.To enhance comprehension and aid in identifying relevant algorithms,we propose a comprehensive classification framework for existing Shapley value-based feature attribution methods from three dimensions:Shapley value type,feature replacement method,and approximation method.Furthermore,we emphasize the practical application of the Shapley value at different stages of ML model development,encompassing pre-modeling,modeling,and post-modeling phases.Finally,this work summarizes the limitations associated with the Shapley value and discusses potential directions for future research.展开更多
The integrated energy system is an important development direction for achieving energy transformation in the context of the low-carbon development era,and an integrated energy system that uses renewable energy can re...The integrated energy system is an important development direction for achieving energy transformation in the context of the low-carbon development era,and an integrated energy system that uses renewable energy can reduce carbon emissions and improve energy utilization efficiency.The electric power network and the natural gas network are important transmission carriers in the en-ergy field,so the coupling relationship between them has been of wide concern.This paper establishes an integrated energy system considering electricity,gas,heat and hydrogen loads;takes each subject in the integrated energy system as the research object;anal-yses the economic returns of each subject under different operation modes;applies the Shapley value method for benefit allocation;and quantifies the contribution value of the subject to the alliance through different influencing factors to revise the benefit allocation value.Compared with the independent mode,the overall benefits of the integrated energy system increase in the cooperative mode and the benefits of all subjects increase.Due to the different characteristics of different subjects in terms of environmental benefits,collaborative innovation and risk sharing,the benefit allocation is reduced for new-energy subjects and increased for power-to-gas sub-jects and combined heat and power generation units after revising the benefit allocation,to improve the matching degree between the contribution level and the benefit allocation under the premise of increased profit for each subject.The cooperative mode effectively enhances the economic benefits of the system as a whole and individually,and provides a useful reference for the allocation of benefits of integrated energy systems.The analysis shows that the revised benefit distribution under the cooperative model increases by 3.86%,4.08%and 3.13%for power-to-gas subjects,combined heat and power generation units,and new-energy units,respectively,compared with the independent function model.展开更多
China＇s market-oriented reform is expected to strengthen the role of the market in allocating resources, which raises concerns over the impact of market transformation on income distribution and earnings inequality i...China＇s market-oriented reform is expected to strengthen the role of the market in allocating resources, which raises concerns over the impact of market transformation on income distribution and earnings inequality in the past decades. This paper decomposes the sources of inequality based on the newly developed Shapley value approach and examines the contributions of the market, along with other nonmarket factors, to total inequality. Using the China Health and Nutrition Survey data over the period 1989-2009, we find that the income gap between laborers with a higher level of education and those with a lower level has widened since the transformational reforms of the economy. Our results suggest that the largest contribution of changes in income inequality can be attributed to the increase in returns to education, while the relative contributions of the household registration （hukou） system, type of sector ownership, geographic location, and gender to inequality experienced a downward trend between 1989 and 2009. The authors argue that rising income inequality is the consequence of efficiency improvements and an imperfect economic system, and that the market is a decisive force in economic development as it releases competitive signals and creates incentive mechanisms for innovation. Creating a more efficient labor market and increasing investment in human capital, particularly equalizing educational opportunities and improving the quality of education in lagging rural and inland regions to disadvantaged groups, are significant for an equitable distribution of income and sustainable development in the long run.展开更多
Freeform surface measurement is a key basic technology for product quality control and reverse engineering in aerospace field.Surface measurement technology based on multi-sensor fusion such as laser scanner and conta...Freeform surface measurement is a key basic technology for product quality control and reverse engineering in aerospace field.Surface measurement technology based on multi-sensor fusion such as laser scanner and contact probe can combine the complementary characteristics of different sensors,and has been widely concerned in industry and academia.The number and distribution of measurement points will significantly affect the efficiency of multisensor fusion and the accuracy of surface reconstruction.An aggregation‑value‑based active sampling method for multisensor freeform surface measurement and reconstruction is proposed.Based on game theory iteration,probe measurement points are generated actively,and the importance of each measurement point on freeform surface to multi-sensor fusion is clearly defined as Shapley value of the measurement point.Thus,the problem of obtaining the optimal measurement point set is transformed into the problem of maximizing the aggregation value of the sample set.Simulation and real measurement results verify that the proposed method can significantly reduce the required probe sample size while ensuring the measurement accuracy of multi-sensor fusion.展开更多
A park hydrogen-doped integrated energy system(PHIES)can maximize energy utilization as a system with multiple supplies.To realize win-win cooperation between the PHIES and active distribution network(ADN),the coopera...A park hydrogen-doped integrated energy system(PHIES)can maximize energy utilization as a system with multiple supplies.To realize win-win cooperation between the PHIES and active distribution network(ADN),the cooperative operation problem of multi-PHIES connected to the same ADN is studied.A low-carbon hybrid game coordination strategy for multi-PHIES accessing ADN based on dynamic carbon base price is proposed in the paper.Firstly,multi-PHIES are constructed to form a PHIES alliance,including a hydrogen-doped gas turbine(HGT),hydrogen-doped gas boiler(HGB),power to gas and carbon capture system(P2G-CCS),and other equipment.Secondly,a hybrid game system model of the ADN and PHIES alliance is constructed,in which the ADN and PHIES alliance constitute a master-slave game,and the members of the PHIES alliance constitute a cooperative game.An improved Shapley value is proposed to deal with the problem of cost share among members in the alliance.Thirdly,an improved stepped carbon trading based on dynamic carbon baseline price is proposed.Thecarbon emissions at each moment and the total carbon emissions in a cycle are set as the dynamic adjustment factors of the carbon baseline price.The pricing mechanism of carbon baseline price increases with carbon emissions is constructed so that carbon emissions decrease.Finally,the quadratic interpolation optimization(QIO)algorithm is combined with Gurobi to solve the model.The results of the example analysis show that the cost of ADN is reduced by 4.47%,the cost of PHIES 1 is reduced by 3.67%,the cost of PHIES 2 is reduced by 0.97%,and the cost of PHIES 3 is reduced by 4.91%respectively.The total carbon emissions of the PHIES alliance are reduced by 7.08%.The low-carbon and economical operation of the multi-PHIES accessing ADN is achieved.展开更多
Coking at the fractionating tower bottom and the decant oil circulation system disrupts the heat balance,leading to unplanned shutdown and destroying the long period stable operation of the Fluid Catalytic Cracking Un...Coking at the fractionating tower bottom and the decant oil circulation system disrupts the heat balance,leading to unplanned shutdown and destroying the long period stable operation of the Fluid Catalytic Cracking Unit(FCCU).The FCCU operates through interconnected subsystems,generating high-dimensional,nonlinear,and non-stationary data characterized by spatiotemporally correlated.The decant oil solid content is the crucial indicator for monitoring catalyst loss from the reactor-regenerator system and coking risk tendency at the fractionating tower bottom that relies on sampling and laboratory testing,which is lagging responsiveness and labor-intensive.Developing the online decant oil solid content soft sensor using industrial data to support operators in conducting predictive maintenance is essential.Therefore,this paper proposes a hybrid deep learning framework for soft sensor development that combines spatiotemporal pattern extraction with interpretability,enabling accurate risk identification in dynamic operational conditions.This framework employs a Filter-Wrapper method for dimensionality reduction,followed by a 2D Convolutional Neural Network(2DCNN)for extracting spatial patterns,and a Bidirectional Gated Recurrent Unit(BiGRU)for capturing long-term temporal dependencies,with an Attention Mechanism(AM)to highlight critical features adaptively.The integration of SHapley Additive exPlanations(SHAP),Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN),2DCNN,and expert knowledge precisely quantifies feature contributions and decomposes signals,significantly enhancing the practicality of risk identification.Applied to a China refinery with processing capacity of 2.80×10^(6) t/a,the soft sensor achieved the R^(2) value of 0.93 and five-level risk identification accuracy of 96.42%.These results demonstrate the framework's accuracy,robustness,and suitability for complex industrial scenarios,advancing risk visualization and management.展开更多
Accurate prediction of pure component physiochemical properties is crucial for process integration, multiscale modelling, and optimization. In this work, an enhanced framework for pure component property prediction by...Accurate prediction of pure component physiochemical properties is crucial for process integration, multiscale modelling, and optimization. In this work, an enhanced framework for pure component property prediction by using explainable machine learning methods is proposed. In this framework, the molecular representation method based on the connectivity matrix effectively considers atomic bonding relationships to automatically generate features. The supervised machine learning model random forest is applied for feature ranking and pooling. The adjusted R^(2) is introduced to penalize the inclusion of additional features, providing an assessment of the true contribution of features. The prediction results for normal boiling point (T_(b)), liquid molar volume (L_(mv)), critical temperature (T_(c)) and critical pressure (P_(c)) obtained using Artificial Neural Network and Gaussian Process Regression models confirm the accuracy of the molecular representation method. Comparison with GC based models shows that the root-mean-square error on the test set can be reduced by up to 83.8%. To enhance the interpretability of the model, a feature analysis method based on Shapley values is employed to determine the contribution of each feature to the property predictions. The results indicate that using the feature pooling method reduces the number of features from 13316 to 100 without compromising model accuracy. The feature analysis results for Tb, Lmv, Tc, and Pc confirms that different molecular properties are influenced by different structural features, aligning with mechanistic interpretations. In conclusion, the proposed framework is demonstrated to be feasible and provides a solid foundation for mixture component reconstruction and process integration modelling.展开更多
Floor heave is a common defect in mountainous tunnels.It is critical but challenging to predict the risk of floor heave,as traditional methods often fail to characterize this phenomenon effectively.This study proposes...Floor heave is a common defect in mountainous tunnels.It is critical but challenging to predict the risk of floor heave,as traditional methods often fail to characterize this phenomenon effectively.This study proposes a data-driven approach utilizing a support vector machine(SVM)optimized by the sparrow search algorithm(SSA)to address the issue.The model was developed and validated using a dataset collected from 100 tunnels.Shapley value analysis was conducted to identify the key features influencing floor heave defects.Moreover,a committee-based uncertainty quantification method is presented to evaluate the reliability of each prediction.The results show that:(1)Data feature engineering and SSA play pivotal roles in expediting the convergence of the SVM model.(2)Groundwater and high in situ stress are key factors contributing to tunnel floor heave.(3)In comparison to backpropagation(BP)neural networks,the SSA-SVM demonstrates superior robustness in handling imperfect and limited data.(4)The committee-based uncertainty quantification method is proven effective to evaluate the trustworthiness of each prediction.This data-driven surrogate model offers an effective strategy for understanding the factors that impact tunnel floor defects and accurately predicting tunnel floor heave deformation.展开更多
During the transitional period of electricity market reforms in China,scheduling simulations of technical virtual power plants(TVPPs)are crucial owing to the lack of operational experience.This study proposes a model ...During the transitional period of electricity market reforms in China,scheduling simulations of technical virtual power plants(TVPPs)are crucial owing to the lack of operational experience.This study proposes a model for TVPPs participating in the current multi-market;that is,TVPP coordinate bidding in the day-ahead energy and ramping ancillary market while purchasing unbalanced power and pro-viding frequency regulation service in the real-time market.A multi-scenario optimization approach was employed in the day-ahead stage to manage uncertainty,and an improved Shapley value was utilized for revenue allocation.By employing linearization techniques,the model is transformed into a mixed-integer second-order cone-programming problem that can be efficiently solved using linear solvers.Numerical simulations based on actual provincial electricity market rules were conducted to validate the effectiveness of a TVPP coalition profitability.展开更多
Background The geo-traceability of cotton is crucial for ensuring the quality and integrity of cotton brands. However, effective methods for achieving this traceability are currently lacking. This study investigates t...Background The geo-traceability of cotton is crucial for ensuring the quality and integrity of cotton brands. However, effective methods for achieving this traceability are currently lacking. This study investigates the potential of explainable machine learning for the geo-traceability of raw cotton.Results The findings indicate that principal component analysis(PCA) exhibits limited effectiveness in tracing cotton origins. In contrast, partial least squares discriminant analysis(PLS-DA) demonstrates superior classification performance, identifying seven discriminating variables: Na, Mn, Ba, Rb, Al, As, and Pb. The use of decision tree(DT), support vector machine(SVM), and random forest(RF) models for origin discrimination yielded accuracies of 90%, 87%, and 97%, respectively. Notably, the light gradient boosting machine(Light GBM) model achieved perfect performance metrics, with accuracy, precision, and recall rate all reaching 100% on the test set. The output of the Light GBM model was further evaluated using the SHapley Additive ex Planation(SHAP) technique, which highlighted differences in the elemental composition of raw cotton from various countries. Specifically, the elements Pb, Ni, Na, Al, As, Ba, and Rb significantly influenced the model's predictions.Conclusion These findings suggest that explainable machine learning techniques can provide insights into the complex relationships between geographic information and raw cotton. Consequently, these methodologies enhances the precision and reliability of geographic traceability for raw cotton.展开更多
基金sponsored by Qinglan Project of Jiangsu Province,and Jiangsu Provincial Key Research and Development Program(No.BE2020084-1).
文摘Opportunistic mobile crowdsensing(MCS)non-intrusively exploits human mobility trajectories,and the participants’smart devices as sensors have become promising paradigms for various urban data acquisition tasks.However,in practice,opportunistic MCS has several challenges from both the perspectives of MCS participants and the data platform.On the one hand,participants face uncertainties in conducting MCS tasks,including their mobility and implicit interactions among participants,and participants’economic returns given by the MCS data platform are determined by not only their own actions but also other participants’strategic actions.On the other hand,the platform can only observe the participants’uploaded sensing data that depends on the unknown effort/action exerted by participants to the platform,while,for optimizing its overall objective,the platform needs to properly reward certain participants for incentivizing them to provide high-quality data.To address the challenge of balancing individual incentives and platform objectives in MCS,this paper proposes MARCS,an online sensing policy based on multi-agent deep reinforcement learning(MADRL)with centralized training and decentralized execution(CTDE).Specifically,the interactions between MCS participants and the data platform are modeled as a partially observable Markov game,where participants,acting as agents,use DRL-based policies to make decisions based on local observations,such as task trajectories and platform payments.To align individual and platform goals effectively,the platform leverages Shapley value to estimate the contribution of each participant’s sensed data,using these estimates as immediate rewards to guide agent training.The experimental results on real mobility trajectory datasets indicate that the revenue of MARCS reaches almost 35%,53%,and 100%higher than DDPG,Actor-Critic,and model predictive control(MPC)respectively on the participant side and similar results on the platform side,which show superior performance compared to baselines.
文摘Under the current long-term electricity market mechanism,new energy and thermal power face issues such as deviation assessment and compression of generation space.The profitability of market players is limited.Simultaneously,the cooperation model among various energy sources will have a direct impact on the alliance’s revenue and the equity of income distribution within the alliance.Therefore,integrating new energy with thermal power units into an integrated multi-energy complementary system to participate in the long-term electricity market holds significant potential.To simulate and evaluate the benefits and internal distribution methods of a multi-energy complementary system participating in long-term market transactions,this paper first constructs a multi-energy complementary system integrated with new energy and thermal power generation units at the same connection point,and participates in the annual bilateral game as a unified market entity to obtain the revenue value under the annual bilateral market.Secondly,based on the entropy weight method,improvements are made to the traditional Shapley value distribution model,and an internal distribution model for multi-energy complementary systems with multiple participants is constructed.Finally,a Markov Decision Process(MDP)evaluation system is constructed for practical case verification.The research results show that the improved Shapley value distribution model achieves higher satisfaction,providing a reasonable allocation scheme for multi-energy complementary cooperation models.
基金Sponsored by the National Natural Science Foundation of China(70771010)the Second Phase of "985 Project" of China (107008200400024)the Graduate Student’s Science and Technology Innovation Project of Beijing Institute of Technology (GB200818)
文摘The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.
基金supported by the National Natural Science Foundation of China(No.62073202,No.61873150)the Young Experts of Taishan Scholar Project(No.tsqn201909076)the Natural Science Fund for Distinguished Young Scholars of Shandong Province(No.JQ201613).
文摘Shapley value is one of the most fundamental concepts in cooperative games.This paper investigates the calculation of the Shapley value for cooperative games and establishes a new formula via carrier.Firstly,a necessary and sufficient condition is presented for the verification of carrier,based on which an algorithm is worked out to find the unique minimum carrier.Secondly,by virtue of the properties of minimum carrier,it is proved that the profit allocated to dummy players(players which do not belong to the minimum carrier)is zero,and the profit allocated to players in minimum carrier is only determined by the minimum carrier.Then,a new formula of the Shapley value is presented,which greatly reduces the computational complexity of the original formula,and shows that the Shapley value only depends on the minimum carrier.Finally,based on the semi-tensor product(STP)of matrices,the obtained new formula is converted into an equivalent algebraic form,which makes the new formula convenient for calculation via MATLAB.
基金the National Natural Science Foundation of China (70471063 , 70171036)the Second Phase of "985"Project of China(107008200400024) the Main/Subject Project of Beijing of China(XK100070534)
文摘Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with fuzzy payoffs by using fuzzy sets theory. Fuzzy Shapley function is defined based on these extended axioms. From the viewpoint the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, a crisp allocation scheme based on fuzzy Shapley values is proposed.
基金the National Natural Science Foundation of China(70771010)the Second Phase of"985 Project"of China (107008200400024)the Graduate Student s Science and Technology Innovation Project of Beijing Institute of Technology (GB200818)
文摘Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.
文摘Under green supply chain mode, how to Carry out the distribution of profits between subjects is an important problem. Through the comparison of the green supply chain benefit allocation of non-cooperative game and cooperative game the payoffmatrix, it is clearly that the necessity of interest distribution cooperative game. Put general manufacturing enterprises of green supply chain as the research object, using Shapley value method for theory analysis and example verification, vertifys that enterprise synergy gains more than their own separate management, and puts forward a feasible path of supply chain collaboration through the construction of the distribution of interests coordination model.
文摘Rural sewage treatment is in need of more capital investment,in which the financing model of PPP(public-private partnership)is able to encourage the investment of social capital in this sector.Risk sharing is one of the core features in the PPP model.In view that the risk loss of projects cannot be accurately estimated,this article describes the uncertainty of risk loss with fuzzy numbers and allocates the distribution of risk loss among the participants of rural sewage treatment PPP projects with interval fuzzy Shapley value to ensure a more reasonable and effective risk distribution.
基金supported by the National Science and Technology Major Project(2021ZD0112802)the National Natural Science Foundation of China(Grant No.62376119).
文摘Tree models have made an impressive progress during the past years,while an important problem is to understand how these models predict,in particular for critical applications such as finance and medicine.For this issue,most previous works measured the importance of individual features.In this work,we consider the interpretation of feature groups,which is more effective to capture intrinsic structures and correlations of multiple features.We propose the Baseline Group Shapley value(short for BGShapvalue)to calculate the importance of a feature group for tree models.We further develop a polynomial algorithm,BGShapTree,to deal with the sum of exponential terms in the BGShapvalue.The basic idea is to decompose the BGShapvalue into leaves’weights and exploit the relationships between features and leaves.Based on this idea,we could greedily search salient feature groups with large BGShapvalues.Extensive experiments have validated the effectiveness of our approach,in comparison with state-of-theart methods on the interpretation of tree models.
文摘An iterative method based on Shapley Value Cooperative Game Theory is proposed for the calculation of local marginal price (LMP) for each Distributed Generator (DG) bus on a network. The LMP value is determined for each DG on the basis of its contribution to reduce loss and emission reduction, which is assessed using the Shapley Value approach. The proposed approach enables the Distribution Company (DISCO) decision-maker to operate the network optimally in terms of loss and emission. The proposed method is implemented in the Taiwan Power Company distribution network 7 warnings consisting of 84 buses and 11 feeders in the MATLAB environment. The results show that the proposed approach allows DISCO to operate the network on the basis of its priority between the reduction of active power loss and emission in the network.
基金supported by the National Key Research and Development Program of China under Grant No.2020AAA0108101the National Natural Science Foundation of China under Grant No.U1964201.
文摘With the tremendous success of machine learning(ML),concerns about their black-box nature have grown.The issue of interpretability affects trust in ML systems and raises ethical concerns such as algorithmic bias.In recent years,the feature attribution explanation method based on Shapley value has become the mainstream explainable artificial intelligence approach for explaining ML models.This paper provides a comprehensive overview of Shapley value-based attribution methods.We begin by outlining the foundational theory of Shapley value rooted in cooperative game theory and discussing its desirable properties.To enhance comprehension and aid in identifying relevant algorithms,we propose a comprehensive classification framework for existing Shapley value-based feature attribution methods from three dimensions:Shapley value type,feature replacement method,and approximation method.Furthermore,we emphasize the practical application of the Shapley value at different stages of ML model development,encompassing pre-modeling,modeling,and post-modeling phases.Finally,this work summarizes the limitations associated with the Shapley value and discusses potential directions for future research.
文摘The integrated energy system is an important development direction for achieving energy transformation in the context of the low-carbon development era,and an integrated energy system that uses renewable energy can reduce carbon emissions and improve energy utilization efficiency.The electric power network and the natural gas network are important transmission carriers in the en-ergy field,so the coupling relationship between them has been of wide concern.This paper establishes an integrated energy system considering electricity,gas,heat and hydrogen loads;takes each subject in the integrated energy system as the research object;anal-yses the economic returns of each subject under different operation modes;applies the Shapley value method for benefit allocation;and quantifies the contribution value of the subject to the alliance through different influencing factors to revise the benefit allocation value.Compared with the independent mode,the overall benefits of the integrated energy system increase in the cooperative mode and the benefits of all subjects increase.Due to the different characteristics of different subjects in terms of environmental benefits,collaborative innovation and risk sharing,the benefit allocation is reduced for new-energy subjects and increased for power-to-gas sub-jects and combined heat and power generation units after revising the benefit allocation,to improve the matching degree between the contribution level and the benefit allocation under the premise of increased profit for each subject.The cooperative mode effectively enhances the economic benefits of the system as a whole and individually,and provides a useful reference for the allocation of benefits of integrated energy systems.The analysis shows that the revised benefit distribution under the cooperative model increases by 3.86%,4.08%and 3.13%for power-to-gas subjects,combined heat and power generation units,and new-energy units,respectively,compared with the independent function model.
基金The authors acknowledge financial support from the National Natural Science Foundation of China （71173020）, and the Visiting Research Scholarship （20123013） awarded to Chunjin Chen by the China Scholarship Council. We would like to thank Yongmei Hu and Yuhong Du for valuable comments.
文摘China＇s market-oriented reform is expected to strengthen the role of the market in allocating resources, which raises concerns over the impact of market transformation on income distribution and earnings inequality in the past decades. This paper decomposes the sources of inequality based on the newly developed Shapley value approach and examines the contributions of the market, along with other nonmarket factors, to total inequality. Using the China Health and Nutrition Survey data over the period 1989-2009, we find that the income gap between laborers with a higher level of education and those with a lower level has widened since the transformational reforms of the economy. Our results suggest that the largest contribution of changes in income inequality can be attributed to the increase in returns to education, while the relative contributions of the household registration （hukou） system, type of sector ownership, geographic location, and gender to inequality experienced a downward trend between 1989 and 2009. The authors argue that rising income inequality is the consequence of efficiency improvements and an imperfect economic system, and that the market is a decisive force in economic development as it releases competitive signals and creates incentive mechanisms for innovation. Creating a more efficient labor market and increasing investment in human capital, particularly equalizing educational opportunities and improving the quality of education in lagging rural and inland regions to disadvantaged groups, are significant for an equitable distribution of income and sustainable development in the long run.
基金supported by the Na‑tional Key R&D Program of China(No.2022YFB3402600)the National Science Fund for Distinguished Young Scholars(No.51925505)+1 种基金the General Program of National Natural Science Foundation of China(No.52275491)Joint Funds of the National Natural Science Foundation of China(No.U21B2081).
文摘Freeform surface measurement is a key basic technology for product quality control and reverse engineering in aerospace field.Surface measurement technology based on multi-sensor fusion such as laser scanner and contact probe can combine the complementary characteristics of different sensors,and has been widely concerned in industry and academia.The number and distribution of measurement points will significantly affect the efficiency of multisensor fusion and the accuracy of surface reconstruction.An aggregation‑value‑based active sampling method for multisensor freeform surface measurement and reconstruction is proposed.Based on game theory iteration,probe measurement points are generated actively,and the importance of each measurement point on freeform surface to multi-sensor fusion is clearly defined as Shapley value of the measurement point.Thus,the problem of obtaining the optimal measurement point set is transformed into the problem of maximizing the aggregation value of the sample set.Simulation and real measurement results verify that the proposed method can significantly reduce the required probe sample size while ensuring the measurement accuracy of multi-sensor fusion.
基金supported by the Central Government Guides the Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in Inner Mongolia Autonomous Region(2022YFHH0019)+4 种基金the Fundamental Research Funds for Inner Mongolia University of Science and Technology(2022053)Natural Science Foundation of Inner Mongolia Autonomous Region(2022LHQN05002)NationalNatural Science Foundation of China(52067018)Natural Science Foundation of InnerMongoliaAutonomous Region of China(2025MS05052)Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology.
文摘A park hydrogen-doped integrated energy system(PHIES)can maximize energy utilization as a system with multiple supplies.To realize win-win cooperation between the PHIES and active distribution network(ADN),the cooperative operation problem of multi-PHIES connected to the same ADN is studied.A low-carbon hybrid game coordination strategy for multi-PHIES accessing ADN based on dynamic carbon base price is proposed in the paper.Firstly,multi-PHIES are constructed to form a PHIES alliance,including a hydrogen-doped gas turbine(HGT),hydrogen-doped gas boiler(HGB),power to gas and carbon capture system(P2G-CCS),and other equipment.Secondly,a hybrid game system model of the ADN and PHIES alliance is constructed,in which the ADN and PHIES alliance constitute a master-slave game,and the members of the PHIES alliance constitute a cooperative game.An improved Shapley value is proposed to deal with the problem of cost share among members in the alliance.Thirdly,an improved stepped carbon trading based on dynamic carbon baseline price is proposed.Thecarbon emissions at each moment and the total carbon emissions in a cycle are set as the dynamic adjustment factors of the carbon baseline price.The pricing mechanism of carbon baseline price increases with carbon emissions is constructed so that carbon emissions decrease.Finally,the quadratic interpolation optimization(QIO)algorithm is combined with Gurobi to solve the model.The results of the example analysis show that the cost of ADN is reduced by 4.47%,the cost of PHIES 1 is reduced by 3.67%,the cost of PHIES 2 is reduced by 0.97%,and the cost of PHIES 3 is reduced by 4.91%respectively.The total carbon emissions of the PHIES alliance are reduced by 7.08%.The low-carbon and economical operation of the multi-PHIES accessing ADN is achieved.
基金supported by the Innovative Research Group Project of the National Natural Science Foundation of China(22021004)Sinopec Major Science and Technology Projects(321123-1)。
文摘Coking at the fractionating tower bottom and the decant oil circulation system disrupts the heat balance,leading to unplanned shutdown and destroying the long period stable operation of the Fluid Catalytic Cracking Unit(FCCU).The FCCU operates through interconnected subsystems,generating high-dimensional,nonlinear,and non-stationary data characterized by spatiotemporally correlated.The decant oil solid content is the crucial indicator for monitoring catalyst loss from the reactor-regenerator system and coking risk tendency at the fractionating tower bottom that relies on sampling and laboratory testing,which is lagging responsiveness and labor-intensive.Developing the online decant oil solid content soft sensor using industrial data to support operators in conducting predictive maintenance is essential.Therefore,this paper proposes a hybrid deep learning framework for soft sensor development that combines spatiotemporal pattern extraction with interpretability,enabling accurate risk identification in dynamic operational conditions.This framework employs a Filter-Wrapper method for dimensionality reduction,followed by a 2D Convolutional Neural Network(2DCNN)for extracting spatial patterns,and a Bidirectional Gated Recurrent Unit(BiGRU)for capturing long-term temporal dependencies,with an Attention Mechanism(AM)to highlight critical features adaptively.The integration of SHapley Additive exPlanations(SHAP),Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN),2DCNN,and expert knowledge precisely quantifies feature contributions and decomposes signals,significantly enhancing the practicality of risk identification.Applied to a China refinery with processing capacity of 2.80×10^(6) t/a,the soft sensor achieved the R^(2) value of 0.93 and five-level risk identification accuracy of 96.42%.These results demonstrate the framework's accuracy,robustness,and suitability for complex industrial scenarios,advancing risk visualization and management.
基金support from China Scholarship Council(CSC)(202406440073).
文摘Accurate prediction of pure component physiochemical properties is crucial for process integration, multiscale modelling, and optimization. In this work, an enhanced framework for pure component property prediction by using explainable machine learning methods is proposed. In this framework, the molecular representation method based on the connectivity matrix effectively considers atomic bonding relationships to automatically generate features. The supervised machine learning model random forest is applied for feature ranking and pooling. The adjusted R^(2) is introduced to penalize the inclusion of additional features, providing an assessment of the true contribution of features. The prediction results for normal boiling point (T_(b)), liquid molar volume (L_(mv)), critical temperature (T_(c)) and critical pressure (P_(c)) obtained using Artificial Neural Network and Gaussian Process Regression models confirm the accuracy of the molecular representation method. Comparison with GC based models shows that the root-mean-square error on the test set can be reduced by up to 83.8%. To enhance the interpretability of the model, a feature analysis method based on Shapley values is employed to determine the contribution of each feature to the property predictions. The results indicate that using the feature pooling method reduces the number of features from 13316 to 100 without compromising model accuracy. The feature analysis results for Tb, Lmv, Tc, and Pc confirms that different molecular properties are influenced by different structural features, aligning with mechanistic interpretations. In conclusion, the proposed framework is demonstrated to be feasible and provides a solid foundation for mixture component reconstruction and process integration modelling.
基金financially supported by the National Natural Science Foundation of China(Grant No.52008039)the Guizhou Provincial Department of Transportation Science and Technology Project(Project No.2024-121-043)the Changsha University of Science and Technology Graduate Research Innovation Project(Grant No.CLSJCX23036).
文摘Floor heave is a common defect in mountainous tunnels.It is critical but challenging to predict the risk of floor heave,as traditional methods often fail to characterize this phenomenon effectively.This study proposes a data-driven approach utilizing a support vector machine(SVM)optimized by the sparrow search algorithm(SSA)to address the issue.The model was developed and validated using a dataset collected from 100 tunnels.Shapley value analysis was conducted to identify the key features influencing floor heave defects.Moreover,a committee-based uncertainty quantification method is presented to evaluate the reliability of each prediction.The results show that:(1)Data feature engineering and SSA play pivotal roles in expediting the convergence of the SVM model.(2)Groundwater and high in situ stress are key factors contributing to tunnel floor heave.(3)In comparison to backpropagation(BP)neural networks,the SSA-SVM demonstrates superior robustness in handling imperfect and limited data.(4)The committee-based uncertainty quantification method is proven effective to evaluate the trustworthiness of each prediction.This data-driven surrogate model offers an effective strategy for understanding the factors that impact tunnel floor defects and accurately predicting tunnel floor heave deformation.
基金supported by Science and Technology Foundation of Global Energy Interconnection Group Co.LTD.(SGGE0000JYJS2310046).
文摘During the transitional period of electricity market reforms in China,scheduling simulations of technical virtual power plants(TVPPs)are crucial owing to the lack of operational experience.This study proposes a model for TVPPs participating in the current multi-market;that is,TVPP coordinate bidding in the day-ahead energy and ramping ancillary market while purchasing unbalanced power and pro-viding frequency regulation service in the real-time market.A multi-scenario optimization approach was employed in the day-ahead stage to manage uncertainty,and an improved Shapley value was utilized for revenue allocation.By employing linearization techniques,the model is transformed into a mixed-integer second-order cone-programming problem that can be efficiently solved using linear solvers.Numerical simulations based on actual provincial electricity market rules were conducted to validate the effectiveness of a TVPP coalition profitability.
基金supported by Agricultural Science and Technology Innovation Program of Chinese Academy of Agricultural Science。
文摘Background The geo-traceability of cotton is crucial for ensuring the quality and integrity of cotton brands. However, effective methods for achieving this traceability are currently lacking. This study investigates the potential of explainable machine learning for the geo-traceability of raw cotton.Results The findings indicate that principal component analysis(PCA) exhibits limited effectiveness in tracing cotton origins. In contrast, partial least squares discriminant analysis(PLS-DA) demonstrates superior classification performance, identifying seven discriminating variables: Na, Mn, Ba, Rb, Al, As, and Pb. The use of decision tree(DT), support vector machine(SVM), and random forest(RF) models for origin discrimination yielded accuracies of 90%, 87%, and 97%, respectively. Notably, the light gradient boosting machine(Light GBM) model achieved perfect performance metrics, with accuracy, precision, and recall rate all reaching 100% on the test set. The output of the Light GBM model was further evaluated using the SHapley Additive ex Planation(SHAP) technique, which highlighted differences in the elemental composition of raw cotton from various countries. Specifically, the elements Pb, Ni, Na, Al, As, Ba, and Rb significantly influenced the model's predictions.Conclusion These findings suggest that explainable machine learning techniques can provide insights into the complex relationships between geographic information and raw cotton. Consequently, these methodologies enhances the precision and reliability of geographic traceability for raw cotton.
