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Research article Special Issues

Navigating the future by fuzzy AHP method: Enhancing global tech-sustainable governance, digital resilience, & cybersecurity via the SME 5.0, 7PS framework & the X.0 Wave/Age theory in the digital age

  • In the rapidly evolving landscape of the digital age, the call for intelligent governance has become paramount. This study offers a nuanced exploration of global sustainable governance, integrating the Seven Pillars of Sustainability (7PS) framework and innovation culture. Utilizing structural equation modeling and data from diverse government organizations, this research empirically established the 7PS framework's pivotal role in enhancing organizational sustainability, supported by a robust 95% confidence level. Notably, it unveiled the transformative influence of innovation culture in amplifying the 7PS's impact. The methodological innovation lies in strategically applying the fuzzy analytic hierarchy process (AHP), assigning priority weights to 7PS criteria, and identifying culture as the linchpin. This approach provided a robust framework for dissecting the complex interplay of emerging technologies, sustainable engineering, and cybersecurity. The study delves into the X.0 wave/age (X.0 = 5.0) theory, offering insights into the intricate dynamics of innovation, sustainability, and governance. Beyond academic discourse, this research informs practical strategies globally, particularly for small and medium-sized enterprises (SMEs) transitioning to SME 5.0/hybrid SMEs. Emphasizing inclusivity and diversity as catalysts for innovation, it scrutinizes contemporary challenges amid technological evolution and cybersecurity threats. Functioning as a visionary compass, the study elucidates the path to a 7PS sustainable future. It signifies a paradigm shift, transcending boundaries between knowledge domains. The fusion of the 7PS framework, X.0 wave theory, and fuzzy AHP navigates global governance, digital resilience, and cybersecurity, offering a transformative roadmap. This research contributes by substantiating the pivotal role of culture in emerging technologies, augmenting global tech-sustainable governance, fortifying digital resilience, and safeguarding cybersecurity.

    Citation: Hamid Doost Mohammadian, Omid Alijani, Mohammad Rahimi Moghadam, Behnam Ameri. Navigating the future by fuzzy AHP method: Enhancing global tech-sustainable governance, digital resilience, & cybersecurity via the SME 5.0, 7PS framework & the X.0 Wave/Age theory in the digital age[J]. AIMS Geosciences, 2024, 10(2): 371-398. doi: 10.3934/geosci.2024020

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  • In the rapidly evolving landscape of the digital age, the call for intelligent governance has become paramount. This study offers a nuanced exploration of global sustainable governance, integrating the Seven Pillars of Sustainability (7PS) framework and innovation culture. Utilizing structural equation modeling and data from diverse government organizations, this research empirically established the 7PS framework's pivotal role in enhancing organizational sustainability, supported by a robust 95% confidence level. Notably, it unveiled the transformative influence of innovation culture in amplifying the 7PS's impact. The methodological innovation lies in strategically applying the fuzzy analytic hierarchy process (AHP), assigning priority weights to 7PS criteria, and identifying culture as the linchpin. This approach provided a robust framework for dissecting the complex interplay of emerging technologies, sustainable engineering, and cybersecurity. The study delves into the X.0 wave/age (X.0 = 5.0) theory, offering insights into the intricate dynamics of innovation, sustainability, and governance. Beyond academic discourse, this research informs practical strategies globally, particularly for small and medium-sized enterprises (SMEs) transitioning to SME 5.0/hybrid SMEs. Emphasizing inclusivity and diversity as catalysts for innovation, it scrutinizes contemporary challenges amid technological evolution and cybersecurity threats. Functioning as a visionary compass, the study elucidates the path to a 7PS sustainable future. It signifies a paradigm shift, transcending boundaries between knowledge domains. The fusion of the 7PS framework, X.0 wave theory, and fuzzy AHP navigates global governance, digital resilience, and cybersecurity, offering a transformative roadmap. This research contributes by substantiating the pivotal role of culture in emerging technologies, augmenting global tech-sustainable governance, fortifying digital resilience, and safeguarding cybersecurity.



    Cyber-physical system (CPS) is an emerging technology that integrates computation, communication, and physical devices. Introduction of network technology in CPS offers significant advantages in system efficiency, scalability, and maintainability. CPS is widely applied in various fields due to its robustness, high reliability, and fast operation speed [1,2,3]. Due to the close interaction among computation, sensing, communication, and actuation in CPS, it is highly susceptible to network security threats.Additionally, intelligent CPS presents new challenges and threats different from existing issues [4,5]. Notably, CPS closely integrated with national infrastructure can lead to immeasurable severe consequences if subjected to malicious attacks. Therefore, ensuring the secure operation of CPS-related devices is an urgent problem that needs to be addressed [6,7].

    There have been many security incidents of CPS in the world, which have brought huge losses [8,9]. In June 2010, Iran's nuclear facilities were attacked by the Stuxnet virus, which seriously damaged nuclear power plants and other facilities, seriously jeopardizing Iran's nuclear security. In 2014, the Havex Trojan attacked numerous European industrial manufacturing systems. In addition to attacks on industrial systems, attacks on the power grid also occur frequently. In 2015, the Ukrainian power grid suffered a Black-Energy attack. In 2016, the Israeli power grid suffered a serious cyber attack, and in 2019, several South American countries suffered a cyber attack on the power system. An attack on the power grid would lead to widespread power outages, which would render factories inoperable and infrastructure paralyzed, causing serious inconvenience and impact to society.

    In recent years, scholars have conducted extensive research on the security of CPSs. Attack detection is one of the important strategies to ensure the safe operation of CPS, aiming to identify malicious behaviors such as network attacks and take appropriate countermeasures as early as possible to minimize or prevent significant losses [10,11]. As the complexity of attacks in CPS increases, traditional anomaly detection methods have limitations and require the design of detection algorithms with specific characteristics for a particular domain [12,13]. Reference [14] tackles the design problem of intrusion detection systems by creatively combining feature-based intrusion detection system (SIDS) and anomaly-based intrusion detection system (AIDS) to form an improved stacked ensemble algorithm (ISEA). This algorithm significantly reduces the false positive rate (FPR) through a false positive elimination strategy (FPES). Reference [15] argues that in the era of Industry 4.0, a layered and distributed approach is required for intrusion detection. This approach includes perception-execution layer monitoring based on Kalman filters, network transmission layer monitoring based on recursive Gaussian mixture models, and application control layer monitoring based on sparse deep belief network models. It enables comprehensive and efficient identification of covert attacks and ensures security protection. Reference [16] proposes a federated deep learning scheme to address the attack problem in large-scale and complex industrial networked physical systems. This scheme utilizes a deep learning-based intrusion detection model combined with federated learning framework and secure communication protocols to enhance the privacy of industrial CPS while ensuring resilience against network threats.

    Data tampering attacks are a prevalent and typical type of network attack targeting CPSs. They have also gained widespread attention in recent years[13,17,18]. The main method of data tampering attacks is to manipulate the data transmitted in the network, affecting the estimation and control center of CPS, leading to incorrect judgments or decisions, and issuing erroneous instructions, which may result in abnormal or even damaged physical devices[19,20,21]. Such attacks are often difficult to be detected by existing intrusion detection systems, thus they can quietly penetrate CPS systems and affect their stable operation[22,23].

    In recent years, the detection algorithms for data tampering attacks have received attention, and some scholars have conducted in-depth analysis and research on these attacks. Reference [24] proposes a solution to mitigate the computational cost and enhance privacy for smart grid aggregation faced with deletion and tampering attacks, targeted specifically at data tampering attacks. Reference [25] addresses firmware tampering attack defense and forensics issues by designing a detection method based on joint testing action groups and memory comparison to detect firmware tampering attacks. Reference [26] addresses the problem of the χ2 detector being difficult to detect false data injection attacks with white noise. It proposes a novel summation (SUM) detector that not only utilizes current compromise information but also collects all historical information to reveal the threat. It also has good identification for improved false data injection. Reference [27] studies the identification problem of finite impulse response (FIR) systems with binary measurements under data tampering, and the optimal attack strategy and defense method are given. Reference [28] introduces a novel secure key aggregation searchable encryption scheme and anti-tampering blockchain technology to propose a data sharing system that selectively shares and retrieves vehicle sensor data, detecting unauthorized data tampering attacks.

    This paper focuses on the data tampering attack problem in binary quantization FIR systems. Under the framework of system identification, a novel algorithm is designed to solve the system parameters and attack strategies using the maximum likelihood method and binary measurement data. The computation method is also provided. To begin, the maximum likelihood function of the measurement data is established. Then, parameter estimation algorithms are proposed for both known and unknown attack strategies. The closeness between the estimated system parameter values obtained from this estimation algorithm and the true values depends on the sample data size and whether the attack strategy is known or unknown. In the case of an unknown attack strategy, the difficulty in algorithm design increases due to the coupling between unknown parameters and attack strategies. The unknown variables in the maximum likelihood function are simplified to the system of equations. The Newton-Raphson iteration method is used to train the back propagation neural network (BPNN), and the attack strategy is estimated in advance. The estimated value of the attack strategy is then substituted into the algorithm to obtain the unknown parameter estimates. The results obtained from the algorithm show that with a small sample data size, the estimation algorithm produces large fluctuations in the solved system parameters. However, as the sample data size increases, the estimated values of the system parameters tend to become closer to the true values.

    The structure of this paper is as follows. Section 2 describes the data tampering detection problem in binary quantization FIR systems; Section 3 presents the expression of the maximum likelihood function of the system; Section 4 discusses the use of maximum likelihood estimation to solve the system parameters in the case of a known attack strategy; Section 5 discusses the step-by-step solution of system parameters and attack strategies in the case of an unknown attack strategy; Section 6 validates the estimation algorithm through numerical simulations; and Section 7 provides a summary and outlook for this paper.

    Consider a single-input single-output discrete-time FIR system:

    yk=a1uk+a2uk1++anukn1+dk=ϕTkθ+dk,k=1,2,, (1)

    where uk is the quantized system input and its possible value is in {μ1,μ2,,μr}, i.e., uk{μ1,μ2,,μr}; ϕk=[uk,,ukn1]T is the regression vector composed of quantized inputs, since uk can only take r different values, ϕk has l=rn possible values, which can be represented as π1,π2,,πl, that is, ϕk{π1,π2,,πl}; θ=[a1,,an]T is the unknown parameters of the system; dk is the system noise; yk is the system output, measured by a binary sensor with threshold C(,), and it can be represented by an indicator function as:

    s0k=I{ykC}={1,ykC;0,else. (2)

    From here on, the superscript T denotes the transpose of a matrix or vector.

    As shown in Figure 1, s0k is transmitted through a communication network to a data center, but it is susceptible to data tampering attacks during the communication process. The data received by the data center is denoted as sk, and its relationship with s0k is as follows:

    {Pr(sk=1|s0k=0)=p0;Pr(sk=0|s0k=1)=p1. (3)
    Figure 1.  System block diagram.

    The above equation essentially describes a data tampering attack strategy, which is denoted as (p0,p1).

    In this paper, a maximum likelihood estimation method is used to provide an estimation algorithm for the unknown parameters θ, and the convergence performance of the algorithm is also analyzed.

    Assumption 1. The system noise {dk} is an independent and identically distributed (i.i.d.) sequence of normal random variables with zero mean and variance σ2, and its probability distribution function and probability density function are denoted as F() and f(), respectively.

    Remark 1. 1) This paper is concerned with the binary observation. For the case of multi-threshold quantization, it can be converted into multiple binary values for processing [29]. 2) The attack process here is independent, and the existing literature often studies the cases where it is dependent and modeled as Markov processes [30]. The method in this paper can provide reference for the case of nonindependent attack process.

    Maximum likelihood estimate is a commonly used parameter estimation method in statistics that estimates model parameters by maximizing the likelihood function of the sample data. This section presents the maximum likelihood function of the data received at the receiving center, laying the foundation for the subsequent algorithm design.

    From Eqs (1) and (2), we can determine the probability of s0k=1 being equal to

    Pr(ykC)=Pr(ϕTkθ+dkC)=Pr(dkCϕTkθ)=F(CϕTkθ). (4)

    Combining this with Eq (3) and using the law of total probability, we obtain:

    Pr(sk=1)=Pr(sk=1|s0k=0)Pr(s0k=0)+Pr(sk=1|s0k=1)Pr(s0k=1)=p0Pr(yk>C)+(1p1)Pr(ykC)=p0(1F(CϕTkθ))+(1p1)F(CϕTkθ)def=gk. (5)

    Then,

    Pr(sk)=gskk(1gk)(1sk). (6)

    Based on Eq (5), gk can be simplified as:

    gk=(1p0p1)F(CϕTkθ)+p0. (7)

    Hence, for a data length of N, the maximum likelihood function of s1,s2,,sN is:

    L(θ|s1,s2,,sN)=Pr(s1,s2,,sN)=Pr(s1)Pr(s2)Pr(sN)=Nk=1gskk(1gk)(1sk). (8)

    The principle of maximum likelihood estimation is based on the intuitive idea that a parameter is the most reasonable estimate if it gives the greatest probability that the sample data will occur. For the maximum likelihood function, the parameters at its maximum value are called the maximum likelihood estimates. In this section, the attack strategy (p0,p1) is assumed to be known. Two functions are defined as follows:

    h1(x)=(1p0p1)f(Cx)(1p0p1)F(Cx)+p0,h2(x)=(1p0p1)f(Cx)(p0+p11)F(Cx)+1p0. (9)

    Let

    θlnL(s1,s2,,sN)=0. (10)

    The solution of the equation is denoted as ˆθN=ˆθN(s1,s2,,sN), which is the maximum likelihood estimate of θ.

    Since Eq (10) is highly nonlinear, an explicit solution generally doesn't exist. Here, an approximate solution method is presented. Taking the logarithm of Eq (8), we have

    lnL(θ|s1,s2,,sN)=Nk=1[sklngk+(1sk)ln(1gk)]=Nk=1skln[F(CϕTkθ)(1p0p1)+p0]+Nk=1(1sk)ln[F(CϕTkθ)(p0+p11)+1p0]. (11)

    Taking the partial derivative of the above equation with respect to θ, we get

    θlnL(θ|s1,s2,,sN)=Nk=1sk(1p0p1)f(CϕTkθ)(ϕTk)(1p0p1)F(CϕTkθ)+p0+Nk=1(sk1)(1p0p1)f(CϕTkθ)(ϕTk)(p0+p11)F(CϕTkθ)+1p0. (12)

    By Eq (9), Eq (12) can be expressed as:

    θlnL(θ)=Nk=1skh1(ϕTkθ)(ϕTk)+Nk=1(sk1)h2(ϕTkθ)(ϕTk). (13)

    Since ϕTk can take the values π1,π2,,πl, grouping the above expression based on these values, we can rearrange it as:

    θlnL(θ)=Nk=1,ϕTk=π1skh1(π1θ)(π1)+Nk=1,ϕTk=π1(sk1)h2(π1θ)(π1)+Nk=1,ϕTk=π2skh1(π2θ)(π2)+Nk=1,ϕTk=π2(sk1)h2(π2θ)(π2)++Nk=1,ϕTk=πlskh1(πlθ)(πl)+Nk=1,ϕTk=πl(sk1)h2(πlθ)(πl). (14)

    In Eq (15), if we have

    Nk=1,ϕTk=πiskh1(πiθ)+Nk=1,ϕTk=πi(sk1)h2(πiθ)=0,i=1,2,,l, (15)

    then θlnL(θ)=0. Thus, the problem of solving the equation θlnL(θ)=0 is reduced to solving the system of Eq (15).

    By rearranging (15), we get

    [h1(πiθ)+h2(πiθ)]Nk=1,ϕTk=πisk=h2(πiθ)Nk=1,ϕTk=πi1.

    As a result, we obtain

    Nk=1skI{ϕTk=πi}Nk=1I{ϕTk=πi}=h2(πiθ)h1(πiθ)+h2(πiθ)=H(πiθ), (16)

    where H(x)=h2(x)h1(x)+h2(x), h1(x), and h2(x) are given by (9). Let the H(x) reverse function be H1(x), and we have

    H(x)=(1p0p1)F(Cx)+p0H(x)p0=(1p0p1)F(Cx)H(x)p01p0p1=F(Cx) (17)
    F1(H(x)p01p0p1)=Cx. (18)

    Therefore, from (16), we have

    πiθ=CF1(Nk=1skI{ϕTk=πi}Nk=1I{ϕTk=πi}p01p0p1),i=1,2,,l.

    Expressing the above equation set in matrix form, we have

    [π1πl]θ=[CF1(Nk=1skI{ϕTk=π1}Nk=1I{ϕTk=π1}p01p0p1)CF1(Nk=1skI{ϕTk=πl}Nk=1I{ϕTk=πl}p01p0p1)]. (19)

    Let Φ=[πT1,πT2,,πTl]T, ηN,i=CF1(Nk=1skI{ϕTk=πi}Nk=1I{ϕTk=πi}p01p0p1), i=1,2,,l. The maximum likelihood estimate of θ is obtained as:

    ˆθN=Φ+[ηN,1,,ηN,l]T, (20)

    where + denotes the Moore-Penrose inverse of the matrix.

    Remark 2. From the above, it can be seen that the distribution function of the system noise plays an important role in the algorithm design. For the unknown case, an estimation algorithm can be designed to estimate it, and then the estimated value can be used instead of the true value, so as to realize the adaptive identification of unknown parameters [29].

    Theorem 1. Consider the system (1) and the binary observation (2) under the data tampering attack (3). If Assumption 1 holds, the matrix Φ generated by the system input is full rank, and Nk=1I{ϕTk=πi} as N for i=1,2,,l, then the maximum likelihood-based parameter estimate ˆθN given by (20) converges strongly to the true value θ, i.e.,

    ˆθNθ,N,w.p.1.

    Proof. By (5), it is known that

    E(skI{ϕTk=πi})=p0(1F(Cπiθ))+(1p1)F(Cπiθ)=p0+(1p0p1)F(Cπiθ).

    According to the Law of Large Numbers, for i=1,2,,l, we have

    Nk=1skI{ϕTk=π1}Nk=1I{ϕTk=π1}p0+(1p0p1)F(Cπiθ),N, (21)

    which implies that

    CF1(Nk=1skI{ϕTk=π1}Nk=1I{ϕTk=π1}p01p0p1)πiθ,N. (22)

    Since Φ is full rank, from (19) and (20), the theorem is proved.

    In the previous section, an identification algorithm with unknown parameters was designed under the assumption of known attack strategies. In the case of unknown attack strategies, the design of the identification algorithm becomes more difficult. This is mainly because the unknown parameters and attack strategies are coupled together. This section primarily addresses this problem.

    Using the maximum likelihood function, Eq (11) is used to obtain the maximum likelihood estimates of θ, p0, and p1, which results in a system of equations consisting of n+2 equations involving θ, p0, and p1. Solving this system of equations yields the estimates ˆθ, ^p0, and ^p1. However, solving a system of n+2 dimensional equations numerically will be challenging and time-consuming. The solution process is illustrated in Figure 2, divided into three steps below.

    Figure 2.  Solution steps.

    Step 1: Construction of system of equations for θ and (p0,p1)

    Based on the analysis process, when the attack strategies are known, the likelihood function L(θ|s1,s2,,sN) is first logarithmically transformed into a logarithmic form and then differentiated. From Eqs (16) and (17), it can be determined that the problem of solving the extremum of the maximum likelihood function is equivalent to the problem of solving the following system of equations:

    {F(Cπ1θ)=Nk=1skI{ϕTk=π1}Nk=1I{ϕTk=π1}p01p0p1;F(Cπ2θ)=Nk=1skI{ϕTk=π2}Nk=1I{ϕTk=π2}p01p0p1;F(Cπlθ)=Nk=1skI{ϕTk=πl}Nk=1I{ϕTk=πl}p01p0p1. (23)

    If πiθ is treated as an unknown variable, then the above system of equations has l+2 unknowns but only l equations. Therefore, it is generally unsolvable. To address this, the correlation between πi is utilized, which leads to the second step.

    Step 2: Solve the system of equations for θ and (p0,p1), and obtain the estimated values of the attack strategies (ˆpN,0,ˆpN,1)

    Let the number of maximal linearly independent sets of π1,π2,,πl be denoted as l0. Without loss of generality, assume that π1,π2,,πl0 form a maximal linearly independent set of π1,π2,,πl. Then, each πi can be expressed as a linear combination of π1,π2,,πl0, as follows:

    πi=l0j=1αi,jπj,i=1,2,,l. (24)

    Substituting the above equation into Eq (23), we get

    {F(Cl0j=1α1,jπjθ)=Nk=1skI{ϕTk=π1}Nk=1I{ϕTk=π1}p01p0p1;F(Cl0j=1α2,jπjθ)=Nk=1skI{ϕTk=π2}Nk=1I{ϕTk=π2}p01p0p1;F(Cl0j=1αl,jπjθ)=Nk=1skI{ϕTk=πl}Nk=1I{ϕTk=πl}p01p0p1. (25)

    The above system of equations consists of l equations, and the number of unknowns is reduced to l0+2. Solving the above system of equations, denoted as g(s1,s2,,sN)=(g1,g2,,gl0+2), which gives the estimated values of π1θ,π2θ,,πl0θ, and (p0,p1) as follows:

    ^π1θN=g1(s1,s2,,sN); (26)
    (27)
    ^πl0θN=gl0(s1,s2,,sN); (28)
    ˆpN,0=gl0+1(s1,s2,,sN); (29)
    ˆpN,1=gl0+2(s1,s2,,sN). (30)

    Equations (29) and (30) provide the estimated values of the attack strategies.

    The most critical part is how to obtain the expression of g(s1,s2,,sN), which can be divided into two cases. One case is when the system of Eq (25) has an analytical solution, in which case the expression of g() can be obtained through mathematical operations. The other case is when (25) does not have an analytical solution, in which case the expression of g() can be approximated using numerical methods and neural networks. The process is as follows.

    Consider the following system of equations:

    {F(Cl0j=1α1,jxj)=β1xl0+11xl0+1xl0+2;F(Cl0j=1α2,jxj)=β2xl0+11xl0+1xl0+2;F(Cl0j=1αl,jxj)=βlxl0+11xl0+1xl0+2, (31)

    where X=[x1,x2,,xl0+2]TRl0+2 is the unknown variable, and β1,β2,,βl are known parameters.

    Given a step size Δ(0,1), we uniformly sample the interval [0,1] to obtain a set

    Γ={(j1)Δ:j=1,2,,1Δ}, (32)

    where denotes the ceiling function. We randomly take any element β=[β1,β2,,βl] from Γl and substitute it into Eq (31). Then, we solve the Eq (31) using the Newton-Raphson iteration method to obtain the solution X=X(β). Specifically, let ϖi(x1,x2,,xl0+2)=F(Cl0j=1αi,jxj)βixl0+11xl0+1xl0+2, i=1,2,,l. Then, the system of Eq (31) can be equivalently written as:

    Ω(X)=[ϖ1(x1,x2,,xl0+2)ϖ2(x1,x2,,xl0+2)ϖl(x1,x2,,xl0+2)]=0. (33)

    The Jacobian matrix of the above equations is given by:

    J(X)=[ϖ1x1ϖ1xl0+2ϖlx1ϖlxl0+2]=[α1,1f(Cl0j=1α1,jxj)1β1xl0+2(1xl0+1xl0+2)2β1+xl0+1(1xl0+1xl0+2)2αl,1f(Cl0j=1α1,jxj)1βlxl0+2(1xl0+1xl0+2)2βl+xl0+1(1xl0+1xl0+2)2]. (34)

    Given an initial value X0, let Xt=[x{t}1,x{t}2,,x{t}l0+2]T represent the zero of the system of equations for the solution of Eq (33) obtained at the t-th iteration. Then,

    Xt=Xt1J1(Xt1)Ω(Xt1). (35)

    Repeat the above process and iteratively calculate until is satisfied, where X(\beta) = X_t is the solution to the system of Eq (31), \|\cdot\| denotes the norm of a vector, and \varepsilon > 0 is a given constant called the iteration stopping tolerance.

    Repeat the above process, letting \boldsymbol{\beta} traverse \Gamma^l , and simultaneously obtaining the solution X = X(\boldsymbol{\beta}) for Eq (31). This way, a set of data \{\boldsymbol{\beta}, X(\boldsymbol{\beta}): \boldsymbol{\beta}\in\Gamma^l\} is obtained. Treat \boldsymbol{\beta} as the input and X(\boldsymbol{\beta}) as the output of a BPNN*, and train the neural network as g^0(\beta_1, \beta_2, \ldots, \beta_l) . As a result, g(s_1, s_2, \ldots, s_N) can be computed as follows:

    *Here we choose BPNN as the fitting algorithm, mainly to show our thinking and method. In specific use, one can also choose other regression algorithms, such as random forest and so on.

    \begin{equation} g(s_1,s_2,\ldots,s_N) = g^0(\frac { \sum_{k = 1}^N s_k I_{\{\phi_k^T = \pi_1\}} } {\sum_{k = 1}^N I_{\{\phi_k^T = \pi_1\}}},\ldots,\frac { \sum_{k = 1}^N s_k I_{\{\phi_k^T = \pi_l\}} } {\sum_{k = 1}^N I_{\{\phi_k^T = \pi_l\}}}). \end{equation} (36)

    The above process can be summarized into the following algorithm:

    Algorithm 1 Algorithm for computing function g(\ldots)
    1. Initial values: sample step size \Delta of (0, 1) ; set D = \emptyset ; iteration tolerance \varepsilon > 0 for stopping Newton-Raphson iteration.
    2. Set \Gamma based on (32), then obtain set \Gamma^ {l} with m elements denoted as \boldsymbol{\beta}_1 , \boldsymbol{\beta}_2, \ldots, \boldsymbol{\beta}_m
    3. Loop: i = 1 , 2 , \ldots , m
      3.1. Substitute \boldsymbol{\beta}_i into system of Eq (31)
      3.2. Initialize X_0 , and use Newton-Raphson iteration to solve (31), obtain solution X_i = X_i(\boldsymbol{\beta}_i)
      3.3. Update data set D = D\cup \{(\boldsymbol{\beta}_i, X_i)\}
    4. End loop
    5. Train the BPNN g^0(\beta_1, \beta_2, \ldots, \beta_l) based on data set D
    6. Calculate g(\ldots) based on (36)

    Step 3: Obtain the estimated values of the unknown parameters \widehat{\theta}_N

    Express the \widehat{\pi_1\theta} _N, \widehat{\pi_2\theta}_N, \ldots, \widehat{\pi_{l_0}\theta}_N obtained in Step 2 in vector form. Based on Eqs (26) and (28), we have:

    \left[ \begin{array}{c} \pi_1 \\ \vdots \\ \pi_{l_0} \\ \end{array} \right]\widehat{\theta}_N = \left[ \begin{array}{c} g_1(s_1,s_2,\ldots,s_N) \\ \vdots \\ g_{l_0}(s_1,s_2,\ldots,s_N)\\ \end{array} \right].

    Letting [\pi_1^T, \ldots, \pi^T_{l_0}]^T = \overline{\Phi} , we can obtain the estimate of \theta as:

    \begin{equation} \widehat{\theta}_N = \overline{\Phi}^+\left[ \begin{array}{c} g_1(s_1,s_2,\ldots,s_N) \\ \vdots \\ g_{l_0}(s_1,s_2,\ldots,s_N)\\ \end{array} \right]. \end{equation} (37)

    In the above equation, the expressions of g_1, \ldots, g_{l_0} may contain the attack strategies (p_0, p_1) as parameters. In this case, replace them with their estimated values from (29) and (30).

    Theorem 2. Under the condition of Theorem 1, if the matrix \overline{\Phi} generated by the system input is full rank, the function g(\cdot) given by Algorithm 1 is the solution to the Eq (33), then the maximum likelihood-based parameter estimate \widehat{\theta}_N given by (37) converges strongly to the true value \theta , i.e.,

    \widehat{\theta}_N\to\theta,\; \; N\to\infty,\; \; {\mbox{w.p.1}}.

    Proof. According to the conditions of the theorem and by (23) and (25), it is known that the solution to (31) is

    \begin{eqnarray} X & = & X([p_0+(1-p_0-p_1)F(C - \pi_1\theta ),\ldots,p_0+(1-p_0-p_1)F(C - \pi_l\theta )]^T) \cr & = & [\pi_1\theta,\ldots,\pi_{l_0}\theta]^T. \end{eqnarray} (38)

    From (21), we have

    \begin{eqnarray*} && g^0(\frac { \sum_{k = 1}^N s_k I_{\{\phi_k^T = \pi_1\}} } {\sum_{k = 1}^N I_{\{\phi_k^T = \pi_1\}}},\ldots,\frac { \sum_{k = 1}^N s_k I_{\{\phi_k^T = \pi_l\}} } {\sum_{k = 1}^N I_{\{\phi_k^T = \pi_l\}}}) \\ &\to& g^0(p_0+(1-p_0-p_1)F(C - \pi_1\theta ),\ldots,p_0+(1-p_0-p_1)F(C - \pi_l\theta )),\; \; N\to\infty, \end{eqnarray*}

    which together with (36) gives

    g(s_1,\ldots,s_N)\to g^0(p_0+(1-p_0-p_1)F(C - \pi_1\theta ),\ldots,p_0+(1-p_0-p_1)F(C - \pi_l\theta ))

    as N\to\infty . Combining the above and (38), by (37), it can be seen that

    \begin{eqnarray} \widehat{\theta}_N = \overline{\Phi}^+\left[ \begin{array}{c} g_1(s_1,s_2,\ldots,s_N) \\ \vdots \\ g_{l_0}(s_1,s_2,\ldots,s_N)\\ \end{array} \right]\to \overline{\Phi}^+\left[ \begin{array}{c} \pi_1\theta\\ \vdots \\ \pi_{l_0}\theta\\ \end{array} \right],\; \; N\to\infty. \end{eqnarray} (39)

    Considering that \overline{\Phi} is full rank, the proof is completed.

    Consider the system

    \begin{align*} \begin{cases} y_k\; \; = & \phi_k^T \theta + d_k ; \\ s_k^0\; \; = & I_{\{y_k \leq C\}} ; \end{cases} \end{align*}

    with the system parameters \theta = [a_1, \dots, a_n]^T = [-2, 4, 8]^T and the system input u_k \in \{1, 3, 5\} ; the threshold for the binary sensor output is C = 30 ; and the system noise follows an independent and identically distributed normal random variable sequence d_k \sim (0, 40^2) . The system output is transmitted to the data center through a communication network and is subjected to data tampering attacks with attack strategy (p_0, p_1) = (0.4, 0.2) .

    The data center receives the tampered data s_k after the original data s_k^0 has been attacked. The relationship between the data is shown in Figure 3. The original data s_k^0 has been randomly altered.

    Figure 3.  Comparison between original data and data after random attacks.

    Experiments are conducted on algorithms (10)–(22) to compute the estimated system parameter values \widehat \theta_N , where the length of the data sample is N = 80,000 . The results are shown in Figure 4, which indicate that: when the data sample size N is small, the estimated parameter values \widehat \theta_N have large convergence biases; When the data sample size N exceeds a critical value, the estimated parameter values \widehat \theta_N are close to the true values \theta ; as the data sample size N further increases, the deviation between the estimated parameter values \widehat \theta_N and the true values decreases.

    Figure 4.  Estimation of system parameters when the attack strategy is known.

    Experiments are conducted on algorithms (23)–(39) for T = 150 times, and the average results of each experiment are computed to obtain \widehat \theta_N , p_0 , and p_1 , where the length of the data sample is N = 60,000 . The results are shown in Figures 5 and 6, which indicate that: As the data sample size N increases, the estimated system parameter values \widehat \theta_N approach the true values, and the estimated attack strategy values \widehat p_0 and \widehat p_1 also approach the true values. Moreover, due to the large number of experiments T , the convergence of each parameter improves as the data sample size N increases.

    Figure 5.  Estimation of system parameters when the attack strategy is unknown.
    Figure 6.  Estimation of the attack strategy when the attack strategy is unknown.

    In the framework of system identification, this paper carried out the research of security issue based on the maximum likelihood estimation method. For FIR systems with binary observations and data tampering attacks, the parameter estimation algorithms are proposed in the two cases of known and unknown attack strategy, and the convergence condition and convergence proof of these algorithms are given.

    The maximum likelihood estimation is a very classical and effective method. This paper explores its application in CPS security identification. In the future, this method can be extended to nonlinear systems, multi-threshold observations, colored noise, and other more general cases.

    The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

    This research was supported in part by the National Natural Science Foundation of China (62173030) and in part by the Beijing Natural Science Foundation (4222050).

    The authors declare there is no conflict of interest.



    [1] Mardani A, Zavadskas EK, Streimikiene D, et al. (2016) Using fuzzy multiple criteria decision making approaches for evaluating energy saving technologies and solutions in five star hotels: A new hierarchical framework. Energy 117: 131–148. https://doi.org/10.1016/j.energy.2016.10.076 doi: 10.1016/j.energy.2016.10.076
    [2] Dobson A (2007) Environmental citizenship: Towards sustainable development. Sustainable Dev 15: 276–285. https://doi.org/10.1002/sd.344 doi: 10.1002/sd.344
    [3] Littig B, Griessler E (2005) Social sustainability: a catchword between political pragmatism and social theory. Int J Sust Dev 8: 65–79. https://doi.org/10.1504/IJSD.2005.007375 doi: 10.1504/IJSD.2005.007375
    [4] Hopwood B, Mellor M, O'Brien G (2005) Sustainable development: mapping different approaches. Sustainable Dev 13: 38–52. https://doi.org/10.1002/sd.244 doi: 10.1002/sd.244
    [5] Dobin C (2008) Measuring innovation culture in organizations: The development of a generalized innovation culture construct using exploratory factor analysis. Eur J Innov Manag 11: 539–559. https://doi.org/10.1108/14601060810911156 doi: 10.1108/14601060810911156
    [6] Eizenberg E, Jabareen Y (2017) Social sustainability: A new conceptual framework. Sustainability 9: 68. https://doi.org/10.3390/su9010068 doi: 10.3390/su9010068
    [7] Mohammadian HD, Langari ZG, Kamalian AR, et al. (2023) Promoting sustainable global innovative smart governance through the 5 th wave theory, via Fuzzy AHP for future SMEs (SME 5.0/hybrid SMEs). AIMS Geosci 9: 123–152. https://doi.org/10.3934/geosci.2023008 doi: 10.3934/geosci.2023008
    [8] Goyal S, Garg D, Luthra S (2021) Sustainable production and consumption: Analysing barriers and solutions for maintaining green tomorrow by using fuzzy-AHP—fuzzy-TOPSIS hybrid framework. Environ Dev Sustain 23: 16934–16980. https://doi.org/10.1007/s10668-021-01357-5 doi: 10.1007/s10668-021-01357-5
    [9] Jamwal A, Agrawal R, Sharma M (2023) Challenges and opportunities for manufacturing SMEs in adopting industry 4.0 technologies for achieving sustainability: Empirical evidence from an emerging economy. Oper Manag Res. https://doi.org/10.1007/s12063-023-00428-2 doi: 10.1007/s12063-023-00428-2
    [10] Mohammadian HD, Langari ZG, Castro M, et al. (2022) A Study of MOOCs Project (MODE IT), Techniques, and Know How-Do How Best Practices and Lessons from the Pandemic through the Tomorrow Age Theory. 2022 IEEE Learning with MOOCS (LWMOOCS), 179–191. https://doi.org/10.1109/LWMOOCS53067.2022.9927790
    [11] Mohammadian HD, Wittberg V, Castro M, et al. (2020) The 5th Wave and i-Sustainability Plus Theories as Solutions for SocioEdu Consequences of Covid-19. 2020 IEEE Learning With MOOCS (LWMOOCS), 118–123. https://doi.org/10.1109/LWMOOCS50143.2020.9234360
    [12] Mohammadian HD, Shahhoseini H, Castro M, et al. (2020) Digital transformation in academic society and innovative ecosystems in the world beyond Covid19-pandemic with using 7PS model for IoT. 2020 IEEE Learning With MOOCS (LWMOOCS), 112–117. https://doi.org/10.1109/LWMOOCS50143.2020.9234328
    [13] Mohammadian HD, Langari ZG, Castro M, et al. (2022) Smart Governance for Educational Sustainability: Hybrid SMEs & the 5 th wave theory Towards Mapping the Future Education in Post-Covid Era. 2022 IEEE Global Engineering Education Conference (EDUCON), 1916–1926. https://doi.org/10.1109/EDUCON52537.2022.9766580
    [14] Mohammadian HD, Bakhtiari AK, Castro M, et al. (2022) The Development of a Readiness Assessment Framework for Tomorrow's SMEs/SME 5.0 for Adopting the Educational Components of future of I4.0. 2022 IEEE Global Engineering Education Conference (EDUCON), 1699–1708. https://doi.org/10.1109/EDUCON52537.2022.9766580
    [15] Mohammadian HD, Castro M, Wittberg V (2022) Doost Sme Ranking Model (DSRM) for the Edu. SMEs Development, based on Guter Mittelstand, MOOCs & Related Projects as German Best Practice Towards: Future Edu Readiness to Achieve SME 5.0. 2022 IEEE Learning with MOOCS (LWMOOCS), 161–178. https://doi.org/10.1109/LWMOOCS53067.2022.9927831
    [16] Mohammadian HD, Langari ZG, Wittberg V (2022) Cyber Government for Sustainable Governance: Examining Solutions to Tomorrow's Crises and Implications through the 5 th wave theory, Edu 5.0 concept, and 9PSG model. 2022 IEEE Global Engineering Education Conference (EDUCON), 1737–1746. https://doi.org/10.1109/EDUCON52537.2022.9766774
    [17] Mohammadian HD (2022) Mapping the Future SMEs' HR Competencies via IoE Technologies and 7PS Model Through the Fifth Wave Theory, Chemma, N, El Amine Abdelli M, Awasthi A, Mogaji E, Ed., Management and Information Technology in the Digital Era: Challenges and Perspectives, Emerald Publishing Limited, 141–171. https://doi.org/10.1108/S1877-636120220000029010
    [18] Spangenberg JH (2004) Reconciling sustainability and growth: criteria, indicators, policies. Sustainable Dev 12: 74–86. https://doi.org/10.1002/sd.229 doi: 10.1002/sd.229
    [19] Hervás-Oliver JL, Parrilli MD, Rodríguez-Pose A, et al. (2021) The drivers of SME innovation in the regions of the EU. Res Policy 50: 104316. https://doi.org/10.1016/j.respol.2021.104316 doi: 10.1016/j.respol.2021.104316
    [20] Shi L, Han L, Yang F, et al. (2019) The evolution of sustainable development theory: Types, goals, and research prospects. Sustainability 11: 7158. https://doi.org/10.3390/su11247158 doi: 10.3390/su11247158
    [21] Camilleri MA (2022) Strategic attributions of corporate social responsibility and environmental management: The business case for doing well by doing good! Sustainable Dev 30: 409–422. https://doi.org/10.1002/sd.2256 doi: 10.1002/sd.2256
    [22] Porter ME, Linde CVD (1995) Toward a new conception of the environment-competitiveness relationship. J Econ Perspect 9: 97–118. https://doi.org/10.1257/jep.9.4.97 doi: 10.1257/jep.9.4.97
    [23] Tang M, Walsh G, Lerner D, et al. (2018) Green innovation, managerial concern and firm performance: An empirical study. Bus Strateg Environ 27: 39–51. https://doi.org/10.1002/bse.1981 doi: 10.1002/bse.1981
    [24] Dempsey N, Bramley G, Power S, et al. (2011) The social dimension of sustainable development: Defining urban social sustainability. Sustainable Dev 19: 289–300. https://doi.org/10.1002/sd.417 doi: 10.1002/sd.417
    [25] Takalo SK, Tooranloo HS, Shahabaldini Parizi Z (2021) Green innovation: A systematic literature review. J Cleaner Prod 279: 122474. https://doi.org/10.1016/j.jclepro.2020.122474 doi: 10.1016/j.jclepro.2020.122474
    [26] El Amine Abdelli M, Sghaier A, Akbaba A, et al. (2023) Smart Cities for Sustainability: Approaches and Solutions, Emerald Publishing Limited, Leeds, 32: 233–242. https://doi.org/10.1108/S1877-636120230000033017
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