
Preventive identification of mechanical parts failures has always played a crucial role in machine maintenance. Over time, as the processing cycles are repeated, the machinery in the production system is subject to wear with a consequent loss of technical efficiency compared to optimal conditions. These conditions can, in some cases, lead to the breakage of the elements with consequent stoppage of the production process pending the replacement of the element. This situation entails a large loss of turnover on the part of the company. For this reason, it is crucial to be able to predict failures in advance to try to replace the element before its wear can cause a reduction in machine performance. Several systems have recently been developed for the preventive faults detection that use a combination of low-cost sensors and algorithms based on machine learning. In this work the different methodologies for the identification of the most common mechanical failures are examined and the most widely applied algorithms based on machine learning are analyzed: Support Vector Machine (SVM) solutions, Artificial Neural Network (ANN) algorithms, Convolutional Neural Network (CNN) model, Recurrent Neural Network (RNN) applications, and Deep Generative Systems. These topics have been described in detail and the works most appreciated by the scientific community have been reviewed to highlight the strengths in identifying faults and to outline the directions for future challenges.
Citation: Giuseppe Ciaburro. Machine fault detection methods based on machine learning algorithms: A review[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 11453-11490. doi: 10.3934/mbe.2022534
[1] | Raimund Bürger, Christophe Chalons, Rafael Ordoñez, Luis Miguel Villada . A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function. Networks and Heterogeneous Media, 2021, 16(2): 187-219. doi: 10.3934/nhm.2021004 |
[2] | Maya Briani, Emiliano Cristiani . An easy-to-use algorithm for simulating traffic flow on networks: Theoretical study. Networks and Heterogeneous Media, 2014, 9(3): 519-552. doi: 10.3934/nhm.2014.9.519 |
[3] | Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina . Conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2007, 2(1): 159-179. doi: 10.3934/nhm.2007.2.159 |
[4] | Raimund Bürger, Kenneth H. Karlsen, John D. Towers . On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. Networks and Heterogeneous Media, 2010, 5(3): 461-485. doi: 10.3934/nhm.2010.5.461 |
[5] | Helge Holden, Nils Henrik Risebro . Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Networks and Heterogeneous Media, 2018, 13(3): 409-421. doi: 10.3934/nhm.2018018 |
[6] | Adriano Festa, Simone Göttlich, Marion Pfirsching . A model for a network of conveyor belts with discontinuous speed and capacity. Networks and Heterogeneous Media, 2019, 14(2): 389-410. doi: 10.3934/nhm.2019016 |
[7] | Christophe Chalons, Paola Goatin, Nicolas Seguin . General constrained conservation laws. Application to pedestrian flow modeling. Networks and Heterogeneous Media, 2013, 8(2): 433-463. doi: 10.3934/nhm.2013.8.433 |
[8] | Raimund Bürger, Stefan Diehl, M. Carmen Martí, Yolanda Vásquez . A difference scheme for a triangular system of conservation laws with discontinuous flux modeling three-phase flows. Networks and Heterogeneous Media, 2023, 18(1): 140-190. doi: 10.3934/nhm.2023006 |
[9] | Giuseppe Maria Coclite, Lorenzo di Ruvo, Jan Ernest, Siddhartha Mishra . Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Networks and Heterogeneous Media, 2013, 8(4): 969-984. doi: 10.3934/nhm.2013.8.969 |
[10] | Wen Shen . Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition. Networks and Heterogeneous Media, 2018, 13(3): 449-478. doi: 10.3934/nhm.2018020 |
Preventive identification of mechanical parts failures has always played a crucial role in machine maintenance. Over time, as the processing cycles are repeated, the machinery in the production system is subject to wear with a consequent loss of technical efficiency compared to optimal conditions. These conditions can, in some cases, lead to the breakage of the elements with consequent stoppage of the production process pending the replacement of the element. This situation entails a large loss of turnover on the part of the company. For this reason, it is crucial to be able to predict failures in advance to try to replace the element before its wear can cause a reduction in machine performance. Several systems have recently been developed for the preventive faults detection that use a combination of low-cost sensors and algorithms based on machine learning. In this work the different methodologies for the identification of the most common mechanical failures are examined and the most widely applied algorithms based on machine learning are analyzed: Support Vector Machine (SVM) solutions, Artificial Neural Network (ANN) algorithms, Convolutional Neural Network (CNN) model, Recurrent Neural Network (RNN) applications, and Deep Generative Systems. These topics have been described in detail and the works most appreciated by the scientific community have been reviewed to highlight the strengths in identifying faults and to outline the directions for future challenges.
Traffic flow models based on scalar conservation laws with continuous flux functions are widely used in the literature. For a general presentation of the models, we refer to the books [11,12,23] and the references therein. Extensions to road traffic networks have been also established. We mention in particular the contributions [6,15], where the authors introduce the coupled network problem and show the existence of solutions. Within this article, we are concerned with the special case of scalar conservation laws with discontinuous flux in the unknown that are motivated in the traffic flow theory by the observation of a gap between the free flow and the congested flow regime [4,5,8]. This phenomenon generates an interesting dynamical behavior called zero waves, i.e., waves with infinite (negative) speed but zero wave strength, and has been investigated in recent years either from a theoretical or numerical point of view, see for instance [2,19,20,22,24] or more generally [1,3,7,13].
To the best of our knowledge, the study of scalar conservation laws with discontinuous flux functions on networks is still missing in the traffic flow literature. However, in the context of supply chains with discontinuous flux such considerations have been already done [10,14]. We remark that supply chain models differ essentially from traffic flow models due to simpler dynamics and different coupling conditions.
In this work, we aim to derive a traffic network model, where the dynamics on each road are governed by a scalar conservation law with discontinuous flux function in the unknown. For simplicity, we restrict to piecewise linear flux functions. Special emphasis is put on the coupling at junction points to ensure a unique admissible weak solution. In particular, we focus on dispersing junctions where the number of incoming roads does not exceed the number of outgoing roads and merging with two incoming and one outgoing road. The latter type of junction can be extended to the case of multiple incoming roads and a single outgoing one. In order to construct a suitable numerical scheme that is not based on regularization techniques we adapt the splitting algorithm originally introduced in [22]. Therein, the discontinuous flux is decomposed into a Lipschitz continuous flux and a Heaviside flux such that a two-point monotone flux scheme, e.g., Godunov, can be employed in an appropriate manner. This algorithm has been studied in [22] for the case of a single road only. However, in the network case, multiple roads with possibly disjunctive flux functions need to be considered at a junction point to ensure mass conservation. Hence, the key challenge is to determine the correct flux through the junction in an appropriate manner. Therefore, a detailed case distinction in accordance with the theoretical investigations is provided for the different types of junctions. The numerical results validate the proposed algorithm for some relevant network problems.
The paper is organized as follows: in Section 2 we discuss the basic model and Riemann problems which permit to derive an exact solution. We extend the modeling framework to networks in Section 3 and focus on the coupling conditions. In Section 4, we introduce how the splitting algorithm [22] can be extended to also deal with the different types of junctions. Finally, we present a suitable discretization and numerical simulations in Section 5.
In this section, we briefly recall the case of the Lighthill-Whitham-Richards (LWR) model [18,21] on a single edge with a flux function having a single decreasing jump at
Following [22], we consider the scalar conservation law Eq (2.1),
{ut+f(u)x=0,(x,t)∈(a,b)×(0,T)=:ΠT,u(x,0)=u0(x)∈[0,umax],x∈(a,b),u(a,t)=r(t)∈[0,umax],t∈(0,T),u(b,t)=s(t)∈[0,umax],F(t)∈˜f(s(t)),t∈(0,T). | (2.1) |
More precisely the flux function is defined as follows Eq (2.2),
f(u)={f1(u) ˆ=Flux1,ifu∈[0,u∗],f2(u) ˆ=Flux2,ifu∈(u∗,umax]. | (2.2) |
We denote
α:=f(u∗−)−f(u∗+). | (2.3) |
As usual we require for the flux function
As in [22], the multivalued version of
˜f(u)={f(u),u∈[0,u∗),[f(u∗+),f(u∗−)],u=u∗,f(u),u∈(u∗,umax]. | (2.4) |
Finally, we have to discuss the imposed boundary conditions at
F(t)={f(u∗−),ifthetrafficaheadofx=bisfree−flowing,f(u∗+),ifthetrafficaheadofx=biscongested. | (2.5) |
The state of traffic ahead of
Remark 2.1. [22,Remark 1.3] We note that for the boundary condition at the left end the state of traffic ahead of
The following assumptions are important for the proof of existence and uniqueness of solutions.
Assumption 2.2. [22,Assumption 1.1] The initial data satisfies
A weak solution is intended in the following sense:
Definition 2.3 [22,Definition 1.1] A function
v(x,t)∈˜f(u(x,t))a.e. |
such that for each
∫T0∫ba(uψt+vψx)dxdt+∫bau0(x)ψ(x,0)dx=0. |
As usual, weak solutions do not lead to a unique solution and additional criteria are necessary to rule out physically incorrect solutions. In particular, the discontinuity of the flux prohibits from directly using the classical approaches. Note that in [22] an adapted version of Oleinik's entropy condition [9] is used to single out the correct solution, while in [24] the convex hull construction [17] is used to construct solutions to Riemann problems.
Here, we will concentrate on the convex hull construction. For completeness we will shortly recall the solutions to Riemann problems considered in [24] as they are essential in order to construct a Riemann solver at a junction.
We consider a Riemann problem with initial data
We consider the following flux function by Eq (2, 6),
f(u)={d1u+d0,x≤u∗(Flux1),e1u+e0,x>u∗(Flux2) | (2.6) |
with the regularized flux function given by Eq (2.7),
fϵ(u)={f1(u)=d1u+d0,0≤u≤u∗,fϵmid(u)=−1ϵ(f1(u∗)−fϵ2(u∗+ϵ))(u−u∗)+f1(u∗),u∗<u<u∗+ϵ,fϵ2(u)=e1u+e0,u∗+ϵ<u≤umax. | (2.7) |
We define
Case 1: Either
This case corresponds to the classical case of solving Riemann problems, where the solution consists of a single rarefaction wave or shock, see [17].
Case 2:
By using the smallest convex hull approach the solution consists of a contact line following
s=f(uL)−f(u∗)uL−u∗<0, |
where we recall that
u(x,t)={uL,ifx<st,u∗,ifst≤x≤d1t,uR,ifx>d1t. | (2.8) |
Case 3:
Here, the solution is given by a shock connecting
s=f(u∗+)−f(uL)u∗−uL<0. |
Note that due to
u(x,t)={uL,ifx<st,u∗,ifst≤x≤e1t,uR,ifx>e1t. | (2.9) |
Case 4:
In this case, we get only one shock connecting
u(x,t)={uL,ifx<st,uR,ifx≥st. | (2.10) |
Remark 2.4. As aforementioned in [19] Riemann solutions for piecewise quadratic discontinuous flux functions are derived. They also cover the case of a piecewise linear flux function if the quadratic terms are zero. For a general quadratic discontinuous flux, the solutions are more involved since no contact discontinuities occur.
Up to now, we have not addressed the case, where one of the boundary conditions equals the critical density
Next, we focus on networks where we allow for discontinuous flux functions. The key idea is to consider the regularized flux function
We start with a short introduction to the network setting. For more details on traffic flow network models we refer the reader to [11] and the references therein.
Let
We call the couple
In order to derive the network solution, we restrict to the description of a single junction
A=(β1,1⋯β1,m⋮⋮⋮βn,1⋯βn,m). |
To conserve the mass we assume
Definition 3.1 (Weak solution at a junction). Let
n∑i=1(∫T0∫Iini(uini(x,t)∂tϕini(x,t)+wini(x,t)∂xϕini(x,t))dxdt)+m∑j=1(∫T0∫Ioutj(uoutj(x,t)∂tϕoutj(x,t)+woutj(x,t)∂xϕoutj(x,t))dxdt)=0, |
for every collection of test functions
ϕini(bini,⋅)=ϕoutj(aoutj,⋅),∂xϕini(bini,⋅)=∂xϕoutj(aoutj,⋅), |
for
Additionally, in order to get unique solutions, we will consider the following concept of admissible solutions, which adapts ref. [11] (rule (A) and (B), p. 81) to the discontinuous setting:
Definition 3.2 (Admissbile Weak Solution). We call
1.
2.
3.
4.
In particular, the maximization of the inflow with respect to the distributions parameters and the technical assumption [11] guarantee the uniqueness of solutions for a continuous flux.
If
For solving the maximization problems imposed by the definition 3.2 so-called supply and demand functions can be used, see [16]. The demand describes the maximal flux the incoming road wants to send. In contrast, the supply describes the maximal flux the outgoing road is able to absorb. The definition of the supply and demand functions of the regularized function is straightforward. As
Definition 3.3. For a network with flux function
D(u)={f(u),u∈[0,u∗),f(u∗−),u∈[u∗,umax]. | (3.1) |
On the contrary, the supply reads as
S(u)={f(u∗−),u∈[0,u∗),f(u),u∈(u∗,umax] | (3.2) |
and
S(u∗)={f(u∗−),freeflowing,f(u∗+),congested. | (3.3) |
Remark 3.4. If we consider the regularized flux function
In order to show existence and uniqueness in the discontinuous case we need to define an additional function. For a regularized flux function we notice that for every flux value, we get two different density values, see left picture in Figure 4. As different density values lead to different solutions, we need to be able to distinguish them and choose the correct solution. In the continuous or regularized case a mapping usually called
Definition 3.5. Let the function
1.
2. For
Note that if
Remark 3.6. We note that the mapping
Now, we present a Riemann solver for two types of junctions. First, we consider a junction with
Theorem 3.7. Let
uini∈{{uini,0}∪(η(uini,0),umax],ifuini,0∈[0,f−1+],{uini,0}∪[u∗,umax],ifuini,0∈(f−1+,u∗),[u∗,umax],ifuini,0∈[u∗,umax], | (3.4) |
and
uoutj∈{[0,u∗],ifuoutj,0∈[0,u∗),[0,u∗],ifuoutj,0=u∗andfreeflowing,{u∗}∪[0,f−1+),ifuoutj,0=u∗andcongested,{uoutj,0}∪[0,η(uoutj,0)),ifuoutj,0∈(u∗,umax]. | (3.5) |
Proof. Using the definition of the supply and demand functions in definition 3.3 and the results from [12,section 5.2.3] we can follow the proof of [12,theorem 5.1.2] and uniquely determine the inflows which maximize the flux through junctions subject to the distribution parameters. It remains to show that by the choice of the density values the correct waves are induced.
We start with considering the outgoing roads. If
For
On the contrary, considering the incoming roads and
Now, let
s=fini−f(uini,0)u∗−uini,0<0. |
Further, if
Now, let us turn to the remaining case of
s=fini−f(uini,0)u∗−uini,0≤0, |
as
Hence, the choices of the densities induce the correct waves.
Now, we consider the case of more incoming than outgoing roads. Exemplary, we study the 2–to–1 situation, even though the results can be easily extended to the
Theorem 3.8. Let
uini∈{{uini,0}∪(η(uini,0),umax],ifuini,0∈[0,f−1+],{uini,0}∪[u∗,umax],ifuini,0∈(f−1+,u∗),[u∗,umax],ifuini,0∈[u∗,umax], | (3.6) |
and
uout1∈{[0,u∗],ifuout1,0∈[0,u∗),[0,u∗],ifuout1,0=u∗andfreeflowing,{u∗}∪[0,f−1+),ifuout1,0=u∗andcongested,{uout1,0}∪[0,η(uout1,0)),ifuout1,0∈(u∗,umax]. | (3.7) |
Proof. Following [11,Section 3.2.2], the flux values at the junction can be calculated with the following steps:
1. Calculate the maximal possible flux
2. Consider the right of way parameter and the flux maximization and calculate the intersection
3. If
4. The flux values are given by
Completely analogous to theorem 3.7 we can show that the choice of the densities admits the correct wave speeds.
The Riemann solutions proposed in theorem 3.7 and theorem 3.8 are the key ingredients for the splitting algorithm on networks in the next section.
Different problems might occur when designing a numerical scheme for a conservation law with discontinuous flux. However, the main difficulties are induced by the zero waves. Since these waves have infinite speed, the regular CFL condition is scaled by the regularization parameter
We consider a flux function
g(u)=−αH(u−u∗), |
where
This case has been already treated in [22] and will be the basis for the splitting algorithm on networks. When solving the scalar conservation law (2.1) on a single road, the boundary value in the case
˜g(u)={0,u∈[0,u∗),[−α,0],u=u∗,−α,u∈(u∗,umax]. | (4.1) |
Furthermore, we define
F(t)=f(u∗−)⇔G(t)=0,F(t)=f(u∗+)⇔G(t)=−α. | (4.2) |
Additionally to the assumptions 2.2, we assume:
Assumption 4.1. [22,Assumption 1.1] The initial data satisfies
Remark 4.2. We emphasize that the original splitting algorithm for a single road [22] is not limited to piecewise linear discontinuous flux functions. Another prominent example might be concave piecewise quadratic flux functions with discontinuity again at
Then, we are able to handle the flux function
λ=ΔtΔx. |
For an integer
As the algorithm splits the function
We denote the backward spatial difference by
rn=rn+12=r(tn),Un+120=Un0=rnsn=sn+12=s(tn)Un+12K+1=UnK+1=sn. |
The function
gn+12K+1=gnK+1=G(tn)={0,ifs(tn)<u∗,0,ifs(tn)=u∗,trafficaheadofx=bisfree−flowing,−α,ifs(tn)=u∗,trafficaheadofx=biscongested,−α,ifs(tn)>u∗. | (4.3) |
That means, we can describe the boundary value
Definition 4.3 [22,Eq (3.7)] Let
˜G(u)={u,u∈[0,u∗),[u∗,u∗+λα],u=u∗,u+λα,u∈(u∗,umax], ˜G−1(u)={u,u∈[0,u∗),u∗,u∈[u∗,u∗+λα),u−λα,u∈[u∗+λα,umax+λα]. |
The splitting algorithm [22] can be then expressed as
{{Un+1/2k=˜G−1(Unk−λgn+1/2k+1),k=K,K−1,…,1,gn+1/2k=(Un+1/2k−Unk+λgn+1/2k+1)/λ,k=K,K−1,…,1,Un+1k=Un+1/2k−λΔ−pg(Un+1/2k+1,Un+1/2k), k∈K. | (4.4) |
Note that the first half step, which includes the first two equations, is implicit. Nevertheless, instead of solving a nonlinear system of equations, the equation can be solved backwards in space starting with
We note that for the implicit equation a CFL condition is not needed, but it is required for the third step. As
As shown in [22,Theorem 5.1] the splitting algorithm (4.4) converges to a weak solution of Eq (2.1). However, obtaining a similar statement about weak entropy solutions is still an open problem.
The key idea to numerically solve such discontinuous conservation laws on networks is to use the splitting algorithm only on the roads and determine the correct in- and outflows at the boundaries by the help of the Riemann solver established in, e.g., theorem 3.7. As the splitting algorithm works with flux values, there is no need to compute the exact densities at the junction. Instead we need to know how the solution at the junction influences the flux values. The algorithm for a single junction is depicted in algorithm 1. The general description of the algorithm allows for either junctions with given distribution or right of way parameters. For simplicity, we assume that each road is represented by the same interval
Remark 4.4. Note that this simplification enables the use of the same grid points on each road which spares further sub- or superindices. However, the algorithm can be easily adapted to different road lengths.
We assume in the following that the space and time grid is the same as in the previous subsection. The approximate solutions are denoted by
The overall strategy of the splitting algorithm on a network consists of three important steps:
1. Solve the optimization problem induced by definition 3.2 (in particular item 4) at the junction to calculate the flux values
Here, it is crucial to use the discontinuous flux function
These flux values bring us now to:
Require: number of incoming roads Ensure: approximate solutions 1: Initilization: 2: 3: 4: 5: for 6: Solve the by definition 3.2 induced optimization problem at the junction based on the flux 7: Compute the densities at the junction with an appropriate Riemann solver 8: Compute the adjusted flux values for the incoming roads 9: for 10: 11: for 12: 13: 14: end for 15: 16: for 17: 18: end for 19: end for 20: for 21: Compute 22: for 23: 24: 25: end for 26: 27: for 28: 29: end for 30: end for 31: end for |
Using the calculated (unadjusted) flux values from step one, we can determine the densities at the junction with the help of the appropriate Riemann solver (theorem 3.7 and Eqs (3.4)–(3.5) or theorem 3.8 and Eqs (3.6)–(3.7)) at the junction (line 7). Then, these density values can be used to calculate the corresponding flux value of
In addition, the first steps give us all the ingredients for the final step:
The adjusted flux values from the previous step are important for the second half step (line 17 or 28) of the splitting algorithm which uses a Godunov type scheme based on
Further boundary data is needed in the first half step of the algorithm, lines 12–13 and 23–24. Here, we start with
gn+1/2,ini,K+1=gn,ini,K+1=fini−fini,adj. | (4.5) |
Note that the definition of
Furthermore, we can decrease the computational costs of the algorithm: In the second step (or in line 7 of algorithm 1) the density at the junction is computed. This can be very expensive and hence we aim to avoid this. In the third step we have seen that for the missing boundary data only the adjusted flux values are necessary and not the densities at the junction themselves. Therefore, studying first each junction type in detail allows to determine the corresponding flux values based on the density values and the supply and demand functions and the intermediate expensive step for the computation of the exact densities can be skipped. Hence, we combine the first and second step of the strategy in one single step. In the following, we will study a 1–to–1 junction in detail and present the tailored algorithm. As the strategy is completely analogous for the 1–to–2 junction and 2–to–1 junction, we will only present the algorithms and discuss important properties. The algorithms can then be used to replace the lines 6 to 8 in algorithm 1.
Remark 4.5. The extension to
Remark 4.6. Further note that the presented strategy and also algorithm 1 can be used for arbitrary junctions and nonlinear discontinuous flux functions once an appropriate Riemann solver similar to theorem 3.7 and 3.8 is established.
First, we consider a junction with one incoming and one outgoing road in detail. Let
Case A: demand and supply are equal
There are two different situations depending on the density value of the incoming road where demand and supply can be equal.
1.
2.
Case B: supply is restrictive
If the supply is restrictive, i.e.
1.
2.
Case C: demand is restrictive
If the demand is restrictive, the outgoing road is able to take the whole amount of vehicles the demand wants to send. Here, we only have one possible situation for the initial condition on the incoming road:
1.
Note that we have the same flux function on each road. Hence, in the case
The whole procedure is summarized in algorithm 2.
Require: Demand Ensure: Flux values 1: 2: 3: if 4: 5: else if 6: 7: 8: end if |
Remark 4.7. Theoretically, the Riemann solver in theorem 3.7 coincides for a 1–to–1 junction with the Riemann solver on a single road. Hence, the procedure described in algorithm 2 leads to the same solution. In contrast to that on the numerical level, the splitting algorithm for a 1–to–1 junction does not exactly coincide with the splitting algorithm used for a single road [22]. The reason for the computational difference is that the splitting algorithm for the 1–to–1 junction considers the exact solution of the Riemann problem at the junction point and hence uses exact values for
The difference to the 1–to–1 junction is now that we have to consider two supplies. So the case distinctions to determine the flux values are a bit more complex. However, the procedure itself does not change. The details can be seen in algorithm 3.
We remark that if the inflow on the first road equals the demand and the restriction given by at least one of the supplies, the latter road needs to be congested. The Riemann solver states congestion such that the flux needs to be adjusted. Then, the incoming road either stays free flowing or the solution is given by
Require: Demand Ensure: Flux values 1: 2: 3: if 4: if 5: 6: else if 7: 8: end if 9: else if 10: if 11: 12: else 13: 14: end if 15: if 16: 17: 18: else if 19: 20: else if 21: 22: end if 23: end if |
If at least one of the supply restrictions is active, we need to adjust the corresponding flux values as in the 1–to–1 case and the incoming road. Nevertheless, here an interesting case (which is not possible in the 1–to–1 situation) can occur. The solution of the Riemann problem at the incoming road can be given by
Recall that for two incoming and one outgoing roads, the maximal possible flux on the outgoing road is given by
Require: Demand Ensure: Flux values 1: 2: 3: if 4: 6: 7: end if 8: 9: if 10: 11:else if 12: if 13: 14: end if 15: if 16: if 17: 18: else 19: 20: end if 21: end if 22: if 23: if 24: 25: else 26: 27: end if 28: end if 29: end if |
As before, no adjustment is needed when the demand on both roads is smaller than the supply. If the supply is active we might need to adjust the outgoing road and in most cases at least one incoming road. As in the 1–to–2 case,
In this section, we present some numerical examples to compare the splitting algorithm on networks with the Riemann solver. Further, we compute the solution using a regularized flux and the Godunov scheme. We consider the following flux function:
f(u)={u,u∈[0,0.5),0.5(1−u),u∈[0.5,1]. | (5.1) |
The corresponding regularization is given by Eq (2.7).
We consider in particular the 1–to–2 and 2–to–1 situations. For our comparison, we choose constant initial data on each road. The junction is always located at
In both scenarios the supply of the first outgoing road is restrictive. The parameter settings are as follows:
The exact solution is given by
uin1(x,t)={0.4,x≥−32t,0.5,−32t<x<−12t,1315,−12t<x<0,uout1(x,t)=0.9,uout2(x,t)={115β20≤x≤841t,0.7,841t<x. |
Apparently, the solution induces two waves on the incoming road.
The exact solution is given by
uin1(x,t)={0.4,x≥−t,0.5,−t<x<0,uout1(x,t)=0.7,1≤x≤3,uout2(x,t)={0.3β21≤x≤t,0.2,t<x. |
This example generates
In Table 1, the
Example 1 | |||||
Splitt. | Reg. | ||||
33.44e-03 | 46.77e-03 | 82.26e-03 | 51.82e-03 | ||
24.17e-03 | 29.05e-03 | 65.59e-03 | 30.69e-03 | ||
14.16e-03 | 20.12e-03 | 60.86e-03 | 24.45e-03 | ||
8.97e-03 | 12.49e-03 | 58.37e-03 | 20.44e-03 | ||
CR | 0.64695 | 0.62453 | 0.1593 | 0.4353 | |
Example 2 | |||||
Splitt. | Reg. | ||||
4.58e-03 | 7.41e-03 | 44.70e-03 | 14.57e-03 | ||
2.97e-03 | 4.24e-03 | 43.47e-03 | 11.28e-03 | ||
2.03e-03 | 2.89e-03 | 42.50e-03 | 10.06e-03 | ||
1.24e-03 | 1.99e-03 | 41.80e-03 | 9.21e-03 | ||
CR | 0.61911 | 0.62327 | 0.0322 | 0.2150 |
We can see that the error terms obtained by the splitting algorithm are the lowest and so the computational costs. Obviously, the error terms increase with a lower CFL due to numerical diffusion. For a direct comparison with the regularized approach, the CFL condition should be the same. Meaning that the second column in Table 1 for the splitting algorithm should be compared with the first one of the regularized approach. In this case, we can see that the splitting algorithm also performs better in both examples. By choosing a smaller regularization parameter the performance of the regularized approach increases, but also the computational costs. To obtain similar error terms as for the splitting algorithm the regularization parameter needs to be further reduced at very high computational costs.
For
Here, we consider two scenarios, where in the first scenario the demand is restrictive while in the second one the supply. The parameter settings are as follows:
The exact solution is given by
uin1(x,t)=0.2,uout1(x,t)={0.450≤x≤t,0.3,t<xuin2(x,t)=0.25. |
The exact solution is given by
uin1(x,t)={0.5x≤−2t,0.6,−2t<x<0,uout1(x,t)={0.50≤x≤t,0.4,t<x,uin2(x,t)={0.8x≤−0.5t,0.7,−0.5t<x<0. |
In particular, the flux value for the first incoming road needs to be adjusted from
Considering the
Example 1 | |||||
Splitt. | Reg. | ||||
9.25e-03 | 16.22e-03 | 16.22e-03 | 17.01e-03 | ||
5.90e-03 | 11.63e-03 | 11.63e-03 | 12.19e-03 | ||
2.98e-03 | 8.13e-03 | 8.13e-03 | 8.52e-03 | ||
8.97e-03 | 5.71e-03 | 5.71e-03 | 5.99e-03 | ||
CR | 0.53838 | 0.50353 | 0.50353 | 0.50347 | |
Example 2 | |||||
Splitt. | Reg. | ||||
14.12e-03 | 20.10e-03 | 85.69e-03 | 27.55e-03 | ||
9.65e-03 | 13.86e-03 | 79.98e-03 | 21.65e-03 | ||
6.41e-03 | 9.57e-03 | 75.96e-03 | 17.49e-03 | ||
4.51e-03 | 6.69e-03 | 73.22e-03 | 14.65e-03 | ||
CR | 0.55295 | 0.52959 | 0.07551 | 0.30432 |
For
We have presented a Riemann solver at a junction for conservation laws with discontinuous flux. We have adapted the splitting algorithm of [22] to networks and demonstrated its validity in comparison with the exact solution. We have also pointed out that the splitting algorithm on networks is faster and more accurate than the approach with a regularized flux. Future research includes the investigation of other network models, where the flux is discontinuous.
J.F. was supported by the German Research Foundation (DFG) under grant HE 5386/18-1 and S.G. under grant GO 1920/10-1.
The authors declare there is no conflict of interest.
[1] |
A. Muller, A. C. Marquez, B. Iung, On the concept of e-maintenance: Review and current research, Reliab. Eng. Syst. Saf., 93 (2008), 1165–1187. https://doi.org/10.1016/j.ress.2007.08.006 doi: 10.1016/j.ress.2007.08.006
![]() |
[2] | K. Gandhi, A. H. Ng, Machine maintenance decision support system: a systematic literature review, in Advances in Manufacturing Technology XXXⅡ: Proceedings of the 16th International Conference on Manufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, September 11–13, University of Skö vde, IOS Press, Sweden, 8 (2018), 349. |
[3] |
A. Garg, S. G. Deshmukh, Maintenance management: literature review and directions, J. Qual. Maint. Eng., 12 (2006), 205–238. https://doi.org/10.1108/13552510610685075 doi: 10.1108/13552510610685075
![]() |
[4] |
D. Sherwin, A review of overall models for maintenance management, J. Qual. Maint. Eng., 6 (2000), 138–164. https://doi.org/10.1108/13552510010341171 doi: 10.1108/13552510010341171
![]() |
[5] | K. C. Ng, G. G. G. Goh, U. C. Eze, Critical success factors of total productive maintenance implementation: a review, in 2011 IEEE international conference on industrial engineering and engineering management, IEEE, Singapore, 269–273. https://doi.org/10.1109/IEEM.2011.6117920 |
[6] |
E. Sisinni, A. Saifullah, S. Han, U. Jennehag, M. Gidlund, Industrial internet of things: Challenges, opportunities, and directions, IEEE Trans. Ind. Inf., 14 (2018), 4724–4734. https://doi.org/10.1109/TⅡ.2018.2852491 doi: 10.1109/TⅡ.2018.2852491
![]() |
[7] |
H. Boyes, B. Hallaq, J. Cunningham, T. Watson, The industrial internet of things (ⅡoT): An analysis framework, Comput. Ind., 101 (2018), 1–12. https://doi.org/10.1016/j.compind.2018.04.015 doi: 10.1016/j.compind.2018.04.015
![]() |
[8] |
J. Wan, S. Tang, Z. Shu, D. Li, S. Wang, M. Imran, et al., Software-defined industrial internet of things in the context of industry 4.0, IEEE Sens. J., 16 (2016), 7373–7380. https://doi.org/10.1109/JSEN.2016.2565621 doi: 10.1109/JSEN.2016.2565621
![]() |
[9] |
Y. Liao, E. D. F. R. Loures, F. Deschamps, Industrial Internet of Things: A systematic literature review and insights, IEEE Internet Things J., 5 (2018), 4515–4525. https://doi.org/10.1109/JIOT.2018.2834151 doi: 10.1109/JIOT.2018.2834151
![]() |
[10] | M. Hartmann, B. Halecker, Management of innovation in the industrial internet of things, in The International Society for Professional Innovation Management ISPIM Conference Proceedings, 2015. |
[11] | M. Mohri, A. Rostamizadeh, A. Talwalkar, Foundations of Machine Learning, MIT press, 2018. |
[12] | C. Sammut, G. I. Webb, Encyclopedia of Machine Learning, Springer Science & Business Media, 2011. |
[13] |
G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, et al., Machine learning and the physical sciences, Rev. Mod. Phys., 91 (2019), 045002. https://doi.org/10.1103/RevModPhys.91.045002 doi: 10.1103/RevModPhys.91.045002
![]() |
[14] |
M. Du, N. Liu, X. Hu, Techniques for interpretable machine learning, Commun. ACM, 63 (2019), 68–77. https://doi.org/10.1145/3359786 doi: 10.1145/3359786
![]() |
[15] | H. Sahli, An introduction to machine learning, in TORUS 1-Toward an Open Resource Using Services: Cloud Computing for Environmental Data, (2020), 61–74. https://doi.org/10.1002/9781119720492.ch7 |
[16] |
R. H. P. M. Arts, G. M. Knapp, L. Mann, Some aspects of measuring maintenance performance in the process industry, J. Qual. Maint. Eng., 4 (1998) 6–11. https://doi.org/10.1108/13552519810201520 doi: 10.1108/13552519810201520
![]() |
[17] |
C. Stenströ m, P. Norrbin, A. Parida, U. Kumar, Preventive and corrective maintenance-cost comparison and cost-benefit analysis, Struct. Infrastruct. Eng., 12 (2016), 603–617. https://doi.org/10.1080/15732479.2015.1032983 doi: 10.1080/15732479.2015.1032983
![]() |
[18] |
H. P. Bahrick, L. K. Hall, Preventive and corrective maintenance of access to knowledge, Appl. Cognit. Psychol., 5 (1991), 1–18. https://doi.org/10.1002/acp.2350050102 doi: 10.1002/acp.2350050102
![]() |
[19] |
J. Shin, H. Jun, On condition based maintenance policy, J. Comput. Des. Eng., 2 (2015), 119–127. https://doi.org/10.1016/j.jcde.2014.12.006 doi: 10.1016/j.jcde.2014.12.006
![]() |
[20] |
R. Ahmad, S. Kamaruddin, An overview of time-based and condition-based maintenance in industrial application, Comput. Ind. Eng., 63 (2012), 135–149. https://doi.org/10.1016/j.cie.2012.02.002 doi: 10.1016/j.cie.2012.02.002
![]() |
[21] | J. H. Williams, A. Davies, P. R. Drake, Condition-Based Maintenance and Machine Diagnostics, Springer Science & Business Media, 1994. |
[22] | R. K. Mobley, An Introduction to Predictive Maintenance, 2nd edition, Elsevier, 2002. https://doi.org/10.1016/B978-0-7506-7531-4.X5000-3 |
[23] | C. Scheffer, P. Girdhar, Practical Machinery Vibration Analysis and Predictive Maintenance, Elsevier, 2004. |
[24] |
K. Efthymiou, N. Papakostas, D. Mourtzis, G. Chryssolouris, On a predictive maintenance platform for production systems, Procedia CIRP, 3 (2012), 221–226. https://doi.org/10.1016/j.procir.2012.07.039 doi: 10.1016/j.procir.2012.07.039
![]() |
[25] |
G. A. Susto, A. Schirru, S. Pampuri, S. McLoone, A. Beghi, Machine learning for predictive maintenance: A multiple classifier approach, IEEE Trans. Ind. Inf., 11 (2014), 812–820. https://doi.org/10.1109/TⅡ.2014.2349359 doi: 10.1109/TⅡ.2014.2349359
![]() |
[26] | R. Isermann, Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer Science & Business Media, 2005. |
[27] |
Z. Gao, C. Cecati, S. X. Ding, A survey of fault diagnosis and fault-tolerant techniques—Part I: Fault diagnosis with model-based and signal-based approaches, IEEE Trans. Ind. Electron., 62 (2015), 3757–3767. https://doi.org/10.1109/TIE.2015.2417501 doi: 10.1109/TIE.2015.2417501
![]() |
[28] |
S. Leonhardt, M. Ayoubi, Methods of fault diagnosis, Control Eng. Pract., 5 (1997), 683–692. https://doi.org/10.1016/S0967-0661(97)00050-6 doi: 10.1016/S0967-0661(97)00050-6
![]() |
[29] | R. J. Patton, P. M. Frank, R. N Clark, Issues of Fault Diagnosis for Dynamic Systems, Springer Science & Business Media, 2013. |
[30] |
M. I. Jordan, T. M. Mitchell, Machine learning: Trends, perspectives, and prospects, Science, 349 (2015), 255–260. https://doi.org/10.1126/science.aaa8415 doi: 10.1126/science.aaa8415
![]() |
[31] | U. S. Shanthamallu, A. Spanias, C. Tepedelenlioglu, M. Stanley, A brief survey of machine learning methods and their sensor and IoT applications, in 2017 8th International Conference on Information, Intelligence, Systems & Applications (ⅡSA), IEEE, (2017), 1–8. https://doi.org/10.1109/ⅡSA.2017.8316459 |
[32] | D. A. Pisner, D. M. Schnyer, Support vector machine, in Machine Learning, Academic Press, (2020), 101–121. https://doi.org/10.1016/B978-0-12-815739-8.00006-7 |
[33] |
W. S. Noble, What is a support vector machine, Nat. Biotechnol., 24 (2006), 1565–1567. https://doi.org/10.1038/nbt1206-1565 doi: 10.1038/nbt1206-1565
![]() |
[34] | L. Wang, Support Vector Machines: Theory and Applications, Springer Science & Business Media, 2005. https://doi.org/10.1007/b95439 |
[35] |
S. I. Amari, S. Wu, Improving support vector machine classifiers by modifying kernel functions, Neural Networks, 12 (1999), 783–789. https://doi.org/10.1016/S0893-6080(99)00032-5 doi: 10.1016/S0893-6080(99)00032-5
![]() |
[36] | O. L. Mangasarian, D. R. Musicant, Lagrangian support vector machines, J. Mach. Learn. Res., 1 (2001), 161–177. |
[37] |
A. Widodo, B. S. Yang, Support vector machine in machine condition monitoring and fault diagnosis, Mech. Syst. Sig. Process., 21 (2007), 2560–2574. https://doi.org/10.1016/j.ymssp.2006.12.007 doi: 10.1016/j.ymssp.2006.12.007
![]() |
[38] |
S. W. Fei, X. B. Zhang, Fault diagnosis of power transformer based on support vector machine with genetic algorithm, Expert Syst. Appl., 36 (2009), 11352–11357. https://doi.org/10.1016/j.eswa.2009.03.022 doi: 10.1016/j.eswa.2009.03.022
![]() |
[39] |
S. D. Wu, P. H. Wu, C. W. Wu, J. J. Ding, C. C. Wang, Bearing fault diagnosis based on multiscale permutation entropy and support vector machine, Entropy, 14 (2012), 1343–1356. https://doi.org/10.3390/e14081343 doi: 10.3390/e14081343
![]() |
[40] | W. Aziz, M. Arif, Multiscale permutation entropy of physiological time series, in 2005 Pakistan Section Multitopic Conference, IEEE, (2005), 1–6. https://doi.org/10.1109/INMIC.2005.334494 |
[41] |
B. Tang, T. Song, F. Li, L. Deng, Fault diagnosis for a wind turbine transmission system based on manifold learning and Shannon wavelet support vector machine, Renewable Energy, 62 (2014), 1–9. https://doi.org/10.1016/j.renene.2013.06.025 doi: 10.1016/j.renene.2013.06.025
![]() |
[42] |
Z. Wang, L. Yao, Y. Cai, J. Zhang, Mahalanobis semi-supervised mapping and beetle antennae search based support vector machine for wind turbine rolling bearings fault diagnosis, Renewable Energy, 155 (2020), 1312–1327. https://doi.org/10.1016/j.renene.2020.04.041 doi: 10.1016/j.renene.2020.04.041
![]() |
[43] |
L. Yao, Z. Fang, Y. Xiao, J. Hou, Z. Fu, An intelligent fault diagnosis method for lithium battery systems based on grid search support vector machine, Energy, 214 (2021), 118866. https://doi.org/10.1016/j.energy.2020.118866 doi: 10.1016/j.energy.2020.118866
![]() |
[44] |
Y. P. Zhao, J. J. Wang, X. Y. Li, G. J. Peng, Z. Yang, Extended least squares support vector machine with applications to fault diagnosis of aircraft engine, ISA Trans., 97 (2020), 189–201. https://doi.org/10.1016/j.isatra.2019.08.036 doi: 10.1016/j.isatra.2019.08.036
![]() |
[45] |
F. Marini, B. Walczak, Particle swarm optimization (PSO). A tutorial, Chemom. Intell. Lab. Syst., 149 (2015), 153–165. https://doi.org/10.1016/j.chemolab.2015.08.020 doi: 10.1016/j.chemolab.2015.08.020
![]() |
[46] |
M. Van, D. T. Hoang, H. J. Kang, Bearing fault diagnosis using a particle swarm optimization-least squares wavelet support vector machine classifier, Sensors, 20 (2020), 3422. https://doi.org/10.3390/s20123422 doi: 10.3390/s20123422
![]() |
[47] |
X. Li, S. Wu, X. Li, H. Yuan, D. Zhao, Particle swarm optimization-support vector machine model for machinery fault diagnoses in high-voltage circuit breakers, Chin. J. Mech. Eng., 33 (2020), 1–10. https://doi.org/10.1186/s10033-019-0428-5 doi: 10.1186/s10033-019-0428-5
![]() |
[48] |
Y. Fan, C. Zhang, Y. Xue, J. Wang, F. Gu, A bearing fault diagnosis using a support vector machine optimised by the self-regulating particle swarm, Shock Vib., 2020 (2020). https://doi.org/10.1155/2020/9096852 doi: 10.1155/2020/9096852
![]() |
[49] | E. Mirakhorli, Fault diagnosis in a distillation column using a support vector machine based classifier, Int. J. Smart Electr. Eng., 8 (2020), 105–113. |
[50] |
S. Gao, C. Zhou, Z. Zhang, J. Geng, R. He, Q. Yin, C. Xing, Mechanical fault diagnosis of an on-load tap changer by applying cuckoo search algorithm-based fuzzy weighted least squares support vector machine, Math. Probl. Eng., 2020 (2020). https://doi.org/10.1155/2020/3432409 doi: 10.1155/2020/3432409
![]() |
[51] |
X. Huang, X. Huang, B. Wang, Z. Xie, Fault diagnosis of transformer based on modified grey wolf optimization algorithm and support vector machine, IEEJ Trans. Electr. Electron. Eng., 15 (2020), 409–417. https://doi.org/10.1002/tee.23069 doi: 10.1002/tee.23069
![]() |
[52] |
Y. Zhang, J. Li, X. Fan, J. Liu, H. Zhang, Moisture prediction of transformer oil-immersed polymer insulation by applying a support vector machine combined with a genetic algorithm, Polymers, 12 (2020), 1579. https://doi.org/10.3390/polym12071579 doi: 10.3390/polym12071579
![]() |
[53] |
Y. Liu, H. Chen, L. Zhang, X. Wu, X. J. Wang, Energy consumption prediction and diagnosis of public buildings based on support vector machine learning: A case study in China, J. Cleaner Prod., 272 (2020), 122542. https://doi.org/10.1016/j.jclepro.2020.122542 doi: 10.1016/j.jclepro.2020.122542
![]() |
[54] |
S. K. Ibrahim, A. Ahmed, M. A. E. Zeidan, I. E. Ziedan, Machine learning techniques for satellite fault diagnosis, Ain Shams Eng. J., 11 (2020), 45–56. https://doi.org/10.1016/j.asej.2019.08.006 doi: 10.1016/j.asej.2019.08.006
![]() |
[55] |
Y. P. Zhao, G. Huang, Q. K. Hu, B. Li, An improved weighted one class support vector machine for turboshaft engine fault detection, Eng. Appl. Artif. Intell., 94 (2020), 103796. https://doi.org/10.1016/j.engappai.2020.103796 doi: 10.1016/j.engappai.2020.103796
![]() |
[56] | M. Guo, L. Xie, S. Q. Wang, J. M. Zhang, Research on an integrated ICA-SVM based framework for fault diagnosis, in SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme-System Security and Assurance (Cat. No. 03CH37483), IEEE, 3 (2003), 2710–2715. https://doi.org/10.1109/ICSMC.2003.1244294 |
[57] | S. Poyhonen, P. Jover, H. Hyotyniemi, Signal processing of vibrations for condition monitoring of an induction motor, in First International Symposium on Control, Communications and Signal Processing, IEEE, Tunisia, (2004), 499–502. https://doi.org/10.1109/ISCCSP.2004.1296338 |
[58] |
M. C. Moura, E. Zio, I. D. Lins, E. Droguett, Failure and reliability prediction by support vector machines regression of time series data, Reliab. Eng. Syst. Saf., 96 (2011), 1527–1534. https://doi.org/10.1016/j.ress.2011.06.006 doi: 10.1016/j.ress.2011.06.006
![]() |
[59] |
K. Y. Chen, L. S. Chen, M. C. Chen, C. L. Lee, Using SVM based method for equipment fault detection in a thermal power plant, Comput. Ind., 62 (2011), 42–50. https://doi.org/10.1016/j.compind.2010.05.013 doi: 10.1016/j.compind.2010.05.013
![]() |
[60] |
K. He, X. Li, A quantitative estimation technique for welding quality using local mean decomposition and support vector machine, J. Intell. Manuf., 27 (2016), 525–533. https://doi.org/10.1007/s10845-014-0885-8 doi: 10.1007/s10845-014-0885-8
![]() |
[61] |
K. Yan, C. Zhong, Z. Ji, J. Huang, Semi-supervised learning for early detection and diagnosis of various air handling unit faults, Energy Build., 181 (2018), 75–83. https://doi.org/10.1016/j.enbuild.2018.10.016 doi: 10.1016/j.enbuild.2018.10.016
![]() |
[62] |
Z. Yin, J. Hou, Recent advances on SVM based fault diagnosis and process monitoring in complicated industrial processes, Neurocomputing, 174 (2016), 643–650. https://doi.org/10.1016/j.neucom.2015.09.081 doi: 10.1016/j.neucom.2015.09.081
![]() |
[63] |
M. M. Islam, J. M. Kim, Reliable multiple combined fault diagnosis of bearings using heterogeneous feature models and multiclass support vector Machines, Reliab. Eng. Syst. Saf., 184 (2019), 55–66. https://doi.org/10.1016/j.ress.2018.02.012 doi: 10.1016/j.ress.2018.02.012
![]() |
[64] |
R. P. Monteiro, M. Cerrada, D. R. Cabrera, R. V. Sánchez, C. J. Bastos-Filho, Using a support vector machine based decision stage to improve the fault diagnosis on gearboxes, Comput. Intell. Neurosci., 2019 (2019). https://doi.org/10.1155/2019/1383752 doi: 10.1155/2019/1383752
![]() |
[65] |
D. Yang, J. Miao, F. Zhang, J. Tao, G. Wang, Y. Shen, Bearing fault diagnosis using a support vector machine optimized by an improved ant lion optimizer, Shock Vib., 2019 (2019). https://doi.org/10.1155/2019/9303676 doi: 10.1155/2019/9303676
![]() |
[66] |
S. Mirjalili, The ant lion optimizer, Adv. Eng. Software, 83 (2015), 80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010 doi: 10.1016/j.advengsoft.2015.01.010
![]() |
[67] |
L. You, W. Fan, Z. Li, Y. Liang, M. Fang, J. Wang, A fault diagnosis model for rotating machinery using VWC and MSFLA-SVM based on vibration signal analysis, Shock Vib., 2019 (2019). https://doi.org/10.1155/2019/1908485 doi: 10.1155/2019/1908485
![]() |
[68] |
A. Kumar, R. Kumar, Time-frequency analysis and support vector machine in automatic detection of defect from vibration signal of centrifugal pump, Measurement, 108 (2017), 119–133. https://doi.org/10.1016/j.measurement.2017.04.041 doi: 10.1016/j.measurement.2017.04.041
![]() |
[69] |
Z. Chen, F. Zhao, J. Zhou, P. Huang, X. Zhang, Fault diagnosis of loader gearbox based on an Ica and SVM algorithm, Int. J. Environ. Res. Public Health, 16 (2019), 4868. https://doi.org/10.3390/ijerph16234868 doi: 10.3390/ijerph16234868
![]() |
[70] | T. W. Lee, Independent component analysis, in Independent Component Analysis, Springer, Boston, (1998), 27–66. https://doi.org/10.1007/978-1-4757-2851-4_2 |
[71] |
W. Liu, Z. Wang, J. Han, G. Wang, Wind turbine fault diagnosis method based on diagonal spectrum and clustering binary tree SVM, Renewable Energy, 50 (2013), 1–6. https://doi.org/10.1016/j.renene.2012.06.013 doi: 10.1016/j.renene.2012.06.013
![]() |
[72] |
M. A. Djeziri, O. Djedidi, N. Morati, J. L. Seguin, M. Bendahan, T. Contaret, A temporal-based SVM approach for the detection and identification of pollutant gases in a gas mixture, Appl. Intell., 52 (2022), 6065–6078. https://doi.org/10.1007/s10489-021-02761-0 doi: 10.1007/s10489-021-02761-0
![]() |
[73] |
G. Ciaburro, G. Iannace, J. Passaro, A. Bifulco, D. Marano, M. Guida, et al., Artificial neural network-based models for predicting the sound absorption coefficient of electrospun poly (vinyl pyrrolidone)/silica composite, Appl. Acoust., 169 (2020), 107472. https://doi.org/10.1016/j.apacoust.2020.107472 doi: 10.1016/j.apacoust.2020.107472
![]() |
[74] |
S. Agatonovic-Kustrin, R. Beresford, Basic concepts of artificial neural network (ANN) modeling and its application in pharmaceutical research, J. Pharm. Biomed. Anal., 22 (2000), 717–727. https://doi.org/10.1016/S0731-7085(99)00272-1 doi: 10.1016/S0731-7085(99)00272-1
![]() |
[75] |
G. Ciaburro, G. Iannace, M. Ali, A. Alabdulkarem, A. Nuhait, An artificial neural network approach to modelling absorbent asphalts acoustic properties, J. King Saud Univ. Eng. Sci., 33 (2021), 213–220. https://doi.org/10.1016/j.jksues.2020.07.002 doi: 10.1016/j.jksues.2020.07.002
![]() |
[76] |
J. Misra, I. Saha, Artificial neural networks in hardware: A survey of two decades of progress, Neurocomputing, 74 (2010), 239–255. https://doi.org/10.1016/j.neucom.2010.03.021 doi: 10.1016/j.neucom.2010.03.021
![]() |
[77] |
Z. Zhang, K. Friedrich, Artificial neural networks applied to polymer composites: a review, Compos. Sci. Technol., 63 (2003), 2029–2044. https://doi.org/10.1016/S0266-3538(03)00106-4 doi: 10.1016/S0266-3538(03)00106-4
![]() |
[78] |
G. Iannace, G. Ciaburro, A. Trematerra, Modelling sound absorption properties of broom fibers using artificial neural networks, Appl. Acoust., 163 (2020), 107239. https://doi.org/10.1016/j.apacoust.2020.107239 doi: 10.1016/j.apacoust.2020.107239
![]() |
[79] |
K. P. Singh, A. Basant, A. Malik, G. Jain, Artificial neural network modeling of the river water quality—a case study, Ecol. Modell., 220 (2009), 888–895. https://doi.org/10.1016/j.ecolmodel.2009.01.004 doi: 10.1016/j.ecolmodel.2009.01.004
![]() |
[80] |
H. Zhu, X. Li, Q. Sun, L. Nie, J. Yao, G. Zhao, A power prediction method for photovoltaic power plant based on wavelet decomposition and artificial neural networks, Energies, 9 (2015), 1–15. https://doi.org/10.3390/en9010011 doi: 10.3390/en9010011
![]() |
[81] |
V. P. Romero, L. Maffei, G. Brambilla, G. Ciaburro, Modelling the soundscape quality of urban waterfronts by artificial neural networks, Appl. Acoust., 111 (2016), 121–128. https://doi.org/10.1016/j.apacoust.2016.04.019 doi: 10.1016/j.apacoust.2016.04.019
![]() |
[82] |
S. Fabio, D. N. Giovanni, P. Mariano, Airborne sound insulation prediction of masonry walls using artificial neural networks, Build. Acoust., 28 (2021), 391–409. https://doi.org/10.1177/1351010X21994462 doi: 10.1177/1351010X21994462
![]() |
[83] |
Y. Zhang, X. Ding, Y. Liu, P. J. Griffin, An artificial neural network approach to transformer fault diagnosis, IEEE Trans. Power Delivery, 11 (1996), 1836–1841. https://doi.org/10.1109/61.544265 doi: 10.1109/61.544265
![]() |
[84] |
J. C. Hoskins, K. M. Kaliyur, D. M. Himmelblau, Fault diagnosis in complex chemical plants using artificial neural networks, AIChE J., 37 (1991), 137–141. https://doi.org/10.1002/aic.690370112 doi: 10.1002/aic.690370112
![]() |
[85] |
J. B. Ali, N. Fnaiech, L. Saidi, B. Chebel-Morello, F. Fnaiech, Application of empirical mode decomposition and artificial neural network for automatic bearing fault diagnosis based on vibration signals, Appl. Acoust., 89 (2015), 16–27. https://doi.org/10.1016/j.apacoust.2014.08.016 doi: 10.1016/j.apacoust.2014.08.016
![]() |
[86] |
T. Sorsa, H. N. Koivo, Application of artificial neural networks in process fault diagnosis, Automatica, 29 (1993), 843–849. https://doi.org/10.1016/0005-1098(93)90090-G doi: 10.1016/0005-1098(93)90090-G
![]() |
[87] |
N. Saravanan, K. I. Ramachandran, Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN), Expert Syst. Appl., 37 (2010), 4168–4181. https://doi.org/10.1016/j.eswa.2009.11.006 doi: 10.1016/j.eswa.2009.11.006
![]() |
[88] |
W. Chine, A. Mellit, V. Lughi, A. Malek, G. Sulligoi, A. M. Pavan, A novel fault diagnosis technique for photovoltaic systems based on artificial neural networks, Renewable Energy, 90 (2016), 501–512. https://doi.org/10.1016/j.renene.2016.01.036 doi: 10.1016/j.renene.2016.01.036
![]() |
[89] |
B. Li, M. Y. Chow, Y. Tipsuwan, J. C. Hung, Neural-network-based motor rolling bearing fault diagnosis, IEEE Trans. Ind. Electron., 47 (2000), 1060–1069. https://doi.org/10.1109/41.873214 doi: 10.1109/41.873214
![]() |
[90] |
B. Samanta, K. R. Al-Balushi, S. A. Al-Araimi, Artificial neural networks and genetic algorithm for bearing fault detection, Soft Comput., 10 (2006), 264–271. https://doi.org/10.1007/s00500-005-0481-0 doi: 10.1007/s00500-005-0481-0
![]() |
[91] |
T. Han, B. S. Yang, W. H. Choi, J. S. Kim, Fault diagnosis system of induction motors based on neural network and genetic algorithm using stator current signals, Int. J. Rotating Mach., 2006 (2006). https://doi.org/10.1155/IJRM/2006/61690 doi: 10.1155/IJRM/2006/61690
![]() |
[92] |
H. Wang, P. Chen, Intelligent diagnosis method for rolling element bearing faults using possibility theory and neural network, Comput. Ind. Eng., 60 (2011), 511–518. https://doi.org/10.1016/j.cie.2010.12.004 doi: 10.1016/j.cie.2010.12.004
![]() |
[93] |
M. A. Hashim, M. H. Nasef, A. E. Kabeel, N. M. Ghazaly, Combustion fault detection technique of spark ignition engine based on wavelet packet transform and artificial neural network, Alexandria Eng. J., 59 (2020), 3687–3697. https://doi.org/10.1016/j.aej.2020.06.023 doi: 10.1016/j.aej.2020.06.023
![]() |
[94] |
G. Iannace, G. Ciaburro, A. Trematerra, Fault diagnosis for UAV blades using artificial neural network, Robotics, 8 (2019), 59. https://doi.org/10.3390/robotics8030059 doi: 10.3390/robotics8030059
![]() |
[95] |
M. Kordestani, M. F. Samadi, M. Saif, K. Khorasani, A new fault diagnosis of multifunctional spoiler system using integrated artificial neural network and discrete wavelet transform methods, IEEE Sens. J., 18 (2018), 4990–5001. https://doi.org/10.1109/JSEN.2018.2829345 doi: 10.1109/JSEN.2018.2829345
![]() |
[96] |
S. Shi, G. Li, H. Chen, J. Liu, Y. Hu, L. Xing, et al., Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter, Appl. Therm. Eng., 112 (2017), 698–706. https://doi.org/10.1016/j.applthermaleng.2016.10.043 doi: 10.1016/j.applthermaleng.2016.10.043
![]() |
[97] |
X. Xu, D. Cao, Y. Zhou, J. Gao, Application of neural network algorithm in fault diagnosis of mechanical intelligence, Mech. Syst. Sig. Process., 141 (2020), 106625. https://doi.org/10.1016/j.ymssp.2020.106625 doi: 10.1016/j.ymssp.2020.106625
![]() |
[98] | A. Viveros-Wacher, J. E. Rayas-Sánchez, Analog fault identification in RF circuits using artificial neural networks and constrained parameter extraction, in 2018 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), IEEE, (2018), 1–3. https://doi.org/10.1109/NEMO.2018.8503117 |
[99] |
S. Heo, J. H. Lee, Fault detection and classification using artificial neural networks, IFAC-PapersOnLine, 51 (2018), 470–475. https://doi.org/10.1016/j.ifacol.2018.09.380 doi: 10.1016/j.ifacol.2018.09.380
![]() |
[100] |
P. Agrawal, P. Jayaswal, Diagnosis and classifications of bearing faults using artificial neural network and support vector machine, J. Inst. Eng. (India): Ser. C, 101 (2020), 61–72. https://doi.org/10.1007/s40032-019-00519-9 doi: 10.1007/s40032-019-00519-9
![]() |
[101] | Y. LeCun, B. E. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. E. Hubbard, et al., Handwritten digit recognition with a back-propagation network, in Advances in Neural Information Processing Systems, (1990), 396–404. |
[102] |
T. Chen, Y. Sun, T. H. Li, A semi-parametric estimation method for the quantile spectrum with an application to earthquake classification using convolutional neural network, Comput. Stat. Data Anal., 154 (2021), 107069. https://doi.org/10.1016/j.csda.2020.107069 doi: 10.1016/j.csda.2020.107069
![]() |
[103] |
F. Perla, R. Richman, S. Scognamiglio, M. V. Wüthrich, Time-series forecasting of mortality rates using deep learning, Scand. Actuarial J., 2021 (2021), 1–27. https://doi.org/10.1080/03461238.2020.1867232 doi: 10.1080/03461238.2020.1867232
![]() |
[104] |
G. Ciaburro, G. Iannace, V. Puyana-Romero, A. Trematerra, A comparison between numerical simulation models for the prediction of acoustic behavior of giant reeds shredded, Appl. Sci., 10 (2020), 6881. https://doi.org/10.3390/app10196881 doi: 10.3390/app10196881
![]() |
[105] |
C. Yildiz, H. Acikgoz, D. Korkmaz, U. Budak, An improved residual-based convolutional neural network for very short-term wind power forecasting, Energy Convers. Manage., 228 (2021), 113731. https://doi.org/10.1016/j.enconman.2020.113731 doi: 10.1016/j.enconman.2020.113731
![]() |
[106] |
G. Ciaburro, Sound event detection in underground parking garage using convolutional neural network, Big Data Cognit. Comput., 4 (2020), 20. https://doi.org/10.3390/bdcc4030020 doi: 10.3390/bdcc4030020
![]() |
[107] |
R. Ye, Q. Dai, Implementing transfer learning across different datasets for time series forecasting, Pattern Recognit., 109 (2021), 107617. https://doi.org/10.1016/j.patcog.2020.107617 doi: 10.1016/j.patcog.2020.107617
![]() |
[108] |
J. Han, L. Shi, Q. Yang, K. Huang, Y. Zha, J. Yu, Real-time detection of rice phenology through convolutional neural network using handheld camera images, Precis. Agric., 22 (2021), 154–178. https://doi.org/10.1016/j.patcog.2020.107617 doi: 10.1016/j.patcog.2020.107617
![]() |
[109] |
G. Ciaburro, G. Iannace, Improving smart cities safety using sound events detection based on deep neural network algorithms, Informatics, 7 (2020), 23. https://doi.org/10.3390/informatics7030023 doi: 10.3390/informatics7030023
![]() |
[110] |
L. Wen, X. Li, L. Gao, Y. Zhang, A new convolutional neural network-based data-driven fault diagnosis method, IEEE Trans. Ind. Electron., 65 (2017), 5990–5998. https://doi.org/10.1109/TIE.2017.2774777 doi: 10.1109/TIE.2017.2774777
![]() |
[111] | Y. LeCun, LeNet-5, Convolutional Neural Networks, 2015, Available from: http://yann.lecun.com/exdb/lenet/, Accessed date: 28 April 2022. |
[112] |
H. Wu, J. Zhao, Deep convolutional neural network model based chemical process fault diagnosis, Comput. Chem. Eng., 115 (2018), 185–197. https://doi.org/10.1016/j.compchemeng.2018.04.009 doi: 10.1016/j.compchemeng.2018.04.009
![]() |
[113] |
W. Zhang, C. Li, G. Peng, Y. Chen, Z. Zhang, A deep convolutional neural network with new training methods for bearing fault diagnosis under noisy environment and different working load, Mech. Syst. Sig. Process., 100 (2018), 439–453. https://doi.org/10.1016/j.ymssp.2017.06.022 doi: 10.1016/j.ymssp.2017.06.022
![]() |
[114] |
L. Jing, M. Zhao, P. Li, X. Xu, A convolutional neural network based feature learning and fault diagnosis method for the condition monitoring of gearbox, Measurement, 111 (2017), 1–10. https://doi.org/10.1016/j.measurement.2017.07.017 doi: 10.1016/j.measurement.2017.07.017
![]() |
[115] |
Z. Chen, C. Li, R. V. Sanchez, Gearbox fault identification and classification with convolutional neural networks, Shock Vib., 2015 (2015). https://doi.org/10.1155/2015/390134 doi: 10.1155/2015/390134
![]() |
[116] |
X. Guo, L. Chen, C. Shen, Hierarchical adaptive deep convolution neural network and its application to bearing fault diagnosis, Measurement, 93 (2016), 490–502. https://doi.org/10.1016/j.measurement.2016.07.054 doi: 10.1016/j.measurement.2016.07.054
![]() |
[117] |
O. Janssens, V. Slavkovikj, B. Vervisch, K. Stockman, M. Loccufier, S. Verstockt, et al., Convolutional neural network based fault detection for rotating machinery, J. Sound Vib., 377 (2016), 331–345. https://doi.org/10.1016/j.jsv.2016.05.027 doi: 10.1016/j.jsv.2016.05.027
![]() |
[118] |
W. Zhang, G. Peng, C. Li, Y. Chen, Z. Zhang, A new deep learning model for fault diagnosis with good anti-noise and domain adaptation ability on raw vibration signals, Sensors, 17 (2017), 425. https://doi.org/10.3390/s17020425 doi: 10.3390/s17020425
![]() |
[119] |
Y. Li, N. Wang, J. Shi, X. Hou, J. Liu, Adaptive batch normalization for practical domain adaptation, Pattern Recognit., 80 (2018), 109–117. https://doi.org/10.1016/j.patcog.2018.03.005 doi: 10.1016/j.patcog.2018.03.005
![]() |
[120] |
T. Ince, S. Kiranyaz, L. Eren, M. Askar, M. Gabbouj, Real-time motor fault detection by 1-D convolutional neural networks, IEEE Trans. Ind. Electron., 63 (2016), 7067–7075. https://doi.org/10.1109/TIE.2016.2582729 doi: 10.1109/TIE.2016.2582729
![]() |
[121] |
Y. Zhang, K. Xing, R. Bai, D. Sun, Z. Meng, An enhanced convolutional neural network for bearing fault diagnosis based on time-frequency image, Measurement, 157 (2020), 107667. https://doi.org/10.1016/j.measurement.2020.107667 doi: 10.1016/j.measurement.2020.107667
![]() |
[122] |
M. Azamfar, J. Singh, I. Bravo-Imaz, J. Lee, . Multisensor data fusion for gearbox fault diagnosis using 2-D convolutional neural network and motor current signature analysis, Mech. Syst. Sig. Process., 144 (2020), 106861. https://doi.org/10.1016/j.ymssp.2020.106861 doi: 10.1016/j.ymssp.2020.106861
![]() |
[123] |
Q. Zhou, Y. Li, Y. Tian, L. Jiang, A novel method based on nonlinear auto-regression neural network and convolutional neural network for imbalanced fault diagnosis of rotating machinery, Measurement, 161 (2020), 107880. https://doi.org/10.1016/j.measurement.2020.107880 doi: 10.1016/j.measurement.2020.107880
![]() |
[124] |
K. Zhang, J. Chen, T. Zhang, Z. Zhou, A compact convolutional neural network augmented with multiscale feature extraction of acquired monitoring data for mechanical intelligent fault diagnosis, J. Manuf. Syst., 55 (2020), 273–284. https://doi.org/10.1016/j.jmsy.2020.04.016 doi: 10.1016/j.jmsy.2020.04.016
![]() |
[125] |
Y. Li, X. Du, F. Wan, X. Wang, H. Yu, Rotating machinery fault diagnosis based on convolutional neural network and infrared thermal imaging, Chin. J. Aeronaut., 33 (2020), 427–438. https://doi.org/10.1016/j.cja.2019.08.014 doi: 10.1016/j.cja.2019.08.014
![]() |
[126] |
Z. Chen, A. Mauricio, W. Li, K. Gryllias, A deep learning method for bearing fault diagnosis based on cyclic spectral coherence and convolutional neural networks, Mech. Syst. Sig. Process., 140 (2020), 106683. https://doi.org/10.1016/j.ymssp.2020.106683 doi: 10.1016/j.ymssp.2020.106683
![]() |
[127] |
J. Antoni, Cyclic spectral analysis in practice, Mech. Syst. Sig. Process., 21 (2007), 597–630. https://doi.org/10.1016/j.ymssp.2006.08.007 doi: 10.1016/j.ymssp.2006.08.007
![]() |
[128] |
D. Zhou, Q. Yao, H. Wu, S. Ma, H. Zhang, Fault diagnosis of gas turbine based on partly interpretable convolutional neural networks, Energy, 200 (2020), 117467. https://doi.org/10.1016/j.energy.2020.117467 doi: 10.1016/j.energy.2020.117467
![]() |
[129] | T. Chen, T. He, M. Benesty, V. Khotilovich, Y. Tang, H. Cho, Xgboost: extreme gradient boosting, R package version 0.4-2, 1 (2015), 1–4. |
[130] |
X. Li, J. Zheng, M. Li, W. Ma, Y. Hu, Frequency-domain fusing convolutional neural network: A unified architecture improving effect of domain adaptation for fault diagnosis, Sensors, 21 (2021), 450. https://doi.org/10.3390/s21020450 doi: 10.3390/s21020450
![]() |
[131] | C. C. Chen, Z. Liu, G. Yang, C. C. Wu, Q. Ye, An improved fault diagnosis using 1D-convolutional neural network model, electronics, 10 (2021), 59. https://doi.org/10.3390/electronics10010059 |
[132] |
Y. Liu, Y. Yang, T. Feng, Y. Sun, X. Zhang, Research on rotating machinery fault diagnosis method based on energy spectrum matrix and adaptive convolutional neural network, Processes, 9 (2021), 69. https://doi.org/10.3390/pr9010069 doi: 10.3390/pr9010069
![]() |
[133] |
D. T. Hoang, X. T. Tran, M. Van, H. J. Kang, A deep neural network-based feature fusion for bearing fault diagnosis, Sensors, 21 (2021), 244. https://doi.org/10.3390/s21010244 doi: 10.3390/s21010244
![]() |
[134] | T. Mikolov, M. Karafiát, L. Burget, J. Černocký, S. Khudanpur, Recurrent neural network based language model, in Eleventh Annual Conference of the International Speech Communication Association, 2010. |
[135] | K. Gregor, I. Danihelka, A. Graves, D. Rezende, D. Wierstra, Draw: A recurrent neural network for image generation, in International Conference on Machine Learning (PMLR), 37 (2015), 1462–1471. |
[136] | T. Mikolov, G. Zweig, Context dependent recurrent neural network language model, in 2012 IEEE Spoken Language Technology Workshop (SLT), IEEE, (2012), 234–239. https://doi.org/10.1109/SLT.2012.6424228 |
[137] | G. Ciaburro, Time series data analysis using deep learning methods for smart cities monitoring, in Big Data Intelligence for Smart Applications, Springer, Cham, (2022), 93–116. https://doi.org/10.1007/978-3-030-87954-9_4 |
[138] |
H. Sak, A. W. Senior, F. Beaufays, Long short-term memory recurrent neural network architectures for large scale acoustic modeling, Interspeech, (2014), 338–342. https://doi.org/10.21437/Interspeech.2014-80 doi: 10.21437/Interspeech.2014-80
![]() |
[139] | J. Kim, J. Kim, H. L. T. Thu, H. Kim, Long short term memory recurrent neural network classifier for intrusion detection, in 2016 International Conference on Platform Technology and Service (PlatCon), IEEE, (2016), 1–5. https://doi.org/10.1109/PlatCon.2016.7456805 |
[140] | Y. Tian, L. Pan, Predicting short-term traffic flow by long short-term memory recurrent neural network, in 2015 IEEE International Conference on Smart City/SocialCom/SustainCom (SmartCity), IEEE, (2015), 153–158. https://doi.org/10.1109/SmartCity.2015.63 |
[141] |
H. Jiang, X. Li, H. Shao, K. Zhao, Intelligent fault diagnosis of rolling bearings using an improved deep recurrent neural network, Meas. Sci. Technol., 29 (2018), 065107. https://doi.org/10.1088/1361-6501/aab945 doi: 10.1088/1361-6501/aab945
![]() |
[142] |
T. De Bruin, K. Verbert, R. Babuška, Railway track circuit fault diagnosis using recurrent neural networks, IEEE Trans. Neural Networks Learn. Syst., 28 (2016), 523–533. https://doi.org/10.1109/TNNLS.2016.2551940 doi: 10.1109/TNNLS.2016.2551940
![]() |
[143] |
R. Yang, M. Huang, Q. Lu, M. Zhong, Rotating machinery fault diagnosis using long-short-term memory recurrent neural network, IFAC-PapersOnLine, 51 (2018), 228–232. https://doi.org/10.1016/j.ifacol.2018.09.582 doi: 10.1016/j.ifacol.2018.09.582
![]() |
[144] |
H. A. Talebi, K. Khorasani, S. Tafazoli, A recurrent neural-network-based sensor and actuator fault detection and isolation for nonlinear systems with application to the satellite's attitude control subsystem, IEEE Trans. Neural Networks, 20 (2008), 45–60. https://doi.org/10.1109/TNN.2008.2004373 doi: 10.1109/TNN.2008.2004373
![]() |
[145] |
S. Zhang, K. Bi, T. Qiu, Bidirectional recurrent neural network-based chemical process fault diagnosis, Ind. Eng. Chem. Res., 59 (2019), 824–834. https://doi.org/10.1021/acs.iecr.9b05885 doi: 10.1021/acs.iecr.9b05885
![]() |
[146] |
Z. An, S. Li, J. Wang, X. Jiang, A novel bearing intelligent fault diagnosis framework under time-varying working conditions using recurrent neural network, ISA Trans., 100 (2020), 155–170. https://doi.org/10.1016/j.isatra.2019.11.010 doi: 10.1016/j.isatra.2019.11.010
![]() |
[147] |
W. Liu, P. Guo, L. Ye, A low-delay lightweight recurrent neural network (LLRNN) for rotating machinery fault diagnosis, Sensors, 19 (2019), 3109. https://doi.org/10.3390/s19143109 doi: 10.3390/s19143109
![]() |
[148] |
K. Liang, N. Qin, D. Huang, Y. Fu, Convolutional recurrent neural network for fault diagnosis of high-speed train bogie, Complexity, 2018 (2018). https://doi.org/10.1155/2018/4501952 doi: 10.1155/2018/4501952
![]() |
[149] |
D. Huang, Y. Fu, N. Qin, S. Gao, Fault diagnosis of high-speed train bogie based on LSTM neural network, Sci. Chin. Inf. Sci., 64 (2021), 1–3. https://doi.org/10.1007/s11432-018-9543-8 doi: 10.1007/s11432-018-9543-8
![]() |
[150] |
H. Shahnazari, P. Mhaskar, J. M. House, T. I. Salsbury, Modeling and fault diagnosis design for HVAC systems using recurrent neural networks, Comput. Chem. Eng., 126 (2019), 189–203. https://doi.org/10.1016/j.compchemeng.2019.04.011 doi: 10.1016/j.compchemeng.2019.04.011
![]() |
[151] |
H. Shahnazari, Fault diagnosis of nonlinear systems using recurrent neural networks, Chem. Eng. Res. Des., 153 (2020), 233–245. https://doi.org/10.1016/j.cherd.2019.09.026 doi: 10.1016/j.cherd.2019.09.026
![]() |
[152] |
L. Guo, N. Li, F. Jia, Y. Lei, J. Lin, A recurrent neural network based health indicator for remaining useful life prediction of bearings, Neurocomputing, 240 (2017), 98–109. https://doi.org/10.1016/j.neucom.2017.02.045 doi: 10.1016/j.neucom.2017.02.045
![]() |
[153] | M. Yuan, Y. Wu, L. Lin, Fault diagnosis and remaining useful life estimation of aero engine using LSTM neural network, in 2016 IEEE international conference on aircraft utility systems (AUS), IEEE, (2016), 135–140. https://doi.org/10.1109/AUS.2016.7748035 |
[154] |
Z. Wu, H. Jiang, K. Zhao, X. Li, An adaptive deep transfer learning method for bearing fault diagnosis, Measurement, 151 (2020), 107227. https://doi.org/10.1016/j.measurement.2019.107227 doi: 10.1016/j.measurement.2019.107227
![]() |
[155] |
A. Yin, Y. Yan, Z. Zhang, C. Li, R. V. Sánchez, Fault diagnosis of wind turbine gearbox based on the optimized LSTM neural network with cosine loss, Sensors, 20 (2020), 2339. https://doi.org/10.3390/s20082339 doi: 10.3390/s20082339
![]() |
[156] |
M. Xia, X. Zheng, M. Imran, M. Shoaib, Data-driven prognosis method using hybrid deep recurrent neural network, Appl. Soft Comput., 93 (2020), 106351. https://doi.org/10.1016/j.asoc.2020.106351 doi: 10.1016/j.asoc.2020.106351
![]() |
[157] |
Z. Wang, Y. Dong, W. Liu, Z. Ma, A novel fault diagnosis approach for chillers based on 1-D convolutional neural network and gated recurrent unit, Sensors, 20 (2020), 2458. https://doi.org/10.3390/s20092458 doi: 10.3390/s20092458
![]() |
[158] |
R. Salakhutdinov, Learning deep generative models, Annu. Rev. Stat. Appl., 2 (2015), 361–385. https://doi.org/10.1146/annurev-statistics-010814-020120 doi: 10.1146/annurev-statistics-010814-020120
![]() |
[159] | A. Gupta, A. Agarwal, P. Singh, P. Rai, A deep generative framework for paraphrase generation, in Proceedings of the AAAI Conference on Artificial Intelligence, 32 (2018). https://doi.org/10.1609/aaai.v32i1.11956 |
[160] | I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, et al., Generative adversarial networks, 2014, preprint, arXiv: 1406.2661. |
[161] | L. Metz, B. Poole, D. Pfau, J. Sohl-Dickstein, Unrolled generative adversarial networks, 2016, preprint, arXiv: 1611.02163. |
[162] | G. Ciaburro, Security systems for smart cities based on acoustic sensors and machine learning applications, in Machine Intelligence and Data Analytics for Sustainable Future Smart Cities, Springer, Cham, (2021), 369–393. https://doi.org/10.1007/978-3-030-72065-0_20 |
[163] | X. Hou, L. Shen, K. Sun, G. Qiu, Deep feature consistent variational autoencoder, in 2017 IEEE Winter Conference on Applications of Computer Vision (WACV), IEEE, (2017), 1133–1141. https://doi.org/10.1109/WACV.2017.131 |
[164] | M. J. Kusner, B. Paige, J. M. Hernández-Lobato, Grammar variational autoencoder, in International Conference on Machine Learning (PMLR), 70 (2017), 1945–1954. |
[165] | Y. Pu, Z. Gan, R. Henao, X. Yuan, C. Li, A. Stevens, et al., Variational autoencoder for deep learning of images, labels and captions, 2016, preprint, arXiv: 1609.08976. |
[166] | A. Makhzani, J. Shlens, N. Jaitly, I. Goodfellow, B. Frey, Adversarial autoencoders, 2015, preprint, arXiv: 1511.05644. |
[167] | Z. Zhang, Y. Song, H. Qi, Age progression/regression by conditional adversarial autoencoder, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2017), 5810–5818. https://doi.org/10.1109/CVPR.2017.463 |
[168] |
H. Liu, J. Zhou, Y. Xu, Y. Zheng, X. Peng, W. Jiang, Unsupervised fault diagnosis of rolling bearings using a deep neural network based on generative adversarial networks, Neurocomputing, 315 (2018), 412–424. https://doi.org/10.1016/j.neucom.2018.07.034 doi: 10.1016/j.neucom.2018.07.034
![]() |
[169] |
S. Shao, P. Wang, R. Yan, Generative adversarial networks for data augmentation in machine fault diagnosis, Comput. Ind., 106 (2019), 85–93. https://doi.org/10.1016/j.compind.2019.01.001 doi: 10.1016/j.compind.2019.01.001
![]() |
[170] |
W. Zhang, X. Li, X. D. Jia, H. Ma, Z. Luo, X. Li, Machinery fault diagnosis with imbalanced data using deep generative adversarial networks, Measurement, 152 (2020), 107377. https://doi.org/10.1016/j.measurement.2019.107377 doi: 10.1016/j.measurement.2019.107377
![]() |
[171] |
Z. Wang, J. Wang, Y. Wang, An intelligent diagnosis scheme based on generative adversarial learning deep neural networks and its application to planetary gearbox fault pattern recognition, Neurocomputing, 310 (2018), 213–222. https://doi.org/10.1016/j.neucom.2018.05.024 doi: 10.1016/j.neucom.2018.05.024
![]() |
[172] | P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, P. A. Manzagol, L. Bottou, Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion, J. Mach. Learn. Res., 11 (2010), 3371–3408. |
[173] |
Q. Li, L. Chen, C. Shen, B. Yang, Z. Zhu, Enhanced generative adversarial networks for fault diagnosis of rotating machinery with imbalanced data, Meas. Sci. Technol., 30 (2019), 115005. https://doi.org/10.1088/1361-6501/ab3072 doi: 10.1088/1361-6501/ab3072
![]() |
[174] |
J. Wang, S. Li, B. Han, Z. An, H. Bao, S. Ji, Generalization of deep neural networks for imbalanced fault classification of machinery using generative adversarial networks, IEEE Access, 7 (2019), 111168–111180. https://doi.org/10.1109/ACCESS.2019.2924003 doi: 10.1109/ACCESS.2019.2924003
![]() |
[175] | Y. Xie, T. Zhang, Imbalanced learning for fault diagnosis problem of rotating machinery based on generative adversarial networks, in 2018 37th Chinese Control Conference (CCC), IEEE, (2018), 6017–6022. https://doi.org/10.23919/ChiCC.2018.8483334 |
[176] |
C. Zhong, K. Yan, Y. Dai, N. Jin, B. Lou, Energy efficiency solutions for buildings: Automated fault diagnosis of air handling units using generative adversarial networks, Energies, 12 (2019), 527. https://doi.org/10.3390/en12030527 doi: 10.3390/en12030527
![]() |
[177] |
D. Zhao, S. Liu, D. Gu, X. Sun, L. Wang, Y. Wei, et al., Enhanced data-driven fault diagnosis for machines with small and unbalanced data based on variational auto-encoder, Meas. Sci. Technol., 31 (2019), 035004. https://doi.org/10.1088/1361-6501/ab55f8 doi: 10.1088/1361-6501/ab55f8
![]() |
[178] | J. An, S. Cho, Variational autoencoder based anomaly detection using reconstruction probability, Spec. Lect. IE, 2 (2015), 1–18. |
[179] |
G. San Martin, E. López Droguett, V. Meruane, M. das Chagas Moura, Deep variational auto-encoders: A promising tool for dimensionality reduction and ball bearing elements fault diagnosis, Struct. Health Monit., 18 (2019), 1092–1128. https://doi.org/10.1177/1475921718788299 doi: 10.1177/1475921718788299
![]() |
[180] | Y. Kawachi, Y. Koizumi, N. Harada, Complementary set variational autoencoder for supervised anomaly detection, in 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, (2018), 2366–2370. https://doi.org/10.1109/ICASSP.2018.8462181 |
[181] |
D. Park, Y. Hoshi, C. C. Kemp, A multimodal anomaly detector for robot-assisted feeding using an LSTM-based variational autoencoder, IEEE Rob. Autom. Lett., 3 (2018), 1544–1551. https://doi.org/10.1109/LRA.2018.2801475 doi: 10.1109/LRA.2018.2801475
![]() |
[182] |
S. Lee, M. Kwak, K. L. Tsui, S. B. Kim, Process monitoring using variational autoencoder for high-dimensional nonlinear processes, Eng. Appl. Artif. Intell., 83 (2019), 13–27. https://doi.org/10.1016/j.engappai.2019.04.013 doi: 10.1016/j.engappai.2019.04.013
![]() |
[183] |
K. Wang, M. G. Forbes, B. Gopaluni, J. Chen, Z. Song, Systematic development of a new variational autoencoder model based on uncertain data for monitoring nonlinear processes, IEEE Access, 7 (2019), 22554–22565. https://doi.org/10.1109/ACCESS.2019.2894764 doi: 10.1109/ACCESS.2019.2894764
![]() |
[184] |
G. Ping, J. Chen, T. Pan, J. Pan, Degradation feature extraction using multi-source monitoring data via logarithmic normal distribution based variational auto-encoder, Comput. Ind., 109 (2019), 72–82. https://doi.org/10.1016/j.compind.2019.04.013 doi: 10.1016/j.compind.2019.04.013
![]() |
[185] |
J. Wu, Z. Zhao, C. Sun, R. Yan, X. Chen, Fault-attention generative probabilistic adversarial autoencoder for machine anomaly detection, IEEE Trans. Ind. Inf., 16 (2020), 7479–7488. https://doi.org/10.1109/TⅡ.2020.2976752 doi: 10.1109/TⅡ.2020.2976752
![]() |
[186] | G. Ciaburro, An ensemble classifier approach for thyroid disease diagnosis using the AdaBoostM algorithm, in Machine Learning, Big Data, and IoT for Medical Informatics, Academic Press, (2021), 365–387. https://doi.org/10.1016/B978-0-12-821777-1.00002-1 |
[187] |
Z. Gao, C. Cecati, S. X. Ding, A survey of fault diagnosis and fault-tolerant techniques—Part I: fault diagnosis with model-based and signal-based approaches, IEEE Trans. Ind. Electron., 62 (2015), 3757–3767. https://doi.org/10.1109/TIE.2015.2417501 doi: 10.1109/TIE.2015.2417501
![]() |
[188] |
M. Djeziri, O. Djedidi, S. Benmoussa, M. Bendahan, J. L. Seguin, Failure prognosis based on relevant measurements identification and data-driven trend-modeling: Application to a fuel cell system, Processes, 9 (2021), 328. https://doi.org/10.3390/pr9020328 doi: 10.3390/pr9020328
![]() |
[189] |
M. Aliramezani, C. R. Koch, M. Shahbakhti, Modeling, diagnostics, optimization, and control of internal combustion engines via modern machine learning techniques: A review and future directions, Prog. Energy Combust. Sci., 88 (2022), 100967. https://doi.org/10.1016/j.pecs.2021.100967 doi: 10.1016/j.pecs.2021.100967
![]() |
[190] |
D. Passos, P. Mishra, A tutorial on automatic hyperparameter tuning of deep spectral modelling for regression and classification tasks, Chemom. Intell. Lab. Syst., 233 (2022), 104520. https://doi.org/10.1016/j.chemolab.2022.104520 doi: 10.1016/j.chemolab.2022.104520
![]() |
[191] |
A. Zakaria, F. B. Ismail, M. H. Lipu, M. A. Hannan, Uncertainty models for stochastic optimization in renewable energy applications, Renewable Energy, 145 (2020), 1543–1571. https://doi.org/10.1016/j.renene.2019.07.081 doi: 10.1016/j.renene.2019.07.081
![]() |
[192] |
M. H. Lin, J. F. Tsai, C. S. Yu, A review of deterministic optimization methods in engineering and management, Math. Probl. Eng., 2012 (2012). https://doi.org/10.1155/2012/756023 doi: 10.1155/2012/756023
![]() |
Require: number of incoming roads Ensure: approximate solutions 1: Initilization: 2: 3: 4: 5: for 6: Solve the by definition 3.2 induced optimization problem at the junction based on the flux 7: Compute the densities at the junction with an appropriate Riemann solver 8: Compute the adjusted flux values for the incoming roads 9: for 10: 11: for 12: 13: 14: end for 15: 16: for 17: 18: end for 19: end for 20: for 21: Compute 22: for 23: 24: 25: end for 26: 27: for 28: 29: end for 30: end for 31: end for |
Require: Demand Ensure: Flux values 1: 2: 3: if 4: 5: else if 6: 7: 8: end if |
Require: Demand Ensure: Flux values 1: 2: 3: if 4: if 5: 6: else if 7: 8: end if 9: else if 10: if 11: 12: else 13: 14: end if 15: if 16: 17: 18: else if 19: 20: else if 21: 22: end if 23: end if |
Require: Demand Ensure: Flux values 1: 2: 3: if 4: 6: 7: end if 8: 9: if 10: 11:else if 12: if 13: 14: end if 15: if 16: if 17: 18: else 19: 20: end if 21: end if 22: if 23: if 24: 25: else 26: 27: end if 28: end if 29: end if |
Example 1 | |||||
Splitt. | Reg. | ||||
33.44e-03 | 46.77e-03 | 82.26e-03 | 51.82e-03 | ||
24.17e-03 | 29.05e-03 | 65.59e-03 | 30.69e-03 | ||
14.16e-03 | 20.12e-03 | 60.86e-03 | 24.45e-03 | ||
8.97e-03 | 12.49e-03 | 58.37e-03 | 20.44e-03 | ||
CR | 0.64695 | 0.62453 | 0.1593 | 0.4353 | |
Example 2 | |||||
Splitt. | Reg. | ||||
4.58e-03 | 7.41e-03 | 44.70e-03 | 14.57e-03 | ||
2.97e-03 | 4.24e-03 | 43.47e-03 | 11.28e-03 | ||
2.03e-03 | 2.89e-03 | 42.50e-03 | 10.06e-03 | ||
1.24e-03 | 1.99e-03 | 41.80e-03 | 9.21e-03 | ||
CR | 0.61911 | 0.62327 | 0.0322 | 0.2150 |
Example 1 | |||||
Splitt. | Reg. | ||||
9.25e-03 | 16.22e-03 | 16.22e-03 | 17.01e-03 | ||
5.90e-03 | 11.63e-03 | 11.63e-03 | 12.19e-03 | ||
2.98e-03 | 8.13e-03 | 8.13e-03 | 8.52e-03 | ||
8.97e-03 | 5.71e-03 | 5.71e-03 | 5.99e-03 | ||
CR | 0.53838 | 0.50353 | 0.50353 | 0.50347 | |
Example 2 | |||||
Splitt. | Reg. | ||||
14.12e-03 | 20.10e-03 | 85.69e-03 | 27.55e-03 | ||
9.65e-03 | 13.86e-03 | 79.98e-03 | 21.65e-03 | ||
6.41e-03 | 9.57e-03 | 75.96e-03 | 17.49e-03 | ||
4.51e-03 | 6.69e-03 | 73.22e-03 | 14.65e-03 | ||
CR | 0.55295 | 0.52959 | 0.07551 | 0.30432 |
Require: number of incoming roads Ensure: approximate solutions 1: Initilization: 2: 3: 4: 5: for 6: Solve the by definition 3.2 induced optimization problem at the junction based on the flux 7: Compute the densities at the junction with an appropriate Riemann solver 8: Compute the adjusted flux values for the incoming roads 9: for 10: 11: for 12: 13: 14: end for 15: 16: for 17: 18: end for 19: end for 20: for 21: Compute 22: for 23: 24: 25: end for 26: 27: for 28: 29: end for 30: end for 31: end for |
Require: Demand Ensure: Flux values 1: 2: 3: if 4: 5: else if 6: 7: 8: end if |
Require: Demand Ensure: Flux values 1: 2: 3: if 4: if 5: 6: else if 7: 8: end if 9: else if 10: if 11: 12: else 13: 14: end if 15: if 16: 17: 18: else if 19: 20: else if 21: 22: end if 23: end if |
Require: Demand Ensure: Flux values 1: 2: 3: if 4: 6: 7: end if 8: 9: if 10: 11:else if 12: if 13: 14: end if 15: if 16: if 17: 18: else 19: 20: end if 21: end if 22: if 23: if 24: 25: else 26: 27: end if 28: end if 29: end if |
Example 1 | |||||
Splitt. | Reg. | ||||
33.44e-03 | 46.77e-03 | 82.26e-03 | 51.82e-03 | ||
24.17e-03 | 29.05e-03 | 65.59e-03 | 30.69e-03 | ||
14.16e-03 | 20.12e-03 | 60.86e-03 | 24.45e-03 | ||
8.97e-03 | 12.49e-03 | 58.37e-03 | 20.44e-03 | ||
CR | 0.64695 | 0.62453 | 0.1593 | 0.4353 | |
Example 2 | |||||
Splitt. | Reg. | ||||
4.58e-03 | 7.41e-03 | 44.70e-03 | 14.57e-03 | ||
2.97e-03 | 4.24e-03 | 43.47e-03 | 11.28e-03 | ||
2.03e-03 | 2.89e-03 | 42.50e-03 | 10.06e-03 | ||
1.24e-03 | 1.99e-03 | 41.80e-03 | 9.21e-03 | ||
CR | 0.61911 | 0.62327 | 0.0322 | 0.2150 |
Example 1 | |||||
Splitt. | Reg. | ||||
9.25e-03 | 16.22e-03 | 16.22e-03 | 17.01e-03 | ||
5.90e-03 | 11.63e-03 | 11.63e-03 | 12.19e-03 | ||
2.98e-03 | 8.13e-03 | 8.13e-03 | 8.52e-03 | ||
8.97e-03 | 5.71e-03 | 5.71e-03 | 5.99e-03 | ||
CR | 0.53838 | 0.50353 | 0.50353 | 0.50347 | |
Example 2 | |||||
Splitt. | Reg. | ||||
14.12e-03 | 20.10e-03 | 85.69e-03 | 27.55e-03 | ||
9.65e-03 | 13.86e-03 | 79.98e-03 | 21.65e-03 | ||
6.41e-03 | 9.57e-03 | 75.96e-03 | 17.49e-03 | ||
4.51e-03 | 6.69e-03 | 73.22e-03 | 14.65e-03 | ||
CR | 0.55295 | 0.52959 | 0.07551 | 0.30432 |