Loading [MathJax]/jax/output/SVG/jax.js
Review

Analysis and prediction of railway accident risks using machine learning

  • The harmful consequences of rail accidents, which sometimes lead to loss of life and the destruction of the system and its environment, are at the basis of the implementation of a "experience feedback" (REX) system considered as the essential means to promote the improvement of safety. REX seeks to identify adverse events with a view to highlighting all the causes that contributed to the occurrence of a particular accident and therefore to avoid at least the reproduction of new accidents and similar incidents. Accident and incident investigation reports provide a wealth of informative information for accident prevention. It would be appropriate to exploit these reports in order to extract the relevant information and suggest ways to avoid the reproduction of adverse events. In this context, knowledge of the causes of accidents results mainly from the contribution of lessons learned and experiences gained, whether positive or negative. However, the exploitation of information and the search for lessons from past events is a crucial step in the REX process. This process of analyzing and using data from experience can be facilitated if there are methods and tools available to technical investigators. It seems advisable to consider the use of artificial intelligence (AI) techniques and in particular automatic learning methods in order to understand the origins and circumstances of accidents and therefore propose solutions to avoid the reproduction of similar insecurity events. The fact that the lessons one can learn from a REX depends on the experiences of the situations experienced in the past, constitutes in itself a key argument in favor of machine learning. Thus, the identification of knowledge about rail accidents and incidents and share them among REX actors constitute a process of learning sequences of undesirable events. The approach proposed in this manuscript for the prevention of railway accidents is a hybrid method built around several algorithms and uses several methods of automatic learning: Learning by classification of concepts, Rule-based machine learning (RBML) and Case-based reasoning (CBR).

    Citation: Habib Hadj-Mabrouk. Analysis and prediction of railway accident risks using machine learning[J]. AIMS Electronics and Electrical Engineering, 2020, 4(1): 19-46. doi: 10.3934/ElectrEng.2020.1.19

    Related Papers:

    [1] Pierre Failler, Claire Montocchio, Adeline Borot de Battisti , Thomas Binet, Jean-Philippe Maréchal, MyriamThirot . Sustainable financing of marine protected areas: the case of the Martinique regional marine reserve of “Le Prêcheur”
    . Green Finance, 2019, 1(2): 110-129. doi: 10.3934/GF.2019.2.110
    [2] Most Nilufa Khatun, Sandip Mitra, Md Nazirul Islam Sarker . Mobile banking during COVID-19 pandemic in Bangladesh: A novel mechanism to change and accelerate people's financial access. Green Finance, 2021, 3(3): 253-267. doi: 10.3934/GF.2021013
    [3] Yafei Wang, Jing Liu, Xiaoran Yang, Ming Shi, Rong Ran . The mechanism of green finance's impact on enterprises' sustainable green innovation. Green Finance, 2023, 5(3): 452-478. doi: 10.3934/GF.2023018
    [4] Reinhard Haas, Amela Ajanovic, Jasmine Ramsebner, Theresia Perger, Jaroslav Knápek, Jan W. Bleyl . Financing the future infrastructure of sustainable energy systems. Green Finance, 2021, 3(1): 90-118. doi: 10.3934/GF.2021006
    [5] Tõnis Mets, Piia Vettik-Leemet . Women in the sustainability new ventures in the digital era: Out from the shadow of the small country male-dominated startup ecosystem. Green Finance, 2024, 6(3): 383-406. doi: 10.3934/GF.2024015
    [6] Amanda-Leigh O'Connell, Johan Schot . Operationalizing transformative capacity: State policy and the financing of sustainable energy transitions in developing countries. Green Finance, 2024, 6(4): 666-697. doi: 10.3934/GF.2024026
    [7] Yicong Huang, Kaidong Yu, Chao Huang . Green finance engagement: An empirical study of listed companies on Chinese main board. Green Finance, 2023, 5(1): 1-17. doi: 10.3934/GF.2023001
    [8] Fu-Hsaun Chen . Green finance and gender equality: Keys to achieving sustainable development. Green Finance, 2024, 6(4): 585-611. doi: 10.3934/GF.2024022
    [9] Shahinur Rahman, Iqbal Hossain Moral, Mehedi Hassan, Gazi Shakhawat Hossain, Rumana Perveen . A systematic review of green finance in the banking industry: perspectives from a developing country. Green Finance, 2022, 4(3): 347-363. doi: 10.3934/GF.2022017
    [10] Mukul Bhatnagar, Sanjay Taneja, Ercan Özen . A wave of green start-ups in India—The study of green finance as a support system for sustainable entrepreneurship. Green Finance, 2022, 4(2): 253-273. doi: 10.3934/GF.2022012
  • The harmful consequences of rail accidents, which sometimes lead to loss of life and the destruction of the system and its environment, are at the basis of the implementation of a "experience feedback" (REX) system considered as the essential means to promote the improvement of safety. REX seeks to identify adverse events with a view to highlighting all the causes that contributed to the occurrence of a particular accident and therefore to avoid at least the reproduction of new accidents and similar incidents. Accident and incident investigation reports provide a wealth of informative information for accident prevention. It would be appropriate to exploit these reports in order to extract the relevant information and suggest ways to avoid the reproduction of adverse events. In this context, knowledge of the causes of accidents results mainly from the contribution of lessons learned and experiences gained, whether positive or negative. However, the exploitation of information and the search for lessons from past events is a crucial step in the REX process. This process of analyzing and using data from experience can be facilitated if there are methods and tools available to technical investigators. It seems advisable to consider the use of artificial intelligence (AI) techniques and in particular automatic learning methods in order to understand the origins and circumstances of accidents and therefore propose solutions to avoid the reproduction of similar insecurity events. The fact that the lessons one can learn from a REX depends on the experiences of the situations experienced in the past, constitutes in itself a key argument in favor of machine learning. Thus, the identification of knowledge about rail accidents and incidents and share them among REX actors constitute a process of learning sequences of undesirable events. The approach proposed in this manuscript for the prevention of railway accidents is a hybrid method built around several algorithms and uses several methods of automatic learning: Learning by classification of concepts, Rule-based machine learning (RBML) and Case-based reasoning (CBR).


    Chaos systems, as a category of nonlinear dynamical systems, are highly dependent on initial conditions, inherent randomness, and a continuous broad spectrum. These characteristics render chaotic systems particularly suitable for communication applications while presenting significant prospects in finance, chemistry, and biology[1,2,3,4,5]. Notably, chaotic systems have garnered considerable attention since the seminal work presented in [6]. A wide range of nonlinear dynamical systems can be expressed as chaotic Lur'e systems (CLS). Therefore, the synchronization problem related to CLS has become a hot topic in recent years[7]. To address the synchronization problem, various control strategies have been proposed, including adaptive control [8], sliding mode control [9], feedback control [10], and sampled-data control [11].

    Sampled-data control requires the system to provide state information only at specific sampling times, which endows it with low control cost, high efficiency, flexibility, and reliability. Over the past few decades, advancements in network communication and associated digital technologies have led to significant progress in sampled-data control systems[12,13]. Consequently, it has been widely used in the field of control [14,15,16,17,18,19]. Many excellent results have also been obtained in the synchronization problem of CLS[20,21,22]. In Reference [6], sampling control is introduced into the CLS, deriving global asymptotic synchronization conditions. An input delay method utilizing the Lyapunov functional to establish synchronization conditions in Reference [23]. Subsequently, References [24,25] further investigate master-slave synchronization of CLS considering system delays. However, these studies do not fully account for the characteristics of the CLS and available information during the sampling process. Therefore, system information was thoroughly considered in References [26,27]. Based on this information, the Lyapunov functional was augmented, and the results were further optimized using linear matrix inequalities (LMIs). However, the augmented function did not sufficiently consider the sampling process's characteristics, and there is still potential for improving the resulting outcomes.

    Only occupying the network channel at the sampling moment can significantly reduce a sampling system's communication pressure and computational burden. Thus, obtaining a more extensive sampling interval is the main issue in the field of sampled-data control, and it is also a critical index that evaluates the conservativeness of the synchronization criterion of CLS [28,29,30]. Two main approaches to achieving a more extensive sampling interval are adopting appropriate Lyapunov functionals and bounding its derivative with lower conservativeness. The field of functionals has seen significant advancements, starting with basic forms of Lyapunov functionals [31], progressing to time-dependent and discontinuous Lyapunov functionals [32], and culminating in the recent development of two-sided looped functionals [33,34,35]. Integral inequalities play a crucial role in limiting the quadratic integral term within the functional derivative. With the development of Jensen's inequality, Wirtinger-based inequality, free-weighting matrix inequality, and augmented forms, conservativeness has been substantially diminished. All these provide beneficial tools for us to study the synchronization problem of CLS.

    In previous studies on the synchronization problem of CLS based on sampled-data control, the solution of the sampled controller was usually obtained by parameter adjustment methods. However, this approach is heavily influenced by the initial values of the chosen parameters, and optimizing these parameters can be quite complex. This complexity may hinder determining the controller and could result in the oversight of specific solutions that satisfy the necessary conditions. In Reference [36], an iterative algorithm of cone complementary linearization based on linear matrix inequalities is proposed and successfully applied in sampling control systems[37]. This algorithm eliminates the need for preset initial parameter values and does not require parameter tuning. Once a stopping condition for the iteration is established, it continuously iterates to discover the optimal solution that meets the specified conditions, thereby significantly enhancing the accuracy of the calculations.

    Motivated by the descriptions discussed above, this paper thoroughly investigates the synchronization problem of CLS by considering the characteristics of the system's sampling process. The key contributions of this paper are outlined as follows:

    1) An augmented two-sided looped Lyapunov functional is constructed, which fully considers the system's state variables and sampling information and leads to the establishment of a stability criterion.

    2) Utilizing the cone complementarity linearization iterative algorithm, a novel iterative condition for the design of sampling controllers has been developed.

    3) Numerical simulation experiments reveal that our method attains a significantly larger sampling interval than that reported in References [22,25,34], suggesting its capability to generate more relaxed outcomes.

    Notations. Throughout this note, Rn denotes the n-dimensional Euclidean space. The superscripts V1 and VT represent the matrix V inverse and transpose, respectively; the space of n×m real matrix is denoted by Rn×m; the condition P>0 indicates that the matrix P is both symmetric and positive definite; He{J} = J+JT; the notation diag{} denoted a block-diagonal matrix; N represents the collection of all natural numbers. rN, Nr={1,2,,r}.

    Consider the following master and slave CLS:

    E:{˙x(t)=Ax(t)+Bσ(Dx(t)),p(t)=Cx(t),F:{˙y(t)=Ay(t)+Bσ(Dy(t))+u(t),q(t)=Cy(t),L:u(t)=K(p(tk)q(tk)),tkt<tk+1, (2.1)

    which comprises the master system E, slave system F, and control input L. where x(t)Rn and y(t)Rn are the states of E and F, respectively; and p(t)Rm and q(t)Rm are the subsystem output, u(t)Rn is the control input of F; A,B, C, and D are constant matrices with appropriate dimensions; K is a controller gain matrix. σ():RlRl is a diagonal and nonlinear function that belongs to the sector [0,gi] for i=1,2,,l,

    0σi(dix(t))σi(diy(t))di(x(t)y(t))gi,x(t)y(t), (2.2)

    where gi>0 represents a scalar, and di denotes the ith row vector of matrix D.

    It is assumed that the time interval between any two consecutive sampling instants is such that

    tk+1tk=hk(0,h].

    From the master system E and slave system F, the synchronization error is given by r(t)=x(t)y(t), and the synchronization error system can be formulated as follows:

    ˙r(t)=Ar(t)+Bf(Dx(t),Dy(t))KCr(tk), (2.3)

    where f(Dx(t),Dy(t))=σ(Dx(t))σ(Dy(t)). To simplify the presentation, let us refer to f(Dx(t),Dy(t)) as f(t).

    To formulate a more permissive synchronization criterion, the subsequent Lemma 2.1 is necessary [38].

    Lemma 2.1. Let RRn×n be a positive-definite matrix. x:[α1,α2]Rn and ˜ξRm be a continuous differentiable function. The following two inequalities hold for NR3n×m:

    α2α1˙xT(θ)R˙x(θ)dθ2˜ξTˉΠTN˜ξ+α˜ξTNTR1N˜ξ,

    where R1=diag{R,3R,5R} and

    α=α2α1,˜ki=[0n×(i1)nIn0n×(4i)n],i=1,24,˜ξ=[xT(α2)xT(α1)α2α1xT(θ)αdθα2α1α2θxT(θ)α2dθds]T,ˉΠ=[˜kT1˜kT2˜kT1+˜kT22˜kT3˜kT1˜kT2+6˜kT312˜kT4]T.

    This section develops a criterion for achieving master-slave synchronization in CLS. Leveraging this criterion, we then apply the cone complementarity linearization iterative algorithm to determine the gain of the sampled-data controller. The following notions are given to help simplify the description of the matrices and vectors of the main results.

    h1(t)=ttk,h2(t)=tk+1t,ν1=ttkr(s)h1(t)ds,ν2=tk+1tr(s)h2(t)ds,ν3=ttkstk2r(θ)h1(t)2dθds,ν4=tk+1ttk+1s2r(θ)h2(t)2dθds,ν=[h1(t)vT1h2(t)vT2h1(t)vT3h2(t)vT4]T,η1=[rT(tk)rT(tk+1)tk+1tkrT(s)ds]T,η2(t)=[rT(tk)rT(tk+1)h1(t)vT1h2(t)vT2h1(t)vT3h2(t)vT4]T,η3(t)=[h2(t)(r(t)r(tk))Th1(t)(r(tk+1)r(t))T]T,η4(t)=[rT(t)rT(tk)rT(tk+1)νT]T,ξ(t)=[rT(t)rT(tk)rT(tk+1)νTvT1vT2vT3vT4f(t)]T.

    Below, Theorem 3.1 explores system (2.1) with a predefined controller gain K. The condition for synchronization is obtained through the application of the two-sided looped function in combination with Lemma 2.1.

    Theorem 3.1. Give scalars h>0 and real matrices K, the master system E, and the slave system F in system (2.1) are globally asymptotically synchronous if there exist real matrices P>0,Yı>0, Q,Gı,Sȷ,X, (ıN2,ȷN4), M1,M2, and diagonal matrix Γ>0 such that the following LMIs (3.1) and (3.2) are satisfied for hk(0,h],

    φa=[φ0+hkφ1hkπT8bM2hkπT0Y1Yb0Y1]<0, (3.1)
    φb=[φ0+hkφ2hkπT8aM1hkπT0Y2Ya0Y2]<0, (3.2)

    where

    φ0=He{eT1Pπ0eT12Γe12+eT12ΓGDe1+eT5G1π1eT4G2π1+πT4Qπ3S1e4S2e5S3e6S4e7+πT8aM1π9+πT8bM2π10},φ1=He{eT1G1π1+eT5G1π2+πT6aQπ3+πT4aQπ5+S1e8+S3e10}πT7Xπ7,φ2=He{eT1G2π1+eT4G2π2+πT6bQπ3+πT4bQπ5+S2e9+S4e11}+πT7Xπ7,

    with

    em=[0n×(m1)nIn0n×(12m)n],m=1,2,,12,Ya=diag{Y1,3Y1,5Y1},Yb=diag{Y2,3Y2,5Y2},π0=Ae1+Be12CKe2,π1=[eT2eT3eT4eT5eT6eT7]T,π2=[00eT1eT12eT8eT102eT9+eT11]T,π3=[eT1eT2eT3eT4eT5eT6eT7]T,π4=[eT2eT1eT3eT1]T,π4a=[0eT3eT1]T,π4b=[eT1eT20]T,π5=[πT000eT1eT12eT8eT102eT9+eT11]T,π6a=[0πT0]T,π6b=[πT00]T,π7=[eT2eT3eT4+eT5]T,π8a=[eT3eT1eT9eT11]T,π8b=[eT1eT2eT8eT10]T,π9=[eT3eT1eT3+eT12eT9eT3eT1+6eT96eT11]T,π10=[eT1eT2eT1+eT22eT8eT1eT26eT8+6eT10]T.

    Proof. Choose a Lyapunov functional below.

    V(rt)=V0(t)+4n=1Vn(t),t[tk,tk+1), (3.3)

    where

    V0(t)=rT(t)Pr(t),V1(t)=h1(t)h2(t)ηT1Xη1,V2(t)=2h1(t)tk+1tr(s)TdsG1η2(t)+2h2(t)ttkr(s)TdsG2η2(t),V3(t)=2η3(t)TQη4(t),V4(t)=h2(t)ttk˙r(s)TY2˙r(s)dsh1(t)tk+1t˙r(s)TY1˙r(s)ds.

    Computing the derivative of (3.3) with respect to the solution of system (2.1) results in

    ˙V0(t)=2ξT(t){eT1Pπ0}ξ(t),˙V1(t)=ξT(t){h2(t)πT7Xπ7h1(t)πT7Xπ7}ξ(t),˙V2(t)=2ξT(t){eT5G1π1h1(t)eT1G1π1+h1(t)eT5G1π2eT4G2π1+h2(t)eT1G2π1+h2(t)eT4G2π2}ξ(t),˙V3(t)=2ξT(t){πT4Qπ3+2h1(t)πT6aQπ3+2h1(t)πT4aQ3π5+2h2(t)πT6bQπ3+2h2(t)πT4bQπ5}ξ(t),˙V4(t)=ξT(t){h1(t)πT0Y1π0+h2(t)πT0Y2π0}ξ(t)+J1+J2,

    where

    J1=tk+1t˙r(s)TY1˙r(s)ds,J2=ttk˙r(s)TY2˙r(s)ds.

    Applying Lemma 2.1, we obtain

    J1ξT(t)[h2(t)ΠT8aM1Ya1M1TΠ8a+2ΠT8aM1Π9]ξ(t), (3.4)
    J2ξT(t)[h1(t)ΠT8bM2Yb1M2TΠ8b+2ΠT8bM2Π10]ξ(t). (3.5)

    Note that, for any matrices Si(iN4), all the subsequent zero-equality equations remain valid

    0=2ξT(t)S1[h1(t)e8e4]ξ(t), (3.6)
    0=2ξT(t)S2[h2(t)e9e5]ξ(t), (3.7)
    0=2ξT(t)S3[h1(t)e10e6]ξ(t), (3.8)
    0=2ξT(t)S4[h2(t)e11e7]ξ(t). (3.9)

    For any diagonal matrix Γ=diag{1,2,,l}>0, it follows from inequality (2.2) that the following inequality holds:

    02ξT(t)(eT12ΓGDe1eT12Γe12)ξ(t) (3.10)

    with G=diag{g1,g2,,gl}. By incorporating (3.4)-(3.10) into the right-hand side of ˙V(rt), the following resulting expression is obtained.

    ˙V(rt)ξT(t)[h1(t)hkφa+h2(t)hkφb]ξ(t), (3.11)

    where

    φa=φ0+hkφ1+hkπT0Y1π0+hkM1T~Ya1M1, (3.12)
    φb=φ0+hkφ2+hkπT0Y2π0+hkM2T~Yb1M2. (3.13)

    If φa<0 and φb<0 are satisfied, then according to the Schur complement, inequalities (3.1) and (3.2) are established, respectively. Then ˙V(t)<γx(t)2 for a suitably small γ>0; the master system E and the slave system F are synchronous. This concludes the proof.

    Remark 3.1. In contrast to the conventional Lyapunov functional, the Lyapunov functional developed in this paper is a two-sided looped functional, comprising two distinct components, V0(t) and 4n=1Vn(t), and does not need to satisfy 4n=1Vn(t)>0, so the qualification conditions are relaxed compared with the traditional functional. Meanwhile, the functional constructed in this paper is augmented with the double integral terms ν3 and ν4 in ξ(t) compared to [32]. All of these measures contribute to reducing the conservativeness of the derived condition.

    To guarantee that the synchronization error system is absolutely stable as defined in Eq (2.3), a method for designing a sampled-data controller is proposed based on Theorem 3.1.

    Theorem 3.2. Given scalars h>0, the synchronization error system (2.3) is absolutely stable, if there exist real matrices W>0,˜Yı>0, ˜Q,˜Gı,˜Sȷ,˜X, (ıN2,ȷN4), ˜M1,˜M2, and diagonal matrix Γ>0, such that the following LMIs (3.14) and (3.15) are satisfied for hk(0,h],

    ˜φa=[˜φ0+hk˜φ1hkπT8b˜M2hkπT0˜Rb0˜R1]<0, (3.14)
    ˜φb=[˜φ0+hk˜φ2hkπT8a˜M1hkπT0˜Ra0˜R2]<0, (3.15)

    where

    ˜φ0=He{eT1P˜π0eT12Γe12eT12ΓGDWe1+eT5˜G1π1eT4˜G2π2+˜S1e4˜S2e5˜S3e6˜S4e7+πT8a˜M1π9+πT8b˜M2π10},˜φ1=He{eT1˜G1π1+eT5˜G1π2+˜S1e8+˜S3e10}πT7˜Xπ7,˜φ2=He{eT1˜G2π1+eT4˜G2π2+˜S2e9+˜S4e11}+πT7˜Xπ7,˜π0=AWe1+Be12CVe2,˜Ra=diag{W˜R11W,3W˜R11W,5W˜R11W},˜Rb=diag{W˜R12W,3W˜R12W,5W˜R12W}.

    Any other symbols not covered above are defined in accordance with Theorem 3.1. Furthermore, the controller gain is given by K=VW1.

    Proof. Define

    W=P1,˜X=J3XJ3,˜Gi=J1GiJ6,˜Sj=˜J11SJ1,˜Ni=J4NiJ3,˜Ri=Y1i,V=KP1,˜J11=diag{J11,I},˜J3a=diag{J3,Y11},˜J3b=diag{J3,Y12},

    where, iN2,jNr and

    Jn=diag{P1,,P1}nelements.

    Set Q=0, then, pre- and post-multiplying (3.1) and (3.2) with diag{˜J11,˜J3a} and diag{˜J11,˜J3b}, we obtain (3.14) and (3.15). This concludes the proof.

    It is evident that inequalities (3.14) and (3.15) contain two nonlinear terms, W˜R12W and W˜R11W. This makes it impossible to directly solve the controller of Theorem 3.2 through standard solvers. Therefore, the cone complementarity linearization iterative algorithm proposed in Reference [36] needs to be applied to handle this non-convex problem. The specific steps are as follows:

    Define two new variables Φ1,Φ1 such that Φ1W˜R11W, Φ2W˜R12W. Replace the conditions (3.14) and (3.15) with

    ˜φa=[˜φ0+hk˜φ1hkπT8b˜M2hk˜πT1˜Φb0˜R1]<0, (3.16)
    ˜φb=[˜φ0+hk˜φ2hkπT8a˜M1hk˜πT1˜Φa0˜R2]<0, (3.17)

    where ˜Φa=diag{Φ1,3Φ1,5Φ1},˜Φb=diag{Φ2,3Φ2,5Φ2} and,

    ΦiW˜R1iW,iN2. (3.18)

    Notice that (3.18) is equal to Φ1iW1˜RiW10. Using the Schur complement, this condition is equivalent to

    [Φ1iW1W1˜R1i]0, (3.19)

    then, by introducing the new variable P,Hi,Yi,iN2, the original conditions (3.14) and (3.15) can be reformulated as (3.16), (3.17), and

    [HiPPYi]0,P=W1,Hi=Φ1i,Yi=˜R1i. (3.20)

    Therefore, the aforementioned non-convex problem is reformulated as a nonlinear minimization problem based on Linear Matrix Inequalities (LMIs) as follows:

    Minimizetr{PW+2i=1(HiΦi+YiRi)}s.t.(3.16),(3.17)and[HiPPYi]0,[WIIP]0,[ΦiIIHi]0,[˜RiIIYi]0. (3.21)

    In the following text, we will introduce an iterative algorithm for solving the controller matrix with the maximization of h.

    Step 1. First, choose a sufficiently small initial value h such that the LMIs in Eqs (3.16), (3.17), and (3.21) are satisfied, and then we set hmax=h.

    Step 2. Find a feasible set P0,W0,H10,H20,Φ10,Φ20,Y10,Y20,˜R10,˜R20 satisfying (3.16), (3.17), and (3.21). And set j=0.

    Step 3. Solve the following LMI problem:

    Minimizetr{PWj+PjW+2i=1(HijΦi+HiΦij+YijRi+Yi˜Rij)},s.t.(3.16),(3.17)and(3.21).setPj+1=W1,Wj+1=W,Φi(j+1)=Φi,Hi(j+1)=Φ1i,˜Ri(j+1)=˜Ri,Yi(j+1)=˜R1i,iN2.

    Step 4. If the LMIs (3.1) and (3.2) are satisfied with the controller gain K obtained in Step 3, then update hmax to h and revert to Step 2 after increasing h2 to a certain degree. If LMIs (3.1) and (3.2) are unsolvable within a set number of iterations, then exit the procedure. Otherwise, set j=j+1 and go back to Step 3.

    Remark 3.2. In contrast to the parameter adjustment methods for controller optimization described in references [27,34], the enhanced cone complementarity linearization iteration iterative algorithm systematically identifies the optimal solution within the feasible region through a step-by-step iterative process. This method not only improves the precision of synchronous control but also effectively minimizes potential errors that may arise during parameter adjustment.

    This section presents a benchmark example based on reference [34], aimed at illustrating the benefits of the proposed standard.

    Consider the CLS defined by the following parameters.

    A=[100010001],B=[1.21.601.2410.902.21.5],C=D=I.

    with nonlinear characteristics

    fi(xi(t))=12(|xi(t)+1||xi(t)1|),

    where fi(xi(t)) belongs to sector [0, 1] for iN3.

    The systems mentioned above have all been examined in Reference [34]. Table 1 presents the maximum sampling periods that were obtained. Utilizing the sampling periods and in accordance with Theorem 3.2, the controller obtained through continuous iterative calculation is as follows:

    K=[1.12541.09420.14340.46070.95650.62370.31701.75401.3261].

    By substituting the obtained controller into Theorem 3.1, the maximum sampling period h for this study is determined to be 0.77. As shown in Table 1, the results of this study are superior to those in other literature, demonstrating that our approach exhibits less conservativeness.

    Table 1.  Maximum values of the upper bound h.
    Methods [25] [22] [34] Theorem 3.1
    h 0.32 0.38 0.71 0.77

     | Show Table
    DownLoad: CSV

    Then, set x(0)=[0.30.50.8]T,y(0)=[0.20.40.9]T, Figure 1 shows the state response of the system without the controller in use. Applying the above controller K, the state trajectories of system (2.3) and its control input are illustrated in Figures 2 and 3 under the sampling period h=0.77. It can be seen that the system is unstable at this time. As shown in Figures 2 and 3, CLS achieved synchronization in a short period of time, and the system was in a stable state at this point.

    Figure 1.  State response of the system with no controller.
    Figure 2.  State response of the system.
    Figure 3.  Control input u(t).

    This paper focuses on examining CLS's synchronization issue. This study thoroughly considers the system's sampling process characteristics and constructs an improved augmented two-sided looped Lyapunov functional to derive the stability criterion. Subsequently, based on the derived conditions, the cone complementary linearization iteration algorithm is employed to design the sampling controller. Numerical simulation results demonstrate the effectiveness and superiority of the proposed approach.

    Xin-Yu Li: writing-original draft, software, methodology, investigation. Wei Wang: Writing-review and editing, formal analysis, validation, conceptualization, supervision, funding acquisition. Jin-Ming Liang: Writing-review and editing.

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

    This study received partial support from the National Natural Science Foundation of China (Grant No. 62173136) and the Natural Science Foundation of Hunan Province (Grant. No. 2020JJ2013). No potential conflict of interest was reported by the authors.

    The authors confirm that the data supporting the findings of this study are available within the article.

    The authors declare no conflict of interest.



    [1] Hadj-Mabrouk H (2018) New approach of assessing human errors in railways. Transactions of the VSB - Technical University of Ostrava, Safety Engineering Series 13: 1-17.
    [2] Hadj-Mabrouk H (2019) Consideration of Human Factors in the Accident and Incident Investigation Process. Application to the Safety of Railway Transport. J Ergon Adv Res 1: 1-20.
    [3] Hadj-Mabrouk H (2016) Knowledge based system for the evaluation of safety and the prevention of railway accidents. International journal of railway 3: 37-44.
    [4] Bergmeir C, Sáinz G, Bertrand CM, et al. (2013) A Study on the Use of Machine Learning Methods for Incidence Prediction in High-Speed Train Tracks. IEA/AIE 2013 Proceedings of the 26th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems 7906: 674-683.
    [5] Fay A (2000) A fuzzy knowledge-based system for railway traffic control. Eng Appl Artif Intel 13: 719-729. doi: 10.1016/S0952-1976(00)00027-0
    [6] Santur Y, Karaköse M, Akin E (2017) A new rail inspection method based on deep learning using laser cameras. International Artificial Intelligence and Data Processing Symposium (IDAP) 16-17.
    [7] Faghih-Roohi S, Hajizadeh S, Núñez A, et al. (2016) Deep convolutional neural networks for detection of rail surface defects. International Joint Conference on Neural Networks (IJCNN) 24-29.
    [8] Ghofrania F, He Q, Goverde R, et al. (2018) Recent applications of big data analytics in railway transportation systems: A survey. Transport Res C-Emer 90: 226-246. doi: 10.1016/j.trc.2018.03.010
    [9] Thaduri A, Galar D, Kumar U (2015) Railway assets: A potential domain for big data analytics. Procedia Comput Sci 53: 457-467. doi: 10.1016/j.procs.2015.07.323
    [10] Attoh-Okine N (2014) Big data challenges in railway engineering. IEEE International Conference on Big Data (Big Data) 27-30.
    [11] Hughes P (2018) Making the railway safer with big data. Available from: http://www.railtechnologymagazine.com/Comment/making-the-railway-safer-with-big-data.
    [12] Hayward V (2018) Big data & the Digital Railway. Available from: https://on-trac.co.uk/big-data-digital-railway/.
    [13] Marr B (2017) How Siemens Is Using Big Data And IoT To Build The Internet Of Trains. Available from: https://www.forbes.com/sites/bernardmarr/2017/05/30/how-siemens-is-using-big-data-and-iot-to-build-the-internet-of-trains/#2b7a4b6e72b8.
    [14] Williams T, Betak J, Findley B (2016) Text Mining Analysis of Railroad Accident Investigation Reports. Proceedings of the 2016 Joint Rail Conference.
    [15] Brown DE (2016) Text Mining the Contributors to Rail Accidents. IEEE Transactions on Intelligent Transportation Systems 17: 346-355. doi: 10.1109/TITS.2015.2472580
    [16] Li J, Wang J, Xu N, et al. (2018) Importance Degree Research of Safety Risk Management Processes of Urban Rail Transit Based on Text Mining Method. Information-an International Interdisciplinary Journal 9: 26
    [17] Williams T, Betakbc J (2018) A Comparison of LSA and LDA for the Analysis of Railroad Accident Text. Procedia Computer Science 130: 98-102. doi: 10.1016/j.procs.2018.04.017
    [18] Syeda K, Shirazi SN, Naqvi SA, et al. (2018) Big Data and Natural Language Processing for Analysing Railway Safety: Analysis of Railway Incident Reports. Innovative Applications of Big Data in the Railway Industry 240-267.
    [19] Van-Gulijk C, Hughes P, Figueres-Esteban M, et al. (2018) The case for IT transformation and big data for safety risk management on the GB railways. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 232: 151-163. doi: 10.1177/1748006X17728210
    [20] Syeda KN, Shirazi SN, Naqvi SAA, et al. (2017) Big Data and Natural Language Processing for Analysing Railway Safety. Innovative Applications of Big Data in the Railway Industry. IGI Global Publishing 240-267.
    [21] Ghomi H, Bagheri M, Fu L, et al (2016) Analyzing injury severity factors at highway railway grade crossing accidents involving vulnerable road users: A comparative study. Traffic Injury Prevention 17: 833-841. doi: 10.1080/15389588.2016.1151011
    [22] Zhang X, Green E, Chen M, et al. (2019) Identifying secondary crashes using text mining techniques. Journal of Transportation Safety & Security 1-21.
    [23] Heidarysafa M, Kowsari K, Barnes LE, et al. (2018) Analysis of Railway Accidents' Narratives Using Deep Learning. International Conference on Machine Learning and Applications (LCMLA) 1446-1453.
    [24] Gibert X, Patel VM, Chellappa R (2017) Deep multitask learning for railway track inspection. IEEE T Intell Transp 18: 153-164. doi: 10.1109/TITS.2016.2568758
    [25] Osman A, Hajij M, Bakhit PR, et al. (2019) Prediction of Near-Crashes from Observed Vehicle Kinematics Using Machine Learning. Transportation Res Rec.
    [26] Nakhaee MC, Hiemstra D, Stoelinga M, et al. (2019) The Recent Applications of Machine Learning in Rail Track Maintenance: A Survey. In: Collart-Dutilleul S., Lecomte T., Romanovsky A. (eds) Reliability, Safety, and Security of Railway Systems. Modelling, Analysis, Verification, and Certification. RSSRail 2019. Lecture Notes in Computer Science.
    [27] Zubair M, Khan MJ, Awais M (2012) Prediction and analysis of air incidents and accidents using case-based reasoning. Third Global Congress on Intelligent Systems 315-318.
    [28] Khattak A, Kanafani A (1996) Case-based reasoning: A planning tool for intelligent transportation systems. Transport Res C-Emer 4: 267-288. doi: 10.1016/S0968-090X(97)82901-4
    [29] Sadeka A, Smith B, Demetsky M (2001) A prototype case-based reasoning system for real-time freeway traffic routing. Transport Res C-Emer 9: 353-380. doi: 10.1016/S0968-090X(00)00046-2
    [30] Sadek A, Demetsky M, Smith B (1999) Case-Based Reasoning for Real-Time Traffic Flow Management. Comput-Aided Civ Inf 14:347-356. doi: 10.1111/0885-9507.00153
    [31] Zhenlong L, Xiaohua Z (2008) A case-based reasoning approach to urban intersection control. 7th World Congress on Intelligent Control and Automation 7113-7118.
    [32] Li K, Waters NM (2005) Transportation Networks, Case-Based Reasoning and Traffic Collision Analysis: A Methodology for the 21st Century. In: Reggiani A, Schintler LA (eds.), Methods and Models in Transport and Telecommunications, 63-92.
    [33] Kofod-Petersen A, Andersen OJ, Aamodt A (2014) Case-Based Reasoning for Improving Traffic Flow in Urban Intersections. International Conference on Case-Based Reasoning 8765: 215-229.
    [34] Louati A, Elkosantini S, Darmoul S, et al. (2016) A case-based reasoning system to control traffic at signalized intersections. IFAC-Papers On Line 49: 149-154.
    [35] Begum S, Ahmed MU, Funk P, et al. (2012) Mental state monitoring system for the professional drivers based on Heart Rate Variability analysis and Case-Based Reasoning. Federated Conference on Computer Science and Information Systems (FedCSIS) 35-42.
    [36] Zhong Q, Zhang G (2017) A Case-Based Approach for Modelling the Risk of Driver Fatigue. International Conference on Intelligence Science 510: 45-56.
    [37] Varma A, Roddy N (1999) ICARUS: Design and deployment of a case-based reasoning system for locomotive diagnostics. Eng Appl Artif Intel 12: 681-690. doi: 10.1016/S0952-1976(99)00039-1
    [38] Johnson C (2000) Using case-based reasoning to support the indexing and retrieval of incident reports. Proceeding of European Safety and Reliability Conference (ESREL 2000): Foresight and Precaution, Balkema, Rotterdam, the Netherlands 1387-1394.
    [39] Cui Y, Tang Z, Dai H (2005) Case-based reasoning and rule-based reasoning for railway incidents prevention. Proceedings of ICSSSM '05. 2005 International Conference on Services Systems and Services Management 2: 1057-1060.
    [40] Li X, Yu K (2010) The research of intelligent Decision Support system based on Case-based Reasoning in the Railway Rescue Command System. International Conference on Intelligent Control and Information Processing 59-63.
    [41] Lu Y, Li Q, Xiao W (2013) Case-based reasoning for automated safety risk analysis on subway operation: Case representation and retrieval. Safety Sci 57: 75-81. doi: 10.1016/j.ssci.2013.01.020
    [42] de Souza VDM, Borges AP, Sato DMV, et al. (2016) Automatic knowledge learning using Case-Based Reasoning: A case study approach to automatic train conduction. International Joint Conference on Neural Networks (IJCNN) 4579-4585.
    [43] Zhao H, Chen H, Dong W, et al. (2017) Fault diagnosis of rail turnout system based on case-based reasoning with compound distance methods. 29th Chinese Control And Decision Conference (CCDC) 4205-4210.
    [44] Hadj-Mabrouk H (2017) Preliminary Hazard Analysis (PHA): New hybrid approach to railway risk analysis. International Refereed Journal of Engineering and Science 6: 51-58.
    [45] Hadj-Mabrouk H (2016) Machine learning from experience feedback on accidents in transport. 7th International Conference on Sciences of Electronics, Technologies of Information and Telecommunications 246-251.
    [46] Ganascia JG (1987) Agape et Charade: deux mécanismes d'apprentissage symbolique appliqués à la construction de bases de connaissances. Thèse d'État, Université Paris-sud, France.
    [47] Quinlan JR (1986) Induction of Decision Trees. Mach Learn 1: 81-106.
    [48] Hadj-Mabrouk H (2016) CLASCA: Learning System for Classification and Capitalization of Accident Scenarios of Railway. Journal of Engineering Research and Application 6: 91-98.
    [49] Hadj-Mabrouk H (2018) A Hybrid Approach for the Prevention of Railway Accidents Based on Artificial Intelligence. International Conference on Intelligent Computing & Optimization 383-394.
    [50] Hadj-Mabrouk H (2019) Contribution of artificial intelligence to risk assessment of railway accidents. Journal of Urban Rail Transit 5: 104-122. doi: 10.1007/s40864-019-0102-3
    [51] Hadj-Mabrouk H, Mejri H (2015) ACASYA: a knowledge-based system for aid in the storage, classification, assessment and generation of accident scenarios. Application to the safety of rail transport systems. Advances in Computer Science an International Journal 4: 7-13.
    [52] Hadj-Mabrouk H (2017) Contribution of learning Charade system of rules for the prevention of rail accidents. Intell Decis Technol 11: 477-485. doi: 10.3233/IDT-170304
    [53] Aamodt A, Plaza E (1994) Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Commun 7: 39-52.
    [54] Harmon P (1991) Case-based reasoning II. Intelligent Software Strategies 7: 1-9.
    [55] Kolodner J (1992) An introduction to case-based reasoning. Artif Intell Rev 6: 3-34. doi: 10.1007/BF00155578
    [56] Leake D (1996) CBR in Context: The present and future. Case-Based Reasoning: Experiences, Lessons, and Future Directions 3-30.
    [57] Mott S (1993) Case-based reasoning: Market, applications, and fit with other technologies. Expert Syst Appl 6: 97-104. doi: 10.1016/0957-4174(93)90022-X
    [58] Pinson S, Demourioux M, Laasri B, et al. (1993) Le Raisonnement à Partir de Cas: panorama et modélisation dynamique. Séminaire CBR, LAFORIA, Rapport 93/42, 1er octobre.
    [59] Slade S (1991) Case-based reasoning: A research paradigm. AI Mag 12: 42-55.
    [60] Hadj-Mabrouk H (2017) Case-Based Reasoning for the Evaluation of Safety Critical Software. Application to The Safety of Railway Transport. International Journal of Engineering Research and Development 13: 37-43.
    [61] Hadj-Mabrouk H (2019) Contribution of artificial intelligence and machine learning to the assessment of the safety of critical software used in railway transport. AIMS Electronics and Electrical Engineering 3: 33-70. doi: 10.3934/ElectrEng.2019.1.33
    [62] Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27: 379-423. doi: 10.1002/j.1538-7305.1948.tb01338.x
  • This article has been cited by:

    1. Kishor Aryal, Rajendra Dhungana, Thakur Silwal, Understanding policy arrangement for wildlife conservation in protected areas of Nepal, 2021, 26, 1087-1209, 1, 10.1080/10871209.2020.1781983
    2. Kishor Aryal, Bhuwan Raj Ojha, Tek Maraseni, Perceived importance and economic valuation of ecosystem services in Ghodaghodi wetland of Nepal, 2021, 106, 02648377, 105450, 10.1016/j.landusepol.2021.105450
    3. Kishor Aryal, Hari Krishna Laudari, Prem Raj Neupane, Tek Maraseni, Who shapes the environmental policy in the global south? Unpacking the reality of Nepal, 2021, 121, 14629011, 78, 10.1016/j.envsci.2021.04.008
    4. Shivaraj Thapa, Subina Shrestha, Ram Kumar Adhikari, Suman Bhattarai, Deepa Paudel, Deepak Gautam, Anil Koirala, Residents’ willingness-to-pay for watershed conservation program facilitating ecosystem services in Begnas watershed, Nepal, 2022, 24, 1387-585X, 7811, 10.1007/s10668-021-01759-5
    5. Kishor Aryal, Tek Maraseni, Armando Apan, How much do we know about trade-offs in ecosystem services? A systematic review of empirical research observations, 2022, 806, 00489697, 151229, 10.1016/j.scitotenv.2021.151229
    6. Kishor Aryal, Tek Maraseni, Armando Apan, Spatial dynamics of biophysical trade-offs and synergies among ecosystem services in the Himalayas, 2023, 59, 22120416, 101503, 10.1016/j.ecoser.2022.101503
    7. Hunggul Yudono Setio Hadi Nugroho, Fitri Nurfatriani, Yonky Indrajaya, Tri Wira Yuwati, Sulistya Ekawati, Mimi Salminah, Hendra Gunawan, Subarudi Subarudi, Markus Kudeng Sallata, Merryana Kiding Allo, Nurhaedah Muin, Wahyudi Isnan, Indra Ardie Surya Liannawatty Purnamawan Putri, Retno Prayudyaningsih, Fajri Ansari, Mohamad Siarudin, Ogi Setiawan, Himlal Baral, Mainstreaming Ecosystem Services from Indonesia’s Remaining Forests, 2022, 14, 2071-1050, 12124, 10.3390/su141912124
    8. Xinwen Lin, Angathevar Baskaran, Yajie Zhang, Watershed Horizontal Ecological Compensation Policy and Green Ecological City Development: Spatial and Mechanism Assessment, 2023, 20, 1660-4601, 2679, 10.3390/ijerph20032679
    9. Kishor Aryal, Nripesh Awasthi, Tek Maraseni, Hari Krishna Laudari, Pabitra Gotame, Dhan Bahadur Bist, Calibrating Nepal's scientific forest management practices in the measure of forest restoration, 2023, 127, 02648377, 106586, 10.1016/j.landusepol.2023.106586
    10. Kishor Aryal, Tek Maraseni, Armando Apan, Transforming agroforestry in contested landscapes: A win-win solution to trade-offs in ecosystem services in Nepal, 2023, 857, 00489697, 159301, 10.1016/j.scitotenv.2022.159301
    11. Christopher Mulwanda, Vincent R. Nyirenda, Ngawo Namukonde, Perceived social-ecological benefits of insect pollinators in Mufulira mining district of Zambia, 2022, 42, 1742-7592, 3245, 10.1007/s42690-022-00759-w
    12. Kishor Aryal, Armando Apan, Tek Maraseni, Comparing global and local land cover maps for ecosystem management in the Himalayas, 2023, 30, 23529385, 100952, 10.1016/j.rsase.2023.100952
    13. Motilal Ghimire, Niroj Timalsina, Wei Zhao, A Geographical approach of watershed prioritization in the Himalayas: a case study in the middle mountain district of Nepal, 2023, 26, 1573-2975, 23527, 10.1007/s10668-023-03610-5
    14. Nisha Silwal, Nabin Dhungana, Rajan Subedi, Suraj Upadhaya, Chun-Hung Lee, Community perspectives on the effectiveness of watershed management institutions in the Himalayas, 2024, 21, 1672-6316, 1119, 10.1007/s11629-023-8424-8
    15. Kishor Aryal, Tek Maraseni, Armando Apan, Preference, perceived change, and professed relationship among ecosystem services in the Himalayas, 2023, 344, 03014797, 118522, 10.1016/j.jenvman.2023.118522
    16. Sarita Mishra, Ajay Kumar Mishra, Jay Prakash Bhatt, 2025, Chapter 7, 978-981-96-1047-1, 93, 10.1007/978-981-96-1048-8_7
    17. Nabin Dhungana, Chun-Hung Lee, Suman Acharya, Adaptive watershed management in a changing climate: an importance-performance analysis of user perspectives in central Nepal, 2025, 2040-2244, 10.2166/wcc.2025.067
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(8155) PDF downloads(977) Cited by(11)

Figures and Tables

Figures(4)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog