Loading [MathJax]/jax/output/SVG/jax.js
Research article Special Issues

A negative correlation ensemble transfer learning method for fault diagnosis based on convolutional neural network

  • With the development of the smart manufacturing, data-driven fault diagnosis has receiving more and more attentions from both academic and engineering fields. As one of the most important data-driven fault diagnosis method, deep learning (DL) has achieved remarkable applications. However, the DL based fault diagnosis methods still have the following two drawbacks: 1) One of the most major branch of deep learning is to construct the deeper structures, however the deep learning models in fault diagnosis is very shadow. 2) As stated by the no-free-lunch theorem, no single model can perform best on every dataset, and the individual deep learning model still suffers from the generalization ability. In this research, a new negative correlation ensemble transfer learning method (NCTE) is proposed. Firstly, the transfer learning based ResNet-50 is proposed to construct a deep learning structure that has 50 layers. Secondly, several fully-connected layers and softmax classifiers are trained cooperatively using negative correlation learning (NCL). Thirdly, the hyper-parameters of the proposed NCTE are determined by cross validation. The proposed NCTE is conducted on the KAT Bearing Dataset, and the prediction accuracy of NCTE is as high as 98.73%. This results show that NCTE has achieved a good results compared with other machine learning and deep learning method.

    Citation: Long Wen, Liang Gao, Yan Dong, Zheng Zhu. A negative correlation ensemble transfer learning method for fault diagnosis based on convolutional neural network[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3311-3330. doi: 10.3934/mbe.2019165

    Related Papers:

    [1] Long Wen, Yan Dong, Liang Gao . A new ensemble residual convolutional neural network for remaining useful life estimation. Mathematical Biosciences and Engineering, 2019, 16(2): 862-880. doi: 10.3934/mbe.2019040
    [2] Guanghua Fu, Qingjuan Wei, Yongsheng Yang . Bearing fault diagnosis with parallel CNN and LSTM. Mathematical Biosciences and Engineering, 2024, 21(2): 2385-2406. doi: 10.3934/mbe.2024105
    [3] Xueyan Wang . A fuzzy neural network-based automatic fault diagnosis method for permanent magnet synchronous generators. Mathematical Biosciences and Engineering, 2023, 20(5): 8933-8953. doi: 10.3934/mbe.2023392
    [4] Yajing Zhou, Xinyu Long, Mingwei Sun, Zengqiang Chen . Bearing fault diagnosis based on Gramian angular field and DenseNet. Mathematical Biosciences and Engineering, 2022, 19(12): 14086-14101. doi: 10.3934/mbe.2022656
    [5] Kunli Zhang, Shuai Zhang, Yu Song, Linkun Cai, Bin Hu . Double decoupled network for imbalanced obstetric intelligent diagnosis. Mathematical Biosciences and Engineering, 2022, 19(10): 10006-10021. doi: 10.3934/mbe.2022467
    [6] Jinyi Tai, Chang Liu, Xing Wu, Jianwei Yang . Bearing fault diagnosis based on wavelet sparse convolutional network and acoustic emission compression signals. Mathematical Biosciences and Engineering, 2022, 19(8): 8057-8080. doi: 10.3934/mbe.2022377
    [7] Xu Zhang, Wei Huang, Jing Gao, Dapeng Wang, Changchuan Bai, Zhikui Chen . Deep sparse transfer learning for remote smart tongue diagnosis. Mathematical Biosciences and Engineering, 2021, 18(2): 1169-1186. doi: 10.3934/mbe.2021063
    [8] Shizhen Huang, ShaoDong Zheng, Ruiqi Chen . Multi-source transfer learning with Graph Neural Network for excellent modelling the bioactivities of ligands targeting orphan G protein-coupled receptors. Mathematical Biosciences and Engineering, 2023, 20(2): 2588-2608. doi: 10.3934/mbe.2023121
    [9] Jun Gao, Qian Jiang, Bo Zhou, Daozheng Chen . Convolutional neural networks for computer-aided detection or diagnosis in medical image analysis: An overview. Mathematical Biosciences and Engineering, 2019, 16(6): 6536-6561. doi: 10.3934/mbe.2019326
    [10] Suqi Zhang, Wenfeng Wang, Ningning Li, Ningjing Zhang . Multi-behavioral recommendation model based on dual neural networks and contrast learning. Mathematical Biosciences and Engineering, 2023, 20(11): 19209-19231. doi: 10.3934/mbe.2023849
  • With the development of the smart manufacturing, data-driven fault diagnosis has receiving more and more attentions from both academic and engineering fields. As one of the most important data-driven fault diagnosis method, deep learning (DL) has achieved remarkable applications. However, the DL based fault diagnosis methods still have the following two drawbacks: 1) One of the most major branch of deep learning is to construct the deeper structures, however the deep learning models in fault diagnosis is very shadow. 2) As stated by the no-free-lunch theorem, no single model can perform best on every dataset, and the individual deep learning model still suffers from the generalization ability. In this research, a new negative correlation ensemble transfer learning method (NCTE) is proposed. Firstly, the transfer learning based ResNet-50 is proposed to construct a deep learning structure that has 50 layers. Secondly, several fully-connected layers and softmax classifiers are trained cooperatively using negative correlation learning (NCL). Thirdly, the hyper-parameters of the proposed NCTE are determined by cross validation. The proposed NCTE is conducted on the KAT Bearing Dataset, and the prediction accuracy of NCTE is as high as 98.73%. This results show that NCTE has achieved a good results compared with other machine learning and deep learning method.


    Flight scheduling (FS) and aircraft routing (AR) present the two-core task of daily airline management. FS is aimed to obtain a series of flight trips from their origins at departure times to destinations at arrival times, while AR is used to arrange several airplanes located at different airports to cover all flight trips. If the integrated operation of FS and AR is neglected, aircraft flight scheduling plans based on an unreasonable fixed timetable would require a larger fleet of airplanes. The output of FS being the input of AR in the interactive process of FS and AR preparation, such integration will significantly reduce operation costs [1,2]. Therefore, it is necessary to find their optimal relationship in the integrated FS and AR (IFSAR), in order to pursue the optimal global solution.

    In the process of developing the IFSAR plan, each airline's aircraft routing schedule (solution of AR) is up to its own discretion, but the timetable of each flight line (solution of FS) is jointly determined by the airlines and the civil aviation administration. The airlines will expect to choose a flight time of maximum load rates in pursuit of more profit. If the civil aviation administration determines that this time is within the feasible time window for an aircraft taking off or landing at an airport and passing through an air route related to air traffic control (which depends on weather conditions and military aspects), this flight is allowed. Otherwise, airlines will need to repeatedly submit the flight timetable before it is approved by the civil aviation authority. However, IFSAR with consideration of the interactions between flexible time window, schedule and load rate is less studied.

    Another major motivation of this paper is to address the IFSAR with multi-type aircraft. In the conventional IFSAR, each flight trip with its own particular aircraft type can only be covered by the respective aircraft-type plane. In the proposed model, flight trip via a small airplane can be alternatively covered by a larger one. Compared to IFSAR with a single aircraft type, the proposed model may reduce the aircraft fleet in the case where the supply and demand of different types of aircrafts are not balanced in time and space. However, to the best of the authors' knowledge, no IFSAR with multi-type aircraft has been comprehensively analyzed yet.

    The main contribution of this study is the development of an optimization framework for IFSAR with multiple aircraft type and flexible time window. The study focused on the following critical research tasks: 1) Coordination of FS and AR to reveal optimal relation between flexible schedule, load rate and operation cost; 2) development of a two-stage heuristic model based on ant colony optimization (ACO) algorithm to efficiently yield the acceptable solution. Finally, a real-world case study is used to illustrate the validity of the proposed method.

    The remainder of the paper is organized as follows. Section 2 summarizes the research status of IFSAR. The optimization framework of IFSAR and its mathematical formulation are described in Section 3. Section 4 presents a two-stage heuristic model based on the ACO algorithm. A real-world case is examined to prove the validity of the proposed model and algorithm in Section 5, and some concluding remarks are given in Section 6.

    In recent years, flight scheduling (FS) and aircraft routing (AR) are two key decision problems in airline planning processes. Although they are typically solved sequentially and independently, integration of some of these solutions in airline planning can further enforce decision consistency and achieve significant savings [3]. These integrated models are classified into leg-based methods and itinerary-based methods, where the former ones are well-justified for small- and medium-sized airline companies with a single flight leg, while the latter ones are more applicable for large airline companies with several flight legs [4,5].

    In FS, a profitable flight schedule is optimized to find optimal relation between aircraft utilization, airline revenue generation, and passenger convenience [6]. There are a variety of FSs, involving various objectives, constraints and solution methods [7,8]. Most of these studies assume that static O/D traffic are inputs to the model, resulting in flight delay. However, the demand is highly uncertain especially 10–12 weeks prior to the departure date of a flight. Compared to static FS, dynamic model reschedules a partial change of flights to meet short-term demand changes, which could improve flight schedule punctuality [2,9,10,11]. AR was firstly proposed for network flow methods by Simpson as early as in 1969 [12] and extended by Daskin and Panayotopoulos [13] in a hub-and-spoke-network, in order to build an integer-programming model. In recent years, such integration of AR with extensions of FS, fleet assignment (FA) and crew scheduling (CS) has caused widespread concern in the academic community. The integrated model of AR and FS was firstly proposed by Desaulniers et al. [14] to formulate a set partitioning model and a multi-commodity network flow model, and also extended by Salazar-Gonzalez [15] with extensions in CS, and by Cacchiani and Salazar-Gonzalez [16] to abide by specific rules to obtain both aircraft and crew routes.

    Since the input of AR is derived from scheduled flight departure and arrival times in FS, many works aimed at finding a robust AR scheme with consideration of delay propagation in FS were conducted, e. g. [17,18,19,20]. These works mainly minimized the occurrence and the amount of flight delay in aircraft routing and/or flight retiming based on historical delay data. Due to the complexity of the problem solved independently, several authors [21,22,23] presented some IFSAR models to avoid some shortcomings of these studies. In particular, Sherali et al. [21] studied an IFSAR model with the extension of FA. Jamili [22] extended this work by considering uncertain travel time. Gürkan et al. [23] presented a leg-based IFSAR model with consideration of fuel and CO2 emission costs. Besides, Faust et al. [24] studied an IFSAR model with consideration of maintenance problems. However, the above-mentioned IFSAR studies were based on the deterministic demand. To reduce the loss of operation profit related to the demand variability and disruptions, Kenan et al. [18] further accounted for the demand uncertainty in the IFSAR model. The solution algorithms include the branch-and-price-and-cut algorithm [19], iterative heuristic approach [20,25], row-and-column generation approach [26], and integrated scenario-based heuristic approach [27].

    The above brief survey of available FS & AR & IFSAR models and their solution methods made it possible to identify the shortlist of issues that require a more in-depth analysis:

    1) Although a variety of FSs & ARs were elaborated in several studies, only a few of them took into account a feasible time for an aircraft's take-off and landing at airports and ban time for a plane passing through a certain air route. Similarly, a few of them consider each flight trip with its own special aircraft type being covered by itself or a larger plane.

    2) The basic assumption of conventional FSs is given flight timetabling that is the output for ARs. It implies a neglect of the integrated operation of FS (guide the airline choice of the most profitable departure time of flight trip by taking fares and seats into account) and AR (guide transits from selected flight trips to an aircraft of a particular type).

    3) IFSAR, as an extension of the classic vehicle routing problem (VRP), is also a nondeterministic polynomial time (NP) hard problem, which implies that the exact algorithm cannot find a feasible solution at the acceptable time. Hence, an efficient heuristic algorithm needs to be designed to solve such a problem.

    An airline operates a set of flight trips belonging to different aircraft routes between some airports. Each flight trip with certain travel time is covered by an aircraft from an origin at departure time to the destination at arrival time. Many different types of airplanes are initially located at the docked airports, so any flight trip via a particular aircraft type can be covered by the latter or a larger plane. The aim of multi-aircraft-type IFSAR is to simultaneously determine the departure time of each flight trip and assign a set of airplanes located at different airports to perform all flight trips. The departure and arrival time of each flight trip must be within a flexible time window in its aircraft's route and origin/destination airports, related to air traffic control. If two adjacent flight trips are covered by the airplane, the arrival time of the previous flight trip plus airplane's maintenance time should not exceed the departure time of the next flight trip, except for the case where the origin airport of the former trip coincides with the destination airport of the latter one. In view of aircraft maintenance and the required leisure time of pilots, an aircraft can perform at least two flight trips, in which origin airport of the first flight trip is the same as the destination airport of the last one. To reveal the optimal relationship between FS and AR to maximize the operational efficiency and passenger sales revenues, an integrated mixed-integer programming model was elaborated to pursue the optimal global value.

    Figure 1 provides a detailed description of the proposed method. There are six flight trips (F1–F6) between three airports (A1–A3). The aircraft type for the first two flight trips is T1, while that of the last four flight trips is T2. In this example, the optimization process yields a trip timetable and two aircraft routes as follows. A T1 aircraft is illustrated by a solid line F1-F2-F4-F6, and a T2 aircraft is illustrated by a solid line F3-F5. The arrival and departure times are 5:20–6:30, 7:30–9:50, 7:00–9:30, 10:30–12:30, 9:50–11:30 and 13:10–14:30, respectively. If departure time of F2 is delayed by an hour in a fixed timetable, the original T1 aircraft can't continue to run the remaining two flights, and a new T2 aircraft is illustrated by a solid line F4-F6. Obviously, traditional FS, being independent of AR, need more than one T2 aircraft, which further proves the validity of our model. Similarly, traditional AR with single aircraft type is worse than our model. Our objective is to find an aircraft flight timetabling and scheduling plan that would simultaneously minimize the weighted operation costs for the fleet of airplanes and the total idle and running time for each flight trips covered by different aircraft, as well as maximize the total passenger sales revenues for all flight trips. To ensure that this approach fits well with the actual situations, the following assumptions are made:

    Figure 1.  Graphical representation of the IAFTSP problem solution.

    (1) Each flight trip is provided by one airplane, which cannot cover two flight trips at the same time.

    (2) According to air traffic control, each airport has its own flexible time window for flight trips to take off or land, which can be given in advance. Similarly, a plane running flight trip must pass through the air route in fixed time windows.

    (3) Passenger sales revenues of each flight trip are related to its departure time, which determines the number of passengers and fares at the time. Through the big data analysis of airline operations, a simple linear piecewise function describing this relationship can be obtained.

    (4) The travel time of each flight trip is a certain value, which is independent of weather conditions, traffic control, etc.

    To facilitate the model elaboration, all definitions and notations used hereafter are summarized in Table 1.

    Table 1.  Parameters and variables in the proposed model.
    Indices
    i,j Flight trip index
    0 Virtual flight
    h Time section
    r Air route
    k Aircraft index
    t Aircraft type index
    d Airport index
    Sets
    F Set of trips
    T Set of aircraft types
    D Set of airports
    H Set of time sections
    Ri Set of air routes related to trip i
    Ktd Set of aircraft belonging to the particular type t located at airport d
    Parameters
    spi Starting (origin) airport of trip i
    dpi Ending (destination) airport of trip i
    Ti Total travel time of trip i
    Tir Travel time for the aircraft flight from the origin airport of trip i to the origin of air route r
    bi The capacity related to the particular aircraft type for trip i
    p(sti) Number of passengers' demand for trip i at its departure time
    Bt The capacity related to aircraft type t
    Ts Minimum safe time
    DTLhd The earliest departure time of a plane at the airport d during time section h
    DTUhd The latest departure time of a plane at the airport d during time section h
    ATLhd The earliest arrival time of a plane at the airport d during time section h
    ATUhd The latest arrival time of a plane at the airport d during time section h
    PTLhr The earliest time of a plane passing through the air route r during time section h
    PTUhr The latest time of a plane passing through the air route r during time section h
    θ Minimum load rate of an aircraft
    c1t Fixed cost of aircraft type t
    c2t Cost of idle time RMB/hour
    c3t Operational cost RMB/hour
    M A very large fixed value
    Decision variables
    xkij Whether trip i precedes trip j on aircraft k or not
    yki Whether trip i is covered by the aircraft k or not
    sti The departure time of trip i
    eti The arrival time of trip i, i.e., sti+Ti=eti
    Uik An auxiliary (real) variable for sub-tour elimination constraint in aircraft k

     | Show Table
    DownLoad: CSV

    The problem under study can be formulated as the following mixed-integer program (MIP), which requires minimization of

    minf1=dDtTkKtd[c1t+iFTiykic2t+i,jFxkij.(stjetiTiTs)c3t] (1)
    maxf2=iFp(sti) (2)

    which is subject to:

    iFyki=1,kKtd  dD  tT (3)
    bi+(1yki)MBt,kKtd  dD  tT (4)
    p(sti)/Bt+(1yki)Mθ,  kKtd  dD  tT (5)
    2xkijyki+ykj,i,jF    kKtd  dD  tT (6)
    jF{0}xkij=jF{0}xkji=yki,iF    kKtd  dD  tT (7)
    UikUjk+|F{0}|xkij|F{0}|1,i,jF    kKtd  dD  tT (8)
    sti+Ti+(1xkij)M+Tsstj,i,jF    kKtd  dD  tT (9)
    dpi+(1xkij)M=spj,i,jF    kKtd  dD  tT (10)
    iFxki0=iFxk0i=1,  kKtd  dD  tT (11)
    d+(1xk0i)M=spj,iF    kKtd  dD  tT (12)
    d+(1xki0)M=dpj,iF    kKtd  dD  tT (13)
    DTLhd(1xk0i)M+stiDTUhd,  hH  iF    kKtd  dD  tT (14)
    ATLhd(1xk0i)M+etiATUhd,  hH  iF    kKtd  dD  tT (15)
    PTLhrsti+TirPTUhr,  hH    rRi  iF (16)

    In the above formulation, the primary objective function is given by Eq (1), which includes three terms: The first term deals with a fixed cost of flight fleet, the second one involves operation cost as the total mileage cost of designed routes; while the third one is related to the loss cost of the total idle time for adjacent flight trips covered by an aircraft. The secondary objective function in Eq (2) aims at maximizing the total number of transported passengers in all flight trips. Constraints (3) and (4) guarantee that each flight trip must be assigned to an aircraft of the same type or a larger one. Constraint (5) ensures that the load factor of an aircraft exceeds a certain value. Constraints (6) and (7) imply that all flight trips served by the aircraft should have the same incoming and outgoing arcs. Constraint (8) is used for the sub-tour elimination in the aircraft routing. Constraints (9) and (10) guarantee that the arrival airport of the former is the same as departure airport of the latter, while the arrival time of the former plus aircraft's maintenance time should not exceed the departure time of the latter if adjacent flight trips are covered by the same aircraft. Constraint (11) guarantees that each plane leaves the base airport and eventually returns to the base airport. Constraints (12) and (13) guarantee that a particular type of aircraft firstly leaves the docked airport, then performs a sequence of flight trips and eventually returns to the docked airport. Constraints (14) and (15) ensure that departure and arrival times of each flight trip are within a flexible time window in its origin/destination airport. Constraint (16) grants that time of a plane passing through the air route is within its flexible time window.

    The proposed mixed-integer model is used to solve the extended classic VRP. Noteworthy that this is also a nondeterministic polynomial time (NP) hard problem, which cannot be solved by any exact method at an acceptable running time, especially for large-scale cases. To improve the computation efficiency, this study further proposes an ant colony optimization-based two-stage heuristic algorithm to yield meta-optimal solutions in a reasonable amount of time.

    The ant colony optimization (ACO) principle proposed by Dorigo in 1997 envisages searching for an optimal path in the graph based on the behavior of ants seeking a path between their colony and source of food. Ants navigate from nest to food source, move at random, and deposit pheromone on their path, while the shortest path is discovered by the maximal amount of pheromone trails left by ants who used this path [28].

    In this section, an ACO-based two-stage heuristic algorithm is designed to realize the proposed model. At the first stage, we assign all flight trips to a set of airplanes initially located at different base airport routes by satisfying each flight trip with its own particular aircraft type being covered by itself or a larger plane. Then, the flight timetable containing the arrival and departure times of each flight trip is scheduled based on the principle of maximizing the total passenger sales revenues for all flight trips at the second stage. Technically, the whole structure is constructed using the ant colony optimization, in which a polynomial algorithm is further embedded for implementing the second stage, as shown in Figure 2.

    Figure 2.  The ACO algorithm flowchart.

    At the first stage, we aim to assign all flight trips to different aircraft routes considering network constraint trajectories. For this purpose, we adopt ACO, in which imaginary ants are placed at the docked airport (aircraft's route origin), and then they will visit the whole trip set for assigning flight trips to routes. The required steps of the proposed algorithm are listed in Table 2.

    Table 2.  Algorithm for assigning flight trips to aircraft routes.
    Step 1. Initialization.
    1) Basic parameters: Number of ants, number of routes, and the maximal number of iterations
    2) Pheromone τij(0) and pheromone increment τij(0)between each arc (i, j) (In our case, pheromone τij represents the desirability of trip j preceding trip i on the route k), in which τij(0) and τij(0)will be initialized to a constant value and zero, respectively;
    Step 2. Network preparation.
    1) A sequence of trips by their pre-defined departure time windows, i.e., sti[PTLhrTir,PTUhrTir];
    2) Place of M ants at the earliest trip;
    Step 3. Generation of candidate routes' set, allowed, for trip i, in which:
    allowed={k|etψ(k)+Tsstidpψ(k)=spi,kK}, where ψ(k) represents the trip proceeding trip i on route k;
    Step 4. Selection of route k from the set, allowed, to visit trip i, where we use a pseudo-random-proportional-based transition rule. A random variable, q, which is uniformly distributed within the interval from 0 to 1, is initialized to compare with a pre-defined parameter q0(0,1]. The route k serving trip i is determined by argmaxkallowed{τψ(k)i(t)[ηik]β} where qq0; otherwise, it will follow the probability function pmik=ταψ(l)i(t)ηikβlϵallowedταψ(l)i(t)ηilβ to decide, which ant (plane) will visit trip i. Note that α and β represent the relative effects of the pheromone trail and heuristic information, respectively, while ηik=1/(stietψ(k)Ts+0.01) means the cost of route k visiting trip i.
    Step 5. Repeat steps 3 and 4 until all trips are successfully assigned.

     | Show Table
    DownLoad: CSV

    Stage Ⅰ has assigned trips to routes, as well as determined the sequence of each route visiting its trips. Stage Ⅱ will be activated to schedule a timetable in a feasible departure time window with the account of the airline revenue maximization. Note that both the route design and air traffic control determine a feasible departure time window. A polynomial algorithm is implemented at this stage, while its detailed procedures are listed in Table 3.

    Table 3.  Algorithm for flight timetable for each trip.
    Step 1. For route k, calculation of departure time window of each trip via Eq (15), sti[PTLhrTir,PTUhrTir].
    Step 2. For route k and trip j linked with trip i;
    1) Obtaining of departure time window of trip j, since it is equal to [PTLhrTir+Ti+Ts,PTUhrTir+Ti+Ts][PTLhrTjr,PTUhrTjr]
    2) Generation of the threshold for the departure time of each flight trip i with its origin airport's flexible working time via Eqs (13) and (14), which belongs to [DTLhd,DTUhd][ATLhdTi,ATUhdTi];
    3) A search of all possible departure times within the threshold of trip i to target the one with the maximization of iFp(sti), sti[PTLhrTir+Ti+Ts,PTUhrTir+Ti+Ts][PTLhrTjr,PTUhrTjr][DTLhd,DTUhd][ATLhdTi,ATUhdTi];
    Step 3. Repeat step 2 until the departure times of all trips in each route are scheduled.

     | Show Table
    DownLoad: CSV

    Feasibility of the initial solution generated by one ant through stages Ⅰ and Ⅱ will be checked, and the objective value will be updated, in case that the solution is feasible for the proposed model. Subsequently, the local pheromone amount data will keep updating until all ants are used in one iteration. The best solution obtained from the current iteration will be stored to update the global pheromone data until reaching the maximal number of iterations. Once all iterations run out, the optimal solution will be generated and stored.

    In this section, a real example of small- to a medium-sized airline in China, consisting of 32 flight trips (F1–F32) between eleven airports (D1–D11), and two types of aircraft for these trips (T1 and T2), is used to illustrate the applicability of the proposed model and algorithm. The departure and arrival times, starting and ending airport, aircraft type, and feasible departure time window of each flight trip are listed in Table 4. Obviously, the departure time of each trip must satisfy the flexible time window in its aircraft's route and origin/destination airports. The key parameters used in the case study are given as follows:

    Table 4.  Basic information on flight trips.
    Trip No. Origin/destination Flexible departure time window Flight time (min) Aircraft type
    F1 D1- > D2 6:30–7:30 60 T1
    F2 D2- > D1 12:30–14:00 90 T1
    F3 D1- > D2 7:00–9:00 120 T1
    F4 D2- > D1 12:00–14:00 70 T1
    F5 D1- > D3 19:00–20:30 60 T2
    F6 D3- > D1 17:00–18:00 60 T2
    F7 D8- > D4 11:00–13:00 80 T2
    F8 D4- > D1 7:00–8:00 90 T2
    F9 D1- > D5 11:00–12:30 90 T2
    F10 D5- > D1 8:00–9:30 120 T2
    F11 D1- > D6 7:00–9:00 120 T1
    F12 D6- > D5 5:00–6:00 60 T1
    F13 D1- > D2 6:00–6:30 60 T1
    F14 D7- > D1 7:00–8:30 80 T1
    F15 D8- > D9 6:30–8:00 60 T2
    F16 D9- > D7 5:00–6:30 60 T2
    F17 D8- > D10 18:00–19:00 150 T1
    F18 D10- > D8 22:00–23:00 70 T1
    F19 D8- > D1 6:00–7:30 60 T2
    F20 D11- > D1 5:00–6:30 60 T2
    F21 D6- > D9 12:00–14:00 80 T1
    F22 D9- > D8 10:00–11:00 60 T1
    F23 D9- > D11 14:00–16:00 90 T2
    F24 D11- > D8 7:30–9:00 150 T2
    F25 D8- > D9 11:00–13:00 90 T1
    F26 D9- > D8 8:00–10:00 90 T1
    F27 D1- > D2 11:00–12:30 60 T1
    F28 D2- > D1 8:00–10:00 80 T1
    F29 D1- > D2 9:00–11:00 60 T2
    F30 D2- > D1 8:00–9:30 90 T2
    F31 D1- > D3 9:30–11:00 120 T2
    F32 D3- > D1 11:00–12:30 70 T2

     | Show Table
    DownLoad: CSV

    ●  Fixed cost of aircraft type t:c1T1 = 10000 RMB/plane and c1T2 = 11000 RMB/plane.

    ●  The idle time cost of aircraft type t:c2T1 = 1.7 RMB/min and c2T2 = 2.5 RMB/min.

    ●  The operational cost of aircraft type t:c3T1 = 1.9 RMB/min and c3T2 = 3 RMB/min.

    ●  Capacity related to aircraft type t:BT1 = 150 persons and BT2 = 200 persons.

    ●  Minimum load rate:θ = 0.7.

    ●  Minimum safe time:Ts = 30 min.

    Table 5 describes the optimal aircraft route and timetable, which include the departure time, assigned aircraft type, and load rate of each flight trip. Two T1 planes (each carrying up to 150 passengers) and nine T2 planes (each carrying up to 200 passengers) were required for covering 32 trips. The total ideal time of 2795 minutes and running time of 2660 minutes were obtained. A total of 133,648 RMB was spent, in order to transport 5035 passengers by these planes, which amounted to 26.55 RMB per capita. Taking route A2 as an example, a T2 aircraft will leave the base airport D11, cover flight trips F20, F1, F30, and F5 and complete its flights at the base airport D3. The flight trip F1 with the T1 plane could be covered by a larger plane T2, which would pick up 140 passengers at 7:05. In this case, the plane load rate was 140/200 = 0.7. Before performing flight trip F1, it will stay at the airport for the expected ideal time of about 60 min.

    Table 5.  Routing and scheduling plan of each plane.
    Aircraft No. Aircrafttype The sequence of flight trips covered by each plane Running time (min) Ideal time (min) Operation cost (RMB)
    A1 T2 D6 - F12 (5:10,150, 0.75) - F10 (8:50,200, 1) -F32 (12:05,200, 1) - F6 (17:45,180, 0.9) - D1 310 737.5 13774
    A2 T2 D11 - F20 (5:05,140, 0.7) - F1 (7:05,140, 0.7) - F30 (8:55,150, 0.75) - F5 (20:10,160, 0.8) - D3 270 575 13248
    A3 T2 D9 - F16 (5:30,160, 0.8) - F14 (8:15,150, 0.75) -F27 (11:55,150, 0.75) - D2 200 165 12013
    A4 T1 D1 - F13 (6:05,140, 0.93) - F2 (13:10,150, 1) - D1 150 325 10838
    A5 T2 D8 - F19 (6:30,160, 0.8) - F31 (10:15,180, 0.9) - D3 180 127.5 11859
    A6 T2 D4 - F8 (7:55,160, 0.8) - F29 (10:00,180, 0.9) - F4 (13:10,140, 0.7) - D1 220 145 12023
    A7 T2 D1 - F3 (7:15,140, 0.7) - F28 (9:35,150, 0.75) - F9 (12:15,180, 0.9) - D5 290 20 11920
    A8 T2 D8 - F15 (7:15,160, 0.8) - F22 (10:40,150, 0.75) - F17 (18:20,150, 0.75) - F18 (22:40,150, 0.75) - D8 340 535 13358
    A9 T1 D1 - F11 (7:25,135, 0.9) - F21 (12:45,150, 1) - D9 200 160 10652
    A10 T2 D11 - F24 (8:15,160, 0.8) - F7 (12:15,170, 0.85) - D4 230 50 11815
    A11 T2 D9 - F26 (9:05,150, 0.85) - F25 (12:15,140, 0.7) - F23 (15:40,160, 0.8) - D11 270 135 12148
    TOTAL: 2660 2795 133648

     | Show Table
    DownLoad: CSV

    Furthermore, the proposed model (AFSRP with multi-type aircraft) has some advantages over the AFSRP with a single aircraft type, which are shown in Table 6. The operation costs defined via the proposed model will be reduced by 26.2%. However, the total number of transported persons via the proposed model will be lower by 5.8% than that determined via the conventional one. This is due to the fact that the flight trip covered by a particular aircraft type increases both the number of needed airplanes and the total idle time for two adjacent flight trips covered by the same airplane. In the case where the departure time of the timetable is more flexible, the airline may schedule flights at a time when more passengers are willing to travel. As shown above, the increase in operation costs is fully compensated by the decrease in fixed cost for fleets, which proves that the proposed model feasibility.

    Table 6.  Comparative analysis of the proposed and conventional models.
    Scenario Number ofT1 planes Number ofT2 planes Total running time (min) Total ideal time (min) Number of passengers Operation costs (RMB)
    Proposed model 2 9 2660 2795 5035 133,648
    Conventional model 8 8 2660 3157.5 5345 181,057
    Difference, % −75 12.5 0 −11.5 5.8 −26.2

     | Show Table
    DownLoad: CSV

    Figures 3 and 4 illustrate how the changes in the load rate affect a trade-off between the operation cost and the number of transported persons. As the load rate β gradually increases from 0.7 to 0.85, both of them are also increased. The reason is that higher load rates lead to more restrictions on the flexible choice of timetables, aiming at scheduling flights at a time when more passengers are willing to travel. In this case, the fleet size cannot be saved by fine-tuning the schedule. The increase in fleet size was accompanied by a rise in the ideal time. Hence, operation costs would also grow.

    Figure 3.  The load rate effect on the number of transported persons.
    Figure 4.  The load rate effect on operation costs.

    This paper presents an integrated optimization framework for IAFTSP with multiple aircraft type to reveal the relationship between temporal and spatial distributions of flight trips, the number of airplanes firstly distributed in the base airports, flight timetabling and scheduling plan. In contrast to available approaches, the proposed one envisages the following two innovations: (ⅰ) It simultaneously coordinates an interactive process of determining the departure times of all flight trips and assigns them to different airplanes, and (ⅱ) it adopts a two-stage heuristic algorithm based on ACO to efficiently yield the acceptable solution. A case study is used to validate the feasibility and applicability of the proposed framework. Results show that operation costs estimated via the proposed model will be reduced by 26.2%, while the total number of transported persons will be increased by 5.8%, as compared to the conventional model. With an increase in the plane load rate, both operation costs and number of transported persons are slightly increased.

    Noteworthy is that, in this study, each flight trip was allocated a certain travel time, which neglected random perturbations and respective changes in the travel time. To this end, robust solutions of IAFTSP with random travel time and the related failure recovery are the two major issues in day-to-day operations. Therefore, extending the IAFTSP to the simultaneous determination of delayed times of some flight trips or canceled ones, and the assignment of uncertain flight trips to airplanes in the follow-up studies is quite expedient.

    This study was financially supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China (20YJCZH176); the central college basic scientific research operating expenses fund in civil aviation university of China (3122020079).

    The authors declare there is no conflict of interest.



    [1] L. Wen, Y. Dong and L. Gao, A new ensemble residual convolutionalneural network for remaining useful life estimation, Math. Biosci. Eng., 16 (2019), 862–880.
    [2] H. D. Shao, H. K. Jiang, X. Zhang, et al., Rolling bearing fault diagnosis using an optimization deepbelief network, Meas. Sci. Tech., 26 (2015), 115002.
    [3] R. Zhao, R. Yan, Z. Chen, et al., Deep learning and itsapplications to machine health monitoring: A survey. arXiv preprint arXiv:1612.07640, 2016.
    [4] M. Cerrada, R. V. Sánchez, C. Li, et al., A review on data-driven fault severityassessment in rolling bearings, Mech. Syst. Signal Proc., 99 (2018), 169–196.
    [5] Y. Bengio, A. Courville and P. Vincent, Representation learning: a review and new perspectives, IEEE T. Pattern Anal. Mach. Intell., 35 (2013), 1798–1828.
    [6] L. Wen, L. Gao and X. Y. Li, A new deep transfer learning based on sparseauto-encoder for fault diagnosis, IEEE T.Syst. Man Cybern. Syst., 49 (2019), 136–144.
    [7] J. L. Wang, J. Zhang and X. X. Wang, A data driven cycle time prediction with featureselection in a semiconductor wafer fabrication system, IEEE T. Semicond. Manuf., 31 (2018), 173–182.
    [8] S. Shao, S. McAleer, R. Yan, et al., Highly-accuratemachine fault diagnosis using deep transfer learning, IEEE T. Ind. Inform., 15 (2019), 2446–2455.
    [9] Z. Y. Wang, C. Lu and B. Zhou, Fault diagnosis for rotary machinery with selectiveensemble neural networks, Mech. Syst.Signal Proc., 113 (2018), 112–130.
    [10] D. H. Wolpert and W. G.Macready, No free lunch theorems for optimization, IEEE T. Evol. Comput., 1 (1997), 67–82.
    [11] H. Y. Sang, Q. K. Pan, J. Q. Li, et al., Effectiveinvasive weed optimization algorithms for distributed assembly permutationflowshop problem with total flowtime criterion, Swarm Evol. Comput., 44 (2019), 64–73.
    [12] X. Y. Li, C. Lu, L. Gao, et al., An Effective Multi-Objective Algorithm forEnergy Efficient Scheduling in a Real-Life Welding Shop, IEEE T. Ind. Inform., 14 (2018), 5400–5409.
    [13] J. Yosinski, J. Clune, Y. Bengio, et al., How transferable arefeatures in deep neural networks? In Advances in neural information processingsystems, (2014), 3320–3328.
    [14] L. Wen, X. Y. Li and L. Gao, A New Two-level Hierarchical Diagnosis Network based onConvolutional Neural Network, IEEE T.Instrum. Meas., (2019).
    [15] H. Y. Sang, Q. K. Pan, P. Y. Duan, et al., Aneffective discrete invasive weed optimization algorithm for lot-streamingflowshop scheduling problems. J. Intell.Manuf., 29 (2018), 1337–1349.
    [16] X.Y. Li, L. Gao, Q. Pan, et al., An effectivehybrid genetic algorithm and variable neighborhood search for integratedprocess planning and scheduling in a packaging machine workshop. IEEE Trans. Syst. Man Cybern. Syst., (2018).
    [17] K. Tidriri, N. Chatti, S. Verron, et al., Bridging data-driven andmodel-based approaches for process fault diagnosis and health monitoring: Areview of researches and future challenges, Annu.Rev. Control, 42 (2016), 63–81.
    [18] Z. Y. Yin and J. Hou, Recent advances on SVMbased fault diagnosis and process monitoring in complicated industrialprocesses, Neurocomputing, 174 (2016), 643–650.
    [19] J. Zheng, L. Gao, H. B. Qiu, et al., Difference mapping methodusing least square support vector regression for variable-fidelityapproximation modelling, Eng. Optimiz., 47 (2015), 719–736.
    [20] T. Han, D. Jiang, Q. Zhao, et al., Comparison of random forest,artificial neural networks and support vector machine for intelligent diagnosisof rotating machinery, Trans. Inst. Meas.Control, (2017), 1–13.
    [21] B. Cai, L. Huang and M. Xie, Bayesian networks in fault diagnosis, IEEE T. Ind. Inform., 13 (2017), 2227–2240.
    [22] L. Wen, L. Gao and X. Y. Li, A new snapshot ensemble convolutional neuralnetwork for fault diagnosis, IEEE Access, 7 (2019), 32037–32047.
    [23] F. Wang, H. K. Jiang, H. D. Shao, et al., An adaptive deepconvolutional neural network for rolling bearing fault diagnosis, Meas. Sci. Technol., 28 (2017), 9.
    [24] J. L. Wang, J. Zhang and X. X. Wang, Bilateral LSTM: Atwo-dimensional long short-term memory model with multiply memory units forshort-term cycle time forecasting in re-entrant manufacturing systems. IEEE T. Ind. Inform., 14 (2018), 748–758.
    [25] J. Pan, Y. Zi, J. Chen, et al., LiftingNet: A novel deep learningnetwork with layerwise feature learning from noisy mechanical data for faultclassification, IEEE T. Ind. Inform., 65 (2018), 4973–4982.
    [26] S. B. Li, G. K. Liu, X. H. Tang, et al., An ensemble deepconvolutional neural network model with improved ds evidence fusion for bearingfault diagnosis, Sensors, 17 (2017), 1729.
    [27] C. Lu, Z. Y. Wang and B. Zhou, Intelligent fault diagnosis of rolling bearing using hierarchicalconvolutional network based health state classification, Adv. Eng. Inform., 32 (2017), 139–151.
    [28] B. Zhang, W. Li, X. Li, et al., Intelligent fault diagnosis undervarying working conditions based on domain adaptive convolutional neural networks, IEEE Access, 6 (2018), 66367–66384.
    [29] J. Donahue, Y. Q. Jia, O, Vinyals, et al., Decaf: A deepconvolutional activation feature for generic visual recognition, Internationalconference on machine learning, (2014),647–655.
    [30] R. Ren, T. Hung and K. C. Tan, A generic deep-learning-based approach for automatedsurface inspection, IEEE T. Cybern., 48 (2018), 929–940.
    [31] J. Wehrmann, G. S. Simoes and R. C. Barros, et al., Adultcontent detection in videos with convolutional and recurrent neural networks, Neurocomputing, 272 (2017), 432–438.
    [32] H. C. Shin, H. R. Roth, M. C. Gao, et al., Deep convolutionalneural networks for computer-aided detection: CNN architectures, datasetcharacteristics and transfer learning, IEEET. Med. Imaging, 35 (2016), 1285–1298.
    [33] E. Rezende, G. Ruppert, T. Carvalho, et al., Malicious softwareclassification using transfer learning of ResNet-50 deep neural network, 201716th IEEE International Conference on Machine Learning and Applications (ICMLA), (2017), 1011–1014.
    [34] O. Janssens, R. Walle, M. Loccufier, et al., Deep learning forinfrared thermal image based machine health monitoring. IEEE-ASME Trans. Mechatron., 23 (2018), 151–159.
    [35] Y. Zhou, W. C. Yi, L. Gao, et al., Adaptive differential evolution with sortingcrossover rate for continuous optimization problems. IEEE T. Cybern., 47 (2017), 2742–2753.
    [36] H. Y. Sang, P. Y. Duan and J. Q. Li, An effective invasive weed optimization algorithm forscheduling semiconductor final testing problem. Swarm Evol. Comput., 38 (2018), 42–53.
    [37] L. K. Hansen and P. Salamon, Neural network ensembles, IEEE T. Pattern Anal. Mach. Intell., 12 (1999), 993–1001.
    [38] H. H. Chen and X. Yao, Regularized negative correlation learning for neuralnetwork ensembles, IEEE T. Neural Netw., 20 (2009), 1962–1979.
    [39] J. C. Fernández, M. Cruz-Ramírez and C. Hervás-Martínez, Sensitivityversus accuracy in ensemble models of artificial neural networks frommulti-objective evolutionary algorithms. NeuralComput. Appl., 30 (2018), 289–305.
    [40] C. Hu, B. D. Youn, P. Wang, et al., Ensemble of data-drivenprognostic algorithms for robust prediction of remaining useful life, Reliab. Eng. Syst. Saf., 1 (2012), 120–35.
    [41] Z. Wu, W. Lin and Y. Ji, An integrated ensemble learning model for imbalanced faultdiagnostics and prognostics. IEEE Access, 6 (2018), 8394–8402.
    [42] U. P. Chong, Signal model-based fault detection and diagnosis forinduction motors using features of vibration signal in two-dimension domain. Strojniski Vestn. J. Mech. Eng., 57 (2011), 655–666.
    [43] L. Wen, X. Y. Li, L. Gao, et al., A new convolutional neuralnetwork based data-driven fault diagnosis method, IEEE Trans. Ind. Electron., 65 (2018), 5990–5998.
    [44] K. M. He, X.Y. Zhang, S. Q. Ren, et al., Deep residuallearning for image recognition, IEEE Conference on Computer Vision and PatternRecognition, (2016),770–778.
    [45] K. M. He, X. Y. Zhang, S. Q. Ren, et al., Delving deep into rectifiers: Surpassing human-level performanceon ImageNet classification. IEEEInternational Conference on Computer Vision, (2015),1026–1034.
    [46] M. Xiao, L. Wen, X. Li, et al., Modelingof the feed-motor transient current in end milling by using varying-coefficientmodel. Math. Probl. Eng., (2015).
    [47] S. Arlot and A. Celisse, A survey ofcross-validation procedures for model selection, Statistics surveys, 4 (2010), 40–79.
    [48] I. H. Witten, E. Frank, M. A. Hall, et al., Data Mining: Practical machinelearning tools and techniques. Morgan Kaufmann, (2016).
    [49] C. Lessmeier, J. K. Kimotho, D. Zimmer, et al., Conditionmonitoring of bearing damage in electromechanical drive systems by using motorcurrent signals of electric motors: A benchmark data set for data-drivenclassification. European Conference of the Prognostics and Health ManagementSociety, 05-08, (2016).
    [50] T. Han, D. Jiang, Q. Zhao, et al., Comparison of random forest, artificial neural networks andsupport vector machine for intelligent diagnosis of rotating machinery. Trans. Inst. Meas. Control, (2017), 1–13.
    [51] Y. H. Chen, G. L. Peng, C. H. Xie, et al., ACDIN: Bridging the gapbetween artificial and real bearing damages for bearing fault diagnosis, Neurocomputing, 294 (2018), 61–71.
    [52] Z. Y. Zhu, G. L. Peng, Y. H. Chen, et al., A convolutional neuralnetwork based on a capsule network with strong generalization for bearing faultdiagnosis, Neurocomputing, 323 (2019), 62–75.
  • This article has been cited by:

    1. Chuan Li, Shaohui Zhang, Yi Qin, Edgar Estupinan, A systematic review of deep transfer learning for machinery fault diagnosis, 2020, 407, 09252312, 121, 10.1016/j.neucom.2020.04.045
    2. Changhe Zhang, Li Kong, Qi Xu, Kaibo Zhou, Hao Pan, Fault diagnosis of key components in the rotating machinery based on Fourier transform multi-filter decomposition and optimized LightGBM, 2021, 32, 0957-0233, 015004, 10.1088/1361-6501/aba93b
    3. Hao Sheng, Zhongsheng Chen, Yemei Xia, Jing He, 2020, Review of Artificial Intelligence-based Bearing Vibration Monitoring, 978-1-7281-5181-6, 58, 10.1109/PHM-Jinan48558.2020.00018
    4. Wentao Luo, Jianfu Zhang, Pingfa Feng, Dingwen Yu, Zhijun Wu, A concise peephole model based transfer learning method for small sample temporal feature-based data-driven quality analysis, 2020, 195, 09507051, 105665, 10.1016/j.knosys.2020.105665
    5. Jinyang Jiao, Ming Zhao, Jing Lin, Kaixuan Liang, A comprehensive review on convolutional neural network in machine fault diagnosis, 2020, 417, 09252312, 36, 10.1016/j.neucom.2020.07.088
    6. Gui-Rong You, Yeou-Ren Shiue, Wei-Chang Yeh, Xi-Li Chen, Chih-Ming Chen, A Weighted Ensemble Learning Algorithm Based on Diversity Using a Novel Particle Swarm Optimization Approach, 2020, 13, 1999-4893, 255, 10.3390/a13100255
    7. Ruqiang Yan, Fei Shen, Chuang Sun, Xuefeng Chen, Knowledge Transfer for Rotary Machine Fault Diagnosis, 2020, 20, 1530-437X, 8374, 10.1109/JSEN.2019.2949057
    8. Gandi Satyanarayana, P. Appala Naidu, Venkata Subbaiah Desanamukula, Kadupukotla Satish kumar, B. Chinna Rao, A mass correlation based deep learning approach using deep Convolutional neural network to classify the brain tumor, 2023, 81, 17468094, 104395, 10.1016/j.bspc.2022.104395
    9. Asefeh Asemi, Andrea Ko, Adeleh Asemi, Infoecology of the deep learning and smart manufacturing: thematic and concept interactions, 2022, 40, 0737-8831, 994, 10.1108/LHT-08-2021-0252
    10. Jin Kyu Oh, Jun Young Lee, Sung-Jong Eun, Jong Mok Park, New Trends in Innovative Technologies Applying Artificial Intelligence to Urinary Diseases, 2022, 26, 2093-6931, 268, 10.5213/inj.2244280.140
    11. Xin Pei, Shaohui Su, Linbei Jiang, Changyong Chu, Lei Gong, Yiming Yuan, Research on Rolling Bearing Fault Diagnosis Method Based on Generative Adversarial and Transfer Learning, 2022, 10, 2227-9717, 1443, 10.3390/pr10081443
    12. Zhiping Song, 2022, Mathematical Modeling Method based on Neural Network and Computer Multi-Dimensional Space, 978-1-7281-8115-8, 1080, 10.1109/ICETCI55101.2022.9832088
    13. Fei Xia, Xiaojun Xie, Zongqin Wang, Shichao Jin, Ke Yan, Zhiwei Ji, A Novel Computational Framework for Precision Diagnosis and Subtype Discovery of Plant With Lesion, 2022, 12, 1664-462X, 10.3389/fpls.2021.789630
    14. Zhang Zhihao, Wang Zumin, 2022, Research on rolling bearing fault diagnosis method based on hybrid deep learning network model, 978-1-6654-5417-9, 406, 10.1109/iThings-GreenCom-CPSCom-SmartData-Cybermatics55523.2022.00091
    15. Lifa Fang, Yanqiang Wu, Yuhua Li, Hongen Guo, Hua Zhang, Xiaoyu Wang, Rui Xi, Jialin Hou, Using Channel and Network Layer Pruning Based on Deep Learning for Real-Time Detection of Ginger Images, 2021, 11, 2077-0472, 1190, 10.3390/agriculture11121190
    16. Marcel Braig, Peter Zeiler, Using Data From Similar Systems for Data-Driven Condition Diagnosis and Prognosis of Engineering Systems: A Review and an Outline of Future Research Challenges, 2023, 11, 2169-3536, 1506, 10.1109/ACCESS.2022.3233220
    17. Cinzia Giannetti, Aniekan Essien, Towards scalable and reusable predictive models for cyber twins in manufacturing systems, 2022, 33, 0956-5515, 441, 10.1007/s10845-021-01804-0
    18. Aniekan Emmanuel Essien, Ilias Petrounias, 2022, chapter 7, 9781799898153, 84, 10.4018/978-1-7998-9815-3.ch007
    19. Chenhui Qian, Junjun Zhu, Yehu Shen, Quansheng Jiang, Qingkui Zhang, Deep Transfer Learning in Mechanical Intelligent Fault Diagnosis: Application and Challenge, 2022, 54, 1370-4621, 2509, 10.1007/s11063-021-10719-z
    20. Eui-Sun Kim, Sung-Jong Eun, Seunghyun Youn, The Current State of Artificial Intelligence Application in Urology, 2023, 27, 2093-6931, 227, 10.5213/inj.2346336.168
    21. Yanhua Guo, Ningbo Wang, Shuangquan Shao, Congqi Huang, Zhentao Zhang, Xiaoqiong Li, Youdong Wang, A review on hybrid physics and data-driven modeling methods applied in air source heat pump systems for energy efficiency improvement, 2024, 204, 13640321, 114804, 10.1016/j.rser.2024.114804
    22. Weijie Shen, Maohua Xiao, Zhenyu Wang, Xinmin Song, Rolling Bearing Fault Diagnosis Based on Support Vector Machine Optimized by Improved Grey Wolf Algorithm, 2023, 23, 1424-8220, 6645, 10.3390/s23146645
    23. Iqbal Misbah, C.K.M. LEE, K.L. KEUNG, Fault diagnosis in rotating machines based on transfer learning: Literature review, 2024, 283, 09507051, 111158, 10.1016/j.knosys.2023.111158
    24. Yaochun Wu, Shaohua Du, Guijun Wu, Xiaobo Guo, Jie Wu, Rongzheng Zhao, Chi Ma, Minimum maximum regularized multiscale convolutional neural network and its application in intelligent fault diagnosis of rotary machines, 2025, 00190578, 10.1016/j.isatra.2025.01.044
    25. Qibin Wang, Jie Xia, Mingqi Li, Lei Yin, Xinming Xie, A multi-sensor fusion and multi-source domain adaptive fault diagnosis method for rotating machinery, 2025, 159, 09521976, 111538, 10.1016/j.engappai.2025.111538
  • Reader Comments
  • © 2019 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(8100) PDF downloads(1253) Cited by(25)

Figures and Tables

Figures(8)  /  Tables(7)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog