Introduction

The world today is facing unprecedented changes in a century, and the complexity and challenges of national security are increasing (Wang et al., 2022). Since China proposed the holistic approach to national security in 2014, national security has expanded to include 20 areas, including political, military, territorial, economic, financial, cultural, social, technological, cyber, food, ecological, resource, nuclear, overseas interests, biological, space, deep sea, polar, artificial intelligence, and data security (Hou and Peng, 2023; Koren and Bukari, 2024; Niu et al., 2024; Perez et al., 2024; Schmidt, 2022; Wang et al., 2024a, 2024b). Within this comprehensive national security framework, political security holds a foundational position. In an era of increasing geopolitical complexity and security challenges, political security has emerged as a critical foundation of national security, as it directly affects the stability of state institutions, governance legitimacy, and national sovereignty (Nyman, 2023; Xu et al., 2024). Political security—encompassing the safety of a nation’s sovereignty, political system, political rights, political order, and ideology—is central to a nation’s survival and development. Threats to political security can undermine the nation’s foundation and trigger chain reactions across other security domains (Schilling et al., 2021). The stability of a nation’s political system directly influences its ability to address challenges in other security areas, making political security a critical component of the overall national security landscape.

In the field of national security research, establishing and improving risk assessment mechanisms are key elements in ensuring national security (Mennen and Van Tuyll, 2015). From a systems engineering perspective, security risk assessment, as a foundational task, not only needs to identify security requirements, assess design plans, and identify potential vulnerabilities but also address challenges arising from the increasing complexity and automation of technical systems (Angermeier et al., 2022; Landoll, 2021; Liu et al., 2012). National security risks are a complex and multidimensional issue, with globalization causing the nature and sources of national security risks to constantly evolve (Mara et al., 2022). Although significant theoretical advancements have been made in national security risk assessment, there is still a lack of consensus both domestically and internationally on standardized requirements, processes, and methods. Furthermore, existing national security risk assessment methods, while providing a scientific basis in theory, still face practical challenges, including a focus on specific areas (e.g., information security), integration of multidimensional risk factors, false alarm risks, and achieving method transparency (Blagden, 2018; Kuzminykh et al., 2021; Lidén, 2023; Vlek, 2013). They have not provided a comprehensive approach to understanding and responding to the ever-changing nature of national security risks. Especially in current risk assessment analysis, although probability assessments can quantify risks, there is still controversy in low-tolerance areas, making effective risk assessment increasingly important in complex decision-making processes (Heyerdahl, 2021).

To address this gap, this study constructs an integrated and standardized national security risk assessment model, with a particular focus on China’s political security as a case study. Building upon existing risk assessment theories, the proposed model systematically incorporates three key dimensions: the risk control process, the relationship among evaluation factors, and the assessment model itself. The model integrates elements such as risk control processes, evaluation indicators, and situation awareness, providing a holistic approach for analyzing, evaluating, and forecasting national security risks, offering practical solutions to enhance national security resilience. While our model is designed to be applicable across all security domains in national security, for the purposes of empirical validation, we have chosen to focus specifically on China’s political security as a case study. This selection allows us to demonstrate the model’s practical application in a domain that has significant implications for overall national security. The insights gained from this political security case study can inform the application of the model to other security domains within the comprehensive national security framework.

We summarize our core contributions: (i) Theoretically, it improves the mechanism and method of national security risk assessment, providing a structured and comprehensive framework that meets the demands of modern security challenges. (ii) Practically, through an empirical analysis of China’s political security, the feasibility of the model is verified, offering actionable insights for policymakers. While this study focuses specifically on political security as a case study, the proposed model provides a methodological framework that can be adapted to other domains of national security, offering theoretical guidance and methodological support for comprehensive national security risk evaluation. By bridging theoretical gaps and addressing practical challenges, this study provides a novel framework for understanding and assessing political security risks. Furthermore, through this research, we aim to promote the understanding and implementation of national security risk assessments, foster high-quality development, and enhance the country’s resilience in an increasingly complex global environment.

Literature review

Related concepts of national security risk assessment

National security risk assessment is an integration of the definitions and connotations of related concepts such as “security,” “national security,” “risk,” and “national security risk.” Security refers to the absence or minimal presence of threats objectively and the absence or minimal sense of fear subjectively. It is the primary prerequisite for human survival and the basic guarantee for national development. The National Security Law of the People’s Republic of China clearly states: National security refers to a state where the national regime, sovereignty, unity, and territorial integrity, the well-being of the people, sustainable economic and social development, and other significant national interests are relatively free from danger and threats from both within and outside, as well as the capability to ensure a continuous state of security. The concept of national security is rich in content. It not only refers to the state of security but also includes the capability of the nation to maintain such a state of security. The International Organization for Standardization (ISO) in its Risk Management Guidelines (ISO 31000:2018) mentions that risk is the effect of uncertainty on objectives, and it is a comprehensive measure of the likelihood and consequence of loss (Rezvani et al., 2022).

By integrating the definitions of national security and risk, and referring to the ISO standard Risk Management—Risk Assessment Techniques (ISO/IEC 31010:2019) (Berov et al., 2024), national security risk can be defined as various internal and external factors (security threats) that pose a threat to the country’s vital interests (assets), as well as inherent security vulnerabilities (weaknesses) within the nation itself. Under certain conditions, these factors may endanger the country’s survival and development, necessitating the implementation of corresponding security measures for mitigation and control. In essence, national security risk is a comprehensive risk composed of four interrelated dimensions: significant national interests, national security threats, national security vulnerabilities, and national security measures. Significant national interests represent the core values and strategic resources that require protection. National security threats manifest as various internal and external challenges that could jeopardize national security. National security vulnerabilities refer to inherent security weaknesses and deficiencies within the national system. National security measures encompass various protective, monitoring, and response strategies implemented to prevent and address risks. These four dimensions are interconnected and interact dynamically, collectively determining the nature, severity, and evolution of national security risks. National security risk assessment is based on these four dimensions, aiming to identify risk sources, analyze influencing factors, and develop effective control strategies to safeguard national security and promote stable development. Accordingly, the national security risk assessment model studied in this paper is a comprehensive framework designed to identify, analyze, and evaluate various security risks faced by the nation. This model integrates key risk assessment elements—including national interests, threats, vulnerabilities, and protective measures—into a systematic framework. By incorporating risk control processes, assessment indicators, and situational awareness, the model provides a holistic approach for analyzing, evaluating, and forecasting national security risks.

Current research on national security risk assessment

Since the founding of the People’s Republic of China, the historical evolution of China’s national security concept has primarily gone through four stages: focusing on military security, comprehensive security, a new type of security concept centered on mutual trust, mutual benefit, equality, and cooperation, and the holistic approach to national security (Ji, 2016). The holistic approach to national security proposed by the 18th National Congress of the Communist Party of China is the basic policy and guiding principle for national security work in the new era, providing a fundamental basis and action plan for our national security work in the new era. Accordingly, with the needs of the international situation and domestic development, China’s national security departments and institutions have been continuously established: such as the Ministry of State Security established in 1983, the National Bureau of Secrets specifically set up by the State Council in 1988, the Central National Security Commission and the National Counter-terrorism Leadership Group established in 2013, the Central Cyberspace Security and Informatization Leading Group established in 2014, and the Emergency Management Department established in 2018. Among these, the Central National Security Commission has improved the national security system and national security strategy, becoming the highest decision-making body for national security work in China. At the same time, in order to better promote national security risk assessment and maintain national security, China has also issued a series of laws, regulations, and national strategic guidelines: the “National Security Law of the People’s Republic of China” passed by the 15th Meeting of the Standing Committee of the Twelfth National People’s Congress in July 2015, which clarifies national security tasks in 11 areas such as politics, territorial, military, cultural, and technological, and specifically provides for national security risk prevention, assessment, and early warning systems in Chapter IV “National Security System”. In addition to this, there are legal provisions related to national security such as the “Anti-Secession Law” (2005), the “Food Security Law” (2009), the “Counter Espionage Law” (2014), the “Counter Terrorism Law” (2015), the “Cybersecurity Law” (2016), the “National Intelligence Law” (2017), the “Nuclear Security Law” (2017), the “Cryptographic Law” (2019), the “Biosecurity Law” (2020), the “Regulations on the Work of Counter Espionage Security” (2021), and the “Foreign Relations Law” (2023). In terms of national strategic guidelines, since the founding of the People’s Republic of China, the term “national security strategy” was not mentioned until January 2015, under the guidance of the holistic approach to national security, the Political Bureau of the CPC Central Committee adopted the “National Security Strategy Outline,” which is the first comprehensive national security strategy since the founding of the People’s Republic of China and is an urgent need to effectively maintain national security, indicating that China has begun to address the relationship between national security and national development from the perspective of national grand strategy(Goldstein, 2020; Hu, 2016; Liu, 2016; Özdemir and Karagül, 2024). Subsequently, the “Opinions on Strengthening National Security Work” passed in December 2016, the “National Security Strategy (2021–2025)” reviewed in November 2021, and the “Opinions on Accelerating the Construction of a National Security Risk Monitoring and Early Warning System” reviewed at the first meeting of the 20th Central National Security Commission on May 30, 2023, all aim to more accurately grasp the historical position and the situation and tasks facing China’s national security, and to recognize the importance of strengthening national security work.

The United States has been committed to further improving its national security risk assessment system to better respond to complex security environments and evolving security threats and challenges. National security risk assessment is an important foundation for the formulation and implementation of U.S. national security policy, such as the “National Security Strategy Report” issued by the U.S. government annually, the “Global Threat Assessment” report published by the U.S (Ihemeson, 2024; Newmann and Christiansen, 2023). The National Intelligence Council, each year, and the “National Cybersecurity Strategy” issued by the U.S. Office of the National Cyber Director. Following the September 11, 2001, terrorist attacks, the U.S. government began to focus on major emergencies such as terrorism and natural disasters, establishing the Department of Homeland Security and releasing the Homeland Security Alert System (in 2002), the National Terrorism Advisory System (in 2011), and the NTAS Bulletin (in 2015) to assess and warn of the risks of terrorism. EU institutions and government departments of other countries also actively carry out national security risk assessment research. The European Commission has released the “EU Internal Security Strategy” and the “EU External Security Strategy” to assess and analyze the security situation within and around the EU. The UK established the National Security Council, the highest national security decision-making and strategic planning body, in 2010, and has developed detailed national security strategy reports. Germany also formulated and released its first “National Security Strategy” on June 14, 2023, mainly addressing all internal and external threats to German security in areas such as defense and military, cyberattacks, critical infrastructure attacks, flood disasters, and climate change. South Korea’s 2023 edition of the “National Security Strategy,” released on June 8, 2023, lists North Korea’s nuclear threat and weapons of mass destruction as the biggest current challenges to South Korean national security. Israel’s “Technical Intelligence Agency,” an important department of the Military Intelligence Directorate, and the Australian Government’s Australian Security Intelligence Organization aim to protect national security and interests, prevent and combat various security threats and risks (AlDaajeh et al., 2022; Eichensehr and Hwang, 2023; Kamp, 2023; Kim, 2023; Levi and Agmon, 2021).

Related risk assessment standards

The existing risk assessment research frameworks are relatively rich and mature, with corresponding international and national standards established for various fields (Kretschmer et al., 2022; Wand et al., 2021). Internationally, the more commonly used risk assessment standards include the ISO risk management family of standards, which consists of four formal standards: “Risk Management—Vocabulary” (ISO Guide 73:2009), “Risk Management—Guidelines” (ISO 31000:2018), “Risk Management—Risk Assessment Techniques” (ISO/IEC 31010:2019), and “Risk Management—Guidance on the Implementation of ISO 31000” (ISO/TR 31004:2013), providing a unified and comprehensive solution for conducting risk management work. Additionally, to reduce the risk of information security vulnerabilities, the ISO has also released “Information Technology—Security Techniques—Information Security Risk Management” (ISO/IEC 27005:2018) for risk assessment in the information security field (Breda and Kiss, 2020). In China, since the establishment of the National Risk Management Standardization Technical Committee (SAC/TC310) in 2007, national standards on risk management and risk assessment techniques have been developed, including “Risk Management—Vocabulary” (GB/T 23694-2024), “Risk Management—Guidelines” (GB/T 24353-2022), and “Risk Management—Risk Assessment Techniques” (GB/T 27921-2023). For information security risk assessment, standards such as “Information Security Technology—Information Security Risk Assessment Methods” (GB/T 20984-2022), “Information Security Technology—Information Security Risk Management Implementation Guide” (GB/T 24364-2023), and “Information Security Technology—Information Security Risk Assessment Implementation Guide” (GB/T 31509-2015) have been established. Moreover, corresponding national standards have also been developed for public security, food security, ecological security, biosecurity, and fire risk assessment, among other fields (Chen et al., 2021; Diana et al., 2020; Schleifer and Sun, 2020; Zeng et al., 2022).

In summary, current research on national security and its risk assessment has made some progress, but there is a need for continuous exploration and improvement. There is no consensus on the requirements, processes, and methods for assessing national security risks, either domestically or internationally, and there are no unified international or national standards. Therefore, there is an urgent need to carry out national security risk assessment work, to standardize the mechanisms and methods for national security risk assessment. This study aims to propose ideas, work processes, and assessment content for national security risk assessment, and to conduct empirical research using national political security as a case study, providing theoretical guidance and methodological support for the practice of national security risk assessment.

Research path of national security risk assessment

National security risk control process

National security risk assessment is a comprehensive process that includes the definition, analysis, evaluation, and control of national security risks. It measures the vulnerabilities, threat levels, and response measures of national security by analyzing and evaluating the security vulnerabilities, threats, and factors affecting a nation’s survival, development, and interests. The national security risk control process should be centered on the national overall security objectives, from formulating national security strategies, to determining national security risk assessment methods, implementing national security risk assessments, identifying national security needs, and selecting national security risk control measures, ultimately verifying the effectiveness of national security measures. By following a cycle of six stages, national security departments can systematically identify and assess potential national security risks to achieve the goal of ensuring national security (Bolbot et al., 2023; Landoll, 2021). By referring to common risk control processes internationally, the entire control process for national security risks can be outlined as shown in Fig. 1.

Fig. 1
figure 1

National security risk control process.

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As can be seen from Fig. 1, the national security risk control process includes the following six stages: (i) Formulating national security strategies: As the first stage of the national security risk control process, this is a crucial step in ensuring national security. National security departments need to conduct a comprehensive assessment of the national security risks, clarify the national overall security objectives and strategic direction based on relevant laws, regulations, national security tasks, and missions, and formulate corresponding national security strategies. (ii) Determining national security risk assessment methods: National security departments need to select appropriate national security risk assessment methods based on the stage and scale of national security system construction, to identify threats, vulnerabilities, and potential risks facing national security, and evaluate the applicability of the risk assessment methods. (iii) Implementing national security risk assessment: National security departments need to use the national security risk assessment methods determined in the previous stage to analyze and identify threats, vulnerabilities, and potential risks that may affect national security, and conduct national security risk assessments based on the risk assessment elements. (iv) Identifying national security needs: National security departments need to combine relevant laws, regulations, national security tasks, missions, and risk assessment results with the national overall security objectives to determine the key national security needs and priority areas, and provide a national security risk needs report. (v) Choosing national security risk control measures: National security departments need to consider the costs, effects, and feasibility of national security risk control measures from the aspects of national security needs, technical limitations, and resource limitations, and choose appropriate risk control measures to mitigate or eliminate identified national security risks, resulting in an effective national security risk management plan. (vi) Verifying the effectiveness of national security measures: National security departments need to monitor, analyze, and evaluate the implementation effects of national security needs and measures to verify whether the selected national security risk control measures have been effectively implemented and whether they have effectively reduced national security risks, to ensure the effectiveness and sustainability of national security measures.

Relationships of national security risk assessment elements

According to the national standard for information security risk assessment, the basic elements of risk assessment are assets, threats, vulnerabilities, and security measures (Ganin et al., 2020; Landoll, 2021). These elements are fundamental and crucial for risk assessment because they can comprehensively and accurately reflect the formation mechanism, influencing factors, and control methods of security risks. In the context of national security risk assessment, as defined in the National Security Law, the ultimate goal of national security is to safeguard significant national interests and ensure that the nation can survive and develop amid various threats and vulnerabilities. Therefore, “assets” correspond to the significant national interests that the nation seeks to protect, “threats” represent the internal and external threats to national security, “vulnerabilities” are the security flaws within the nation, and “security measures” are the various means and measures taken to maintain significant national interests. Figure 2 illustrates the relationships among these elements in national security risk assessment.

Fig. 2
figure 2

Relationships of national security risk assessment elements.

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In Fig. 2, the elliptical sections represent the four basic elements of national security risk assessment: significant national interests, national security threats, national security vulnerabilities, and national security measures. The arrows indicate the relationships among the basic elements. (i) Significant national interests are the object, starting point, and ultimate goal of national security risk assessment. Only by clearly defining the significant national interests that need protection can the scope and objectives of the risk assessment be determined, as well as the value and importance of these interests. (ii) National security threats are the motivation and core of national security risk assessment. Only by identifying threats that may harm significant national interests can the sources, motivations, capabilities, likelihoods, and severity of the threats, as well as the impacts they cause, be analyzed. (iii) National security vulnerabilities are the conditions and key to national security risk assessment. Only by identifying vulnerabilities or defects in significant national interests when defending against threats can the risk levels, resilience, and improvement measures of these interests be assessed. (iv) National security measures are the means and results of national security risk assessment. Only by taking effective technical, management, or legal measures to protect significant national interests can the threats to national security and the vulnerabilities be reduced, thus lowering the level of national security risks.

Construction of a national security risk assessment model

In conducting research on national security risk assessment, it is important to note that the risk assessment process is not a sequential completion of assessment indicators but a comprehensive processing of all indicators simultaneously based on their importance. Therefore, the selection of assessment indicators, the determination of indicator weights, and the appropriate assessment model are critical in constructing the national security risk assessment model. When researching and applying risk assessment models, it is essential to always maintain the feasibility and scientificity of these three aspects. At the same time, based on the above three aspects, national security risk situation awareness can be achieved to predict and provide early warning for future national security risks, providing important reference information for decision-makers and better safeguarding national security.

Construction of assessment indicator system

The holistic approach to national security in China covers 20 areas of security, including politics, military, territory, economy, finance, culture, society, technology, cyberspace, food, ecology, resources, nuclear, overseas interests, biology, space, deep sea, polar regions, artificial intelligence, and data. When constructing the national security risk assessment indicator system, it is necessary to focus on the 20 security fields and start from four aspects: national security threats, national security vulnerabilities, significant national interests, and national security measures. By following principles such as comprehensiveness, scientificity, systematicness, standardization, and operability, the indicators for each field’s security risks can be selected to establish a comprehensive and scientific national security risk assessment indicator system. Due to the characteristics of multi-source, heterogeneous, large-scale, and dynamic changes in the data related to national security risks, it is necessary to obtain the original data of indicators from various official websites, statistical bureaus, and statistical yearbooks, as well as extract potential events, behaviors, trends affecting national security from text, images, videos, and other multi-source, heterogeneous data. After removing redundancy, organizing, and processing related elements through technical means, quantitative indicators can be formed into a national security risk situation data information database. Furthermore, as society continues to develop, science and technology advance rapidly, and the global political landscape changes rapidly, China’s internal and external environment and risk challenges are also changing. The connotation of the holistic approach to national security will also continue to expand, requiring continuous dynamic adjustments to adapt to the changing security threats and challenges, thus better ensuring national security. Therefore, the national security risk assessment indicator system will also need to be adjusted in line with the changes in the connotation of the holistic approach to national security.

Construction of the assessment model

Before conducting a risk assessment, it is necessary to determine the weights of the assessment indicators. Currently, the methods for determining the weights of risk assessment indicators are mainly divided into subjective weighting methods and objective weighting methods. When applied, subjective weighting methods such as the Delphi method and analytic hierarchy process are often used, or objective weighting methods such as the entropy weighting (EW) method and CRITIC method are used. Even when combining subjective and objective weighting methods, the integration of weights is often done simply through addition or multiplication, and the subjective factors in the subjective and objective weighting coefficients remain significant. Therefore, this study can use game theory or moment estimation theory to integrate the subjective and objective weighting methods and obtain a comprehensive weight, thereby avoiding the excessive subjectivity or objectivity of single weighting methods and improving the scientificity and rationality of the weighting of assessment indicators. In the study of risk assessment models, researchers at home and abroad have commonly used methods such as the analytic hierarchy process, fuzzy comprehensive evaluation, EW method, TOPSIS method, principal component analysis, grey relational analysis, and projection pursuit method (Xu et al., 2024). Therefore, this study can combine intelligent optimization algorithms, such as the simulated annealing algorithm, with the projection pursuit method to improve the assessment effect of the model and achieve the assessment of national security risks.

Construction of the situation awareness model

The concept of situation awareness was first proposed by Endsley in 1988 and has since been applied to national competitive intelligence, military warfare, cybersecurity, major emergencies, and government crisis decision-making in national security scenarios (Endsley, 2021; Yang et al., 2023). Applying the concept of situation awareness to national security risk assessment, national security risk situation awareness refers to the analysis and assessment of the current state of national security risks by understanding and obtaining all environmental elements that may lead to changes in the national security risk situation. It also includes predicting the future trends of the national security risk situation. Specifically, national security risk situation awareness includes three sub-models: national security risk situation element acquisition, national security risk situation assessment, and national security risk situation prediction. (i) The sub-model for acquiring national security risk situation elements is the foundational work for achieving national security risk assessment. Its main function is to identify and obtain relevant situation elements from various data sources. The national security risk assessment indicator system constructed in the previous section can form a national security risk situation data information database. Situation assessment is the core of situation awareness, so the sub-model for national security risk situation assessment is the key and core part of the national security risk assessment situation awareness model. Its main function is to integrate and analyze the situation elements identified by the sub-model for acquiring national security risk situation elements. The determination of indicator weights and the construction of assessment models in the previous section are two important steps in the sub-model for national security risk situation assessment. (ii) By mining, analyzing, and modeling the national security risk data information database, the sub-model for national security risk situation assessment can discover patterns and trends, analyze and judge the likelihood, severity, and coping ability of national security risks, and form a deep understanding and assessment of the national security risk situation. This provides important support for the subsequent sub-model for national security risk situation prediction. (iii) Situation prediction is the highest-level requirement of situation awareness. Therefore, the sub-model for national security risk situation prediction is an important part of the national security risk assessment situation awareness model. National security risk situation prediction is based on a full understanding of the national security environment information and activity patterns, combined with the situation elements obtained in the previous stage and the situation assessment model constructed. It predicts and provides early warning for the future national security risk situation. The sub-model for national security risk situation prediction is an important part of the national security risk assessment situation awareness model. National security risk situation prediction can use mathematical models such as linear regression, grey prediction, time series prediction, and neural network prediction. By analyzing and researching the national security risk data information database, it can predict and provide early warning for the national security risk situation that may occur in the future, providing important reference information for decision-makers. It can also take proactive measures to reduce national security risks and protect national interests, thus better maintaining national security.

Methodology

Game theory combination weighting model

Considering the subjective irrelevance of national political security risks, the inherent relationship of the indicators to be assessed, and the weight gradient over time, this study first uses the analytical hierarchy process (AHP) to calculate the subjective weights of the political security risk indicators. Then, the EW method is employed to calculate the objective weights. Finally, the game theory combination weighting (GTCW) model is utilized to integrate the subjective and objective weights to obtain a comprehensive weight. This approach avoids the excessive subjectivity or objectivity of single weighting methods, thereby improving the scientificity and rationality of the indicator weight assignment.

Analytical hierarchy process

The AHP is a method for subjectively and statistically analyzing the hierarchical nature (Cranmer et al., 2021). It divides the important decision factors into three layers: the goal layer, the criteria layer, and the scheme layer. It determines the benefits and drawbacks of the decision-making scheme based on the experienced judgment of decision-makers. This is the foundation for qualitative and quantitative analysis. The specific procedure is as follows: (i) Build a hierarchy model. (ii) Construct a judgment matrix A. (iii) Hierarchical ranking and testing for consistency. (iv) Hierarchical general ranking and consistency testing.

Entropy weighting method

Information entropy is a measure of information uncertainty. The EW method is a weighting method that generates the indicator weight coefficient based on the effect of each indicator’s relative change degree on the overall system (Xu, 2023). The specific procedure is as follows: (i) Construct a decision matrix X. (ii) Indicator standardization: homogeneity of diverse indicators. (iii) Calculate the characteristic proportion of i evaluation object under indicator j. (iv) Determine the entropy value of indication j. (v) Calculate the coefficient of variation in indicator j. (vi) Determine the weight coefficient of indication j.

Game theory combination weighting model

GTCW model is widely used in system evaluation. To seek the optimal solution for the overall interests of the target system, game theory assumes that each plan is a rational decision outcome, and the final result is achieved collectively by all decision-makers (Zhao, 2024). Let \({{\bf{w}}}_{i}(i=1,2)\) be the weight vectors obtained from the ORA method and the EW method, respectively. An arbitrary linear combination of the two weight vectors is denoted as \({\bf{w}}={\sum }_{i=1}^{2}{\alpha }_{i}{{\bf{w}}}_{i}^{{\rm{T}}}({\alpha }_{i} > 0)\), where \({\alpha }_{i}\) is the linear combination coefficient of the weight vectors. By optimizing \({\alpha }_{i}\), we minimize the deviation between w and \({{\bf{w}}}_{i}\), as follows:

$$\min {\left\Vert \mathop{\sum }\limits_{i=1}^{2}({\alpha }_{i}{{\boldsymbol{w}}}_{i}^{{\rm{T}}}-{{\boldsymbol{w}}}_{i})\right\Vert }_{2}$$
(1)

According to the differential properties of matrices, the optimal first-order derivative of the equation is derived as:

$$\left(\begin{array}{cc}{{\boldsymbol{w}}}_{1}{{\boldsymbol{w}}}_{1}^{{\rm{T}}} & {{\boldsymbol{w}}}_{1}{{\boldsymbol{w}}}_{2}^{{\rm{T}}}\\ {{\boldsymbol{w}}}_{2}{{\boldsymbol{w}}}_{1}^{{\rm{T}}} & {{\boldsymbol{w}}}_{2}{{\boldsymbol{w}}}_{2}^{{\rm{T}}}\end{array}\right)\left(\begin{array}{c}{\alpha }_{1}\\ {\alpha }_{2}\end{array}\right)=\left(\begin{array}{c}{{\boldsymbol{w}}}_{1}{{\boldsymbol{w}}}_{1}^{{\rm{T}}}\\ {{\boldsymbol{w}}}_{1}{{\boldsymbol{w}}}_{1}^{{\rm{T}}}\end{array}\right)$$
(2)

From Eq. (2), the optimal weight coefficient \(({\alpha }_{1},{\alpha }_{2})\) are obtained, and after normalization, the optimal distribution ratio coefficient of the weight is \(({\alpha }_{1}^{\ast },{\alpha }_{2}^{\ast })\). Through Eq. (3), the optimal combined weight can be calculated.

$${{\boldsymbol{w}}}^{\ast }=\mathop{\sum }\limits_{i=1}^{2}{\alpha }_{i}^{\ast }{{\boldsymbol{w}}}_{i}^{{\rm{T}}}$$
(3)

Simulated annealing optimization projection pursuit evaluation model

Projection pursuit evaluation method is an effective statistical method for handling multi-factor complex problems. The main idea is to project high-dimensional data into a lower-dimensional space according to a certain combination, and by determining the optimal projection value, the evaluation value becomes more meaningful. This paper combines the simulated annealing algorithm with the projection pursuit evaluation method to establish a simulated annealing optimization projection pursuit evaluation (SAO-PPE) model (Xu, 2025), with the main steps as follows: (i) Standardize the indicator data. (ii) Construct the linear projection of the evaluation object in the low-dimensional space. (iii) Construct the indicator function of the projection. (iv) Optimize the projection direction using the SA algorithm. (v) Calculate the comprehensive evaluation value. The objective function of the SAO-PPE model is

$$\begin{array}{l}\max Q(A)={S}_{Z}\cdot {D}_{Z}\\ s.t.\left\{\begin{array}{l}A > 0\\ \mathop{\sum }\limits_{j=1}^{m}{a}_{j}^{2}=1,-1 < {a}_{j} < 1\end{array}\right.\end{array}$$
(4)
$$\left\{\begin{array}{l}{S}_{Z}=\sqrt{\frac{1}{n-1}\mathop{\sum }\limits_{i=1}^{n}{({z}_{i}-\bar{z})}^{2}}\\ {D}_{Z}=\mathop{\sum }\limits_{i=1}^{n}\mathop{\sum }\limits_{j=1}^{m}(R-{r}_{ij})\cdot I(R-{r}_{ij})\end{array}\right.$$
(5)

where \({S}_{Z}\) is the sample standard deviation of the projection eigenvalues, with a larger value indicating a more uniform distribution of the sample data. \({D}_{Z}\) is the local density of the projection eigenvalues. The value of the local density window radius R depends on the structure of the sample data. \({r}_{ij}\) is the distance between the projection eigenvalues. \(I(R-{r}_{ij})\) is the unit step function.

The specific optimization process of the SA algorithm is as follows: (i) Calculate \({S}_{Z}\) and \({D}_{Z}\) according to Eq. (5) to serve as the optimal initial point of the model. (ii) Calculate the objective function value according to Eq. (4). (iii) Set the initial temperature \({T}_{0}=100\) and the number of iterations \(L=100\). (iv) Generate new points near \({S}_{Z}\) and \({D}_{Z}\) randomly, calculate their objective function values and the increments \(\Delta\). (v) If \(\Delta < 0\), accept the current point as the optimal point, otherwise, with a probability of \(P={e}^{(-\Delta /{T}_{0})}\), select a new point as the optimal point.

Security risk situation prediction model

This paper employs five prediction models, including regression prediction (RP), grey prediction, triple exponential smoothing (TES), time series prediction, and neural network prediction. By conducting a comparative analysis of the effectiveness of these five models, the model with the best performance is ultimately selected to predict the development situation of political security risks in China.

Regression prediction model

RP is a statistical technique that estimates the future values of a dependent variable based on its historical relationship with one or more independent variables. By analyzing past data, a regression model is formulated, which can then be used to forecast outcomes under new conditions. Commonly applied in various fields, such as economics, finance, and social sciences, it helps in understanding the impact of predictors on the response variable, facilitating data-driven decision-making. The strength of the prediction depends on the model’s fit, the relevance of the independent variables, and the assumption that the historical pattern will continue.

Grey prediction model

The grey prediction model is a forecasting method based on grey system theory, suitable for data prediction with small samples and uncertain information. By generating and processing partial known information, it establishes a differential equation model to predict the future behavior of the system. Grey prediction models are particularly useful for short-term forecasting of time series data in fields like economics, environment, and technology (Wang et al., 2024a, 2024b). The core of this model is transforming the original data with strong randomness into generated data with strong regularity through the processes of accumulated generating operation and inverse accumulated generating operation, thereby improving the accuracy of predictions.

Triple exponential smoothing method

TES, also known as the Holt–Winters method, considers the trend and seasonal factors of past observations through a weighted average for prediction. This method builds upon simple and double exponential smoothing by incorporating the handling of seasonal components, making it suitable for data with significant seasonal fluctuations. TES consists of three smoothing equations: one for the level component, one for the trend component, and another for the seasonal component. The method adjusts smoothing parameters to balance the weights of historical data, aiming to reduce forecasting errors.

Time series prediction model

Time series prediction models are statistical models used to analyze and predict data points arranged in chronological order. These models assume that future values can be predicted by the patterns of past values, typically considering time-dependent features such as trends, seasonality, and cyclical patterns (Pereira da Veiga et al., 2024). Common models include Autoregressive, Moving Average, Autoregressive Moving Average, and Seasonal ARIMA. Time series prediction has wide applications in financial market analysis, weather forecasting, sales forecasting, and more, helping to uncover the underlying patterns in data and support decision-making.

Neural network prediction model

Neural network prediction models are forecasting techniques based on artificial intelligence that mimic the working principle of the human brain’s neurons to process and analyze data (Jiang et al., 2024). These models are constructed with multiple layers of nodes (or neurons), where each node performs simple computational tasks and processes input signals through weights and activation functions. Neural networks can learn complex patterns and relationships from data, making them suitable for various nonlinear forecasting problems. By learning from training datasets, neural networks adjust internal parameters to minimize prediction errors. They excel in fields such as financial market forecasting, speech recognition, and image processing.

Empirical study: political security risk assessment in China

National security is a complex, multi-layered, multi-domain, and multi-type grand system. Existing research indicates that political security serves as the foundation and core of national security (D’Amato et al., 2022; Wæver, 2011). The security of a nation’s sovereignty, political system, rights, order, and ideology is central to its survival and development. Threats to political security can undermine the nation’s foundation and trigger a chain reaction across other security domains. As the cornerstone of maintaining national interests and overall security, ensuring political security is of paramount importance. Therefore, this study takes national political security in China as an example to conduct an empirical analysis of the constructed national security risk assessment model, verifying its feasibility and effectiveness. It should be noted that the national security risk assessment model proposed in this study is designed to be applicable across all security domains within the comprehensive national security framework. However, to demonstrate its practical application and validate its effectiveness, we focus on China’s political security as a case study. The methodology outlined above illustrates how the model can be applied to political security risk assessment, but the same methodological framework can be adapted to other security domains by adjusting the specific indicators while maintaining the same structural approach.

Indicator construction

Political security encompasses the objective state of a country’s sovereignty, political system, political rights, political order, and ideology not being threatened, infringed upon, or destroyed. It is related to the overall security of a country. Through extensive literature research, based on existing research on national political security risk assessment, this paper starts from four aspects: political security threats, political security vulnerabilities, political security interests, and political security measures (Abdullah et al., 2020; Hagmann and Cavelty, 2012; Henisz et al., 2010; Kośmider, 2021; Wolford and Ritter, 2016). Adhering to principles such as systematicness, scientificity, and operability, the national political security risk assessment indicator system is constructed and listed in Table 1.

Table 1 Indicator system for national political security risk assessment.
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Data source

Based on the principles of scientificity, rationality, and accessibility, this study selects the period from 2001 to 2022 as the research time frame. The primary data sources include the World Governance Indicators (http://info.worldbank.org/governance/wgi/#home), the International Country Risk Guide (https://epub.prsgroup.com/products/international-country-risk-guide-icrg), the Geopolitical Risk Index (GRI, https://www.matteoiacoviello.com/gpr.htm), the Positive Peace Index (PPI, https://www.visionofhumanity.org/maps/positive-peace-index/#/), the Corruption Perceptions Index (CPI, https://countryeconomy.com/government/corruption-perceptions-index), the Global Terrorism Index (GTI, https://www.visionofhumanity.org/maps/global-terrorism-index/#/), the Fragile States Index (https://fragilestatesindex.org/), the Edelman Trust Barometer (https://www.edelman.com/trust/archive), the Trading Economics (https://tradingeconomics.com/country-list/rating), and the Database of Political Institutions (https://datacatalog.worldbank.org/search/dataset/0039819). For missing data in some years, methods such as cubic linear interpolation and linear extrapolation are employed to supplement the data. Additionally, the range normalization method is used to eliminate the impact of dimensionality for each indicator, converting the values into the range of 0–1.

Optimal weighting results

This paper employs the GTCW model to integrate the weights obtained from the AHP method and the EW method, resulting in the comprehensive weights, which are shown in Fig. 3.

Fig. 3: Weight results of China’s political security risk assessment indicators.
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a Political security threats. b Politicalsecurity vulnerabilities. c Political security interests. d Political security measures.

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Figure 3a–d displays the radar charts of the secondary indicator weights for political security threats, political security vulnerabilities, political security interests, and political security measures, respectively. The weight ranking of China’s primary political security risk indicators is as follows: political security interests (0.3303), political security vulnerabilities (0.2655), political security threats (0.2279), and political security measures (0.1763). Among the 22 secondary indicators, the weight of political stability (I14, 0.1016) is the highest, indicating that political stability has the greatest impact on China’s political security risk. The higher a country’s political stability, the more secure its sovereignty, government, system, and ideology are, meaning its economic development, social order, and citizens’ living and working environment are relatively stable, which in turn lowers the political security risk. Therefore, political stability is the cornerstone of ensuring national political security. A country with high political stability can effectively safeguard its dignity and core national interests, maintain political unity and social order, resist external interference and subversion, prevent internal unrest and division, and promote the healthy and orderly development of its economy and society.

Assessment results of China’s political security risk

This study applied the SAO-PPE model to assess China’s political security risks from 2001 to 2022, with the results shown in Fig. 4.

Fig. 4
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Assessment results of China’s political security risk assessment from 2001 to 2022.

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As depicted in Fig. 4, the political security risk assessment index for China from 2001 to 2022, along with the risks associated with political security threats, vulnerabilities, interests, and measures, all show certain fluctuations but generally demonstrate a decreasing trend year by year. Specifically, China’s political security risk decreased from 76.39 in 2001 to 24.99 in 2022. (i) Regarding political security threat risks, although China faces challenges such as the U.S. containment and suppression and the increasing complexity of regional hotspot issues, leading to cyclical fluctuations in China’s GRI and a slow overall upward trend, in recent years, China has made significant progress in participating in international affairs, conducting counter-terrorism and anti-separatism efforts, advancing the Belt and Road Initiative, and maintaining multilateralism. Consequently, the GTI, the degree of friendly relations with neighboring countries, external conflicts, and foreign interventions have all decreased year by year, reducing political security threat risks. (ii) In terms of political security vulnerability risks, China’s CPI has risen from 35 points in 2001 to 45 points in 2022, indicating some success in the anti-corruption efforts. Improvements in information quality, reductions in indices such as group grievance, gender inequality, public sector theft, and the fragile state index all reflect the increased stability of the Chinese government and its enhanced governance capabilities, which have lowered political security vulnerability risks. (iii) Concerning political security interest risks, China has increased government transparency and integrity through measures such as strengthening the anti-corruption campaign and improving people’s well-being. Public trust in the government has risen from 63 points in 2001 to 89 points in 2022. Additionally, government efficiency and the rule of law have shown a consistent upward trend, while government stability, citizen participation, and the global peace index have remained relatively stable, leading to fluctuating but overall declining political security interest risks. (iv) As for political security measures risks, China’s government credit rating, regulatory quality, and corruption control from 2001 to 2022 show fluctuations with a steady upward trend. This demonstrates the improvement of government credibility, the enhancement of regulatory frameworks, and the increased intensity of the anti-corruption campaign in recent years. Moreover, the positive peace index (PPI) has steadily declined, indicating that China’s political stability has been maintained and is increasingly resilient to internal and external shocks, thereby reducing political security measures risks.

Prediction results of China’s political security risk situation

This paper employs five prediction models to forecast the development situation of China’s political security risks. Based on Fig. 4, which shows the yearly trend of China’s political security risks, a linear function prediction is chosen for the RP model; the grey prediction selects the first-order differential equation GM(1,1) model; the weighted coefficients in the TES method are set to 0.5, 0.5, and 0.3, respectively; the time series model chooses the ARIMA(4,1,3) model for prediction; and the neural network prediction selects the BP neural network (BPNN) model with a network structure of 1-4-1. Simultaneously, this paper compares and evaluates the predictive performance of these five models through metrics such as Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE), Sum of Squared Errors (SSE), and Coefficient of Determination (R2). Among these, except for R2 where values closer to 1 indicate better prediction performance, lower values for the remaining six metrics suggest better prediction effects. The model results are shown in Table 2 and Fig. 5.

Table 2 Comparison of 5 prediction models under different metrics.
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Fig. 5
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Prediction results of China’s political security risk situation.

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As shown in Table 2, by comparing the values of six evaluation metrics across different models, it is evident that among the five prediction models, the BPNN model significantly outperforms the other four models in all six evaluation metrics, with an R2 value reaching 0.9967, indicating the best predictive performance. Therefore, this study selects the BP neural network to forecast China’s political security risk trends for the next 10 years, with the forecast values for 2023–2032 shown in Fig. 5. The figure reveals that over the next decade, China’s political security risk level will continue the trend of fluctuations and a year-on-year decrease observed in the previous period, with the downward trend slowing down. By 2032, the political security risk is expected to drop to 11.00. These results demonstrate that the BP neural network prediction model aligns with the actual situation and can be applied in predicting national political security risks, as well as extended to national security risk assessment studies under the holistic approach to national security.

Conclusion

The world today is facing a major transformation that has not been seen in a century. In response to the complex and severe national security situation, and to accelerate the modernization of the national security system and capabilities, there is an urgent need to explore more forward-looking, standardized, and systematic research on national security risk assessment. National security risk assessment plays a crucial role in national security decision-making, crisis prevention and resolution, and the protection of national interests across multiple security domains.

This paper delves into the research path of national security risk assessment from three aspects: the national security risk control process, the relationship between assessment elements, and the assessment model. While our model is designed to be applicable across all security domains, we have demonstrated its application through a case study of political security in China, which serves as a foundational element of the broader national security framework. The empirical analysis of China’s political security validates the model’s feasibility and effectiveness, showing that China’s political security risk decreased from 76.39 in 2001 to 24.99 in 2022, with projections suggesting a continued decline to 11.00 by 2032. This case study demonstrates how the model can be applied to specific security domains while maintaining its broader applicability to the comprehensive national security framework. The national security risk assessment model proposed in this study can be extended beyond political security to other domains such as military, economic, technological, social, and environmental security. By adjusting the specific indicators while maintaining the same methodological framework, the model provides a versatile tool for comprehensive national security risk assessment. This flexibility is particularly valuable given the interconnected nature of different security domains and the need for an integrated approach to national security.