Fast-slow dynamics of a hydropower generation system with multi-time scales

Mechanical Systems and Signal Processing 110 (2018) 458–468

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Fast-slow dynamics of a hydropower generation system with multi-time scales Huanhuan Li a, Diyi Chen a,b,c,⇑, Xiang Gao a, Xiangyu Wang c,d, Qingshuang Han a, Changzhi Wu c a

Institute of Water Resources and Hydropower Research, Northwest A&F University, Yangling, Shaanxi 712100, PR China Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, Yangling, Shaanxi 712100, PR China c Australasian Joint Research Centre for Building Information Modelling, School of Built Environment, Curtin University, WA 6102, Australia d Department of Housing and Interior Design, Kyung Hee University, Seoul, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 16 August 2017 Received in revised form 3 March 2018 Accepted 13 March 2018

Keywords: Fast-slow dynamics Hydropower generation system Multi-time scales Instability Analysis

a b s t r a c t This paper reports on fast-slow dynamical analysis of a typical complex engineering system coupling with hydraulic-mechanical-electric power. Here, we find a high-dimensional hydropower generation system that fast-slow effect manifesting as spiking states and quiescent states exists by means of multi-time-scale structure mining. In our experimental analysis, we extract critical fast-slow variant parameters used to further study the behaviors of the presented system. Our results reveal that the change of fast-slow variant parameters has remarkable impact on the fluctuation interval of spiking states and quiescent states, which provides guidance for system parameter setting; meanwhile, we experimentally demonstrate that multi-time-scale physical phenomena reflect the stability and operational feature of the complex hydropower generation system. This work, combined with multiscale dynamic analysis and a snapshot of macro-significance of engineering, enables us to develop a novel framework for investigating instability of complex engineering systems. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Multi-scale Dynamics refers to the significant magnitude differences between change rates of state variables for a multiscale coupled system in different groups over time [1]. In general, the multi-scale coupled system includes two forms on the basis of its dimensionless mathematical model: (i) the coupling of vector fields with different orders of magnitude exists in time domain, and (ii) there are magnitude differences of natural frequencies between different subsystems [2–5]. The response of a multi-scale coupled system is performed by the alternate change of sharp oscillation (i.e., spiking state) and relative small oscillation (i.e., quiescent state) [6,7]. Besides, the changing behavior connecting the fast and slow processes is defined as bursting that is caused by the regulating impact of slow-variant parameters on fast-variant parameters (which refer to such system parameters that can lead to fast-slow effects of the system) [8–11]. Multi-scale dynamics, as an important branch of nonlinear dynamics, has significant advantage to reveal the nonlinearity essence of multi-time-scale complex systems; meanwhile, it has been widely used in various fields, such as Biology, Chemistry, Medical Science and Life Science [12–15]. For example, Rinzel first presented analysis theory of fast-slow ⇑ Corresponding author at: Institute of Water Resources and Hydropower Research, Northwest A&F University, Yangling, Shaanxi 712100, PR China. E-mail address: [email protected] (D. Chen). https://doi.org/10.1016/j.ymssp.2018.03.028 0888-3270/Ó 2018 Elsevier Ltd. All rights reserved.

H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468

459

Nomenclature d

x x0 D Tab E0 q q1 Vs x0 d xq xT xL Tj Aj Gh(s) Hr Qr h2 h3 hf1 Tw1 Tw3 Y

the the the the the the the the the the the the the the the the the the the the the the the

relative deviation of the rotor angle, p.u. relative deviation of the generator rotor speed, p.u. unit generator rotor speed, rad/s damping coefficient mechanical starting time, s transient internal voltage of armature, p.u. relative deviation of the flow in penstock, p.u. voltage of infinite bus, p.u. direct axis transient reactance, p.u. quartered axis reactance, p.u. short-circuit reactance of transformer, p.u. transmission line reactance, p.u. starting time of surge tank, s sectional area of surge tank, m2 flow-pressure transfer function with respect to the section of surge tank reference value of head, m reference value of flow, m3/s relative deviation for the base head of surge tank, p.u. relative deviation for the inlet head of hydro-turbine, p.u. frictional head loss of penstock water starting time of diversion pipe, s water starting time of draft pipe, s guide vane opening, p.u.

dynamics to reveal triggering mechanisms of complex system under multi-time scales in 1985 [16]. Belykh et al. researched the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons, finding that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition [17]. Strizhak et al. presented the induced mechanism of bursting and oscillation under multi-time scales in different B-Z chemical reactions [18]. Yoshioka used chemical synapse with periodical excitation to study dynamical behaviors of neuron network, which explained the stability of neuron network with interaction strength in bursting states [19]. Bi et al. investigated the fast-slow behavior of a class of generalized Chua’s circuit and discussed the impact of excitation intensity on bursting [2,5]. However, the vast majority of contributions regarding multiscale coupled system focus on the analysis of low-order simplified model due to the complexity of system and the diversity of slow-variant process. Therefore, to study high-dimensional nonlinear systems with multi-time scales is a crucial and challenging field, not fully explored, of scientific research. Hydropower generation system is a typical high-dimensional complex system with multi-time scales including several components, such as hydro-turbines, generators, penstocks and governors [20–26]. Some complicated nonlinear phenomena that are defined as risks appear frequently during the operating of hydropower generation systems, like the nonlinearity of generator rotor speed, the water-hammer of penstock, the mechanical movement with delayed feedback, and the fast-slow effect caused by magnitude differences of system state variables [27–34]. Correspondingly, most exiting published papers have paid attention to study the nonlinear bifurcations or chaos mechanism, controller design, as well as fault diagnose. Conversely, few existing studies in literature have been proved successful in applying fast-slow effect to hydropower generation systems. Therefore, it is pretty important to study the fast-slow dynamical behaviors of hydropower generation systems in order to reveal the nonlinearity essence of such multi-scale system. Motivated by the above discussions, the main innovations of this paper can be classified into three aspects. First, a multitime-scale high-dimensional hydropower generation system taking into consideration the upstream surge tank and the nonlinearity of generator rotor speed is found. Second, the critical fast-slow variant parameters are extracted based on the presented complex engineering system. Third, the fast-slow dynamical analysis of the proposed system with two scales is performed by numerical experiments. This paper proceeds as follows: Section 2 builds a sixth-order dynamical model of a complex hydropower generation system. Section 3 shows the experimental results related to the performance of the fast-slow dynamical behaviors of the proposed multi-time-scale system. Conclusions and discussion are presented in Section 4.

2. Model of complex hydropower generation system Hydropower generation system is a dynamic coupled hydraulic-mechanical-electric coupled system for hydropower station. In this work, we study a hydropower generation system taking into account an upstream surge tank that aims to reduce

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H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468

Fig. 1. Structural diagram of a hydropower generation system with upstream surge tank.

water-hammer pressure and to limit the propagation of water-hammer waves. The structural diagram of the hydropower generation system is shown in Fig. 1.

2.1. Model of electrical system From Refs. [35,36], the mathematical model of electrical system considering the nonlinear characteristic of generator is

8_ > < d ¼ x0 x E0 V

2

_ ¼ T1 mt  x0 qPs sin d þ V2s > :x ab d

x0 d

! P xq P ; x sin 2d  D P Px

x0

ð1Þ

q

d

where d, x, x0 , D, T ab , E0q , V s , x0d and xq denote the relative deviation of the rotor angle, the deviation of the generator rotor speed, the unit generator rotor speed, the damping coefficient, the mechanical starting time, the transient internal voltage of armature, the voltage of infinite bus, the direct axis transient reactance and the quartered axis reactance, respectively. x0 is the steady-state generator rotor speed, x0 = 314. x0 dP and xq P in Eq. (1) is expressed as

8 0 < xd P ¼ x_ d þ xT þ 12 xL : x P ¼ xq þ x T þ 1 x L q 2

;

ð2Þ

where xT and xL refer to the short-circuit reactance of transformer and the transmission line reactance, respectively.

emy y u

1

eqh eqy

q3

Tw3 s

Ty s 1

q2 q1

Gh ( s )

h3

emh

mt

h2

1 Tw1s h f 1

Fig. 2. Diagram of the hydraulic-mechanical system with upstream surge tank.

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461

2.2. Model of hydraulic-mechanical system In this part, the penstock system (as mentioned in Fig. 1, which includes a diversion pipe and a pressure pipe) with rigid water-hammer is adopted. When we ignore the water damping of surge tank, the flow-pressure transfer function with respect to the section of surge tank is

Gh ðsÞ ¼

1 ; Tjs

ð3Þ

where T j is the starting time of surge tank, T j ¼

Aj H r . Qr

Aj , Hr and Q r are the sectional area of surge tank, the reference value of

head and the reference value of flow, respectively. According to Fig. 2, the state equation (Please see Ref. [37] to further details regarding the state equation) for the hydraulic-mechanical system implemented in Eq. (3) is obtained as

8 hf 1 > q_ 1 ¼  T w1 q1  Thw12 > > > < e e e h_ 2 ¼ qT1j  Tqhj h2  Tqhj h3  Tqyj y : >   > > eqh eqh eqy eqy > q 1 _ 1 : h3 ¼  þ h2 þ  e T w3 h3 þ T y  e y T T T j

j

j

qh

j

ð4Þ

qh

Meanwhile, the hydro-turbine torque is

mt ¼ emh ðh2 þ h3 Þ þ emy y;

ð5Þ

where q1 , h2 and h3 represent the relative deviations for the flow in penstock, the base head of surge tank and the inlet head of hydro-turbine, respectively. hf 1 , T w1 and T w3 are respectively the frictional head loss of penstock, the water starting time of diversion pipe and the water starting time of draft pipe. A common PID control method is used in this paper, therefore hereby the output signal u is

Z u ¼ kp x  ki

0

t

xdt  kd x_ ¼ kp x 

ki

x0

_: d  kd x

ð6Þ

Based on the dynamic characteristic of the hydraulic servo system (as shown in Ref. [38], which is defined as T y y_ þ y ¼ u), the guide vane opening y is expressed as

y_ ¼

  1 ki _y ; kp x  d  kd x Ty x0

ð7Þ

where T y is the engager relay time constant. 2.3. High-dimensional model of hydropower generation system In light of the above consideration, a sixth-order dynamical model of the complex hydropower generation system is obtained as

8 > d_ ¼ x0 x > > ! > x0 P x P > > q > E0q V s V 2s d 1 >x _ > ¼ m  x sin 2d  D sin d þ 0 0 P t > x P 2 x Px T ab > q > d d > > > > < q_ ¼  hf 1 q  h2 1 T w1 1 T w1 : eqh eqh > eqy q1 _ > h ¼  h  h  y > 2 2 3 > Tj Tj Tj Tj > >   > > > _h3 ¼  q1 þ eqh h2 þ eqh  1 h3 þ eqy y  eqy y > > e T T T T Tj eqh > j j j qh w3 >   > > > k 1 : y_ ¼ _y kp x  xi0 d  kd x Ty

ð8Þ

3. Numerical calculation and dynamical analysis 3.1. Numerical calculation We carry out the numerical experiment analysis based on an existing hydropower station [22,26,27,36], and its engineering metrics and basic system parameters are respectively shown in Tables 1 and 2. In this study, the Runge-Kutta method is a family of implicit and explicit iterative approach used to calculate numerical results. The main idea of Runge-Kutta method is that it uses the iteration theory to solve differential equations (Detailed

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H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468 Table 1 Engineering metrics of an existing hydropower station. The hydro-turbine type

HL638-LJ-140

The nominal head HR The nominal power PR The nominal speed NR

116.38 m 9540 Kw 500 r/min

Table 2 Basic system parameters of an existing hydropower station. Parameters

Tab

D

hf1

Tw1

E0 q

Vs

Values (p.u.) Parameters Values (p.u.)

8 xqP 2

0.5 x0 dP 1

0.1435 Tw3 0.8322

0.1 ki 1

1.35 kp 2

1 kd 1

description of Runge-Kutta method is obtained from Refs. [35,39–41]). To date, the Runge-Kutta method has been widely applied in numerical experiments of engineering due to the characteristic of high precision. For the Runge-Kutta method of this work, the iteration step is 1000, and the initial value is (0.001, 0.1, 0, 0, 0, 0). 3.2. Fast-slow dynamical analysis In light of the magnitude differences of system state variables, the fast-slow dynamical behavior of the presented hydropower generation system is studied in this section. Based on the repeated numerical experiments, it is found that the fastslow dynamical characteristics exist in the relative deviations of the generator rotor speed x, the base head of surge tank h2 and the inlet head of hydro-turbine h3. Thus, the system variables x, h2 and h3 are finally selected to perform the fast-slow dynamical analysis. Moreover, the critical fast-slow variant parameters referring to the engager relay time constant Ty and the starting time of surge tank Tj are selected. The dynamical responses of the system with changing Ty and Tj, as shown in Figs. 3–8, are performed on the basis of an existing hydropower station. 3.2.1. System responses as Ty changes In this subsection, the engager relay time constant Ty (Ty equals to 1, 2 and 3, respectively) is determined to investigate fast-slow dynamical behaviors of the hydropower generation system. The corresponding phase trajectories regarding the relative deviations of the generator rotor speed x, the inlet head of hydro-turbine h3 and the base head of surge tank h2 are shown in Fig. 3. Comparing the results in Fig. 3, it is shown that fast-slow effect manifesting as spiking states and quiescent states exists in both relative deviations of the generator rotor speed x and inlet head of hydro-turbine h3 with increasing Ty. The reason is attributed to the main cause: the magnitude differences of system state variables (i.e., different time scales). That is, hydropower generation system is a typical mutual feedback system coupling hydraulic-mechanical-electric power. During the operation of the hydropower generation system, the response rate of electrical system is obviously faster than that of mechanical and hydraulic system. Therefore hereby it enables hydropower generation system to generate multi-time scales. From engineering standpoint, the fast-slow effect is viewed as risk in hydropower stations. As highlighted in Fig. 3, there are periodic bursting behaviors for the phase trajectories of x-h3 and h2-h3 at the parameter value of Ty = 1 or Ty = 2, while the phase trajectories result in non-periodic bursting behaviors at the parameter value of Ty = 3. The periodic bursting herein means that the quiescent state and spiking state appear alternately in the busting state. Conversely, the non-periodic bursting is that the bursting property of the system performs without specific periodic motion regularities. Moreover, the bursting rate and the change interval of spiking states and quiescent states are significantly different, which is shown in Figs. 4 and 5. Figs. 4 and 5 show the change intervals of x and h3 in different time scales and their fluctuation ranges for peak points in spiking states. Fig. 4 not only reveals the change range of state variables, but gives the logicality with respect to change rules of state variables. Note that the change intervals of x and h3 gradually decrease for the quiescent states one and two with the increase of Ty. Differently, the development rule for the change interval of x is virtually unchanged in the spiking states one and two. The change interval of h3 firstly decreases and then slightly expands in the spiking states one and two. From Fig. 5, both fluctuation ranges of x and h3 for peak points have the decreasing trend when the parameter value of Ty increases from 1 to 3 during the spiking states one and two. The above phenomena imply that the stability of the studied hydropower generation system has a tendency to deteriorate as parameter Ty reduces. 3.2.2. System responses as Tj changes To study the fast-slow dynamical behaviors of the presented hydropower generation system in depth, the starting time of surge tank Tj (Tj are respectively 1, 4.5 and 8) is also extracted in this work. In doing so, the results are shown in Fig. 6.

463

H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468 -3

1

-3

x 10

1

x 10

0.8

Quiescent state 1

0.6

Spiking state 2

0.5

0.4

Spiking state 2

0.2

h3

Quiescent state 2

Quiescent state 1

0

h3 0 Spiking state 1

-0.2 -0.4

-0.5

Spiking state 1

-0.6

Quiescent state 2

-0.8 -1

-1

-0.06

0

-0.03

0.06

-0.01

(a)

(b)

-4

8

-4

x 10

8

x 10

Quiescent state 1

6

6

4

h3

2

0

h3 0

-2

-2 Spiking state 1

-4

Quiescent state 1

4

Spiking state 2

2

Spiking state 1

-4

Spiking state 2

Quiescent state 2

-6

-6

Quiescent state 2

-8

-8

-0.06

0

-0.03

0.06

-0.01

0.01

h2

ω

(c)

(d)

-3

1.5

0.01

h2

ω

x 10

1.5

x 10

-3

Quiescent state 1

1

1 Spiking state 2

Quiescent state 1

0.5

0.5

h3 0

h3 0

Spiking state 1 Spiking state 2

-0.5

-0.5

Quiescent state 2

Spiking state 1

-1

-1

Quiescent state 2

-1.5

-1.5 -0.06

0

0.06

-0.03

-0.01

ω

h2

(e)

(f)

0.01

Fig. 3. System responses with different values of the engager relay time constant Ty (Ty equals to 1, 2 and 3, respectively). (a) Phase trajectory of x-h3 with Ty = 1. (b) Phase trajectory of h2-h3 with Ty = 1. (c) Phase trajectory of x-h3 with Ty = 2. (d) Phase trajectory of h2-h3 with Ty = 2. (e) Phase trajectory of x-h3 with Ty = 3. (f) Phase trajectory of h2-h3 with Ty = 3.

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H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468

Quiescent states

Quiescent states

Spiking states

State 1

State 1

State 2

State 2

Spiking states

Ty=2

Ty=1

Ty=1

Ty=2

Ty=1

Ty=3

Ty=2

Ty=2

Ty=3

Ty=1 Ty=3

Ty=3

(a)

(b)

Fig. 4. Change intervals regarding the relative deviations of the generator rotor speed x and the inlet head of hydro-turbine h3 for different time scales with the engager relay time constant Ty. (a) Change interval of the relative deviation of the generator rotor speed x with Ty. (b) Change interval of the relative deviation of the inlet head of hydro-turbine h3 with Ty.

0.045

Spiking State One

Spiking State Two

0.04 T =1

Fluctuation Ranges at Peak Points

y

0.035

T =2 y

T =3

0.03

y

0.025

0.02

0.015

0.01

0.005

0

h

3

h

3

Fig. 5. Fluctuation ranges for the relative deviations of the generator rotor speed x and the inlet head of hydro-turbine h3 at peak points with changing engager relay time constant Ty.

Time waveforms and phase trajectories in Fig. 6 show that, there are multi-time scales in the hydropower generation system when the critical fast-slow variant parameter Tj is assigned different values (i.e., 1, 4.5, 8). More specifically, the single oscillation periods of state variables (i.e., x and h3) are respectively 320 s, 330 s and 270 s with respect to Tj given 1, 4.5 and 8. The behaviors of x-h3 implemented in phase trajectories are the periodic bursting as Tj sets 1, 4.5 and 8. In addition to this, the detailed information regarding the variation intervals of state variables in various fast-slow states is performed in Figs. 7 and 8. As shown in Fig. 7, both change intervals of x and h3 gradually decrease with the increase of Tj in the quiescent states one and two. For the spiking states one and two, the change interval of x is almost unchanged, while the interval of h3 has the significant change when the parameter value of Tj increases from 1 to 8. Specifically, the change interval of h3 for spiking states rapidly decreases from Tj = 1 to Tj = 4.5, while it slightly decreases between Tj = 4.5 and Tj = 8. The above analyses imply that, the fluctuation stability for the inlet head of hydro-turbine improves with the increase of Tj, but there is not any significant improvement on the fluctuation process of the generator rotor speed. The fluctuation ranges of peak points regarding system state variables x and h3 are emphasized in Fig. 8. From Fig. 8, the fluctuation ranges of x increase in both quiescent states one and two, while h3 tends to decreasing during the spiking states one and two. This can reflect the running feature of the studied hydropower generation system. That is, the generator rotor speed rises as the inlet head of hydro-turbine falls from Tj = 1 to Tj = 8.

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H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468 -3

5

-3

x 10

5

x 10

Quiescent state 1

Quiescent states

ω

Spiking state 2

h3 0

0

Spiking states

-5 0

100

200

300

400

500

600

700

800

900

1000

-5 -0.06

0

0.06

ω

Iterations

(a)

(b)

-3

1.5

Quiescent state 2

Spiking state 1

-3

x 10

1.5

x 10

Quiescent states

ω

1

1

0.5

0.5

0

h3 0

-0.5

-0.5

-1

Spiking state 2

Quiescent state 2

Quiescent state 1 Spiking state 1

-1 Spiking states

-1.5 0

100

200

300

400

500

600

700

800

900

1000

-1.5

-0.06

0

(c)

(d) -3

-3

1

0.06

ω

Iterations

x 10

1

x 10 Quiescent state 1

0.5

ω

0.5

Spiking states

0

Spiking state 2

h3 0 Spiking state 1

-0.5

-0.5 Quiescent state 2

Quiescent states

-1 0

100

200

300

400

500

600

Iterations

(e)

700

800

900

1000

-1 -0.06

0

0.06

ω

(f)

Fig. 6. System responses with different values of the starting time of surge tank Tj (Tj are respectively 1, 4.5 and 8). (a) Time waveform of h3 with Tj = 1. (b) Phase trajectory of x-h3 with Tj = 1. (c) Time waveform of h3 with Tj = 4.5. (d) Phase trajectory of x-h3 with Tj = 4.5. (e) Time waveform of h3 with Tj = 8. (f) Phase trajectory of x-h3 with Tj = 8.

H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468

Spiking states

Quiescent states

Spiking states

State 1 Ty=1

Ty=4.5

Ty=1

Ty=8

Ty=4.5

State 2

State 2

Quiescent states

Ty=8

Ty=4.5

Ty=8 Ty=4.5

Ty=1

State 1

466

Ty=8 Ty=1

(a)

(b)

Fig. 7. Change intervals regarding the relative deviations of the generator rotor speed x and the inlet head of hydro-turbine h3 for different time scales with the starting time of surge tank Tj. (a) Change interval of the relative deviation of the generator rotor speed x with Tj. (b) Change interval of the relative deviation of the inlet head of hydro-turbine h3 with Tj.

-5

4

x 10 Spiking State Two

Spiking State One 3.5

T =1

Fluctuation Ranges at Peak Points

j

T =4.5

3

j

T =8 j

2.5

2

1.5

1

0.5

0

h3

h3

Fig. 8. Fluctuation ranges for the relative deviations of the generator rotor speed x and the inlet head of hydro-turbine h3 at peak points with changing starting time of surge tank Tj.

4. Conclusions and discussion In this work, we have found that multi-time-scale physical phenomena exist in the complex hydropower generation system by identifying its fast-slow variant parameters. From the perspective of engineering, the critical fast-slow variant parameters, i.e., the engager relay time constant Ty and the starting time of surge tank Tj, have been extracted in light of the multi-time scales coupling with faster electrical system and relative slower mechanical-hydraulic system. From an experimental point of view, the fast-slow effect, with changing system parameters (i.e., Ty and Tj), has been revealed by employing time waveforms and phase trajectories. Our experimental results clearly demonstrate that, combing multiscale dynamical analysis with practical engineering structure, the operational characteristics of the hydropower generation system can be obtained. For example, based on the fluctuation ranges of system state variables at peak points, we get that the generator rotor speed rises as the inlet head of hydro-turbine falls with the increase of Tj. The fast-slow dynamical analysis developed in the experiment can find applications in the evolving systems, such as living system [17,19]. In order to enrich the outcome of Multi-scale Dynamics, our work successfully reveals that the fast-slow dynamics is also applicable to some complex engineering systems. Hence, for future projects, it would be interesting to investigate the fast-slow dynamics of modern industry process model by means of multi-level structural knowledge mining. This will open up a new field for minimizing engineering risks.

H. Li et al. / Mechanical Systems and Signal Processing 110 (2018) 458–468

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Acknowledgements This work was supported by the scientific research foundation of National Natural Science Foundation of China--Outstanding Youth Foundation (51622906), National Natural Science Foundation of China (51479173), Fundamental Research Funds for the Central Universities (201304030577), Scientific Research Funds of Northwest A&F University (2013BSJJ095), Science Fund for Excellent Young Scholars from Northwest A&F University (Z109021515) and Shaanxi Nova program (2016KJXX-55).

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