中国科学院数学与系统科学研究院期刊网

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  • WANG Bo, YUAN Jiaxin, YE Xue, HAO Jun
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2363-2375. https://doi.org/10.12341/jssms240834
    Considering the high volatility and complexity of electricity spot price time series, a combined forecasting model based on wavelet transform and LGBM (light gradient boosting machine, LGBM) is proposed. By introducing rolling time window and wavelet transform, the dynamic multi-scale decomposition of electricity spot price series can be realized, and the frequency characteristics can be extracted to reduce its modal complexity and effectively avoid data leakage. In this study, the proposed model is constructed by utilizing the complex nonlinear feature extraction ability of the LGBM algorithm. The spot market data of Shanxi electric power is used to verify the validity of the proposed model. The results show that the proposed model is superior to the mainstream forecasting methods such as long-term and short-term memory model, support vector machine, elastic network regression model and extreme gradient lifting model in many key performance indexes, such as root mean square error, average absolute error and determination coefficient, among which the $ R^2 $ reaches 0.9792, showing high forecasting accuracy. At the same time, the proposed model shows robustness and adaptability under different market conditions, which shows the proposed model can be seen as a reliable forecasting tool for power market participants and helps to optimize trading strategies and reduce market risks.
  • LIU Zhifeng, ZHANG Qin, ZHANG Tingting
    Journal of Systems Science and Mathematical Sciences. 2025, 45(10): 3111-3134. https://doi.org/10.12341/jssms240211
    This study approaches typhoon landfalls as exogenous climate risk events, designating the moment of landfall as the critical intervention point. Utilizing the difference-in-differences (DID) methodology, the research examines the influence of typhoon disasters on the stock returns of publicly traded companies in China, and assesses how financial risks propagate through supply chain networks triggered by typhoon disasters. To gain a more nuanced understanding of these effects, the paper engages in a detailed mechanism analysis by examining the intensity of digital transformation. The results suggest that typhoon disasters have a significant and detrimental impact on the stock returns of firms located in affected areas, with this effect rippling through to their suppliers and customers via the intricate web of supply chain connections. Moreover, the study uncovers a distinct asymmetry in the spillover effects between suppliers and customers. Specifically, the research highlights that the level of digital transformation is instrumental in alleviating the financial risks associated with typhoons and serves as a protective barrier against the adverse effects on stock returns. Finally, a comprehensive suite of robustness checks reinforces the validity and reliability of the study’s conclusions.
  • WANG Li, LI Qi, ZHOU Xiancheng, YANG Lingling
    Journal of Systems Science and Mathematical Sciences. 2026, 46(3): 990-1010. https://doi.org/10.12341/jssms240803
    With the increasing demand for rural delivery in mountainous areas, the routing problem of rural delivery logistics in mountainous areas (RPRDLMA) has become an academic hotspot. Based on the background of rural passenger, cargo and postal integration development, the RPRDLMA under the cooperative distribution of bus-electric vehicle-drone (RPRDLMA-CDBEVD) is studied in this paper. Firstly, the village service points are divided into type TC and type FC, meaning that they are served by EVs or by drones, according to their geographic location, distribution characteristics and volume of cargo delivered or mailed. Next, a continuous function of bus idle capacity is established based on the tidal rural passenger flow characteristics. Then, the RPRDLMA-CDBEVD model is constructed with the goal of total cost minimization. Specifically, the total cost includes commissioning cost, capacitybased cost, distance-based cost, time-based cost and electricity consumption cost. In order to solve the model, a hybrid algorithm of multi-constraint modified clustering algorithm and improved adaptive genetic algorithm (MCDCA-IAGA) is designed. The experimental results and case studies show that the collaborative delivery mode of passenger shuttle bus electric vehicle unmanned aerial vehicle effectively reduces delivery costs by 2.9% and delivery time by 8.6%, providing a feasible solution for logistics path planning in mountainous and rural areas.
  • SU Yanyuan, CHENG Simin, ZHANG Xiaoyue, ZHANG Yaming
    Journal of Systems Science and Mathematical Sciences. 2025, 45(12): 3870-3902. https://doi.org/10.12341/jssms240046
    Individual selection preferences and the abuse of recommendation algorithms have trapped the public in an information cocoon dilemma. It would trigger differentiated collective behavior, exacerbate the formation of opinion polarization, and even have a serious impact on social public order. In this paper, we systematically analyze the effects of differences in public behavior within the information cocoon on the interaction between heterogeneous opinion groups, including the intra-group homogeneity restriction weakening-strengthening effect and the inter-group inhibition-promotion combination interaction effect. Then, based on the Lotka-Volterra modeling approach, the opinion polarization dynamic model with the interaction of heterogeneous opinions is constructed. Besides, the equilibrium points and their stabilities are estimated, too. Moreover, we also explore the law of opinion polarization through numerical simulations and empirical analysis. The results show that under the influence of the information cocoon, the weaker the intra-group homogeneity restriction and the stronger the inter-group promotion effect, the faster and the larger the expansion of the two groups, and the more likely to generate binary polarization situation. What's more, when the inter-group inhibition effect is stronger and the intra-group homogeneous restriction of heterogeneous opinion is weaker, the expansion rate of the group would slow down and the size would decrease and even disappear after reaching the peak, and generate single polarization situation. In addition, the potential diffusion range positively affects the expansion rate and final size of the group itself. Furthermore, the potential diffusion range would also slow down the expansion of the heterogeneous group under the inter-group promotion effect, but does not affect its final size.
  • CHENG Weitao, PAN Xianli, ZHANG Xinyu
    Journal of Systems Science and Mathematical Sciences. 2025, 45(7): 2075-2092. https://doi.org/10.12341/jssms240013
    In time series forecasting, prediction error metrics cannot assist researchers in determining whether poor prediction performance is due to an inappropriate model choice or if the data inherently lacks predictive information. Intrinsic predictability characterizes "the upper limit of prediction accuracy" for the data, which can help researchers assess the compatibility of the current model and data. In this paper, we briefly review the concepts of predictability and provide a detailed introduction to the studies of time series predictability based on permutation entropy. Based on this, we propose permutation entropy with covariates to characterize the complexity of target time series when covariates are available and demonstrate its effectiveness through experiments with real glass bubble data. Additionally, we further present a strategy for model selection based on intrinsic predictability, aiming to choose simpler models and reduce the time cost of modeling and forecasting while maintaining reasonable accuracy. Numerical experiments on economic data validate the efficacy of this strategy.
  • LI Meijuan, LIN Xiaxin, HU Huifang, WANG Lili
    Journal of Systems Science and Mathematical Sciences. 2025, 45(7): 2244-2262. https://doi.org/10.12341/jssms241085
    In response to the scenario of a two-stage production structure that includes undesirable outputs and shared input factors, a two-stage data envelopment analysis (DEA) model has been developed. This model not only enables the rational allocation of shared resources between the two stages but also addresses undesirable outputs by applying the weak disposability theory, which aligns with real-world production dynamics. Furthermore, drawing on the concept of non-cooperative games, the model decomposes the efficiency of subprocesses by considering scenarios in which either the first or second stage is dominant, thereby establishing subprocess efficiency models. Ultimately, we employ the proposed model to evaluate the innovation efficiency of Specialized, Refined, Distinctive, and Innovative (SRDI) small and medium-sized enterprises in Fujian Province. By conducting a thorough analysis of both the overall efficiency and the subprocess efficiency of these enterprises, more accurate and comprehensive evaluation results can be obtained. Additionally, comparisons with various models further enhance the rationale and feasibility of the model presented in this paper.
  • CONG Yuyue, YU Zhongfu, YANG Ying, CHAI Jian
    Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1149-1166. https://doi.org/10.12341/jssms240464
    This paper examines the impact of digital inclusive finance on the operational performance of regional commercial banks using a fixed-effects model based on balanced panel data from 78 urban and rural commercial banks spanning from 2011 to 2021. The results indicate a significant negative relationship between the two. This conclusion remains valid after addressing endogeneity issues and conducting robustness tests, suggesting that the current competitive crowding-out effect still exerts a substantial influence. Further analysis through moderation and threshold effects reveal that the technology spillover effect of digital inclusive finance drives business innovation and enhances risk-taking capacity among regional commercial banks, thereby mitigating their negative effects, with the moderation effect on risk-taking being more pronounced. The threshold parameter estimates show that business innovation has a more significant negative convergence moderation effect on rural commercial banks, while risk-taking exhibits a more significant negative convergence moderation effect on urban commercial banks. The findings of this study provide important practical insights for the digital transformation of regional commercial banks and the sustainable and healthy development of regional economies.
  • ZHANG Yuwei, LI Zhenping, LI Xin, ZHANG Ziting, FANG Yong
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2389-2411. https://doi.org/10.12341/jssms240843
    Aiming at the dynamic changes in freshness levels of fresh products over time, a joint optimization problem of fresh products allocation and cold chain distribution with multiple levels of freshness is studied. Considering the constraints of both soft and hard time windows and customers' requirements for product freshness, a joint optimization model for fresh product allocation and cold chain distribution is constructed with different levels of freshness product allocation and cold chain distribution paths as decision variables. Under the premise of satisfying constraints such as vehicle capacity, hard time windows, and product quality, the objective function is to minimize the sum of fixed vehicle costs, transportation costs, refrigeration costs, penalty costs for violating soft time windows, product damage costs, and customer stockout losses. A two-stage hybrid heuristic algorithm based on large neighborhood search is designed according to the characteristics of the model. We use the Solomon dataset to construct the examples and solve the models by Gurobi solver and the two-stage heuristic algorithm, respectively. The results verify the correctness of the model and the fast effectiveness of the two-stage heuristic algorithm. The superiority of joint optimization of multi-level freshness product allocation and cold chain distribution is verified by comparing with the staged optimization strategy, and the results show that the joint optimization strategy can significantly reduce the cost of expired and spoiled goods of fresh products and the loss of customers' out-of-stock loss, which can reduce the total distribution cost by about 45% on average. Finally, the effectiveness of the algorithm in solving practical problems is verified through a real case.
  • WU Hongxu, FANG Yong, DENG Zhibin
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2447-2465. https://doi.org/10.12341/jssms240199
    With the rapid development of deep learning technology, its application in the field of asset pricing has attracted widespread attention. This paper delves into the theoretical foundation of factor pricing models and proposes a latent factor model constructed with deep neural networks based on characteristic ranking. The proposed model overcomes the limitations of traditional factor models in dealing with nonlinearity and hypothesis testing. It uses appropriate activation functions to accurately simulate the real process of portfolio construction. In the empirical analysis of the China A-share market, the proposed deep neural network model significantly outperforms the benchmark models in performance for out-of-sample prediction and achieves the highest cumulative returns and the best Sharpe ratio in constructing mean-variance efficient frontier portfolios. Furthermore, by analyzing the importance of the characteristic gradients of the model outputs, it is found that the monthly returns of the A-share market are significantly influenced by transaction-related factors, reflecting the unique characteristic of the Chinese stock market as an emerging market. This paper provides new insights into the construction of latent factor models and the patterns of market behavior of the A-share market.
  • LIU Xinyue, LIU Pingfeng, JIANG Shan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(1): 70-96. https://doi.org/10.12341/jssms240348
    Small and medium-sized enterprises (SMEs) in supply chains often face significant financing difficulties, which hinder their high-quality development. Block-chain technology-driven third-party financial service platforms offer a new approach to solving this issue. This paper explores the government's regulatory behavior strategy, the third-party financial service platform's blockchain information sharing behavior strategy, and the small and medium-sized enterprises' financing integrity behavior strategy by constructing a tripartite evolutionary game model of “government-third-party financial service platform-SMEs". It conducts an analysis on the stability of the equilibrium points in the tripartite evolutionary game and discusses the impact of blockchain technology cost, government regulatory cost, government reward and punishment intensity, and enterprise income on the equilibrium of the tripartite evolutionary game through parameter sensitivity analysis. The results show that: 1) Whether a third-party financial service platform chooses to share information through blockchain depends not only on the cost of blockchain technology but also on the government's rewards and punishments for the platform and small and medium-sized enterprises (SMEs), as well as the size of the returns from default risks. 2) Conventional wisdom holds that digital supply chain finance driven by blockchain is inevitably superior to traditional supply chain finance. However, this study finds that only when the government dynamically rewards and punishes platforms to improve the transparency of supply chain financial information and constrains enterprises to reduce financing default rates under specific circumstances, will the financing efficiency of blockchain supply chain finance surpass that of traditional supply chain finance.
  • WANG Yufang, WANG Nan, ZHANG Shuhua
    Journal of Systems Science and Mathematical Sciences. 2025, 45(10): 3245-3266. https://doi.org/10.12341/jssms240059
    To solve the problem of instability and imprecision of carbon price prediction with single information source, single decomposition technology and single prediction method, a hybrid prediction model of carbon price based on multi-source data feature and multi-scale analysis is proposed, called CPS-MEMD-SVR-MLR. 1) Multi-source data analysis: This effectively integrates historical carbon trading prices related to carbon prices, macroeconomic development levels, fossil energy prices, exchange rates, and social media sentiment data based on news text information; 2) Multi-scale analysis: This uses multiple empirical mode decomposition technology (MEMD) to decompose multi-source data into prediction features under different modes; 3) Hybrid prediction analysis: This uses fuzzy entropy theory to orderly integrate econometric model and machine learning models, and then integrates the predicted values of each mode into the final result. This paper takes the carbon price of the European Union (EU) from February 11, 2015 to February 27, 2023 as a case study. Based on seven scenarios and DM tests, the results show that: 1) The prediction accuracy of the hybrid model proposed in this paper is better than other comparison models; 2) Social media sentiment can improve the prediction accuracy of carbon price, and it is better than the single factor prediction; 3) The introduction of MEMD decomposition can significantly improve the prediction accuracy of carbon price.
  • XIANG Pengcheng, ZHAO Xiaping, YANG Yingliu
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 462-479. https://doi.org/10.12341/jssms240542
    To enhance the scientific nature of risk prevention and control in the supply chain network of new energy vehicle (NEV), and to strengthen safety production and operational management in China’s NEV industry, we integrate complex network theory with SEIR (susceptible-exposed-infectious-recovered) modeling to simulate the process of risk propagation in the NEV supply chain network, aiming to uncover the mechanisms of risk propagation. Firstly, typical NEV companies such as Tesla and XPeng are selected as case studies, with suppliers as nodes and supplier cooperation relationships as edges to construct the topological networks of their automotive supply chains. Secondly, topological parameters such as average degree, clustering coefficient, and average path length are used to explore the characteristics of the supply chain networks of these two companies. Finally, based on the characteristics of the topological networks, an SEIR epidemic model is constructed for the supply chain networks to simulate the impact of different immunization strategies on the speed and scope of risk propagation in the supply chain. The results indicate: 1) The supply chain networks of both NEV companies exhibit scale-free network structures, with comparable network densities (average degrees of 2.293 for Tesla’s and 1.845 for XPeng’s supply chain networks). 2) Comparing the simulation results of risk prevention strategies between the two companies shows that their performances are largely similar. The proposed model effectively explores the characteristics of risk propagation in the NEV supply chain. Specifically, extending the incubation period of risks can significantly slow down the spread of risks, providing nearly three months of adjustment time for the companies, with Tesla experiencing a shorter delay of about 2 weeks to the peak risk period compared to XPeng; Shortening the duration of infection can notably reduce the scale of risk spread by approximately 20%, with Tesla showing a 4% greater reduction in the scope of risk impact compared to XPeng. Additionally, increasing the complexity of the supply chain network may accelerate the propagation of risks. The research findings can provide a reference for NEV companies to formulate effective risk response measures, ensuring the stability and safety of the supply chain.
  • HUANG Shuai, LIU Yongchao, AN Yaxin
    Journal of Systems Science and Mathematical Sciences. 2025, 45(7): 2025-2039. https://doi.org/10.12341/jssms240152
    For a class of strict-feedback nonlinear systems with unknown control direction, a dynamic event-triggered control method based on backstepping is proposed, which can solve the problem of unknown control direction and reduce the data transmission in the network. Firstly, the Nussbaum gain function is introduced to solve unknown control direction. Secondly, a dynamic event-triggered scheme is introduced in the actual controller design, and a dynamic variable is introduced to adjust the trigger threshold, which further reduce the number of events. The stability of the closed loop system is proved based on Lyapunov function, and Zeno behavior does not appear. Finally, the simulation results show that the dynamic event-triggered control method can reduce the data transmission in the network and save network resources.
  • TAN Xurui, ZHANG Baoyou, WANG Tingting
    Journal of Systems Science and Mathematical Sciences. 2025, 45(7): 2154-2172. https://doi.org/10.12341/jssms240224
    Logistics standardization is a crucial avenue for enhancing the development of the modern circulation industry. China has actively initiated pilot projects on logistics standardization to explore solutions to the "bottleneck" issues in circulation. Against the backdrop of the goal of circulation integration, attracting more participants from the circulation entities to engage in deep collaboration in logistics standardization and building a smooth and efficient circulation system are key to the development of modern circulation. This paper, based on the perspective of collaborative governance, constructs a three-party evolutionary game model, namely, "manufacturer-third-party logistics enterprise-retailer" to depict the behavioral relationships of supply chain participants in collaborative logistics standardization. The study investigates the key factors influencing the collaborative mode selection among entities within the chain, explores the relationships of interests among entities, and further discusses different stable states of the system and the strategic choices of entities through simulation analysis. The research reveals that: 1) The ideal state of three-party collaboration can be directly achieved when the initial potential for each entity's participation reaches a certain threshold. 2) Increasing the intensity of government rewards and penalties for each entity promotes the establishment of standardized collaborative relationships. 3) The reduction of standardization costs can attract the participation of entities in collaborative standardization, and its incentive effect is more independent of the initial intentions of enterprises compared to government subsidies. 4) Third-party logistics enterprises sacrificing profits for cost savings upstream and downstream can benefit entities in converging to the ideal state. In conclusion, the study proposes corresponding policy recommendations based on the findings.
  • LIU Qing, ZHANG Dan
    Journal of Systems Science and Mathematical Sciences. 2025, 45(9): 2775-2790. https://doi.org/10.12341/jssms240235
    In this paper, the problem of output consensus control for heterogeneous multi-agent systems with denial-of-service (DoS) attacks is studied. First, aiming at the problem that the cyber attack behavior is changeable and its statistical characteristics of attack modeling method based on dual hidden Markov model is proposed, which converts the communication interruption caused by the attack behavior into the communication topologies switching of multi-agent system. Second, a distributed asynchronous dynamic observer is designed to solve the asynchronous problem when the communication topology mode (CTM) and the transition probability mode (TPM) do not match. Third, based on the stochastic Lyapunov theory and linear matrix inequality technique, sufficient conditions for the solvability of the system output consensus problem are obtained. Finally, the feasibility and effectiveness of the results are illustrated through a simulation example.
  • ZHANG Yu, LI Kaili, WANG Jinting
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2376-2388. https://doi.org/10.12341/jssms240640
    Privatization reform is regarded as an effective strategy to reduce waiting times in the public healthcare system. This paper focuses on two modes of privatization reform: One is the competition mode, which allows private hospitals to enter the market and compete with public hospitals; the other is the collaboration mode, where public hospitals and private hospitals cooperate to achieve common goals. This paper employs a queueing model to describe the patient consultation process, analyzes the service rates and prices of public and private hospitals under different privatization reforms, and studies the impact of these reforms on the number of patients covered by medical services, patient waiting times, patient welfare and social welfare. The study finds that the competitive mode can significantly reduce patient waiting time, thereby expanding the number of patients covered by medical services and enhancing patient utility and social welfare. In contrast, while the cooperative mode can also reduce patient waiting time, it exhibits uncertainty in increasing the number of patients, patient utility, and social welfare, and can effectively promote the expansion of the number of patients covered by medical services, patient utility, and social welfare only when the service capacity of public-private partnership hospitals is relatively large or the degree of privatization is high. Finally, when private hospitals choose between the cooperative or competitive mode, it mainly depends on the subsidy rate provided by the government to public hospitals and the level of privatization pursued by public-private partnership hospitals for their own interests. Specifically, when the subsidy rate or the level of privatization is high, private hospitals are more inclined to choose the cooperative mode; conversely, they are more inclined to choose the competitive mode.
  • LIU Qinming, XIANG Haodong, LIU Wenyi, HE Jiwei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(2): 480-499. https://doi.org/10.12341/jssms240044
    A data-model dual-driven stochastic process model is proposed for equipment health diagnosis and remaining life prediction problems. Firstly, a new signal scalarization method is proposed for non-vibration signals, so that continuous signals can be scalarized to form a data type that can be input to the hidden semi-Markov model. Secondly, a new deterioration kernel-based modified hidden semi-Markov model (DK-MHSMM) is proposed to realize the process of mapping the observation scales of mechanical equipment to the potential states, and to dynamically screen the equipment state patterns. Then, the adhesion coefficient is introduced into DKMHSMM, and the genetic algorithm and the co-evolutionary algorithm of the Sea Sheath swarm algorithm are used to estimate the model parameters instead of the conventional EM parameter estimation method, and the corresponding remaining life prediction method is proposed according to the characteristics of the whole life distribution of the equipment and the current state values of the equipment. Finally, the method is validated using the turbofan engine dataset, which verifies the effectiveness and feasibility of the method.
  • LI Meng, WANG Zhengqi, GAO Haoyu
    Journal of Systems Science and Mathematical Sciences. 2025, 45(12): 3787-3809. https://doi.org/10.12341/jssms240597
    The national independent innovation demonstration zone (NIIDZ), as an important engine leading innovative development, takes institutional and policy reforms as a starting point to radiate and drive the coordinated development of surrounding regions. The gradual improvement of the high-speed rail (HSR) network has opened up a new pattern for the “ual circulation” and expanded the scope of the NIIDZ's innovation spillover effects. Based on data of HSR city pairs from 2008 to 2019 in China, this paper examines the impacts and mechanisms of the improvement in innovation levels of ordinary cities after the opening of HSR connected to NIIDZs by applying a staggered DID model. The empirical results are as follows. Firstly, the opening of HSR connected to NIDDZs significantly improves the innovation levels of ordinary cities. Secondly, the innovation spillover effects are more pronounced for cities in the eastern region, cities with a better innovation environment, and large-scale cities. Thirdly, the innovation spillover effects are realized by utilizing innovation endowment, government-guided innovation and demonstration driving effects. This paper provides empirical evidence and policy insights for innovation-driven development in the context of HSR network. It optimizes the spatial allocation of innovation resources and accelerates the development of new quality productive forces, achieving high-quality economic development.
  • XIONG Zikang, QIN Hong, NING Jianhui, HUANG Yuning
    Journal of Systems Science and Mathematical Sciences. 2025, 45(12): 4004-4015. https://doi.org/10.12341/jssms240678
    Design of experiments with mixtures has been widely used in food industry manufacturing, mixed drug research and development, investment portfolio optimization and other fields. In order to ensure that the design is robust to the changes of the model, many scholars have proposed uniform designs for experiments with mixtures under different criteria. However, the methods of constructing mixture designs based on the acceptance-rejection algorithm or inverse transformation method become inefficient and complex when the number of mixture compositions is large and the constraints are complex. In this paper, we propose an efficient construction method with representative points method for uniform mixture design on a general restricted region. The main idea is to generate uniform training samples on the experimental region based on the Gibbs sampling algorithm, and then compress them into the optimal representative point set under the energy distance criterion by the optimization algorithm. Through numerical example analysis, the design generated by the new construction method has good uniformity and model robustness.
  • WANG Jun, CAI Xueqiang
    Journal of Systems Science and Mathematical Sciences. 2025, 45(11): 3635-3656. https://doi.org/10.12341/jssms240271
    This paper addresses the fault-tolerant consensus problem in heterogeneous multi-agent systems based on an adaptive distributed event-triggered mechanism, with a focus on actuator faults and bounded external disturbances. Compared to existing research, this paper introduces distributed intermediate variables to model the closed-loop error in heterogeneous multi-agent systems. Additionally, a fault observer is designed to estimate actuator fault states in real time and compensate for actuator faults by adjusting control gains online. Furthermore, an adaptive distributed event-triggered mechanism is designed, which conserves communication resources and successfully avoids the Zeno phenomenon through dynamic interactions and information sharing among agents. Moreover, a fault-tolerant controller based on a distributed adaptive event-triggered mechanism is designed to ensure that agents maintain consistent behavior even in the presence of actuator faults or external disturbances. Finally, the feasibility and effectiveness of the proposed method are validated through Matlab simulations, providing a practical solution for real-world applications.
  • QIAN Wuyong, GUO Kaiyi, WANG Xuan, XU Hanrong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(5): 1599-1623. https://doi.org/10.12341/jssms240811
    Vehicle routing problem in takeout delivery is characterized by dynamic order arrivals and the need for continuous updates on rider status. To address this challenge, a multi-objective dynamic optimization model maximizes the interests of customers, platforms, and riders while considering rider physical condition and road familiarity. A dynamic weights multi-objective heuristic algorithm adaptively adjusts the weights of different objectives based on real-time data, optimizing delivery paths dynamically. Results demonstrate superior performance compared to the Gurobi solver in key metrics such as order fulfillment time, rider idle time, and platform profit. This highlights the effectiveness of the method in handling the complexities of real-world takeout delivery operations. Analysis of dispatch strategies for different types of riders provides valuable insights for operational decision-making. In summary, this research offers a practical solution to enhance delivery efficiency and customer satisfaction while ensuring fair treatment of riders, contributing to improved operational strategies for takeout platforms.
  • XU Shuling, DA Pengfei, CHEN Haodong, HONG Wei
    Journal of Systems Science and Mathematical Sciences. 2025, 45(11): 3462-3479. https://doi.org/10.12341/jssms240823
    This study explores the enhancement of “first mile” logistics in the low-altitude economy, focusing on optimizing the harvesting and distribution of fruits and vegetables, which are characterized by seasonality, freshness, perishability, and regional specificity. We address the collaborative routing of trucks and multi-drones under time constraints by proposing a two-stage mixed integer linear programming model. The first stage minimizes the combined travel and activation costs for both drones and trucks, while the second stage reduces total transportation costs. Extensive numerical experiments validate the model’s feasibility and effectiveness, and an empirical analysis using operational data from SF Express demonstrates its practical applicability. The results reveal that the model provides optimal solutions within specified time limits, significantly improving logistics efficiency while ensuring product maturity and freshness. This research offers valuable insights for modernizing agricultural supply chains and identifies new opportunities for applying low-altitude economy principles in agriculture.
  • ZHENG Ziyi, YU Yang, WANG Wei
    Journal of Systems Science and Mathematical Sciences. 2025, 45(11): 3657-3669. https://doi.org/10.12341/jssms240343
    This paper studies the formation control problem of multi-unmanned ground vehicles with uncertain nonlinear dynamics. First, a formation motion model of multi-unmanned ground vehicles is established based on leader-follower method, which describes the leader-follower relationship among individual unmanned vehicles. The uncertain nonlinear dynamics are learned online by neural networks. Then, based on the target tracking mechanism, an adaptive neural network direction controller is designed by introducing a sliding mode surface. Simultaneously, combining with backstepping control technique, a target tracking mechanism based adaptive neural network propulsion controller is presented to achieve integrated longitudinal and lateral formation driving of multiple unmanned vehicles. Lyapunov stability theory is used to analyze and prove the stability of the closed-loop multi-unmanned vehicle formation control system, and the formation tracking error can converge to the neighborhood of origin. Finally, the simulation results verify that the formation control and formation maintenance are realized under the proposed control algorithm.
  • GAO Kaiye, LIU Qiming, PENG Rui, FU Bo, YE Hengqing
    Journal of Systems Science and Mathematical Sciences. 2025, 45(7): 2114-2132. https://doi.org/10.12341/jssms240107
    As an important supplement to the offline healthcare system, the popularization of online healthcare provides new pathways for patients to access medical services, promoting the sound and orderly development of the social healthcare environment. This study consolidates and reanalyzes empirical research on patients' physician selection behavior in online healthcare communities, addressing inconsistencies in prior findings, clarifying the effect intensity of different antecedent variables on users' physician selection behavior, and providing references for subsequent research and practical applications. Using meta-analysis, we analyze 23 antecedent variables and 3 moderating variables affecting patients' online physician selection behavior, encompassing 190 independent effect sizes from 55 studies. The findings reveal that all 23 antecedent variables positively influence patients' online physician selection behavior, with patient satisfaction and total review count demonstrating significant strong correlations. Platform types, study timeframes, and data collection methods function as moderators in the relationships between certain antecedent variables and online physician selection.
  • SHE Chengxi, ZHANG Caiping, ZHAO Piaoyang, WANG Qingyang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(3): 709-724. https://doi.org/10.12341/jssms240362
    The integration of intelligent fault diagnosis and alarm technology into automatic production lines can avoid production interruptions and economic losses caused by faults. Traditional fault diagnosis method collects physical characteristic data reflecting mechanical fatigue faults through technologies such as machine vision for prediction. But a significant cost for high-precision fault diagnosis will be induced by the large amount of noise present in complex working conditions. Therefore, a method for mining potential occurrence patterns of faults based on production line data was proposed. Firstly, five types of highly generalized derived feature variables were constructed to characterize the faults based on the direct production data of the production line. Secondly, a CNN-LSTM-Attention model was constructed for fault diagnosis and early warning with the scarce fault data balanced by near neighbor under-sampling (Near Miss). Finally, numerical experiments were conducted using a total of 75 million data from 10 production lines, and compared with traditional machine learning, CNN, and LSTM models. The experimental results illustrated that the prediction accuracy of the model reached 99.97%. It demonstrated that effective production line fault diagnosis and warning can be achieved at the level of data mining and feature engineering without advanced learning methods and mechanism features.
  • TANG Huiyun, LI Yang, WANG Feifei
    Journal of Systems Science and Mathematical Sciences. 2025, 45(12): 3972-3987. https://doi.org/10.12341/jssms240383
    Multi-source data are commonly encountered nowadays. The analysis of multi-source data is important for unleashing the data potential and realizing data value. However, many multi-source data still exist in the form of “ata silos”. Interconnection between data remains extremely challenging. Meanwhile, the data security issue is a significant concern, making it crucial to achieve secure development of multi-source data while protecting data privacy. To address these challenges, we propose a privacy-protected paradigm for multi-source data analysis. This method is based on the federated learning framework, enabling different data sources to collaborate on data analysis tasks without exposing their raw data. Meanwhile, to further prevent malicious attacks on data, we incorporate differential privacy into federated learning by adding noise to the transmitted data to protect individual-level information. Finally, we demonstrates the practical application of the proposed paradigm using the example of predicting violation risks of enterprises. By combining data from various departments, the prediction accuracy can be well enhanced.
  • LUO Ming-Min, WANG Jun
    Journal of Systems Science and Mathematical Sciences. 2025, 45(11): 3619-3634. https://doi.org/10.12341/jssms240467
    In response to the significant parameter uncertainties, completely unknown external disturbances, and actuator failures faced by quadrotor UAVs during flight, this paper proposes a robust adaptive controller. Firstly, a quadrotor UAV model is established that is affected by external environmental disturbances and actuator failures, while considering the uncertainties in system parameters. To address the shortcomings of traditional sliding mode reaching laws in eliminating chattering and improving convergence speed, a nonlinear robust adaptive sliding mode controller based on a novel sliding mode reaching law is proposed. Additionally, adaptive laws are designed to estimate system parameters, external disturbances, and actuator failure information that are difficult to measure directly and accurately. To ensure the stability of the closed-loop system, the controller employs the upper bound of unknown lumped disturbances as the switching gain. Experimental results demonstrate that the proposed controller exhibits significantly stronger fault tolerance and disturbance rejection performance compared to two other algorithms.
  • GUO Jingjun, MA Aiqin, CHENG Zhiyong
    Journal of Systems Science and Mathematical Sciences. 2025, 45(9): 2970-2983. https://doi.org/10.12341/jssms23505
    Comprehensively considering the assumptions of the option pricing model and the change characteristics of the underlying asset price of carbon options, based on the EUA DEC22 carbon futures option market data from January 4, 2021 to September 27, 2021, the genetic algorithm is used to estimate the parameters of the pricing model. The option pricing performance of the B-S model, fractal Brownian motion model and Heston stochastic volatility model are compared and analyzed according to the stabilized parameter estimates, the most suitable pricing model for the carbon option market is selected, and to provide relevant suggestions for the improvement and smooth operation of the carbon market pricing mechanism. The results show that the Heston stochastic volatility model has the best pricing performance in the carbon option market, followed by the fractal Brownian motion model, and the B-S model is relatively poor. Therefore, the pricing of carbon options based on the Heston stochastic volatility model can improve the pricing accuracy of carbon options, help complete the pricing mechanism of the carbon market, avoid the risk of carbon market transactions, ensure the smooth operation of the carbon market, and promote the realization of the “dual carbon” strategic goal.
  • JIA Xiaojing, YU Changjiang, MOU Shandong
    Journal of Systems Science and Mathematical Sciences. 2025, 45(9): 2819-2841. https://doi.org/10.12341/jssms240902
    China has introduced a large-scale equipment upgrade policy that can renovate livestock manure collection and processing facilities. However, the impact of this policy on manure management has not yet been explored in existing research. Additionally, there is a gap in the analysis of refined market strategies regarding the collaboration between third-party companies (TPCs) and small to medium-sized livestock farmers (SMS-LFs). To address these issues, this paper constructs an evolutionary game-theoretic model that examines the equipment upgrade strategy of SMS-LFs and the classified pricing strategy of TPCs. The study incorporates prospect theory and mental accounting theory (PT-MA) to explore how farmers decide whether to invest in equipment upgrades, considering their risk preferences. By combining the expected utility function with the value perception function and adhering to the principle of those who invest receive the subsidies, the paper analyzes which party would benefit more from implementing the upgrades in the context of effective policy execution. The study conducts simulation analyses of strategies and summarizes the systemic archetypes for upgrading manure collection and processing facilities. The findings are as follows: 1) Providing large-scale equipment upgrade subsidies to TPCs, allowing them to enhance the manure collection and processing facilities for SMS-LFs, is the most effective strategy for advancing the policy. 2) TPCs should actively implement a classified pricing strategy. 3) The large-scale renewal and upgrading of livestock manure collection and treatment systems exemplify a limits to growth archetype. The solution is removing constraints from balancing loops through a policy mechanism allowing TPCs to obtain equipment renewal subsidies. This subsidy mechanism encourages TPCs to invest in upgrading manure collection and treatment facilities for SMS-LFs. Subsequently, these companies can implement a classified charging strategy to secure higher-quality manure-based raw materials. This creates an incentive mechanism that motivates SMS-LFs to increase their investments in manure treatment. Ultimately, this virtuous cycle enhances the proportion of subsidies received by SMS-LFs through improved environmental performance.
  • GU Nannan, XING Mengjie, LIN Peng, CHEN Haibao
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2581-2598. https://doi.org/10.12341/jssms240506
    Semi-supervised graph-based dimensionality reduction is a kind of meth-od that utilizes data structure graph to deal with semi-supervised dimensionality reduction problem. However, most of these algorithms only take account of data information while ignore class label information; And they don't take account of the differences among samples in the training process, which reduces the robustness of the algorithms in the case of noise or outliers. In this paper, by combining sparse representation with self-paced learning, a self-paced learner is proposed to obtain the linear dimensionality reduction mapping based on sparse discriminant graph. In detail, the proposed method firstly constructs a sparse discriminant graph by integrating the propagation of class labels with sparse representation of data. Then, by considering the distance between each low-dimensional data point and the corresponding class anchor, and the ability of low-dimensional data to maintain the discriminative sparse structure of the original high-dimensional data, this paper proposes a self-paced learning problem for dimensionality reduction. On the one hand, the proposed method constructs a sparse discriminant graph that can extract the discriminative information of data more effectively; On the other hand, the proposed method is based on self-paced learning mechanism, which makes it can automatically calculate the importance values of training data, suppress the negative impact of unreliable data or labels, and improve the robustness of the model to noise or outliers. The results of five experimental data sets demonstrate the effectiveness of the proposed algorithm.
  • KANG Jijia, YANG Xiaoguang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(4): 1039-1063. https://doi.org/10.12341/jssms241052
    Using ESG rating data of Sino-Securities Index Information Service from 2009 to 2020, this paper examines the impact of listed companies' ESG rating on the level of stock price, financial and operational risk in the next year. The study finds that better ESG rating has a significant inhibitory effect on all three risk levels of enterprises in the next year. Specifically, for the risk of stock price crash, ESG rating higher than the benchmark level, as a strong market signal, has a more significant reduction in the risk level of stock price crash. The trading volume of individual stocks, which reflects the attention of investors, has an intermediary effect on ESG to reduce the risk of enterprise stock price crash. ESG of large-scale enterprises that occupy an important position in the market and attract more attention from investors has a stronger inhibitory effect on the risk of stock price crash; In addition, the negative relationship between ESG and the risk of stock price crash is more significant after the implementation of the “Environmental Protection Law”. For financial risk, ESG has a marginal diminishing effect on reducing corporate financial risk, and the improvement of ESG rating from low to medium can improve the level of corporate financial risk. At the same time, enterprises' voluntary disclosure of non-financial information could strengthen the inhibitory effect of ESG on financial risks. For operational risk, ESG rating has a marginal diminishing effect on reducing operational risk; At the same time, the nature of equity has a moderating effect on the reduction of operating risks by ESG rating. Compared with private enterprises, ESG has a stronger inhibition effect on the operation risk of state-owned enterprises. Finally, the sub-sample heterogeneity test results based on the length of enterprise life in this paper show that the inhibitory effect of ESG rating on risk is stronger for enterprises with a long establishment age, but weaker for enterprises with a short establishment age.
  • TAO Tielai, YU Kaizhi
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2616-2633. https://doi.org/10.12341/jssms240097
    This study presents the construction of a $p$ th-order autoregressive integer-valued time series model, predicated on a Poisson thinning operator. This model is characterized by its inherently time-varying parameters, which may conform to a particular random distribution. Building upon this foundation, we derive the theoretical attributes pertaining to its ergodicity, point estimation, interval estimation, and the associated statistical properties of hypothesis testing. Additionally, we propose a variable selection methodology, expressly tailored for this model, and substantiate its theoretical underpinnings. The validity and reliability of these properties are thoroughly corroborated through meticulous numerical simulations. Ultimately, the practical applicability and robustness of this model are vividly demonstrated through its successful deployment within an empirically derived real-world data set.
  • WANG Zongrun, NI Xuekai, REN Xiaohang
    Journal of Systems Science and Mathematical Sciences. 2025, 45(7): 2133-2153. https://doi.org/10.12341/jssms240167
    When a sudden public health emergency occurs, the demand for emergency medical supplies surges, and ensuring the effective supply of emergency medical materials becomes a crucial issue concerning public safety. To investigate the strategic choices among emergency medical supplies stakeholders during sudden public health emergencies, this paper constructs an evolutionary game model involving medical material suppliers, hospitals, and local governments. Based on the real-world scenario during the COVID-19 pandemic where some medical material suppliers engaged in speculative sales, disrupting market order, this paper constructs an evolutionary game model involving medical material suppliers, hospitals, and local governments. It analyzes the stability of strategies adopted by each stakeholder in the game and further employs the Lyapunov first law to analyze the stability of combined strategies in the game system. Subsequently, simulation analysis is conducted to discuss the influence of different parameters on the evolution of the tripartite game system. The research indicates that evolutionarily stable strategies are significantly influenced by hospital complaint costs and the strict supervision costs imposed by local governments. Excessively high hospital complaint costs can result in insufficient proactive supervision feedback from hospitals, consequently leading to ineffective strict government supervision, especially given the relatively high costs associated with such supervision. Ultimately, the strategic choices of the three parties in the game tend towards speculative sales, acceptance, loose supervision. The intensity of rewards and penalties implemented by local governments on the decision-making entities of the other two parties plays a decisive role in the stability of the system. Insufficient rewards and penalties by local governments on medical material suppliers or inadequate compensation by hospitals, coupled with excessive punishment, can lead to the failure of strict government supervision. When local governments adopt a lax supervisory stance, emergency medical material suppliers naturally lean towards speculative sales. To ensure the effective supply of emergency medical supplies, local governments must consistently enforce strict supervision.
  • YE Xiaji, YU Lichao
    Journal of Systems Science and Mathematical Sciences. 2025, 45(12): 4016-4034. https://doi.org/10.12341/jssms240258
    This paper focuses on the situation where the response variable in sampling surveys does not obey the normal distribution as required by traditional small area estimation models. It investigates the small area estimation method for the target parameters of the Fay-Herriot model (FH model) based on the transformed response variable, proposing an empirical best predictor (EBP) for the target parameters and its mean square error (MSE) estimator. When inversely transforming the transformed EBP, a conditional expectation bias correction term is added to correct the bias introduced by the inverse transformation. A second-order approximate MSE estimator is introduced that is not restricted by the estimation method of the model parameters. Through numerical simulation, the MSE estimation method presented in this paper is compared with existing methods, revealing that the method enhances the adaptability of small area estimation models to data with response variables that have a skewed distribution and improves the precision of target parameter estimation, with the added benefit of having a simple estimator form. Finally, the research method of this paper is used to measure the per capita financial assets of urban and rural residents in some provinces and counties of China, and the effectiveness of the method is verified through the measurement results.
  • GU Hengyang, DU Xuewu
    Journal of Systems Science and Mathematical Sciences. 2025, 45(10): 3371-3384. https://doi.org/10.12341/jssms240367
    Among traditional gradient-like methods for solving unconstrained optimization problems, conjugate gradient method has the advantages of small storage requirement, simple iterative form and fast speed of computation. Barzilai-Borwein (BB) gradient methods are a class of improved algorithms for steepest descent method. They have good theoretical convergence and can avoid the zigzag phenomenon of steepest descent method. Spectral conjugate gradient methods are a class of conjugate gradient methods with good numerical performance and they use one of stepsizes in BB gradient methods as the spectral parameter. In this paper, we choose the parameter in a family of Dai-Kou (DK) conjugate gradient methods as the negtive of the reciprocal of another stepsize in the BB gradient methods. Furthermore, by combining Fletcher-Reeves (FR) conjugate gradient method which has good theoretical convergence with a variant of Polak-Ribière-Polyak (PRP) conjugate gradient method which has good computational performance, we present a class of hybrid truncated conjugate gradient methods with a convex combination form. In order to improve the numerical performance of this class of methods, we present a class of hybrid truncated spectral conjugate gradient methods with a restart step by combining a restart strategy and the idea of spectral conjugate gradient method. The choice of the spectral parameter guarantees that the methods in this paper possess the sufficient descent property without relying on any line search. Numerical experiment results show that the algorithm given in this paper has better numerical performance than the DK, DK+, PRP and a hybrid Dai-Yuan (HDY) conjugate gradient algorithms. Finally, we verify again the effectiveness of our algorithm by applying them for solving image restoration problems.
  • WANG Nan, WANG Hanquan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(1): 283-299. https://doi.org/10.12341/jssms240354
    In recent years, uncertainty quantification (UQ) has garnered considerable attention. Surrogate models based on polynomial chaos expansion are widely applied in addressing UQ problems. However, in practical applications, the distribution functions of random data are often unknown, posing significant challenges. Based on polynomial chaos expansion, This paper constructs a surrogate model based on polynomial chaos expansion and data, and uses such model to estimate data statistics, such as moment estimation, probability density function estimation and cumulative distribution function estimation. Firstly, synthetic data is employed to validate the effectiveness and feasibility of the surrogate model, and then the data-driven polynomial chaos expansion method is applied to deal with some real-world data. Numerical results show that our method yields stable and reliable predictions for a certain class of random data.
  • YANG Gang, CHEN Zhu, CAO Xianjie
    Journal of Systems Science and Mathematical Sciences. 2025, 45(12): 3937-3954. https://doi.org/10.12341/jssms240360
    In the context of global climate warming, China is experiencing increasingly frequent extreme high-temperature events, which leads to a rising trend towards climate risks and severe losses of crops. In this paper, the deep learning algorithm N-BEATS model is used to iteratively forecast the future evolution trend of temperatures. Based on the intensity and duration of extreme high temperatures during a day, a novel extreme heat index and corresponding weather derivatives contracts are constructed. These contracts are used to hedge the extreme weather risks faced by crops. The results demonstrate that the proposed model significantly improves the prediction accuracy of future temperature changes, and the newly developed weather derivatives provide an effective hedging tool for extreme high-temperature risks.
  • LU Xunfa, HUANG Nan, ZHANG Zhengjun, LAI Kin Keung
    Journal of Systems Science and Mathematical Sciences. 2026, 46(3): 796-815. https://doi.org/10.12341/jssms240612
    The cryptocurrency mining activities has a high energy consumption, which means that there is a potential linkage mechanism between the cryptocurrency market and the energy market. The frequent occurrences of various unexpected events have brought a huge impact on the global financial market, which has further intensified the risk transmission among financial markets. This study firstly uses the TVP-VAR extended joint correlation method to measure the total spillover between cryptocurrency and energy markets. Subsequently, the time-varying causality method and quantile-to-quantile regression method are used to study the impact mechanism of unexpected events on the risk spillover between cryptocurrency and energy markets. This can help to understand the magnitude and direction of the impact of news media coverage (such as, media coverage rate of the COVID-19 and news sentiment of the Russia-Ukraine conflict) and uncertainties (such as, geopolitical risks and economic policy uncertainty) on total spillovers between the two markets. Finally, the empirical results show that: First, the total spillovers between the two markets increase significantly during the Sino-US trade friction, the COVID-19 and the Russia-Ukraine conflict, and reach the highest point during the COVID-19 epidemic. Second, the impact mechanism of diverse unexpected events on total spillovers is different. During Sino-US trade frictions, geopolitical risks have a causal effect on total spillovers between the two markets, and exhibit a positive effect at the higher quantile. During the COVID-19 pandemic, both the media coverage rate of the COVID-19 and the economic policy uncertainty index have a causal effect on the total spillovers between the two markets, and also show a positive effect at the higher quantile. During the Russian-Ukrainian conflict, the Russian-Ukrainian conflict news sentiment index has no significant causal effect on the total spillovers between the two markets, but it has a negative effect at the higher quantile. In terms of the degree of impact, the media coverage rate of the COVID-19 has the strongest impact on the total spillovers between the cryptocurrency market and the energy market.
  • FU Yingxiong, XIE Huajun, ZHAN Jingjing, ZHANG Xin
    Journal of Systems Science and Mathematical Sciences. 2025, 45(8): 2517-2534. https://doi.org/10.12341/jssms240135
    In view of the current increasingly severe air pollution problem in China, it is especially critical to conduct an effective atmospheric environmental efficiency assessment. This paper proposes a dynamic network slacks-based measure (NSBM) model that considers the internal structure of the system and the inter-period activities in the neighboring periods to dynamically evaluate the inter-provincial atmospheric environmental efficiency in China. The model overcomes the shortcomings of the traditional network data envelopment analysis (DEA) method that ignores the lagged effects of carry-over variables. The model is applied to analyze the efficiency of the overall atmospheric environment and its sub-stages in 30 selected Chinese provinces (municipalities and autonomous regions) from 2016 to 2021. The empirical results show that: 1) In general, the overall efficiency of the atmospheric environment and the efficiency scores of each sub-stage in Eastern China are higher than those in central and Western China; 2) Low pollutant generation efficiency combined with high atmospheric pollutant control efficiency, or high pollutant generation efficiency combined with low atmospheric pollution control efficiency, are the main reasons for the overall inefficiency of the atmospheric environment in some provinces; 3) In the Beijing-Tianjin-Hebei region, Beijing and Tianjin have higher overall atmospheric environmental efficiency and sub-stage efficiency than Hebei Province.
  • LIN Jinguan, REN Yang, WANG Jiangyan
    Journal of Systems Science and Mathematical Sciences. 2025, 45(10): 3299-3317. https://doi.org/10.12341/jssms240127
    Covariance estimation poses a crucial challenge in the analysis of high dimensional data, which in turn is prone to the two phenomena of heavy-tailed distributions, small samples, and in these cases, the traditional estimation methods (e.g., sample covariance matrix) prove inadequate for such heavy-tailed data, given their lack of accuracy. In cases where heavy-tailed high dimensional data represented as tensors (multi-dimensional arrays), harnessing the tensor structure is a good choice for achieving dimensionality reduction. To this end, this paper proposes novel structured regularization methods for estimating the covariance of heavy-tailed tensor-valued data. In this paper, the heavy-tailed tensor data are first truncated, then the truncated sample covariance matrix is computed, and the CP decomposition will be applied to find an approximation in the form of Kronecker product of multiple matrices of the truncated sample covariance matrix, and finally imposes a banded or tapering structure for each of the small matrices obtained by the decomposition. Simulation results show that the proposed estimators have excellent performance for different degree of heavy tailing and different sample sizes. Anomalous temperature datasets with heavy-tailed distributions is analysed using the estimation method proposed in this paper.