Rough-strip energy dissipators (R-SEDs) at the bottom of spillway bends have energy dissipation and flow diversion effects on bend flow. In this paper, twelve Plackett-Burman tests were conducted. Energy dissipation rate and coefficient of variation of superelevation were used as evaluation indices. Influencing factors (i.e., relative height, height ratio, spacing, angle and thickness of R-SEDs as well as centerline radius, width, angle and bottom slope of the bend) of R-SEDs' energy dissipation and flow diversion effects were analyzed using Minitab 21.1 in combination with the entropy weight method and the TOPSIS method. Relative height of R-SED and bend angle were significant factors affecting energy dissipation effects; height ratio of R-SED and centerline radius of the bend were significant factors affecting flow diversion effects; the coefficient of variation of superelevation had a larger weight (0.549) than the energy dissipation rate (0.451), indicating that R-SEDs' flow diversion effects were larger than their energy dissipation effects; height ratio of R-SED, centerline radius of the bend and bend angle were significant factors affecting overall energy dissipation and flow diversion effects and selected as key factors for further steepest climbing tests and response surface design.

  • R-SEDs were proposed for curved spillways, with a simple structure to facilitate construction.

  • The Plackett–Burman design as the experimental method reduced the number of experiments and effectively facilitated the selection of key influencing factors.

  • A new index coefficient of variation of superelevation was established for evaluating flow diversion effects of R-SEDs, with simple calculation for application.

hr

Relative height of R-SED

λ

Height ratio of R-SED

α

R-SED spacing

θ

R-SED angle

δ

R-SED thickness

R

Centerline radius of the bend

B

Bend width

β

Bend angle

i

Bottom slope of the bend

Average water depth of the inlet cross-section of the bend

h1

Height of the R-SED at the concave bank

h2

Height of the R-SED at the convex bank

M

Marking point of an enlarged view of the R-SED at the concave bank

N

Marking point of an enlarged view of the R-SED at the convex bank

L1

Length of inlet straight section

L2

Length of outlet straight section

h

Water depth at each measurement point

Q

Discharge flow rate of the spillway

C0

Flow rate coefficient of the right triangular thin-walled weir

H

The head over the right triangular thin-walled weir

P1

Height of the right triangular thin-walled weir

B1

Width of the flow diversion canal at the upstream of the right triangular thin-walled weir

pij

Proportion of the ith evaluation object under the jth index

Ej

Entropy value of the jth index

Wj

Weight of the jth index

,

Euclidean distance between each object and the ideal solution

Relative closeness of each object to the ideal solution

η

Energy dissipation rate of R-SEDs

E1

Total mechanical energy per unit weight of water in the upstream flow cross-section

Z1

Minimum elevation of the spillway bottom of the upstream flow cross-section

H1

Average water depth of the upstream flow cross-section

v1

Average flow velocity of the upstream flow cross-section

E2

Total mechanical energy per unit weight of water in the downstream flow cross-section

Z2

Minimum elevation of the spillway bottom of the downstream flow cross-section

H2

Average water depth of the downstream flow cross-section

v2

Average velocity of the downstream flow cross-section

φ

Kinetic energy correction factor

g

The acceleration of gravity

SCV

Coefficient of variation of superelevation

σi

Standard deviation of transverse water surface superelevation Δy for all calculated sections under the ith condition

μi

Average transverse water surface superelevation Δy of all the calculated sections under the ith condition

Δyij

The difference between the water level at the concave bank of the bend and the horizontal plane where the center of the water surface is located at the jth calculated cross-section under the ith condition

k

Superelevation coefficient

vij

Average velocity of the jth calculated section under the ith condition

Bi

Water surface width of the open channel based on the centerline water surface elevation under the ith condition

ri

Centerline radius of the bend under the ith condition

Δy

Transverse water surface superelevation of the bend

W(η)

Weight of the energy dissipation rate

W(SCV)

Weight of the coefficient of variation of superelevation

Influenced by topographic and geological conditions, engineering characteristics, construction conditions and economic indicators (Seo & Shin 2018; Yang et al. 2019; Damarnegara et al. 2020), some spillways or natural river channels must have corners, thus forming bends. The water flowing through the bend is called bend flow, which is different from straight-section water flow. When water flows through a bend, uneven distribution of water flow (Zhang et al. 2015) and cross-sectional flow velocity (Pradhan et al. 2018) occurs on both banks of the bend due to centrifugal inertia forces. Thus, secondary flows are developed (Seyedashraf & Akhtari 2015). These unfavorable flow structures lead to sediment movement, riverbed evolution and river channel deformation (Olsen 2003).

The bend flow is one of the topics in the field of hydraulics research. In 1876, Thomson (1876) first proposed the problem of bend circulating flow through experimental research. Currently, various research methods of bend flow have been developed, mainly including model tests, numerical simulations and theoretical studies. The research on bend flow is mainly divided into the study of basic water flow characteristics and the study of engineering measures to improve the flow pattern of bend flow. The study of the basic characteristics of the bend flow is focused on the water depth distribution (Seyedashraf & Akhtari 2015; Zhang et al. 2015; Qin et al. 2016; Zhou et al. 2017; Maatooq & Hameed 2020), flow velocity distribution (Han et al. 2011; Seyedashraf & Akhtari 2015; Vaghefi et al. 2015; Qin et al. 2016; Zhou et al. 2017; Moncho-Esteve et al. 2018; Pradhan et al. 2018; Schreiner et al. 2018; Seo & Shin 2018; Hu et al. 2019; Kim et al. 2020; Yan et al. 2020) and secondary flow evolution (Booij 2003; Huai et al. 2012; Ramamurthy et al. 2013; Seyedashraf & Akhtari 2015; Engel & Rhoads 2016; Gu et al. 2016; Zhou et al. 2017; Moncho-Esteve et al. 2018; Schreiner et al. 2018; Seo & Shin 2018; Hu et al. 2019; Shaheed et al. 2021). Based on the understanding of the basic bend flow characteristics, scholars have improved the bend flow pattern using engineering measures such as permeable spurs (Yang et al. 2019), guide walls (Zhang et al. 2015), vanes (Ranjan et al. 2006; Han et al. 2011) and riprap (Martín-Vide et al. 2010). However, compared with the research on the basic characteristics of bend flow, the research on related engineering measures is still rare. Thus, in this paper, a simpler rough-strip energy dissipator (R-SED) was added to the bend of curved spillways. The simple shape and convenient construction of R-SEDs can effectively solve the adverse hydraulic phenomena in the curved spillway, which will facilitate the safe and stable operation of the curved spillway and the continuous downstream water supply (such as industrial and irrigation water).

The research on the R-SED was first conducted based on the hydraulic model test (the geometric scale of the model was 1:50) of the curved spillway of Project 635 Reservoir in Xinjiang, China, and the research was mainly based on the laboratory test. The actual operation of the spillway reveals that the water depth and flow velocity of the concave and convex banks of the spillway differed greatly at a discharge flow rate of 800 m3/s. The water flow in the bend was splashing and turbulent. In order to solve the above adverse water flow problem, the R-SED was arranged at the bottom of the bend, exhibiting good energy dissipation and flow diversion effects in the bend (Li 2016). Due to the different scaling ratios (geometric ratios) of different curved spillway test models and the special and different geological conditions of each project, laboratory-scale model dimensions were adopted for the research and analysis in this study.

The R-SED has both energy dissipation and flow diversion effects on the bend flow, and the influencing factors affecting these effects are generally divided into R-SED layout parameters (such as relative height of R-SED, height ratio of R-SED, R-SED spacing, R-SED angle and R-SED thickness) and curved spillway engineering parameters (such as centerline radius of the bend, bend width, bend angle and bottom slope of the bend). In the existing R-SED study, Li (2016) mainly analyzed the results of the R-SED in the hydraulic model test of the curved spillway of Project 635 Reservoir in Xinjiang, China, using the single-factor test method. Li (2016) only considered the influence of three parameters of the R-SED arrangement (i.e., height ratio of R-SED, R-SED angle and R-SED thickness) on the energy dissipation and flow diversion effect without including the influence of the engineering parameters of the curved spillway. Li et al. (2020) mainly analyzed the influence law of six factors (height ratio of R-SED, R-SED spacing, R-SED angle, centerline radius of the bend, bend width and discharge flow rate) on the effect of energy dissipation and flow diversion of R-SEDs using the orthogonal test method (six factors and three levels), and the energy dissipation rate and the water flux dispersion coefficient for evaluation energy dissipation and flow diversion effects were adopted, respectively. However, the influence considered influencing factors are still not comprehensive and the calculation formula of the water flux dispersion coefficient is complicated for practical application.

Thus, in this paper, the Plackett–Burman experimental design, the entropy weight method and the TOPSIS method were used to comprehensively analyzes nine factors (relative height of R-SED, height ratio of R-SED, R-SED spacing, R-SED angle, R-SED thickness, centerline radius of the bend, bend width, bend angle, bottom slope of the bend) on the energy dissipation and flow diversion effect of R-SEDs. The energy dissipation rate was used as the evaluation index of the energy dissipation effect of R-SEDs (Li et al. 2020) and a new evaluation index of the R-SED's flow diversion effect was established, i.e., coefficient of variation of superelevation. The newly established formula for calculating the coefficient of variation of superelevation is simple, easy to understand and convenient for practical engineering applications. The study can be used for the next steepest climbing test and response surface test design in order to select the key factors and provide reference for the R-SED design of similar curved spillways. The research on the parameter optimization of the R-SED in curved spillways is divided into two parts, as shown in Figure 1.
Figure 1

Research process.

Figure 1

Research process.

Close modal

Test apparatus

The test was conducted in a curved spillway flume at the Xinjiang Key Laboratory of Hydraulic Engineering Safety and Water Disaster Prevention, China. The testing system includes a model test section and a water circulation system. The overall layout is shown in Figure 2. The model test section is divided into an inlet straight section, a bend section and an outlet straight section along the discharge direction of the spillway. The inlet straight section (L1 = 0.7 m) can ensure the smooth flow of inlet water into the bend section. According to Table 2, eight bends of different sizes were designed and prepared for the test. The outlet straight section (L2 = 1.5 m) can smoothly connect with the flow out of the bend. The water circulation system consists of a water pump, a rectangular water storage tank, a water measuring weir, an underground water reservoir and underground water flow diversion pipelines.
Table 1

Factors and levels of Plackett–Burman tests

Levelhr (cm)λ (–)α (°)θ (°)δ (cm)R (cm)B (cm)β (°)i (–)
−1 0.4  (1/6) β 15 (1/100) B 150 50 30 0.02 
0.8  (1/3) β 30 (1/50) B 300 100 60 0.04 
Levelhr (cm)λ (–)α (°)θ (°)δ (cm)R (cm)B (cm)β (°)i (–)
−1 0.4  (1/6) β 15 (1/100) B 150 50 30 0.02 
0.8  (1/3) β 30 (1/50) B 300 100 60 0.04 

Note: is the average water depth of the inlet cross-section of the bend.

Table 2

Plackett–Burman test scheme

Test Numberhr (cm)λ (–)α (°)θ (°)δ (cm)R (cm)B (cm)β (°)i (–)
0.4  (1/6) β 15 (1/100)B 300 100 60 0.02 
0.8  (1/6) β 15 (1/50)B 300 100 30 0.04 
0.4  (1/3) β 15 (1/50)B 150 50 30 0.04 
0.4  (1/6) β 15 (1/100)B 150 50 30 0.02 
0.4  (1/3) β 30 (1/50)B 150 100 60 0.02 
0.4  (1/6) β 30 (1/50)B 300 50 60 0.04 
0.4  (1/3) β 30 (1/100)B 300 100 30 0.04 
0.8  (1/3) β 15 (1/50)B 300 50 60 0.02 
0.8  (1/6) β 30 (1/100)B 150 50 60 0.04 
10 0.8  (1/3) β 15 (1/100)B 150 100 60 0.04 
11 0.8  (1/6) β 30 (1/50)B 150 100 30 0.02 
12 0.8  (1/3) β 30 (1/100)B 300 50 30 0.02 
Test Numberhr (cm)λ (–)α (°)θ (°)δ (cm)R (cm)B (cm)β (°)i (–)
0.4  (1/6) β 15 (1/100)B 300 100 60 0.02 
0.8  (1/6) β 15 (1/50)B 300 100 30 0.04 
0.4  (1/3) β 15 (1/50)B 150 50 30 0.04 
0.4  (1/6) β 15 (1/100)B 150 50 30 0.02 
0.4  (1/3) β 30 (1/50)B 150 100 60 0.02 
0.4  (1/6) β 30 (1/50)B 300 50 60 0.04 
0.4  (1/3) β 30 (1/100)B 300 100 30 0.04 
0.8  (1/3) β 15 (1/50)B 300 50 60 0.02 
0.8  (1/6) β 30 (1/100)B 150 50 60 0.04 
10 0.8  (1/3) β 15 (1/100)B 150 100 60 0.04 
11 0.8  (1/6) β 30 (1/50)B 150 100 30 0.02 
12 0.8  (1/3) β 30 (1/100)B 300 50 30 0.02 
Figure 2

Test apparatus, (a) schematic diagram of the test apparatus arrangement (top view), (b) schematic diagram of the three-dimensional structure of the curved spillway physical model.

Figure 2

Test apparatus, (a) schematic diagram of the test apparatus arrangement (top view), (b) schematic diagram of the three-dimensional structure of the curved spillway physical model.

Close modal

Test program

The Plackett–Burman design is a two-level partial factorial experimental design method, which is mainly used for experimental designs with a large number of factors and where the significance of these factors relative to the response variable is not determined (Abdel-Fattah et al. 2005; Ghanem et al. 2017). The method mainly analyzed two levels of each factor and determined the significance of each factor by comparing the difference between the two levels of each factor with the overall difference. Two levels (i.e., high (1) and low (−1)) were selected for each influencing factor in the experimental design, with the high level two times larger than the low level.

Considering the influence of R-SED arrangement parameters and spillway engineering parameters on the energy dissipation and flow diversion effect of R-SEDs, two types of influencing factors were selected, including R-SED parameters (i.e., relative height (hr), height ratio (λ), spacing (α), angle (θ) and thickness (δ)) and spillway bend parameters (i.e., centerline radius (R), width (B), angle (β) and bottom slope (i)). Based on the research needs and findings of our group (Li 2016; Li et al. 2020), the values of each factor were selected. The test factors and levels are shown in Table 1 and the symbols are illustrated in Figure 3.
Figure 3

Schematic illustration of parameters in Plackett–Burman tests, (a) schematic diagram of spillway engineering parameters and rough-strip energy dissipators (R-SEDs) arrangement parameters, (b) schematic diagram of the transverse and longitudinal structure of R-SEDs.

Figure 3

Schematic illustration of parameters in Plackett–Burman tests, (a) schematic diagram of spillway engineering parameters and rough-strip energy dissipators (R-SEDs) arrangement parameters, (b) schematic diagram of the transverse and longitudinal structure of R-SEDs.

Close modal

The R-SEDs were installed at the bottom of the spillway bend. Each R-SED extended continuously from the concave bank to the convex bank, close to the bottom of the bend. The roughness of the bend bottom increased after the R-SEDs were added, and the water flow between adjacent R-SEDs collided and swirled, thus strengthening the energy dissipation effect of R-SEDs. Without the R-SED, the water flow in the spillway bend showed a phenomenon of increased flow depth at the concave bank and decreased flow depth at the convex bank; the discharge water flow continuously scoured the sidewall of the bend at the concave bank, which was not conducive to the structural safety and stability. Thus, in order to better improve the uneven distribution of water flow between the concave and convex banks of the bend and improve the flow diversion effect of R-SEDs, the height (h1) of the R-SED at the concave bank was designed to be larger than the height (h2) at the convex bank, i.e., h1 > h2. Therefore, the R-SED had a trapezoidal longitudinal section.

The relative height of R-SED (hr) is the ratio between the height of the R-SED at the concave bank (h1) to the average water depth at the inlet cross-section of the bend (), i.e., hr=h1/. The height ratio of R-SED (λ) is the ratio of the height of the R-SED at the concave bank (h1) to the height at the convex bank (h2), i.e., λ=h1/h2. R-SED spacing (α) is the angle corresponding to the arc length between two adjacent R-SED centerlines along the bend centerline direction. R-SED angle (θ) is the angle between the centerline of the R-SED and the direction perpendicular to the bend centerline. R-SED thickness (δ) is the horizontal distance between the upstream and downstream faces of the R-SED, which is defined as the ratio of the horizontal distance to the bend width (B) for nondimensionalization. The centerline radius of the bend (R) is the distance between the bend centerline and the center of the curvature of the bend. Bend width (B) is the horizontal distance between the two banks of the spillway. Bend angle (β) is the angle corresponding to the bend flow path along the bend centerline. Bottom slope of the bend (i) is the slope along the spillway bottom. The schematic diagram of these parameters is shown in Figure 3.

Based on Table 1, the Plackett–Burman experimental design was developed. The specific test program is shown in Table 2.

Measurement arrangement

  • (a)

    Water depth measurement

The water level measurement probe was used to measure the water depth, with an accuracy of 0.1 mm. A total of 19 water depth measurement cross-sections were arranged along the spillway model, i.e., 0#–18#. Each cross-section was arranged with five measurement points (i.e., A–E). Considering the viscous resistance of the sidewall to the water flow, two near-bank measurement points (A and E) were located at 1 cm from the sidewalls of the concave and convex banks, respectively.

  • (b)

    Flow velocity measurement

The hourly average flow velocity was measured using a Pitot tube. A total of 10 measurement cross-sections (i.e., 0#, 2#, 4#, 6#, 8#, 10#, 12#, 14#, 16# and 18#) were selected as flow velocity measurement sections and three measurement points (i.e., A, C and E) were selected for each section. The vertical measurement position of each measurement point was located at 2 h/3 from the bottom (h is the water depth at the measurement point).

The measurement cross-sections of water depth and flow velocity as well as the location of measurement points are shown in Figure 4.
  • (c)

    Discharge flow rate measurement

Figure 4

Schematic diagram of the model measurement cross-section and cross-section measurement point arrangement.

Figure 4

Schematic diagram of the model measurement cross-section and cross-section measurement point arrangement.

Close modal
A right triangular thin-walled weir was used to measure the flow from the spillway, and the form of the weir is shown in Figure 5. The discharge flow rate is expressed as:
(1)
where Q is the discharge flow rate (L/s); H is the head over the weir (m); C0 is the flow rate coefficient of the weir, which is related to the size of the opening and can be calculated by:
(2)
where P1 is the height of the weir (m); B1 is the width of the flow diversion canal at the upstream of the weir (m).
Figure 5

Illustration of the opening shape of the right triangular thin-walled weir.

Figure 5

Illustration of the opening shape of the right triangular thin-walled weir.

Close modal

Construction of evaluation indices

The R-SED has a dual effect of energy dissipation and flow diversion on the bend flow. Evaluation indices need to be constructed to assess the energy dissipation effect and flow diversion effects of the R-SED under twelve test scenarios.

Energy dissipation rate

In order to quantify the energy dissipation effect of the continuous energy dissipation process of the R-SED in the bend, the energy dissipation rate (η) was introduced as an evaluation index. The change interval of energy dissipation rate is (0, 1) and a larger energy dissipation rate indicates a larger energy dissipation effect. The energy dissipation rate is calculated through:
(3)
(4)
(5)
where η(i) is the energy dissipation rate under the ith condition (%), E1 is the total mechanical energy per unit weight of water in the upstream flow cross-section (m), Z1 is the minimum elevation of the upstream flow cross-section (m), H1 is the average depth of the upstream flow cross-section (m), v1 is the average velocity of the upstream flow cross-section (m/s), E2 is the total mechanical energy per unit weight of water in the downstream flow cross-section (m), Z2 is the minimum elevation of the downstream flow cross-section (m), H2 is the average depth of the downstream flow cross-section (m), v2 is the average velocity of the downstream flow cross-section (m/s); α for the kinetic energy correction factor, taken as 1.0 and g is the acceleration of gravity, taken as 9.81 m/s2.

Cross-sections 4# and 12# were selected as the upstream and downstream sections of the bend, respectively. The horizontal plane where the bottom elevation of cross-section 12# was located was taken as the reference plane. The energy dissipation rate in the 12 test scenarios was calculated using Equations (3)–(5). The calculation results of the energy dissipation rate are shown in Table 3.

Table 3

Plackett–Burman test results

Test Numberhr (cm)λ (–)α (°)θ (°)δ (cm)R (cm)B (cm)β (°)i (–)η (–)SCV (–)
0.4  (1/6) β 15 (1/100)B 300 100 60 0.02 0.535 0.188 
0.8  (1/6) β 15 (1/50)B 300 100 30 0.04 0.557 0.473 
0.4  (1/3) β 15 (1/50)B 150 50 30 0.04 0.318 0.357 
0.4  (1/6) β 15 (1/100)B 150 50 30 0.02 0.153 0.516 
0.4  (1/3) β 30 (1/50)B 150 100 60 0.02 0.461 0.413 
0.4  (1/6) β 30 (1/50)B 300 50 60 0.04 0.662 0.318 
0.4  (1/3) β 30 (1/100)B 300 100 30 0.04 0.335 0.140 
0.8  (1/3) β 15 (1/50)B 300 50 60 0.02 0.656 0.211 
0.8  (1/6) β 30 (1/100)B 150 50 60 0.04 0.623 0.301 
10 0.8  (1/3) β 15 (1/100)B 150 100 60 0.04 0.643 0.605 
11 0.8  (1/6) β 30 (1/50)B 150 100 30 0.02 0.419 0.380 
12 0.8  (1/3) β 30 (1/100)B 300 50 30 0.02 0.402 0.306 
Test Numberhr (cm)λ (–)α (°)θ (°)δ (cm)R (cm)B (cm)β (°)i (–)η (–)SCV (–)
0.4  (1/6) β 15 (1/100)B 300 100 60 0.02 0.535 0.188 
0.8  (1/6) β 15 (1/50)B 300 100 30 0.04 0.557 0.473 
0.4  (1/3) β 15 (1/50)B 150 50 30 0.04 0.318 0.357 
0.4  (1/6) β 15 (1/100)B 150 50 30 0.02 0.153 0.516 
0.4  (1/3) β 30 (1/50)B 150 100 60 0.02 0.461 0.413 
0.4  (1/6) β 30 (1/50)B 300 50 60 0.04 0.662 0.318 
0.4  (1/3) β 30 (1/100)B 300 100 30 0.04 0.335 0.140 
0.8  (1/3) β 15 (1/50)B 300 50 60 0.02 0.656 0.211 
0.8  (1/6) β 30 (1/100)B 150 50 60 0.04 0.623 0.301 
10 0.8  (1/3) β 15 (1/100)B 150 100 60 0.04 0.643 0.605 
11 0.8  (1/6) β 30 (1/50)B 150 100 30 0.02 0.419 0.380 
12 0.8  (1/3) β 30 (1/100)B 300 50 30 0.02 0.402 0.306 

Coefficient of variation of superelevation

In order to quantify the flow diversion effect of the R-SED on the bend flow, the coefficient of variation of superelevation (SCV) was introduced as an evaluation index. The coefficient of variation of superelevation varied between (0, 1) and is negatively correlated with flow diversion effects, i.e., a smaller coefficient of variation of superelevation indicates better flow diversion effects of the R-SED. The coefficient of variation of superelevation is expressed as:
(6)
(7)
(8)
(9)
where SCV(i) is the coefficient of variation of superelevation under the ith condition; σi is the standard deviation of the superelevation of transverse water surface (Δy) of all calculated sections under the ith condition (m); μi is the mean value of superelevation of transverse water surface of all calculated sections under the ith condition (m); Δyij is the difference between the water surface at the concave bank of the bend and the horizontal surface of the center point at the jth calculated section under the ith condition (m); k is the superelevation coefficient, taken as 0.5 for a simple circular-curved bend of a rectangular open channel; vij is the average velocity of the jth calculated section under the ith condition (m/s); Bi is the water surface width of the open channel based on the centerline water surface elevation under the ith condition (m); g is the acceleration of gravity, taken as 9.81 m/s2; ri is the radius of the center of the bend under the ith condition (m). The calculation of transverse water surface superelevation of the bend (Δy) is illustrated in Figure 6.
Figure 6

Schematic diagram of the calculation of the transverse water surface superelevation of the bend (Δy).

Figure 6

Schematic diagram of the calculation of the transverse water surface superelevation of the bend (Δy).

Close modal

The addition of R-SEDs in the bend can induce the secondary distribution of water flow in the bend and the straight section downstream. To fully measure the flow diversion effect of R-SEDs, cross-section 4# at the bend and cross-section 18# at the straight section downstream were selected as the inlet and outlet cross-sections for the calculation of the coefficient of variation of superelevation. The calculation results are shown in Table 3.

Multi-objective evaluation based on entropy weight method and TOPSIS method

  • (a)

    Establishing a comprehensive performance evaluation system

Twelve groups of Plackett–Burman tests were used as feasibility study schemes, and the energy dissipation rate and the coefficient of variation of superelevation were used as target variables to construct the original matrix .

  • (b)

    Determining the weight of each evaluation index using the entropy weight method

The entropy weight method is to calculate the entropy weight of each index according to the degree of variation of each index by using the information entropy, and then to calibrate the weight of each index by the entropy weight, so as to obtain a more objective index weight (Cheng et al. 2021). The matrix Y was derived from the nondimensionalization of the original matrix and then the entropy weight Wj of each evaluation index was determined. A larger entropy weight indicates that the evaluation index is more important. The calculation formula is expressed as:
(10)
(11)
(12)
(13)
where i denotes the number of evaluation objects (i = 1, 2, …, m); j denotes the number of evaluation indices (j = 1, 2, …, n); pij is the proportion of the ith evaluation object under the jth index; Ej is the entropy value of the jth index.
  • (c)

    Obtaining the overall ranking of each program using the TOPSIS method

The TOPSIS method is commonly used to evaluate the relative strengths and weaknesses of existing objects by ranking them according to their closeness to the ideal target (Wang et al. 2019). Firstly, the original matrix is normalized to obtain a matrix and the matrix B is multiplied by the entropy weight Wj to obtain the weighting matrix Z. Secondly, the Euclidean distance and between each object and the ideal solution as well as the relative closeness of each object is calculated. A larger relative closeness indicates that the solution is closer to the ideal solution and that the rating is better. Finally, the solutions are comprehensively ranked according to the relative closeness of each solution to form a decision basis. The calculation equations are as follows:
(14)
(15)
(16)
(17)
(18)

Statistical analysis of data

Minitab 21.1 software was used for statistical analysis of the data, including the energy dissipation rate, the coefficient of variation of superelevation and relative closeness.

Analysis of influencing factors of energy dissipation effects

Analysis of variance for the energy dissipation rate

Analysis of variance (ANOVA) was performed on the nine factors (predictor variables) using the energy dissipation rate as the response variable, as shown in Table 4. The significance level was selected as 0.05 and the factor was significant when P < 0.05. Table 4 shows that the probability P corresponding to the main effect was less than 0.05, rejecting the original hypothesis and indicating that the total effect of the regression was significant. Particularly, the relative height of R-SED and the bend angle were significant.

Table 4

Analysis of variance of the energy dissipation rate

SourceDFAdj SSAdj MSF-valueP-valueSignificance
Model 0.280806 0.031201 19.43 0.050 
 Linear 0.280806 0.031201 19.43 0.050 
  hr 0.058277 0.058277 36.3 0.026 
  λ 0.000005 0.000005 0.00 0.960  
  α 0.001497 0.001497 0.93 0.436  
  θ 0.000129 0.000129 0.08 0.803  
  δ 0.012136 0.012136 7.56 0.111  
  R 0.023419 0.023419 14.59 0.062  
  B 0.001587 0.001587 0.99 0.425  
  β 0.161996 0.161996 100.90 0.010 
  i 0.021759 0.021759 13.55 0.067  
Error 0.003211 0.001605    
Total 11 0.284017      
R-sq = 0.9887 R-sq (adj) = 0.9378 
SourceDFAdj SSAdj MSF-valueP-valueSignificance
Model 0.280806 0.031201 19.43 0.050 
 Linear 0.280806 0.031201 19.43 0.050 
  hr 0.058277 0.058277 36.3 0.026 
  λ 0.000005 0.000005 0.00 0.960  
  α 0.001497 0.001497 0.93 0.436  
  θ 0.000129 0.000129 0.08 0.803  
  δ 0.012136 0.012136 7.56 0.111  
  R 0.023419 0.023419 14.59 0.062  
  B 0.001587 0.001587 0.99 0.425  
  β 0.161996 0.161996 100.90 0.010 
  i 0.021759 0.021759 13.55 0.067  
Error 0.003211 0.001605    
Total 11 0.284017      
R-sq = 0.9887 R-sq (adj) = 0.9378 

Pareto chart of energy dissipation rate

In the Pareto chart, the absolute values of the t-values of each effect from the t-test are taken as vertical coordinates; the critical values of the t-values are determined according to the selected significance level; the effects with absolute values exceeding the critical values are selected, indicating that these effects are significant. In this study, the energy dissipation rate was used as the response variable and a significance level was set as 0.05. Thus, the Pareto chart of each factor was obtained, as shown in Figure 7. From Figure 7, the relative height of R-SED and the bend angle were significant factors, which was consistent with the results in Table 4. In terms of their significance, the factors influencing the energy dissipation effect of R-SEDs were in the following order: bend angle > relative height of R-SED > centerline radius of the bend > bottom slope of the bend > R-SED thickness > bend width > R-SED spacing > R-SED angle > height ratio of R-SED.
Figure 7

Pareto chart with the energy dissipation rate as the response variable.

Figure 7

Pareto chart with the energy dissipation rate as the response variable.

Close modal

Main effect plot of energy dissipation rate

The main effect plot is obtained by plotting the average characteristic value at each factor level; the average response at each factor level is connected through regression; then, whether there is a main effect of a factor is determined by comparing the slope of the regression line; a larger slope of the regression line indicates a more significant main effect. The main effect of the energy dissipation rate is shown in Figure 8. From Figure 8, the regression lines of the height ratio and the angle of R-SEDs were relatively flat, with a slope tending to zero, indicating that the main effect was not significant. It means that the energy dissipation rate was not sensitive to the changes of these two factors, and their values had slight effects on the energy dissipation effect of the R-SED. The energy dissipation rate showed a negative correlation with the R-SED spacing, while the relative height of R-SED, R-SED thickness, centerline radius of the bend, bend width, bend angle and bottom slope of the bend were positively correlated with the energy dissipation rate. The slope of the regression line of the bend angle was the largest, indicating that its main effect was the most significant. The energy dissipation rate was larger at a larger bend angle. To maximize the energy dissipation rate, all six positively correlated factors were taken as large as possible: relative height of R-SED, 0.8 cm; R-SED thickness, (1/50) B; centerline radius of the bend, 300 cm; bend width, 100 cm; bend angle, 60°; bottom slope of the bend, 0.04. The energy dissipation rate was larger at a smaller R-SED spacing, i.e., α = (1/6) β.
Figure 8

Main effect plot of the energy dissipation rate.

Figure 8

Main effect plot of the energy dissipation rate.

Close modal

Analysis of the interaction between the factors

Further analysis was performed to evaluate the correlation of these nine factors and the interaction between each two factors was plotted. A total of 36 groups of interactions were obtained, as shown in Figure 9. In Figure 9, the interaction plots for the two significant factors (relative height of R-SED and bend angle) show that the regression lines of these two factors were relatively non-parallel, indicating that there was a correlation between these two factors. The regression lines of the five interaction groups (i.e., bend angle and bottom slope of the bend, bend angle and R-SED spacing, bend angle and height ratio of R-SED, bend width and R-SED spacing as well as R-SED thickness and R-SED angle) tended to be parallel, indicating that the interaction between two factors in the above five groups was not significant. The regression lines of the remaining 31 interaction groups were not parallel, indicating that the two-factor interaction was significant, and the factors were correlated.
Figure 9

Interaction plot of the energy dissipation rate.

Figure 9

Interaction plot of the energy dissipation rate.

Close modal
In order to study the correlation between the energy dissipation rate and each two-factor combination in the 31 factor combinations with significant interactions, response surface plots are presented in Figure 10. The holding values in the plots were set as the optimal values of each predictor variable. Figure 10 (f7) shows the response surface plot of two significant factors: relative height of R-SED and bend angle. A larger relative height of R-SED (0.8 cm) and a larger bend angle (60°) induced a larger energy dissipation rate of the R-SED. In the process of R-SED design, the results in Figure 10 can be used to understand the correlation between different factors affecting the energy dissipation effect of R-SEDs and to predict the energy dissipation effect of the R-SED.
Figure 10

Response surface plot of the energy dissipation rate, (f1)–(f31) show the correlation between the energy dissipation rate and each two-factor combination.

Figure 10

Response surface plot of the energy dissipation rate, (f1)–(f31) show the correlation between the energy dissipation rate and each two-factor combination.

Close modal

Analysis of influencing factors of flow diversion effects

Analysis of variance of the coefficient of variation of superelevation

The coefficient of variation of superelevation was used as the response variable. The significance level was selected as 0.05. The ANOVA was performed on the nine factors, as shown in Table 5. Table 5 shows that the P-value corresponding to the main effect of the coefficient of variation of superelevation was less than 0.05, indicating that the original hypothesis was rejected and that the total effect of the regression was considered significant. The height ratio of R-SED and the centerline radius of the bend were significant.

Table 5

Analysis of variance of the coefficient of variation of superelevation

SourceDFAdj SSAdj MSF-ValueP-ValueSignificance
Model 0.205751 0.022861 20.02 0.048 
 Linear 0.205751 0.022861 20.02 0.048 
  hr 0.009858 0.009858 8.63 0.099  
  λ 0.092728 0.092728 81.22 0.012 
  α 0.001762 0.001762 1.54 0.34  
  θ 0.020137 0.020137 17.64 0.052  
  δ 0.0008 0.0008 0.7 0.491  
  R 0.07317 0.07317 64.09 0.015 
  B 0.003022 0.003022 2.65 0.245  
  β 0.001546 0.001546 1.35 0.365  
  i 0.002729 0.002729 2.39 0.262  
Error 0.002283 0.001142    
Total 11 0.208034      
R-sq = 0.9890 R-sq (adj) = 0.9396 
SourceDFAdj SSAdj MSF-ValueP-ValueSignificance
Model 0.205751 0.022861 20.02 0.048 
 Linear 0.205751 0.022861 20.02 0.048 
  hr 0.009858 0.009858 8.63 0.099  
  λ 0.092728 0.092728 81.22 0.012 
  α 0.001762 0.001762 1.54 0.34  
  θ 0.020137 0.020137 17.64 0.052  
  δ 0.0008 0.0008 0.7 0.491  
  R 0.07317 0.07317 64.09 0.015 
  B 0.003022 0.003022 2.65 0.245  
  β 0.001546 0.001546 1.35 0.365  
  i 0.002729 0.002729 2.39 0.262  
Error 0.002283 0.001142    
Total 11 0.208034      
R-sq = 0.9890 R-sq (adj) = 0.9396 

Pareto chart of coefficients of variation of superelevation

The coefficient of variation of superelevation was used as the response variable. The significance level was selected as 0.05. The Pareto chart of the nine factors is shown in Figure 11. It is found that the height ratio of R-SED and the centerline radius of the bend were significant factors, which is consistent with the results in Table 5. The factors influencing the flow diversion effect of the R-SED were in the following order: height ratio of R-SED > centerline radius of the bend > R-SED angle > relative height of R-SED > bend width > bottom slope of the bend > R-SED spacing > bend angle > R-SED thickness.
Figure 11

Pareto chart with the coefficient of variation of superelevation as the response variable.

Figure 11

Pareto chart with the coefficient of variation of superelevation as the response variable.

Close modal

Main effect plot of coefficients of variation of superelevation

The main effect plots of the coefficient of variation of superelevation are presented in Figure 12. Figure 12 shows that the regression line of the height ratio of R-SED and the centerline radius of the bend had the largest slope, indicating that their main effects were the most significant. It shows that the coefficient of variation of superelevation was more sensitive to the variation of the height ratio of R-SED and the centerline radius of the bend. The coefficient of superelevation variation was a decreasing indicator. The height ratio of R-SED, the R-SED spacing, the R-SED angle, the centerline radius of the bend and the bend angle was negatively correlated with the coefficient of variation of superelevation; this indicates that at larger values of these five factors (i.e., height ratio of R-SED, 2; R-SED spacing, (1/3) β; R-SED angle, 30°; centerline radius of the bend, 300 cm; bend angle, 60°), the coefficient of variation of superelevation was smaller, while flow diversion effects of R-SEDs were larger. However, the relative height of R-SED, R-SED thickness, bend width and bottom slope of the bend were positively correlated with the coefficient of variation of superelevation. The slopes of the regression line of these four factors were close, indicating that they had a similar effect on the coefficient of variation of superelevation. In order to minimize the coefficient of variation of superelevation, these four factors were taken as small as possible: relative height of R-SED, 0.4 cm; R-SED thickness, (1/100) B; bend width, 50 cm; bottom slope of the bend, 0.02.
Figure 12

Main effect plot of the coefficient of variation of superelevation.

Figure 12

Main effect plot of the coefficient of variation of superelevation.

Close modal

Analysis of the interaction between influencing factors

The coefficient of variation of superelevation was used as the response variable to analyze the correlation of these nine factors. The interaction plots of 36 groups of two-factor combinations are shown in Figure 13. In Figure 13, the interaction plots of the height ratio of R-SED and the centerline radius of the bend show that their regression lines were relatively parallel, indicating that there was no significant correlation between these two factors. The regression lines of four groups of two-factor combinations (i.e., bend angle and relative height of R-SED, centerline radius of the bend and height ratio of R-SED, R-SED spacing and relative height of R-SED as well as height ratio and relative height of R-SED) also tended to be parallel, indicating that the interactions within these two-factor combinations were not significant. The regression lines of the remaining 32 groups of two-factor combinations were not parallel, indicating that the two-factor interaction was significant, and these factors were correlated.
Figure 13

Interaction plot of the coefficient of variation of superelevation.

Figure 13

Interaction plot of the coefficient of variation of superelevation.

Close modal
In order to study the correlation between the coefficient of variation of superelevation and each two-factor combination in the 32 factor combinations with significant interactions, response surface plots are presented in Figure 14. The holding values in the plots were set as the optimal values of each predictor variable. In the process of R-SED design, the results in Figure 14 can be used to understand the correlation between different factors affecting the flow diversion effect of R-SEDs and to predict the flow diversion effect of the R-SEDs.
Figure 14

Response surface plot of the coefficient of variation of superelevation, (f1)–(f32) show the correlation between the coefficient of variation of superelevation and each two-factor combination.

Figure 14

Response surface plot of the coefficient of variation of superelevation, (f1)–(f32) show the correlation between the coefficient of variation of superelevation and each two-factor combination.

Close modal

Analysis of influencing factors on the overall energy dissipation and flow diversion effects

Determination of the weights of each evaluation index using the entropy weight method

The weights of each evaluation index were calculated using Equations (10)–(13) and the calculated parameters are shown in Table 6. The weight of the energy dissipation rate (W(η)) and the coefficient of variation of superelevation (W(SCV)) were 0.451 and 0.549, respectively, i.e., W(SCV)> W(η). This indicates that in these 12 Plackett–Burman tests, the coefficient of variation of superelevation carried more information than the energy dissipation rate and that the flow diversion effect of R-SEDs on the bend flow was larger than the energy dissipation effect.

Table 6

Calculation of the weight of each evaluation index using the entropy weight method

Test numberηSCVη*SCV*
0.535 0.188 0.752 0.896 0.097 0.137 0.943 0.930 0.451 0.549 
0.557 0.473 0.795 0.283 0.103 0.043 
0.318 0.357 0.324 0.532 0.042 0.081 
0.153 0.516 0.000 0.191 0.000 0.029 
0.461 0.413 0.606 0.412 0.078 0.063 
0.662 0.318 1.000 0.616 0.129 0.094 
0.335 0.140 0.358 1.000 0.046 0.153 
0.656 0.211 0.989 0.847 0.128 0.129 
0.623 0.301 0.924 0.653 0.120 0.100 
10 0.643 0.605 0.964 0.000 0.125 0.000 
11 0.419 0.380 0.524 0.483 0.068 0.074 
12 0.402 0.306 0.490 0.643 0.068 0.098 
Test numberηSCVη*SCV*
0.535 0.188 0.752 0.896 0.097 0.137 0.943 0.930 0.451 0.549 
0.557 0.473 0.795 0.283 0.103 0.043 
0.318 0.357 0.324 0.532 0.042 0.081 
0.153 0.516 0.000 0.191 0.000 0.029 
0.461 0.413 0.606 0.412 0.078 0.063 
0.662 0.318 1.000 0.616 0.129 0.094 
0.335 0.140 0.358 1.000 0.046 0.153 
0.656 0.211 0.989 0.847 0.128 0.129 
0.623 0.301 0.924 0.653 0.120 0.100 
10 0.643 0.605 0.964 0.000 0.125 0.000 
11 0.419 0.380 0.524 0.483 0.068 0.074 
12 0.402 0.306 0.490 0.643 0.068 0.098 

Determination of the overall ranking of each program using the TOPSIS method

The relative closeness was a comprehensive evaluation index of the energy dissipation and flow diversion effects of R-SEDs. Based on the calculation results in Table 6, the relative closeness of each scenario to the ideal solution was calculated using Equations (14)–(18). Then, the overall ranking of the energy dissipation and flow diversion effect of R-SEDs on the bend flow under each test scenario was obtained, as shown in Table 7. Table 7 shows that, among the 12 test scenarios, Scenario 8 had the largest relative closeness and the highest overall rating.

Table 7

Calculation of the overall ranking of each test scenario using the TOPSIS method

Test numberηSCV1-SCVRank
0.535 0.188 0.812 0.306 0.354 0.138 0.194 0.035 0.140 0.802 
0.557 0.473 0.527 0.319 0.229 0.144 0.126 0.084 0.109 0.564 
0.318 0.357 0.643 0.182 0.280 0.082 0.154 0.103 0.073 0.415 11 
0.153 0.516 0.484 0.088 0.211 0.040 0.116 0.159 0.021 0.118 12 
0.461 0.413 0.587 0.264 0.256 0.119 0.140 0.083 0.092 0.524 
0.662 0.318 0.682 0.379 0.297 0.171 0.163 0.043 0.148 0.776 
0.335 0.140 0.860 0.192 0.375 0.087 0.206 0.084 0.121 0.589 
0.656 0.211 0.789 0.375 0.344 0.169 0.189 0.017 0.160 0.904 
0.623 0.301 0.699 0.356 0.305 0.161 0.167 0.040 0.141 0.780 
10 0.643 0.605 0.395 0.368 0.172 0.166 0.094 0.111 0.127 0.532 
11 0.419 0.380 0.620 0.240 0.270 0.108 0.148 0.085 0.087 0.507 10 
12 0.402 0.306 0.694 0.230 0.302 0.104 0.166 0.078 0.096 0.553 
Test numberηSCV1-SCVRank
0.535 0.188 0.812 0.306 0.354 0.138 0.194 0.035 0.140 0.802 
0.557 0.473 0.527 0.319 0.229 0.144 0.126 0.084 0.109 0.564 
0.318 0.357 0.643 0.182 0.280 0.082 0.154 0.103 0.073 0.415 11 
0.153 0.516 0.484 0.088 0.211 0.040 0.116 0.159 0.021 0.118 12 
0.461 0.413 0.587 0.264 0.256 0.119 0.140 0.083 0.092 0.524 
0.662 0.318 0.682 0.379 0.297 0.171 0.163 0.043 0.148 0.776 
0.335 0.140 0.860 0.192 0.375 0.087 0.206 0.084 0.121 0.589 
0.656 0.211 0.789 0.375 0.344 0.169 0.189 0.017 0.160 0.904 
0.623 0.301 0.699 0.356 0.305 0.161 0.167 0.040 0.141 0.780 
10 0.643 0.605 0.395 0.368 0.172 0.166 0.094 0.111 0.127 0.532 
11 0.419 0.380 0.620 0.240 0.270 0.108 0.148 0.085 0.087 0.507 10 
12 0.402 0.306 0.694 0.230 0.302 0.104 0.166 0.078 0.096 0.553 

Selection of main influencing factors

The relative closeness was used as the response variable and a significance level of 0.05 was selected. An ANOVA was conducted to examine the importance of these nine influencing factors on the relative closeness, as shown in Table 8. Table 8 shows that the model was significant (P < 0.05). Particularly, the height ratio of R-SED, the centerline radius of the bend and the bend angle were significant for the relative closeness.

Table 8

Analysis of variance of relative closeness

SourceDFAdj SSAdj MSF-ValueP-ValueSignificance
Model 0.479869 0.053319 22.79 0.043 
 Linear 0.479869 0.053319 22.79 0.043 
  hr 0.031554 0.031554 13.49 0.067  
  λ 0.072006 0.072006 30.77 0.031 
  α 0.000079 0.000079 0.03 0.871  
  θ 0.012849 0.012849 5.49 0.144  
  δ 0.008324 0.008324 3.56 0.2  
  R 0.143629 0.143629 61.38 0.016 
  B 0.000064 0.000064 0.03 0.884  
  β 0.206204 0.206204 88.13 0.011 
  i 0.00516 0.00516 2.21 0.276  
Error 0.00468 0.00234    
Total 11 0.484549     
R-sq = 0.9903 R-sq (adj) = 0.9469 
SourceDFAdj SSAdj MSF-ValueP-ValueSignificance
Model 0.479869 0.053319 22.79 0.043 
 Linear 0.479869 0.053319 22.79 0.043 
  hr 0.031554 0.031554 13.49 0.067  
  λ 0.072006 0.072006 30.77 0.031 
  α 0.000079 0.000079 0.03 0.871  
  θ 0.012849 0.012849 5.49 0.144  
  δ 0.008324 0.008324 3.56 0.2  
  R 0.143629 0.143629 61.38 0.016 
  B 0.000064 0.000064 0.03 0.884  
  β 0.206204 0.206204 88.13 0.011 
  i 0.00516 0.00516 2.21 0.276  
Error 0.00468 0.00234    
Total 11 0.484549     
R-sq = 0.9903 R-sq (adj) = 0.9469 

The Pareto chart of these nine factors is presented in Figure 15. From Figure 15, the influencing factors of the overall energy dissipation and flow diversion effects of R-SEDs were in the following order: bend angle > centerline radius of the bend > height ratio of R-SED > relative height of R-SED > R-SED angle > R-SED thickness > bottom slope of the bend > R-SED spacing > bend width. Among them, the height ratio of R-SED, the centerline radius of the bend and the bend angle were the key factors influencing the overall energy dissipation and flow diversion effect of R-SEDs, which will be selected for further steepest climbing tests and response surface tests.
Figure 15

Pareto chart with relative closeness as the response variable.

Figure 15

Pareto chart with relative closeness as the response variable.

Close modal

In this paper, based on 12 groups of Plackett–Burman tests, the R-SEDs set at the bottom of the curved spillway were studied using the entropy weight method and the TOPSIS method. Statistical analysis of the test results was performed using Minitab 21.1 software. The conclusions are drawn as follows:

  • (1)

    The relative height of R-SED and the bend angle had significant effects on the energy dissipation effect of the R-SEDs. The height ratio and angle of R-SED had no significant effect on the energy dissipation effect of the R-SEDs. R-SED spacing was a negatively correlated factor, i.e., a smaller spacing of the R-SED can induce better the energy dissipation effects of the R-SEDs. The relative height of R-SED, R-SED thickness, the centerline radius of the bend, bend width, bend angle and bottom slope of the bend were positively correlated with the energy dissipation rate. The factors affecting the energy dissipation effect of the R-SED were in the following order: bend angle > relative height of R-SED > centerline radius of the bend > bottom slope of the bend > R-SED thickness > bend width > R-SED spacing > R-SED angle > height ratio of R-SED.

  • (2)

    The height ratio of R-SED and the centerline radius of the bend had significant effects on the flow diversion effect of R-SEDs. The height ratio of R-SED, R-SED spacing, R-SED angle, the centerline radius of the bend and the bend angle had a negative correlation with the coefficient of variation of superelevation. The relative height of R-SED, R-SED thickness, the bend width and the bottom slope of the bend showed a positive correlation with the coefficient of variation of superelevation. The factors influencing the flow diversion effect of R-SEDs were in the following order: height ratio of R-SED > centerline radius of the bend > R-SED angle > relative height of R-SED > bend width > bottom slope of the bend > R-SED spacing > bend angle > R-SED thickness.

  • (3)

    The weights of the energy dissipation rate and the coefficient of variation of superelevation were 0.451 and 0.549, respectively, indicating that the flow diversion effect of the R-SEDs was larger than their energy dissipation effect. The height ratio of R-SED, the centerline radius of the bend and the bend angle had significant effects on the overall energy dissipation and flow diversion effects of the R-SEDs. These three factors will be selected as the key factors for further steepest climbing tests and response surface test design. The factors influencing the overall energy dissipation and flow diversion effect of R-SEDs were in the following order: bend angle > centerline radius of the bend > height ratio of R-SED > relative height of R-SED > R-SED angle > R-SED thickness > bottom slope of the bend > R-SED spacing > bend width.

  • (4)

    The R-SED performance achieved the highest overall rating with the following parameter selection: hr = 0.8 cm, λ = 2, α = (1/3) β, θ = 15°, δ = (1/50) B, R = 300 cm, B = 50 cm, β = 60° and i = 0.02. This can be used as a reference for the R-SED design of similar curved spillway projects.

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51769037) and the University Research Program Innovation Team Project of Xinjiang Uygur Autonomous Region (Grant No. XJEDU2017T004).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

Abdel-Fattah
Y. R.
,
Saeed
H. M.
,
Gohar
Y. M.
&
El-Baz
M. A.
2005
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