Received April 23, 2016, accepted May 9, 2016, date of publication May 17, 2016, date of current version June 3, 2016. Digital Object Identifier 10.1109/ACCESS.2016.2569537
Intelligent Hybrid Taguchi-Genetic Algorithm for Multi-Criteria Optimization of Shaft Alignment in Marine Vessels WEN-HSIEN HO1 , JINN-TSONG TSAI2 , JYH-HORNG CHOU1,3,4 , AND JIANN-BEEN YUE5 1 Department
of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Kaohsiung 807, Taiwan of Computer Science, National Pingtung University, Pingtung 900, Taiwan of Electrical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan 4 Institute of Electrical Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 824, Taiwan 5 Design Section, China Shipbuilding Corporation, Keelung 202, Taiwan 2 Department 3 Department
Corresponding author: J.-H. Chou (
[email protected]) This work was supported by the Ministry of Science and Technology, Taiwan, under Grant NSC 102-2221-E-151-021-MY3 and Grant MOST 105-2218-E-151-001.
ABSTRACT An intelligent hybrid Taguchi-genetic algorithm (IHTGA) is used to optimize bearing offsets and shaft alignment in a marine vessel propulsion system. The objectives are to minimize normal shaft stress and shear force. The constraints are permissible reaction force, bearing stress, shear force, and bending moment in the shaft thrust flange under cold and hot operating conditions. Accurate alignment of the shaft for a main propulsion system is important for ensuring the safe operation of a vessel. To obtain a set of acceptable forces and stresses for the bearings and shaft under operating conditions, the optimal bearing offsets must be determined. Instead of the time-consuming classical local search methods with some trial-and-error procedures used in most shipyards to optimize bearing offsets, this paper used IHTGA. The proposed IHTGA performs Taguchi method between the crossover operation of the conventional GA. Incorporating the systematic reasoning ability of Taguchi method in the crossover operation enables intelligent selection of genes used to achieve crossover, which enhances the performance of the IHTGA in terms of robustness, statistical performance, and convergence speed. A penalty function method is performed using the fitness function as a pseudo-objective function comprising a linear combination of design objectives and constraints. A finite-element method is also used to determine the reaction forces and stresses in the bearings and to determine normal stresses, bending moments, and shear forces in the shaft. Computational experiments in a 2200 TEU container vessel show that the results obtained by the proposed IHTGA are significantly better than those obtained by the conventional local search methods with some trial-and-error procedures. INDEX TERMS Marine vessel propulsion system, bearing offsets, shaft alignment, optimal design, genetic algorithm. I. INTRODUCTION
The propulsion shaft is a critical component of a marine vessel [1]–[3]. Excessive bearing heat and wear caused by a misaligned shaft can lead to catastrophic failure. One example of such a failure is Hull no. (Hno.) ×26 B× × × M× × ×, which won a Royal Institution of Naval Architects award for excellence in 1999 and was the largest heavy-lift transportation ship in the world. After transporting the USS Cole (DDG 51) from the Middle East to an American port in July 1999, the ship repeatedly had high temperature alarms for the aft stern tube bearing and intermediate shaft bearing. Inspections
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showed that improper shaft alignment caused the bearings to wear out after only 6 months. The vessel required longitudinal and vertical alignments of bearings to ensure that shear forces, bending moments and normal stresses on the shaft were acceptable and to ensure that reaction forces and bearing stresses were acceptable under cold and hot conditions. The rule of thumb for longitudinal bearing position is l/d;12 for d=400 mm, where l/d is the relative bearing distance over shaft diameter. If all bearings are placed in a straight line, the bearing reaction forces and shaft stresses will reveal the following undesirable properties [4]:
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(1) The forward stern tube bearing will have a negative or upward load. (2) The aftermost bearing will support the uppermost load. (3) The next bearing forward will have a negative or uppermost load. (4) The other bearings will load erratically. That is, some will overload, and some will underload. (5) The shaft stresses will widely vary. (6) Bearing reaction forces and shaft stresses will substantially differ between cold and hot conditions. The above undesirable states can be avoided or minimized by carefully controlling the elevation or depression of the vertical positions of various bearings in order to obtain a set of acceptable limits for bearing and shaft forces and stresses under operating conditions. Designers generally develop their own techniques for calculating bearing offsets. Conventional iterative methods arbitrarily perturb the vertical position of a bearing in a baseline design according to the experience of the user. An acceptable position for the vertical bearing is eventually achieved by the trial and error method [5]. In this study, the intelligent hybrid Taguchi-genetic algorithm (IHTGA), which is proposed by modifying the works given by Tsai et al. [6], Chang et al. [7] and Tsai et al. [8]–[10] is presented to optimize bearing offsets for shaft alignment in a marine vessel propulsion system to obtain acceptable limits for shear forces, bending moments, and normal stresses in the shaft and for reaction forces and stresses in the bearings under cold and hot conditions. Bearing and main engine vertical offsets are conventionally determined in the shipyard by using the time-consuming classical local search methods with some trial-and-error procedures. Alignment usually requires direct measurements of the bearings and shaft. Forrest, Jr., and Labasky [11] developed an alignment method that used strain gauges, and Grant [12] developed an alignment method that uses strain gauges and load cells. Currently, however, alignment is performed by using computer techniques to construct fair curves. Rao et al. [13] used finite element analysis of strain gauge measurements to perform shaft alignment. Mourelatos and Papalambros [14] used the generalized reduced gradient method to construct a mathematical model for optimizing the strength and alignment of a shaft system. In the proposed IHTGA, Taguchi method [15], [16] is performed between the crossover operation of conventional GA. The systematic reasoning capability of the Taguchi method is incorporated in crossover operations to enable intelligent selection of the better genes. Crossover operations can then be tailored to find new representative chromosomes for use as potential offspring. That is, incorporating the Taguchi experimental design method in the IHTGA enhances robustness, statistical analysis, and convergence speed. To evaluate the performance of the IHTGA proposed in this study, the IHTGA was used to optimize bearing offsets during shaft alignment in a marine vessel propulsion system. This paper is organized as follows. Section 2 VOLUME 4, 2016
describes the shaft alignment model. Section 3 describes the use of IHTGA to optimize the shaft alignment. To evaluate the efficiency and effectiveness of the proposed IHTGA, section 4 compares the performance of the IHTGA and conventional approaches in optimizing bearing offsets for two sister vessels (2200-TEU Hno. ×62 delivered in 1999 and Hno. ×96 delivered in 2002), which are real-world practical design cases in the China Shipbuilding Corporation (CSBC) (http://www.csbcnet.com.tw/csbc/EN/index.asp). Finally, Section 5 concludes the study. II. PROBLEM STATEMENT
The optimum alignment problem can be formulated as a typical mathematical model of design optimization as follows: Minimize f (X )u, u = 1, 2, 3 . . . , m, Subject to h(X )w = 0, w = 1, 2, 3 . . . , p, g(X )v 5 0, v = 1, 2, 3 . . . , q,
(1) (2) (3)
where the design objectives f (X )u are the maximum normal stresses and shear forces in the shaft; the design variables X =[x1 , x2 , x3 ] are the bearing vertical offsets; m is the number of the objectives; the equal constraints h(X )w = 0 are the bearing stresses under hot and cold conditions; p is the number of equal constraints; the unequal constraints g(X )v 5 0 are reaction forces of bearings, shear forces, and bending moments of the shaft thrust flange under hot and cold conditions; and q is the number of unequal constraints. When using GA to optimize vertical offsets of bearings in the shaft alignment problem, an appropriate and flexible alternative is to define the fitness function as a linear combination of the design objectives and constraints. Here, the fitness function is a pseudo objective equation. Therefore, penalty function method is used to process the design objectives and constraints into the following pseudo objective equation: 8(X ) =
m X {Wu f (X )u } u=1
) p q X X [hw (X )] , +R {max[0, gv (X )]} + (
v=1
(4)
w=1
where R is a constant penalty factor and Wu (u = 1, 2, . . . , m) is a set of weighting factors for design objectives. The system parameter values are R of 0.8, m of 2, W1 of 0.7, and W2 of 0.3. Because the above pseudo objective equation contains different engineering units, membership functions are used to normalize the objective functions and constraints to 0 or 1 for the lowest and highest fitness, respectively. To obtain an adjustable gradient curve for each objective, the sigmoid function is used to describe the normal stresses and shear forces on the shaft. Figure 1 shows that the sigmoid function can be expressed in the following mathematical form: 1 , (5) uf (x) = 1 + exp(b0 × f − a0 ) 1 − S1 a0 = b0 × fmin − ln( ), (6) S1 2305
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FIGURE 1. Sigmoid function for the minimum objective.
1 1 − S1 1 − S2 b0 = × ln( ) − ln( ) , (fmin − C0 ) S1 S2 C0 = (fmax − fmin ) × d0 + fmin ,
FIGURE 3. Piece ramp function for the unequal constraint.
(7) (8)
where fmax and fmin are the maximum and minimum values of the objective under the constraints, respectively; d0 , s1 and s2 are adjustable parameters; and s1 > s2 due to their minimum objectives.
FIGURE 2. Trianglar function for the equal constraint.
The values for allowable bearing stresses under cold and hot conditions are limited by the upper and lower bounds. In this study, the target value for bearing stress was set to the arithmetic average of the above two values to maintain an even distribution of each bearing stress value. Therefore, each bearing stress value is an equal constraint (h(x) = b). Each value is then defined by the triangular function in Figure 2. The triangular function is expressed as 0, h(x) < b− , |h(x) − b| (9) µh = 1 − + , b− ≤ h(x) ≤ b+ , b − b 0, h(x) > b+ , where b is the target bearing stress value and b+ and b− are loose values (33.3% of the target value). The permissible reaction forces of bearings under cold and hot conditions are unequal constraints (g(x) > b). In Figure 3, 2306
the above unequal constraints are then specified by a piece ramp function expressed as 1, g(x) > b, |g(x) − b| (10) µg = 1 − , b− ≤ g(x) ≤ b, − b − b 0, g(x) < b− .
FIGURE 4. Twin ramp function for the unequal constraint.
The shear forces and bending moments of a shaft thrust flange under cold and hot conditions are unequal constraints (a 6 g(x) 6 b). In Figure 4, the above unequal constraints are then specified by a twin ramp function |g(x)| − b , b ≤ g(x) ≤ b+ , 1 − + b −b µg = 1, (11) a < g(x) < b, |g(x)| − a 1 − , a− ≤ g(x) ≤ a, a − a− where a to b is the range of target values for shear forces and bending moments of the shaft thrust flange and where a− and b+ are loosening values set to 20% of the target value. For multi-criteria optimization of a marine vessel shaft alignment, the IHTGA obtains better and more robust results compared to other improved GAs reported in the literature [6], [17]. The IHTGA codes the solution space (the VOLUME 4, 2016
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FIGURE 5. Configuration of shaft model for 2,200 TEU container.
FIGURE 6. Bearing vertical offset for 2,200 TEU container.
design variable space) as strings. The pseudo objective equation can be used as an objective function for evaluating the fitness of the string in the environment. As in nature, the population (strings) are selected by the environment according to their fitness. The strings with the highest fitness dominate the reproduction process and have the best chance of surviving in the environment. The string with the highest fitness is the optimal solution corresponding to the given objectives. III. ILLUSTRATION OF SHAFT ALIGNMENT PROBLEM
This section illustrates the use of the IHTGA to solve shaft alignment problems in 2200 TEU container series vessels, which are real-world practical design cases in the CSBC (http://www.csbcnet.com.tw/csbc/EN/index.asp). The problem was considered in Hno. ×62 (delivered at Keelung shipyard, Taiwan in 2001) and Hno. ×96 (to be delivered at Kaohsiung shipyard, Taiwan at the end of 2003). Although Hnos. ×62 and ×96 had different designers, shaft alignment is performed by the classical local search methods with some trial-and-error procedures in both vessels. Figure 5 shows the layouts of their shaft systems. The shaft alignment problem is to optimize the vertical offsets of bearings to minimize normal stresses and shear forces on the shaft under normal conditions and under the constraints of cold and hot conditions. The system is considered a static system because the maximum rotary speed of the shaft is quite low (approximately 91 rpm). Figure 6 shows that the design variables considered in this system are the intermediate shaft bearing vertical VOLUME 4, 2016
offset (X1 and X2 ) and the main engine bearing vertical offset (X3 ). In Figures 5 and 6, No.1 is the after stern bearing, No.2 is the forward stern bearing, No.3 is the #2 intermediate bearing, No.4 is the #1 intermediate bearing, and No.5 is the thrust bearing; Nos. 6-11 are the main engine bearings. The design parameters, which are considered known and constant during the optimization process, are the following: (1) Modulus of elasticity (E), 2×105 N/mm2 (2) Yield strength of shaft, 295 N/mm2 (3) Specific gravity of shaft, 76,930 N/ m3 (4) Weight of propeller cap and nut, 12,544 N (5) Weight of propeller (in water), 301,781 N (6) Weight of propeller shaft, 321,263 N (7) Weight of No. 1 intermediate shaft, 189,600 N (8) Weight of No. 2 intermediate shaft, 123,911 N (9) Weight of flywheel, 115,826 N (11,819 kgf) (10) Weight of piston, 235,984 N (24,080 kgf) (11) Chain force of main engine, 160,100 N (up) Under the constraints of cold and hot conditions, the two objectives are (1) Minimize the maximum normal stress σb on the shaft (2) Minimize the maximum shear force Sy on the shaft Subject to constraints (at cold and hot conditions) (1) Minimum bearing reaction force, Pb > 30000 N (2) Intermediate bearing stress, 0 6 Pb /A 6 80 (N/cm2 ) The permissible shear force and bending moment of the shaft thrust flange is 57.6-0.84M 6 F + G 6192–1.8M (N), 2307
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FIGURE 7. Approach loci for (a) IHTGA and (b) GA.
FIGURE 8. Shaft system deflection profiles for (a) Hno. ×62, (b) Hno. ×96, and (c) IHTGA (see Figure 5 for bearing locations).
where M is the bending moment, F is the shear force, and G is the flywheel weight. Notably, the allowable bearing stress according to the design specifications was 40 N/cm2 . In this study, the target value is 30 N/cm2 . IV. RESULTS AND DISCUSSIONS
The IHTGA is performed in the following evolutionary environment: an orthogonal array L4 (23 ) with a maximum generation number of 30, a population size of 50, a crossover rate of 0.95, and a mutation rate of 0.03. Three variables that must be determined are X1 , X2 and X3 (ranges, 1 < X1 < 10 mm, 1 < X2 < 10 mm, and 1 < X3 < 10 mm, respectively). Since each variable is coded with 10 binary bits, a solution for design variables requires a chromosome string of 30 binary bits. Figure 7 compares the approach loci of the IHTGA and GA for the subject vessel. The computation times for thirty generations are 51.5 minutes for IHTGA and 36.6 minutes for GA. The best fitness values are 1.191254041 for IHTGA (Figure 7 (A)) and 1.16546342 for GA (Figure 7 (B)). 2308
For IHTGA, the best and worst fitness values converge to the same value after 12 generations (20.75 minutes). The IHTGA achieves robust convergence by the 12th generation whereas the GA is still divergent. For the GA, the worst fitness value remains near zero. Both the proposed IHTGA and GA substantially reduces shaft alignment time compared to the classical local search method with some trial-and-error procedures, which requires at least 4 days to perform shaft alignment in Hnos. ×62 and ×96. Notably, however, IHTGA outperforms GA. Figure 8 shows the deflection profiles for the shaft system. The figure clearly shows that, compared to the classical local search methods with some trial-and-error procedures, the IHTGA obtains better deflection profiles and smoother elastic curves for Hnos. ×62 and ×96. Table 1 shows the bearing offset values for X1 , X2 and X3 . Table 2 and Figure 9 show the bearing reaction forces. The IHTGA obtains reaction forces of 33.9 kN and 207.7 kN for the engine aftermost bearing (No. 5) under cold and hot conditions, respectively. For the engine aftermost main bearing (No. 6), the IHTGA obtains reaction forces VOLUME 4, 2016
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TABLE 1. Designed bearing offset values (mm).
FIGURE 9. Shaft bearing load distributions for (a) Hno. ×62, (b) Hno. ×96, and (c) IHTGA (see Figure 5 for bearing locations).
TABLE 2. Bearing reaction force (kN).
of 167.0 kN and 29.5 kN under cold and hot conditions, respectively. These values are far lower than the maximum tolerance value (573 kN) and far higher than the minimum tolerance value (28 kN, 5% of 573 kN). In contrast, Hno. ×96 reveals a reaction force of 23.2 kN for the engine aftermost bearing (No. 5) under a hot condition whereas Hno. ×62 reveals a negative reaction force (−7.0 kN) for the engine aftermost main bearing (No. 6) under a cold condition. That is, some constraints of Hnos. ×96 and ×62 are lower than the minimum specified by the American Bureau of VOLUME 4, 2016
Shipping. The bearing reaction forces obtained by the IHTGA are not only acceptable, they are almost ideal. Figure 8 shows that, for the No. 5 and No.6 bearings (at the borders of the shaft thrust flange), reaction forces vary widely between cold and hot conditions. Therefore, the alignment is difficult to optimize by the classical local search methods with some trial-and-error procedures but easy to optimize by IHTGA. Table 3 shows the bearing stresses of the shaft system. The bearing stress values obtained by IHTGA range from 21.1 N/cm2 to 40.9 N/cm2 . For all 2309
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TABLE 3. Bearing stress (N/mm2 ).
FIGURE 10. Bending moment and external force of shaft thrust bearing flange for (a) Hno. ×62, (b) Hno. ×96, and (c) IHTGA.
bearings, the average bearing stresses ((hot condition + cold condition)/2) approach the target value of 30 N/cm2 . In contrast, the values obtained by the classical local search methods with some trial-and-error procedures range from 6.6 N/cm2 to 58.5 N/cm2 for Hno. ×62 and from 13.0 N/cm2 to 49.2 N/cm2 for Hno. ×96. The average stresses range from 7.7 N/cm2 to 48.6 N/cm2 for Hno. ×62 and from 13.7 N/cm2 to 46.2 N/cm2 for Hno. ×96. These data imply that, because IHTGA achieves a better load distribution, the bearings optimized by IHTGA require less maintenance compared to those optimized by the classical local search methods with some trial-and-error procedures, which are susceptible to overheating and burnout. Figure 10 shows the bending moments and shear forces for the shaft thrust flange under cold and hot conditions. The horizontal axis is the bending 2310
moment, and the vertical axis is the external force (shear force + flywheel weight). The bending moments and shear forces are represented by points in the figure. The shaft alignment is acceptable if the points are located within the two limit lines under hot and cold conditions according to the design requirements specified by manufacturer of the main engine. Safe operation of the shaft is ensured under hot and cold conditions. Notably, Hno. ×62 does not meet the above criterion as its hot condition is not within the range considered safe. In contrast, the hot condition for Hno.×96 optimized by IHTGA is within the safe range. In this case, the acceptable range is too narrow to include the points for both the hot and cold conditions. When the IHTGA is used, however, both points are within the range, and the point for the cold condition is quite near VOLUME 4, 2016
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FIGURE 11. Bending stress distribution in shaft system for (a) Hno. ×62, (b) Hno. ×96, and (c) IHTGA (see Figure 5 for bearing locations).
FIGURE 12. Shear force distribution of shaft system for (a) Hno. ×62, (b) Hno. ×96, and (c) IHTGA (see Figure 5 for bearing locations).
the lower line. Therefore, the main engine can withstand the temperature increase under at hot condition. This also demonstrates the excellent shaft alignment results obtained by IHTGA. The diagrams in Figures 11 and 12 show a series of results for shaft bending stresses, and shear forces, respectively, under cold and hot conditions. Figure 11 shows that the IHTGA obtains maximum bending stresses of 16.82 and 8.39 N/mm2 for the propeller and intermediate shaft, which are lower than the maximum allowable bending stress (29.6 N/mm2 , 10% of yield stress). Therefore, the shaft can be considered sufficiently safe. The objectives of the IHTGA are to minimize the maximum shaft bending stresses and shear forces under the given
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constraints and conditions. Figures 11 and 12 show that the IHTGA reduces the maximum shaft bending stresses and shear forces of Hnos. ×62 and ×96, respectively. As noted above, however, some parameters of Hnos. ×62 and ×96 breach their constraints. On the other hand, from a practical perspective, in the CSBC (http://www.csbcnet.com.tw/csbc/EN/index.asp), the classical local search methods with some trial-and-error procedures usually are used to design the proposed problems. For example, the classical local search method with some trialand-error procedures requires at least 4 days to performing shaft alignment in Hnos. ×62 and ×96. However, the design time of using GA-based methods is shortened to about a day. This illustrates that the GA-based methods are necessary. 2311
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The Taguchi GA was developed more than one decade and, from a theoretical perspective, the proposed IHTGA approach appears to be a relatively minor novelty. But the practical results in this study confirmed that the proposed IHTGA, instead of the time-consuming classical local search methods with some trial-and-error procedures used in most shipyards, can not only increase the accuracy of shaft alignment in marine vessels, but also can avoid to exceed the constraints in the shaft thrust flange under cold and hot operating conditions. In addition, the proposed IHTGA method has immediate real-world applications. This paper is an applications-oriented study, and this practical article discusses a new application technique and provides interesting solutions to the shaft alignment in marine vessels. Here it should be noticed that the obtained results, obtained by using the proposed IHTGA approach, were adopted in the CSBC (http://www.csbcnet.com.tw/csbc/EN/index.asp). V. CONCLUSIONS
By combining conventional GA with Taguchi method, the IHTGA effectively optimizes bearing offsets in terms of the maximum normal stresses and shear forces under permissible reaction forces and in terms of the bearing stresses, shear forces, and bending moments of the shaft thrust flange under cold and hot conditions. In computer simulations of bearing offset optimization in Hnos. ×62 and ×96, the proposed IHTGA had a significantly shorter search time compared to the conventional local search methods with some trial-anderror procedures. Whereas the IHTGA obtained satisfactory results, the conventional local search methods with some trial-and-error procedures exceeded the constraints for bearing reaction force in Hnos. ×62 and ×96 and for bending moment and external force of shaft thrust bearing flange in Hno. ×62. Based on the IHTGA results, an alignment plan was established for setting the longitudinal and vertical positions of bearings to ensure acceptable parameter values under actual operating conditions. One potential extension of the proposed method is optimizing the longitudinal positions of bearings in terms of lateral shaft vibration. Here it should be noticed that the CSBC (http://www.csbcnet.com.tw/csbc/EN/index.asp) have already adopted the proposed integrative and systematic design approach to optimizing bearing offsets and shaft alignment in a marine vessel propulsion system. That is, the CSBC has benefited from use of the developed method. REFERENCES [1] H.-J. Yang, C.-D. Che, W.-J. Zhang, and T. Qiu, ‘‘Transient torsional vibration analysis for ice impact of ship propulsion shaft,’’ J. Ship Mech., vol. 19, no. 1, pp. 176–181, 2015. [2] T.-T. Zhou, X.-M. Zhu, C.-J. Wu, and W.-C. Peng, ‘‘Marine propulsion shaft system fault diagnosis method based on partly ensemble empirical mode decomposition and SVM,’’ J. Vibroeng., vol. 17, no. 4, pp. 1783–1795, 2015.
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[3] H. S. Han, K. H. Lee, and S. H. Park, ‘‘Parametric study to identify the cause of high torsional vibration of the propulsion shaft in the ship,’’ Eng. Failure Anal., vol. 59, pp. 334–346, Jan. 2016. [4] R. T. Bradshaw, ‘‘The optimum alignment of marine shafting,’’ Marine Technol., vol. 11, no. 3, pp. 260–269, 1974. [5] L. Vassilopoulos, ‘‘Methods for computing stiffness and damping properties of main propulsion thrust bearing,’’ Int. Shipbuilding Prog., vol. 29, no. 329, pp. 13–31, 1982. [6] J.-T. Tsai, T.-K. Liu, and J.-H. Chou, ‘‘Hybrid Taguchi-genetic algorithm for global numerical optimization,’’ IEEE Trans. Evol. Comput., vol. 8, no. 4, pp. 365–377, Aug. 2004. [7] H.-C. Chang, Y.-P. Chen, T.-K. Liu, and J.-H. Chou, ‘‘Solving the flexible job shop scheduling problem with makespan optimization by using a hybrid Taguchi-genetic algorithm,’’ IEEE Access, vol. 3, pp. 1740–1754, 2015. [8] J.-T. Tsai, J.-H. Chou, and C.-F. Lin, ‘‘Designing micro-structure parameters for backlight modules by using improved adaptive neuro-fuzzy inference system,’’ IEEE Access, vol. 3, pp. 2626–2636, 2015. [9] J.-T. Tsai, K.-Y. Chiu, and J.-H. Chou, ‘‘Optimal design of SAW gas sensing device by using improved adaptive neuro-fuzzy inference system,’’ IEEE Access, vol. 3, pp. 420–429, 2015. [10] J.-T. Tsai, C.-T. Lin, C.-C. Chang, and J.-H. Chou, ‘‘Optimized positional compensation parameters for exposure machine for flexible printed circuit board,’’ IEEE Trans. Ind. Informat., vol. 11, no. 6, pp. 1366–1377, Dec. 2015. [11] A. W. Forrest, Jr., and R. F. Labasky, ‘‘Shaft alignment using strain gages,’’ Marine Technol., vol. 18, no. 3, pp. 276–284, 1981. [12] R. B. Grant, ‘‘Shaft alignment methods with strain gages and load cells,’’ Marine Technol., vol. 17, no. 1, pp. 8–15, 1980. [13] M. N. K. Rao, M. V. Dharaneepathy, S. Gomathinayagam, K. Ramarju, P. K. Chakravorty, and P. K. Mishra, ‘‘Computer-aided alignment of ship propulsion shafts by strain-gage methods,’’ Marine Technol., vol. 28, no. 2, pp. 84–90, 1991. [14] Z. Mourelatos and P. Papalambros, ‘‘A mathematical model for optimal strength and alignment of a marine shafting system,’’ J. Ship Res., vol. 29, no. 3, pp. 212–222, 1985. [15] G. Taguchi, S. Chowdhury, and S. Taguchi, Robust Engineering. New York, NY, USA: McGraw-Hill, 2000. [16] Y. Wu, Taguchi Methods for Robust Design. New York, NY, USA: ASME, 2000. [17] J.-T. Tsai, J.-H. Chou, and T.-K. Liu, ‘‘Tuning the structure and parameters of a neural network by using hybrid Taguchi-genetic algorithm,’’ IEEE Trans. Neural Netw., vol. 17, no. 1, pp. 69–80, Jan. 2006.
WEN-HSIEN HO received the B.S. degree in marine engineering from National Taiwan Ocean University, in 1991, the B.S. degree in industrial and information management from National Cheng Kung University, in 1998, and the M.S. degree in mechanical and automation engineering and the Ph.D. degree in engineering science and technology from the National Kaohsiung First University of Science and Technology, Taiwan, in 2002 and 2006, respectively. He was an Engineer of the Design Department with CSBC Corporation, Taiwan, from 1991 to 2006. He is currently a Professor with the Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Taiwan. His research interests include intelligent systems and control, computational intelligence and methods, robust control, and quality engineering.
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JINN-TSONG TSAI received the B.S. and M.S. degrees in mechanical and electro-mechanical engineering from National Sun Yat-sen University, Taiwan, in 1986 and 1988, respectively, and the Ph.D. degree in engineering science and technology from the National Kaohsiung First University of Science and Technology, Taiwan, in 2004. He was a Lecturer with the Vehicle Engineering Department, Chung Cheng Institute of Technology, Taiwan, from 1988 to 1990. From 1990 to 2004, he was a Researcher and the Chief of the Automation Control Section of Metal Industries Research and Development Center, Taiwan. From 2004 to 2006, he was an Assistant Professor with the Medical Information Management Department, Kaohsiung Medical University, Kaohsiung, Taiwan. From 2006 to 2014, he was an Assistant and Associate Professor with the Department of Computer Science, National Pingtung University of Education, Pingtung, Taiwan. He is currently a Professor with the Department of Computer Science, National Pingtung University, Pingtung. His research interests include evolutionary computation, intelligent control and systems, neural networks, and quality engineering.
JIANN-BEEN YUE received the B.S. degree in mechanical engineering from Chengshih University, Taiwan, in 1984, the B.S. degree in mechanical engineering from the National Taiwan University of Science and Technology, in 1988, and the M.S. degree in mechanical and automation engineering from the National Kaohsiung First University of Science and Technology, Taiwan, in 2003. He is currently a Manager of the Marine Design Department with China Shipbuilding Corporation, Taiwan. His research interests include shafting alignment of vessel, intelligent systems and control, and computational intelligence.
JYH-HORNG CHOU (SM’04–F’15) received the B.S. and M.S. degrees in engineering science from National Cheng Kung University, Tainan, Taiwan, in 1981 and 1983, respectively, and the Ph.D. degree in mechatronic engineering from National Sun Yat-sen University, Kaohsiung, Taiwan, in 1988. He is currently the Chair Professor with the Electrical Engineering Department, National Kaohsiung University of Applied Sciences, Taiwan. He has co-authored four books, and published over 270 refereed journal papers. He also holds six patents. His research and teaching interests include intelligent systems and control, computational intelligence and methods, automation technology, robust control, and robust optimization. He was a recipient of the 2011 Distinguished Research Award from the National Science Council of Taiwan, the 2012 IEEE Outstanding Technical Achievement Award from the IEEE Tainan Section, the 2014 Distinguished Research Award from the Ministry of Science and Technology of Taiwan, the Research Award and the Excellent Research Award from the National Science Council of Taiwan 12 times, and numerous academic awards/honors from various Societies. Based on the IEEE Computational Intelligence Society evaluation, his Industrial Application Success Story has got the 2014 winner of highest rank, thus being selected to become the first internationally industrial success story being reported on the IEEE CIS website. He is also a fellow of the Institution of Engineering and Technology, the Chinese Automatic Control Society, the Chinese Institute of Automation Engineer, and the Chinese Society of Mechanical Engineers.
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