A New Scheme for Fault Detection and Classification Applied to DC Motor

ABSTRACT

This study presents an approach for fault detection and classification in a DC drive system. The fault is detected by a classical Luenberger observer. After the fault detection, the fault classification is started. The fault classification, the main contribution of this paper, is based on a representation which combines the Subctrative Clustering algorithm with an adaptation of Particle Swarm Clustering.

Keywords:
Fault Detection and Classification 1; Luenberger Observer 2; Particle Swarm Clustering 3

1 INTRODUCTION

Fault detection and analysis is a very important strategy that is commonly employed in the industry with the purpose of allowing a cost-effective maintenance policy, keeping productivity standards and ensuring safety. The fault analysis gives support for the design of corrective actions, system redundancies, and safety policies in order to mitigate the effects of a fault ¹⁹. In this paper, a fault diagnosis procedure is divided into two tasks: i) fault detection, indicating the occurrence of some fault in a monitored system; and ii) fault classification, establishing the type and/or location of the fault.

The literature presents several classes of strategies to deal with fault detection and isolation (FDI) ⁷. These strategies can be, in general, divided in approaches based on quantitative models ³⁶ and on qualitative models ^{34), (35}.

Considering the quantitative model-based approaches (used for fault detection), many works with different emphases have been published over the past years. Among them, the main approaches focus on knowledge of mathematical models of the plant, and are based on observers ^{7), (4), (32). (31), (8), (28}On the other hand, considering the qualitative model-based approaches (used for fault classification), focusing on the pattern analysis of the historic process data, the main related approaches are: signed directed graphs ^{24), (9), (2}, fault trees ¹⁶, fuzzy systems ^{17), (29), (15}, qualitative trend analysis ^{25), (18), (14), (13}, mutual information ³⁸, neural networks ³, ¹¹ (neural networks also can be used as observer ^{33), (26}), artificial immune systems ^{22), (23), (30}, Bayesian networks ^{39), (37} and the combination of techniques ^{21), (12}.

In this paper, an approach for fault detection (first step) and classification (second step) is presented. The classical Luenberger observer is used in the first step, and this information is used for the classification system start. The idea of the second step, the main contribution of this paper, is to deal with the fault classification in a new way, using an adaptation of Particle Swarm Clustering. To illustrate the efficiency of the proposed methodology, the problem of fault detection in a DC Motor Benchmark Model ⁵ has been solved. An overview of the FDI framework proposed in this paper is illustrated in Figure 1.

Figure 1:
Framework for fault detection and classification.

1.1 Contributions

In this paper is proposed an algorithm, adapted from cPSC (²⁷) and denoted as New cPSC (NcPSC), which optimizes the hit rate and the total number of groups (classes) of a data set. It is a supervised algorithm which combines the following functionalities:

• A routine, detailed in subsection 3.2, was developed for generating the initial particle set;

• While the cPSC algorithm implements the cosine distance for computing the similarity measure, the NcPSC uses the Euclidean distance for computing the similarity between a particle and the input data set.

• A particle growing procedure, presented in Algorithm 2, was developed;

• A particle stagnation mechanism, described in Algorithm 3, was implemented.

It is important to note that the proposed functionalities may be adapted in several metaheuristics.

Paper organization. Section 2 presents and analyzes the DC Motor modeling considering the case of different types of faults and the observer design for fault detection. Section 3 describes the adaptive methodology based on Particle Swarm Clustering, the main contribution of this paper, for fault classification. Section 4 shows the new proposed approach applied to the DC motor fault classification problem. Finally, section 5 presents the concluding remarks.

2 LUENBERGER OBSERVER DESIGN FOR DC MOTOR

The DC motor benchmark model, evaluated in ⁵, is descripted as a drive system which consists of two power supplies, controlled static converters, a DC motor and a mechanical load. The system can be represented as shown in Figure 2.

Figure 2:
Representation of the DC drive system.

In Figure 2, each variable as the following:

• v_a is the armature voltage,

• v_fd is the field voltage,

• i_a is the armature current,

• i_fd is the field current.

• ω_r represents mechanical rotation speed in rad/s,

• r_a is the armature resistance,

• L_a is the armature inductance,

• r_fd is the field resistance,

• L_fd is the field inductance,

• e_a is the counter electromotive force and is dependent of L _afd (mutual inductance).

A discrete model for the DC motor is given in (2.1) and presented in ⁵, where i _a = x ₁, i _fd = x ₂, and ω _r = x ₃. All state variables are measured, i.e., y(t)=I x(t).

$\left[\begin{array}{c}{x}_1(k+1)\\ x_2(k+1)\\ x_3(k+1)\end{array}\right]=\left[\begin{array}{ccc}{a}_1& a_2\left(k\right)& 0\\ 0& a_3& 0\\ a_4\left(k\right)& 0& a_5\end{array}\right]\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\end{array}\right]+\left[\begin{array}{ccc}{b}_1& 0& 0\\ 0& b_2& 0\\ 0& 0& d_1\end{array}\right]\left[\begin{array}{c}{v}_a\left(k\right)\\ v_{fd}\left(k\right)\\ T_L\end{array}\right]$ (2.1)

As the following: $a_1=a_1(r_a,L_a)=e^{-\frac{r_a}{L_a}h};$

$$\begin{gathered} a_3=a_3(r_{fd},L_{fd})=e^{-\frac{r_{fd}}{L_{fd}}h}; \\ {a}_5=a_5(B_m,J_m)=e^{-\frac{B_m}{J_m}h}; \\ {a}_2\left(k\right)=a_2(r_a,L_a,r_{fd},L_{fd},x_3(k\left)\right)=\frac{1}{r_{fd}La-r_a{L}_{fd}}\left[L_{afd}{L}_{fd}(a_3-a_1)x_3\left(k\right)+r_a{L}_{fd}{a}_1-r_{fd}{L}_a{a}_3\right]; \\ {a}_4\left(k\right)=a_5(B_m,J_m,x_2(k\left)\right)=L_{afd}\frac{(1-a_5)}{B_m}{x}_2\left(k\right); \\ {b}_1=b_1(r_a,L_a)=\frac{1-a_1}{ra}{b}_2=b_2(r_{fd},L_{fd})=\frac{1-a_3}{r_{fd}}{d}_1; \\ {d}_1=d_1(B_m,J_m)=-\frac{1-a_5}{B_m}. \end{gathered}$$

where B _m is the coefficient of viscous friction, J _m is the moment of inertia and T _L is the mechanical torque of the load.

Faults on the DC drive system may occur in: actuators (armature and field converters), plant or process (DC Machine) and sensors (current meters and speed). The faults on actuators are: armature converter disconnection, field converter disconnection, armature converter short circuit and field converter short circuit. The faults in DC Machine are: armature turns short-circuit, field turns short-circuit, ventilation system fault and bearing lubrication fault. The faults on sensors are: armature current sensor fault, field current sensor fault and machine speed sensor fault. Considering these fault types (see Table 1), the complete model is described in (2.2). For more details see the full modeling in ⁵⁾ and ³⁰.

$$\begin{gathered} \left[\begin{array}{c}{x}_1(k+1)\\ x_2(k+1)\\ x_3(k+1)\end{array}\right]=\left[\begin{array}{ccc}{k}_{aa}{a_1}^f& k_{aa}{a_2}^f\left(k\right)& 0\\ 0& k_{afd}{a_3}^f& 0\\ {a_4}^f\left(k\right)& 0& {a_5}^f\end{array}\right]\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\end{array}\right]+\left[\begin{array}{ccc}{b_1}^f& 0& 0\\ 0& {b_2}^f& 0\\ 0& 0& {d_1}^f\end{array}\right]\left[\begin{array}{c}{k}_{aa}{k}_{cca}{v}_a\left(k\right)\\ k_{afd}{k}_{ccfd}{v}_{fd}\left(k\right)\\ T_L\end{array}\right] \\ \left[\begin{array}{c}{y}_1\left(k\right)\\ y_2\left(k\right)\\ y_3\left(k\right)\end{array}\right]=\left[\begin{array}{ccc}{k}_{{i_a}^f}& 0& 0\\ 0& k_{{i_{fd}}^f}& 0\\ 0& 0& k_{{{\omega }_r}^f}\end{array}\right]\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\end{array}\right] \end{gathered}$$ (2.2)

where: ${r_a}^f={k_{ca}}^{r_a}{k_{fv}}^{r_a}{r}_a,{L_a}^f={k_{ca}}^{L_a}{L}_a,{r_{fd}}^f={k_{cfd}}^{r_{fd}}{k_{fv}}^{r_{fd}}{r}_{fd},{L_{fd}}^f={k_{cfd}}^{L_{fd}}{L}_{fd},{B_m}^f=k_{fl}{B}_m.$

Table 1:
Summary of DC motor system faults.

Fault	Fault Type	Affected Fault Indicator Parameter	Index Variables	Parameters Values
1	Armature converter disconnection	ia = 0	k aa	{0;1}
2	Field converter disconnection	ifd = 0	kafd .	{0;1}
3	Armature converter short circuit	va = 0	k cca	{0;1}
4	Field converter short circuit	vfd = 0	kccfd .	{0;1}
5	Armature turns short-circuit	ra and L a	kraca and kLa ca	[0;1]
6	Field turns short-circuit	rfd and L fd	${k^{r_{fd}}}_{cfd}\text{and}{k^{L_{fd}}}_{cfd}$	[0;1]
7	Ventilation system fault	ra and r fd	${k_{fv}}^{r_a}\text{and}{k_{fv}}^{r_{fd}}$	[1;∞)
8	Bearing lubrication fault	B m	k fl	[1;∞)
9	Armature current sensor fault	i a	${k_{i_a}}^f$	{0;1}
10	Field current sensor fault	i fd	${k_{i_{fd}}}^f$	{0;1}
11	Machine speed sensor fault	ω r	${k_{{\omega }_r}}^f$	{0;1}

Simulations were made to show some situations of DC motor operation mode. The normal operation of the machine and the four faults in the actuators were simulated and the values of the variables are shown in Figs 3 to 7.

Figure 3:
Simulation of the DC motor in normal scenario.

Figure 4:
Simulation of the DC motor with disconnection of the armature converter.

Figure 5:
Simulation of the DC motor with disconnection of the field converter.

Figure 6:
Simulation of the DC motor with short circuit in the armature converter.

Figure 7:
Simulation of the DC motor with short circuit in the field converter.

We obtained 4000 points (corresponding to a test of 4 seconds, as each 1s corresponds to 1000 points) and each fault occurs 2s after the beginning of the tests. In these scenarios, it is possible to see which variables are affected after the occurrence of faults.

2.1 Observer-based fault detection

The aim of the observer-based fault detection method is to generate a residual, used for fault indication. Considering the state space model:

$\dot{x}\left(t\right)=Ax\left(t\right)+Bu\left(t\right)$ (2.3)

$y\left(t\right)=Cx\left(t\right)$ (2.4)

where u(t) is the input, x(t) is the state and y(t) is the output.

The observer can be designed as follows to provide the system observability:

$\dot{\hat{x}}\left(t\right)=A\hat{x}\left(t\right)+Bu\left(t\right)+Le\left(t\right)$ (2.5)

$e\left(t\right)=y\left(t\right)-C\hat{x}\left(t\right)$ (2.6)

$\hat{x}$ is the estimated system state, L is the matrix of the observer feedback gains that is designed to provide the required performance of the observer and e(t) is the output error.

Replacing (2.6) in (2.5):

$\dot{\hat{x}}\left(t\right)=[A-LC]\hat{x}\left(t\right)+Bu\left(t\right)+Ly\left(t\right)$ (2.7)

The state error is given by:

$\dot{\tilde{x}}\left(t\right)=\dot{x}\left(t\right)-\dot{\hat{x}}\left(t\right)$ (2.8)

Replacing (2.3) and (2.7) in (2.8):

$\dot{\tilde{x}}\left(t\right)=[A-LC]\tilde{x}\left(t\right)$ (2.9)

The observer design results in:

$\underset{t\to \infty }{\lim }\tilde{x}\left(t\right)=0$

Considering the matrices A and C of the discrete system (2.1) to A?LC, and imposing pole placement to gain L observer, of the form:

$A-LC=\left[\begin{array}{ccc}{\lambda }_1& 0& 0\\ 0& {\lambda }_2& 0\\ 0& 0& {\lambda }_3\end{array}\right]$

the observer gain is obtained by:

$L=\left[\begin{array}{ccc}{a}_1-{\lambda }_1& a_2\left(k\right)& 0\\ 0& a_3-{\lambda }_2& 0\\ a_4\left(k\right)& 0& a_5-{\lambda }_3\end{array}\right]$

Note: for discrete systems, the pole placement of A?LC is inside unit circle, |λ_i |< 1.

Figure 8 shows residuals for observer gain with λ₁ = λ₂ = λ₃ = 0.3 for armature converter disconnection.

Figure 8:
Residual for observer gain with λ₁ = λ₂ = λ₃ = 0.3.

3 ADAPTIVE APPROACH FOR FAULT CLASSIFICATION

In this section, we present the NcPSC algorithm which is an adaptation of the cPSC algorithm. In ⁶ a new unsupervised mechanism based on the particle swarm optimization (PSO)²⁰ algorithm, called Particle Swarm Clustering - PSC, is proposed for solving clustering problems. The PSC creates a population of individuals (particles), initially randomly, where each particle represents a candidate solution which moves through the search space. Specifically for data clustering problems, a particle identifies a cluster (or a prototype for a cluster). However, having to pass the value of k (cluster number) to the algorithm may not be interesting. Thus, ²⁷ developed the cPSC(ConstructivePSC) (an adaptation of PSC) algorithm which identifies automatically the total of groups in a set. The cPSC implements a dynamic mechanism for particles growthing (cloning) and pruning to compute the total of groups in a set. The cloning mechanism works as follows: i) Firstly, it computes how many data from input data set each particle represents. If it is equal zero (or a fixed iteration number) the particle is removed from the swarm. Otherwise, it is a candidate particle for cloning; ii) Also, if the similarity between a particle x and an input data is greater than a constant ε, x will be cloned. The cosine metric is used to calculate the similarity between a particle and an input data. The clone particle is positioned between the cloned particle and the most similar input data item. Finally, the NcPSC algorithm The NcPSC introduces some functionality in the cPSC to insert supervised characteristics, since the problem deal with classification. Next we detail each functionality implemented by NcPSC algorithm.

3.1 Concentration level and hit rate

The NcPSC implements a mechanism for growing and pruning particles based on its concentration level and hit rate. The concentration level of a particle p (p _cl ) is computed as:

Algorithm 1:
Computing CL (p, X).

p.I_x is a list associated to every particle p used for storing input data.

3.2 Generating initial particle set

The initial population plays a key role in terms of convergence rate and may affect the success of an EA in finding high quality or satisfactory solutions ¹. For this reason, the NcPSC algorithm also implements a simple mechanism for generating initial particles set: Firstly it generates a swarm with N particles. The initial position of each particle is determined using the following mechanism: It calculates N centroids for the training data set using the subtractive clustering (SC) method¹⁰.

3.3 Particle growing mechanism

The growing procedure implemented by NcPSC was proposed for generating new particles and it is based on concentration level and hit rate values of a particle. The proposed method, detailed in Algorithm 2, clones a particle p, resulting in a clone particle p’. A particle p is cloned if its concentration level (p.cl) value is greater than ℰ₁ and its hit rate (p.hh) value is less than γ₁ - it means that p concentrates many input data from more than one class ((₁ and γ₁ are parameters of NcPSC). It is noted that a particle with low hit rate worsens (or deteriorates) the final hit rate of the swarm.

Algorithm 2:
Particle growing (p, (₁; γ₁)

Finally, a simple mutation is performed over a dimension (chosen randomly) of the clone particle. It is expected that clone particles present better hit rates values.

3.4 Particle stagnation

A mechanism for particle stagnation was proposed for NcPSC because when choosing the most similar particle to the input data, generally more particles move to the crowded regions of the search space. If these crowded regions concentrate several classes, the hit rate values of the attracted particles may be reduced.

The stagnation routine, presented in Algorithm 3, checks the concentration level and hit rate values of a particle. It means if a particle concentration level value is above (₂ and its hit rate value is above γ₂, the particle will not move in current NcPSC iteration ((₂ and γ₂ are parameters of NcPSC).

Algorithm 3:
Particle stagnation (p, (₂; γ₂).

3.5 General structure of the NcPSC algorithm

The proposed NcPSC, detailed in Algorithm 4, is an adaptation of cPSC algorithm and it has a set of input parameters presented in the following:

• Number of particles: Variable;

• Input Data: Dataset for clustering;

• (₁ = 0.60, (₂ = 0.90, γ₁ =21 and γ₂ = 15

• ω = 0.20;

• Stop condition: 20 (twenty) iterations.

The NcPSC works as: Firstly, it generates a swarm with N particles. In the next, the following steps are executed in an ordered and repetitive manner until a termination criterion is found:

• All particles which concentration level value greater than (₂ and hit rate value greater than γ₂ are marked as stagnated (line 6);

• It identifies the most similar particle from the swarm for each item in the input data. This particle is denoted as the winner particle (X _w ). The following operations are applied over each winner particle (It is moved):

• - Its velocity is updated through expression 3.1:

$$\begin{gathered} V_w(t+1)=\omega V_w\left(t\right)+{\phi }_1\otimes \left(PBes{t}_{wj}\right(t)-X_w(t\left)\right)+ \\ {\phi }_2\otimes \left(GBes{t}_j\right(t)-X_w(t\left)\right)+{\phi }_3\left(Y_j\right(t)-X_w(t\left)\right) \end{gathered}$$ (3.1)

where V _w (t) is the particle velocity in iteration t, ω is the inertia component and φ_1, φ₂ and φ₃ are random number vectors. While PBest denotes the best (most similar) position of a particle in relation to an input data, GBest identifies the best (most similar) particle position (from all PBest particles) in relation to an input data.

• - Its position is updated using equation:

$X_w(t+1)=X_w\left(t\right)+V_w(t+1)$ (3.2)

• - Its p _b est and p _b est components are updated;

• It removes particles from swarm: All particles with concentration level equal zero are removed from the swarm;

• It clones particles from swarm: All particles with concentration level greater than (₁ and with hit rates less than γ₁ are cloned.

Algorithm 4:
NcPSC algorithm (ID, (₁, γ₁, (₂, γ₂).

4 PROPOSED APPROACH APPLIED TO THE FAULT CLASSIFICATION IN DC MOTOR

To investigate the main functionalities of the proposed methodology, we analyze the performance of several algorithms which implement some functionalities (isolated or combined) of the NcPSC algorithm. The developed algorithms with their implemented functionalities are:

• cPSC: The original cPSC algorithm proposed in ²⁷;

• cPSC_ED: A version of cPSC algorithm which implements the Euclidean distance for similarity measure;

• cPSC_PG: An adaptation of cPSC algorithm which develops only the Particle_stagnation routine;

• cPSC_EP: A Version of cPSC_ED which combines both the Euclidean distance for similarity measure and the Particle_stagnation mechanism;

• cPSC_Ps: An adaptation of cPSC_EP algorithm which develops the Particle_stagnation mechanism;

• NcPSC: The proposed NcPSC algorithm which implements all mentioned functionalities.

To assess the performance of the developed algorithms they were applied to a clustering problem of a data set with 252 operation points representing 11 (eleven) fault points (Problem with 11 classes). Each algorithm was executed 100 times and each execution performed 20 (twenty) iterations. Some data (Larger, Smaller and average values of hit rate and total of particles) were computed for each algorithm and the obtained results are shown in Table 2.

Table 2:
Performance results (Hit rate and Number of particles) for the problem generated by each algorithm.

Description	Hit Rate (%)			Number of particles
	Larger	Smaller	Average	Larger	Smaller	Average
cPSC	88.10	41.67	73.19	172	9	54.41
cPSC ED	83.73	73.02	80.99	155	76	125.76
cPSC PG	90.48	65.48	81.19	25	16	20.66
cPSC EP	96.04	76.98	86.37	24	15	19.90
cPSC PS	91.67	54.37	78.91	18	10	14.56
NcPSC	100	82.14	91.30	20	11	13.43

Some comments about the performance of the 06 algorithms are presented in the following:

• The cPSC _ED and the cPSC algorithms produced the worst hit rate results. Their greater and average hit rate value are smaller than the values of the remaining algorithms. Also, their greater and average number of particles (classes) values are worse than the values generated by the others algorithms. In summary, the Euclidean distance mechanism is not sufficient to produce good results in solving the proposed clustering problem;

• When comparing the three algorithms (cPSC _PG , cPSC _EP and cPSC _PS ), it is noted that the cPSC _EP produced better hit rate results than cPSC _PG and cPSC _PS algorithms. On the other hand, the cPSC _PS produced best number of particles (near or equal to the number of classes) results than the other two algorithms (cPSC _PG and cPSC _EP algorithms). In addition, the number of classes found by cPSC _EP is a little better than cPSC _PG ;

• NcPSC was capable of providing a better clustering than all algorithms. Its hit rate (greater, smaller and average) values better than the others algorithms. Its number of particles (smaller and average) values are better than the results produced by the remaining algorithms. It is important to comment that the NcPSC algorithm found the exact number of classes of the proposed problem. Despite its greater number of classes value is greater than the value found by cPSC _Ps algorithm, its average value is closer to the real value than the average value produced by cPSC _Ps algorithm.

The results generated by the six algorithms are presented in a boxplot perspective shown in Figure 9. Firstly, the hit rate results, illustrated in Figure 9(a), evidence the good performance of the cPSC _PG , cPSC _EP , cPSC _PS and NcPSC algorithms when compared with cPSC and cPSC _ED methods.

Figure 9:
Boxplot illustrating the performance of the six implemented algorithms.

Also, this perspective emphasizes the good results (both hit rate and particles number) presented by the NcPSC algorithm when compared to the others implementations. The lower boundary of its central box is above the upper boundary of the central box of all others implementations. Figure 9(a) reveals that cPSC _ED , cPSC _EP , cPSC _PS and NcPSC (they developed the euclidian distance as similarity metric) have a more homogeneous behavior than cPSC and cPSC _EG algorithms (both implemented the cossin distance as similarity metric). Furthermore, the symmetry is more pronounced in cPSC _EP and NcPSC implementations. The results generated by cPSC _PS algorithm, which only implements the particle stagnation mechanism, are worser than cPSC _EP results. However, a version which implements all funcionalities (NcPSC algorithm) produced better results than all versions presented in this paper. Also, the total of particles found by each algorithm is presented in a boxplot style (See Figure 9(b)). Again, the figure illustrates the good results produced by algorithms cPSC _PG , cPSC _EP , cPSC _PS and NcPSC and cPSC _PG , cPSC _EP , cPSC _PS and NcPSC are more homogenic and generated better results than cPSC and cPSC _ED algorithms. The total of particles (classes) found by both implementations are closer to the real context than the others algorithms.

5 CONCLUSION

In this paper, a new strategy for fault detection and classification is proposed. The strategy is based on the classical Luenberger observer, for fault detection, associated with an adaptive approach, for fault classification. The adaptive approach for fault classification, the main contribution of this paper, is based on the Particle Swarm Clustering algorithm. This methodology has been successfully applied to the fault detection and classification problem in a DC motor. The simulation results presented illustrate the effectiveness of the proposed method.

ACKNOWLEDGMENT

This work has been supported in part by the Brazilian agencies CNPq and FAPEMIG.

REFERENCES

• ¹
  D. Bajer, G. Martinović & J. Brest. A population initialization method for evolutionary algorithms based on clustering and Cauchy deviates. Expert Systems with Applications, 60 (2016), 294-310.
• ²
  T. Boukhobza, F. Hamelin & S. Canitrot. A graph-theoretic approach to fault detection and isolation for structured bilinear systems. International Journal of Control, 81(4) (2008), 661-678.
• ³
  J.M.F. Calado, J. Korbicz, K. Patan, R.J. Patton & J.M.G.S. da Costa. Soft computing approaches to fault diagnosis for dynamic systems. European Journal of Control, 7(2-3) (2001), 248-286.
• ⁴
  W.M. Caminhas & R.H.C. Takahashi. Dynamic system failure detection and diagnosis employing sliding mode observers and fuzzy neural networks. In “Proceedings of the Joint 9th IFSA and 20th NAFIPS”. Vancouver (2001), pp. 304-309.
• ⁵
  W.M. Caminhas & R.H.C. Takahashi. Dynamic system failure detection and diagnosis employing sliding mode observers and fuzzy neural networks. In “Joint nineth IFSA world congress and 20th NAFIPS international conference” (2001), pp. 304-309.
• ⁶
  L.N. Castro & S.C.M. Cohen. Data Clustering with Particle Swarms. International Conference on Evolutionary Computation, Proceedings of World Congress on Computational Intelligence, (2006), 1792-1798.
• ⁷
  J. Chen & R.J. Patton. “Robust model-based fault diagnosis for dynamic systems”, volume 3. Springer Science & Business Media (2012).
• ⁸
  W. Chen & M. Saif. Observer-based strategies for actuator fault detection, isolation and estimation for certain class of uncertain nonlinear systems. IET Control Theoty and Applications, 1(6) (2007), 1672-1680.
• ⁹
  H. Cheng, M. Nikus & S. Jamsa-Jounela. Fault diagnosis of the paper machine short circulation process using novel dynamic causal digraph reasoning. Journal of Process Control, 18(7-8) (2008), 676-691.
• ¹⁰
  S.L. Chiu. Method and software for extracting fuzzy classification rules by subtractive clustering. Biennial Conf. North American Fuzzy Information Processing Soc., (1996), 461-465.
• ¹¹
  M.F.S.V. D’Angelo & P.P. Costa. Detection of shorted turns in the field winding of turbogenerators using the neural network MLP. In “Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics”. Tucson (2001), pp. 1930-1935.
• ¹²
  M.F.S.V. D’Angelo, R.M. Palhares, L.B. Cosme, L.A. Aguiar, F.S. Fonseca & W.M. Caminhas. Fault detection in dynamic systems by a Fuzzy/Bayesian network formulation. Applied Soft Computing, 21 (2014), 647-653.
• ¹³
  M.F.S.V. D’Angelo, R.M. Palhares, R.H.C. Takahashi & R.H. Loschi. Fuzzy/Bayesian change point detection approach to incipient fault detection. IET Control Theory & Applications, 5(4) (2011), 539-551.
• ¹⁴
  M.F.S.V. D’Angelo, R.M. Palhares, R.H.C. Takahashi, R.H. Loschi, L.M.R. Baccarini & W.M. Caminhas. Incipient fault detection in induction machine stator-winding using a fuzzy-Bayesian change point detection approach. Applied Soft Computing, 11(1) (2011), 179-192.
• ¹⁵
  K.P. Detroja, , R.D. Gudi & S.C. Patwardhan. A possibilistic clustering approach to novel fault detection and isolation. Journal of Process Control, 16(10) (2006), 1055-1073.
• ¹⁶
  Y. Dutuit & A. Rauzy. Approximate estimation of system reliability via fault trees. Reliability Engineering & System Safety, 87(2) (2005), 163-172.
• ¹⁷
  S.M. El-Shal & A.S. Morris. A fuzzy expert system for fault detection in statistical process control of industrial processes. IEEE Transactions on Systems, Man and Cybernetics, Part C, 30(2) (2000), 281-289.
• ¹⁸
  K.F. Fong, A.P. Loh & W.W. Tan. A frequency domain approach for fault detection. International Journal of Control, 81(2) (2008), 264-276.
• ¹⁹
  R. Isermann & P. Balle. Trends in the application of model-based fault detection and diagnosis of technical processes. Control Engineering Practice, 5(5) (1997), 707-719.
• ²⁰
  J. Kennedy & R. Eberhart. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks (1995), pp. 1942-1948.
• ²¹
  C.A. Laurentys, C.H.M. Bomfim, B.R. Menezes & W.M. Caminhas. Design of a pipeline leakage detection using expert system: A novel approach. Applied Soft Computing, 11(1) (2011), 1057-1066.
• ²²
  C.A. Laurentys, R.M. Palhares & W.M. Caminhas. Design of an artificial immune system based on Danger Model for fault detection. Expert Systems with Applications, 37(7) (2010), 5145-5152.
• ²³
  C.A. Laurentys, R.M. Palhares & W.M. Caminhas. A novel Artificial Immune System for fault behavior detection. Expert Systems with Applications, 38(11) (2011), 6957-6966.
• ²⁴
  M.R. Maurya, R. Rengaswamy & V. Venkatasubramanian. A signed directed graph-based systematic framework for steady-state malfunction diagnosis inside control loops. Chemical Engineering Science, 61(6) (2006), 1790-1810.
• ²⁵
  M.R. Maurya, R. Rengaswamy & V. Venkatasubramanian. Fault diagnosis using dynamic trend analysis: A review and recent developments. Engineering Applications of Artificial Intelligence, 20(2) (2007), 133-146.
• ²⁶
  K. Patan & T. Parisini. Identification of neural dynamic models for fault detection and isolation: the case of a real sugar evaporation process. Journal of Process Control, 15(1) (2005), 67-79.
• ²⁷
  A.K.F. Prior & L.N. Castro. cPSC: Um algoritmo de enxame construtivo para agrupamento de dados. In “Anais do XVIII Congresso Brasileiro de Automática” (2010), pp. 3300-3307.
• ²⁸
  V. Puig, A. Stancu, T. Escobet, F. Nejjari, J. Quevedo & R. Patton. Passive robust fault detection using interval observers: Application to the DAMADICS benchmark problem. Control Engineering Practice, 14(6) (2006), 621-633.
• ²⁹
  J. Ragot & D. Maquin. Fault measurement detection in an urban water supply network. Journal of Process Control, 16(9) (2006), 887-902.
• ³⁰
  G.C. Silva, R.M. Palhares & W.M. Caminhas. Immune inspired Fault Detection and Diagnosis: A fuzzy-based approach of the negative selection algorithm and participatory clustering. Expert Systems with Applications, 39(16) (2012), 12474-12486.
• ³¹
  R.H.C. Takahashi, R.M. Palhares & P.L.D. Peres. Discrete-time Singular Observers: ℋ₂/ℋ_∞ Optimality and Unknown Inputs. International Journal of Control, 72(6) (1999), 481-492.
• ³²
  R.H.C. Takahashi & P.L.D. Peres. Unknown input observers for uncertain systems: A unifying approach. European Journal of Control, 5(2-4) (1999), 261-275.
• ³³
  F.J. Uppal, R.J. Patton & M. Witczak. A neuro-fuzzy multiple-model observer approach to robust fault diagnosis based on the DAMADICS benchmark problem. Control Engineering Practice, 14(6) (2006), 699-717.
• ³⁴
  V. Venkatasubramanian, R. Rengaswamy & S.N. Kavuri. A review of process fault detection and diagnosis - Part II: Qualitative models and search strategies. Computers and Chemical Engineering, 27(3) (2003), 313-326.
• ³⁵
  V. Venkatasubramanian, R. Rengaswamy, S.N. Kavuri & K. Yin. A review of process fault detection and diagnosis - Part III: Process history based methods. Computers and Chemical Engineering, 27(3) (2003), 327-346.
• ³⁶
  V. Venkatasubramanian, R. Rengaswamy, K. Yin & S.N. Kavuri. A review of process fault detection and diagnosis - Part I: Quantitative model-based methods. Computers and Chemical Engineering, 27(3) (2003), 293-311.
• ³⁷
  S. Verron, J. Li & T. Tiplica. Fault detection and isolation of faults in a multivariate process with Bayesian network. Journal of Process Control, 20(8) (2010), 902-911.
• ³⁸
  S. Verron, T. Tiplica & A. Kobi. Fault detection and identification with a new feature selection based on mutual information. Journal of Process Control, 18(5) (2008), 479-490.
• ³⁹
  B.G. Xu. Intelligent fault inference for rotating flexible rotors using Bayesian belief network. Expert Systems with Applications, 39(1) (2012), 816-822.

Publication Dates

• Publication in this collection
  May-Aug 2018

History

• Received
  19 Oct 2017
• Accepted
  12 Mar 2018