International Journal of Engineering and Technology, Vol. 8, No. 5, October Model Systems. Yang Jianjun and Li Wenjin

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1 Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October Relablty Optmzaton Desgn of Submarne Free-Runnng Model Systems Yang Janjun and L Wenjn Abstract Wth regard to the relablty desgn of submarne free-runnng model system, ths paper puts forward a focused desgn method for optmzaton of relablty. After constructng a matrx task profle, the relablty modelng theory of phased msson system s employed to buld a system relablty model, and the measures for techncal mprovement are brought forward accordng to the results of FMEA analyss. Relablty redundancy optmzaton model s establshed based on volume, weght and cost and solved by usng partcle swarm optmzaton. A case s presented to llustrate the effectveness and relablty of optmzaton desgn. Index Terms Submarne free-runnng model, relablty optmzaton, phased msson system, redundancy desgn. I. INTRODUCTION Submarne free-runnng model s a test platform featured by hgh safety, operablty, vvd smulaton of flow feld, reasonable change of workng condton, and some other benefts, so t plays a very sgnfcant role n the study on the performance of varous submarnes. After USS Albacore (AGSS-569) submarne, the Unted States has always employed the free-runnng model for submarne tests and studes on smulaton of submarne propertes. Along wth the development of submarne technology, free-runnng model system becomes more and more complcated, and there are hgher and hgher requrements for relablty. The qualty of relablty desgn drectly determnes whether the desgn of submarne free-runnng model test system s successful. Submarne free-runnng model test contans salng and other phases, whch requre dfferent equpment, so t s a typcal phased msson system [1]. Snce the study on phased msson system relablty [2] was proposed n 1975, t has always been the focus n the feld of system relablty. Now, there are already some researches on the relablty optmzaton of phased msson systems of dfferent types [3-5]. Ths paper wll regard submarne free-runnng model system as a non-reparable phased msson system to analyze the mssons and structure of submarne free runnng model test system. After constructng a msson profle, analyzng the weak unts and conductng techncal mprovement and redundancy mprovement of the system, ths paper brngs Manuscrpt receved December 9, 2014; revsed Aprl 23, Yang Janjun s wth Navy Unversty of Engneerng, Wuhan, , Chna (e-mal: @163.com). L Wenjn s wth Management Scence and Engneerng, Navy Unversty of Engneerng, Wuhan, , Chna (e-mal: lwenjn2012@163.com). forward a relablty optmzaton desgn method for submarne free-runnng model system, so as to effectvely mprove the relablty of system. II. STUDY ON RELIABILITY OPTIMIZATION METHOD A. Basc Idea of Free-Runnng Model Relablty Optmzaton The basc procedure of relablty optmzaton desgn for a submarne free-runnng model system s as follows: 1). Analyze system relablty desgn, construct msson profle and relablty block dagram and estmate system relablty; 2). If the estmated relablty does not satsfy the requrements, carry out the relablty optmzaton desgn for the system; 3). Perform FMECA analyss on the system to fnd out the weak unts of the system, conduct techncal mprovement toward the weak unts causng low relablty n the system desgn, and then estmate the relablty of system agan; 4). If the relablty s stll unacceptable, carry out redundancy optmzaton toward the weak unts of the system tll system relablty falls nto the specfed range of constrants (system cost, system volume and system weght) and satsfes the requrements. The whole procedure s presented n Fg. 1. Techncal optmzaton Unt relablty Desgn Msson profle Relablty block dagram Redundancy optmzaton (dstrbuton) Estmaton of system relablty Noncomplance FMECA Requrements Complance Optmzaton of desgn scheme Fg. 1. Basc dea of relablty optmzaton of submarne free-runnng model system. B. Free-Runnng Model Relablty Optmzaton Steps Accordng to the basc procedure of relablty optmzaton desgn, the followng steps are arranged for free-runnng relablty optmzaton: Step 1. Construct the msson profle of free-runnng model system. Msson profle refers to the tme sequence descrpton of events and envronments experenced when the system completes the specfed msson [6]. When constructng the msson profle of free-runnng model system, matrx msson profle can be employed. The schematc dagram of msson profle for a submarne free-runnng model system s presented n Table I. DOI: IJET.2016.V

2 Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 Step 2. Construct the relablty model of free-runnng model system. Free-runnng model system s a phased msson system, so the relablty modelng theory for such type of system can be employed to buld a system relablty model n the form of block dagram. Step 3. Estmate the relablty of free-runnng model system. By buldng the mathematc model for system relablty, t s able to estmate system relablty. The estmaton helps fnd out whether system relablty satsfes the requrements and whether relablty optmzaton s requred. TABLE I: MISSION PROFILE OF SUBMARINE FREE-RUNNING MODEL SYSTEM Course-keepn Load Msson Phase Brake Test g Test Rejecton Test Phase Duraton 55s 20s 55s Batteres Propeller AC ServoDrve Inverter Hgh-pressure Gas Cylnder Note: In the matrx, the columns present the msson phases of system and the lnes contan the descrpton of envronment and the descrpton of workng state of equpment n each msson phase. If left blank at the ntersecton of msson phase and equpment, t means that the equpment operates n the msson phase. If t s flled wth, t means that the equpment does not operate n the msson phase. Step 4. FMECA analyss. FMECA (falure mode, effect and crtcalty analyss)[7] analyzes all possble falure modes and ther causes and consequences to fnd out the weak unts n system equpment, n order to carry out the optmzaton desgn of system toward such weak unts and mprove the relablty of system. The nstructons for FMECA are detaled n Reference [8]. If t s estmated that system relablty does not satsfy the requrements, t s necessary to perform FMECA analyss on the system and fnd out the weak unts of the system, so as to conduct techncal mprovement and redundancy optmzaton n the focused manner and mprove system relablty to the requrements. Step 5. Techncal mprovement. Techncal mprovement means to select more reasonable technology accordng to the techncal problems n the system desgn when any weak unt of the system causes lower system relablty due to mproper relablty desgn of the system, so as to techncally mprove the system and enhance ts relablty. Step 6. Redundancy Optmzaton. Redundancy refers to the mantenance of redundant resources. When a system or ts equpment fals, the faled part can be replaced by the redundant part, n order to guarantee the normal completon of specfed functon as scheduled. Redundancy optmzaton means to select one or several modes of redundancy based on the features and propertes of system and add the redundant parts, n order to acheve the deal relablty of the system [9]. Redundancy optmzaton focuses on the falure of system relablty to satsfy the requrements after techncal mprovement, and optmzes the redundancy of the system. When techncal mprovement fals to enhance the relablty of system, redundant unts can be added to any weak unt whose lower relablty leads to the low relablty of system and mprove the relablty of weak unts, so as to enhance system relablty. Step 7. Judge whether system relablty satsfes the requrements after techncal mprovement and redundancy optmzaton. If satsfyng the requrements, the system wth optmzed relablty s confrmed as the fnal desgn scheme for system relablty. If not, optmzaton must be adjusted. III. CASE ANALYSIS A. Relablty Desgn Analyss A submarne free-runnng model does not receve systematc relablty desgn, so ts system relablty fals to satsfy the requrements of testng program and severely obstructs the test and study of the submarne free-runnng model system. As test perod s delayed, ts cost ncreases constantly. Therefore, t s analyzed n ths paper. 1) Msson profle A msson profle s constructed based on the relablty desgn analyss of the submarne free-runnng model system, as shown n Fg. 2. Due to lmted space, ths paper wll present the msson profle of drve subsystem for only three msson phases n the submarne free-runnng model system. In practce, t s necessary to fully descrbe the envronment parameters and workng state of each equpment n each phase among 13 msson phases ncludng course-keepng and 7 subsystems ncludng drve subsystem, n order to construct ther ntegrated msson profles. More detals are gven n Reference [10]. 2) Relablty modelng and estmaton Accordng to the msson profle of the submarne free-runnng model system, a system relablty block dagram s constructed to analyze the functonal relatons between equpment durng the desgn of system relablty, n order to provde the theoretcal bass for constructng the mathematc model of ts relablty and estmatng the relablty of system. A submarne free-runnng system contans 13 msson phases, so t should be constructed by followng the phased msson theory. The relablty block dagrams for three msson phases of free-runnng model system are presented for llustraton n Fg. 2-Fg. 4. The relablty block dagrams of the submarne free-runnng model are analyzed to buld ts mathematc model of relablty, and the unt relablty parameters gven by experts are utlzed to calculate the relablty of the submarne free-runnng model system. The estmaton s detaled n Reference [10]. The calculated relablty of ths system s 0.753, whch does not satsfy the requrements. As revealed n the practcal test, the test perod s changed from 15d to 45d due to low relablty, whch s very hazardous. Hence, relablty optmzaton s desgned for ths system to mprove ts relablty. 3) FMECA analyss The FMECA analyss process of AC servo drve n the system s llustrated n Table II. As revealed n ths analyss 324

3 Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 process, the severty of AC servo drve s Level I. FMECA analyss s carred out for all equpment unts n the system to dentfy the equpment wth hgh level of crtcalty as the weak unts of the system, ncludng AC servo drve, water tank (also known as atttude control), acoustc postonng system, water pump, batteres, hgh-pressure gas cylnder, water nlet (outlet) controller, exhaust controller and pressure, etc. Batteres On-board computer Pressure AC servo drve Inverter Master propulson motor Rudder Propeller Two-shaft tlt Drectonal gyroscope Underwater sound transducer Sync clock Water leakage Acoustc postonn g system Bow plane After plane Fg. 2. Relablty block dagram of course-keepng test. Batteres On-board computer Pressure AC servo drve Inverter Master propulson motor Front controller Rear controller Acoustc postonng system Water leakage Sync clock Underwater sound transducer Two-shaft tlt Drectonal gyroscope Hgh-pressure gas cylnder Fg. 3. Relablty block dagram of load rejecton test. Acoustc postonng system Batteres On-board computer Pressure Drectonal gyroscope Sync clock Water leakage Underwater sound transducer Drectonal gyroscope Fg. 4. Relablty block dagram of brake system. TABLE II: FMECA ANALYSIS OF AC SERVO DRIVE B. Relablty Optmzaton 1) Techncal mprovement The techncal mprovement of the submarne free-runnng model system s analyzed as follows: AC servo drve s used for frequency converson n the system. However, the submarne free-runnng model system employs batteres to supply the power for AC servo drve. As batteres supply the drect current, t s necessary to convert the drect current nto alternatng current through nverter. As nverter may generate strong electromagnetc nterference durng operaton, t affects the normal operaton of some equpment n the system and causes the low relablty of system. Ths s caused by electromagnetc compatblty. Thus, DC servo drve s used to replace AC servo drve n ths system, so nverter can be removed to elmnate the problem of electromagnetc compatblty and enhance the relablty of system. The test has proven the feasblty and effectveness of such techncal mprovement. In ths system, four water tanks are used to adjust the atttude devaton of free-runnng model durng navgaton by controllng ther water level. In the practcal test, t s very dffcult to approprately control the water level due to nsuffcent accuracy of judgment. Thus, only two out of 16 water levels, that s, dranng and fllng, can be realzed to adjust the navgaton atttude of free-runnng model n the system relablty desgn. Therefore, the system relablty s qute low. Ths s caused by mproper selecton of equpment. Based on the torque prncple, the controller wth a 100kg 1m horzontal torque and a 40kg 0.2m vertcal torque s desgned n the submarne free-runnng model to replace water tanks for adjustng navgaton atttude. A pressure s used to control the adjustment szes of two torques to the accuracy of mllmeter, so as to mprove the accuracy of judgment. The test has proven that ths optmzaton guarantees the accuracy of free-runnng model navgaton atttude and enhances the relablty of submarne free-runnng model system. Acoustc postonng devce can montor the navgaton state of free-runnng model. Durng test, every acoustc postonng devce can montor a range of 75 degrees, so t may easly overlook some areas and s unable to montor whether free-runnng model goes beyond the specfed testng waters. Ths lowers the relablty of free-runnng 325

4 Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 model. Ths s caused by selecton of equpment. Thus, 360-degree acoustc postonng devces can replace these devces and an emergency acoustc postonng system s added to montor whether free-runnng model goes beyond the specfed testng waters. When t goes beyond the specfed testng waters, emergency surfacng functon wll be mmedately trggered. TABLE III: FAILURE RATE PARAMETERS (IF THE RELIABILITY OF OTHER EQUIPMENT AND THE SYSTEM IS 1 WITHOUT ANY FAILURE) Parameter Phase 1 Phase 2 Phase 3 1 A h B 1 h C 1 h D 1 h E 1 h F 1 h G 1 h A 1 Note: h B 1 s the falure rate of batteres, h s the falure rate of hgh-pressure gas cylnder, D 1 h E 1 ( h C 1 h s the falure rate of water pump, )s the falure rate of water supply (dranage) controller, F 1 h G 1 s the falure rate of exhaust controller, and h rate of pressure. TABLE IV: EQUIPMENT PARAMETERS s the falure Parameter Vcm 3 mkg C Equpment A Equpment B Equpment C Equpment D Equpment E Equpment F Equpment G System Constrant After techncal mprovement, ths system can be put nto relablty analyss and ts msson profle and relablty block dagram are constructed. The relablty of the submarne free-runnng model system after techncal mprovement s estmated to be [10]. The estmaton of relablty proves that the relablty of the system s mproved but stll fals to satsfy the requrements. B. Redundancy Optmzaton Consderng that the relablty of the submarne free-runnng model system stll fals to satsfy the requrements after techncal mprovement, ths paper carres out the redundancy optmzaton for the system to mprove ts relablty. Snce the submarne free-runnng model system s an automatc navgaton model, the parallel redundancy optmzaton wth good feasblty and relablty s more sutable for ts redundancy desgn. 1) The relablty parallel redundancy model of free-runnng model s constructed as follows P P P P P P P P s 3A 3B 3C 1D 3G 3E 3F Note: P s system relablty; P s s the relablty of redundant module n the equpment n the phase ; A s batteres; B s hgh-pressure gas cylnder; C s water pump; D s water supply controller; F s dranage controller; F s exhaust controller; G s pressure. The formula of relablty redundancy s utlzed to determne the relablty of redundant module n the equpment n the phase. The relablty of redundant module for batteres A s calculated as follows: (1) 1 A 1 At1 m 1A 1 2At2 m 1 1A k 1A 1 At1 m 1 1A k 1A 1 At1 k 1A k 1A 3 1 A 1A 1A 2A 0 1 m 1 P [1 (1 e ) [1 (1 e ) ]( e ) (1 e ) C A m k k 1 A 0 t m k k 1 t m k k 1 [1 (1 e ) ]( e ) (1 e k t k k ) C m k 3A 3 1 A 1 A 2A 2A 2 1A 1A 2A 2A 2 2A 2A 1A 1A 1 m 1 (2) Smlarly, the relablty of redundant module n equpment B, C, D, E, F and G s calculated and substtuted nto the system relablty redundancy model to calculate the redundancy relablty of the system. Ths s detaled n Reference [10]. 2) Redundancy optmzaton model P s The system redundancy desgn for mprovng system relablty s actually a dfferent form of relablty dstrbuton. Ths method s effectve and feasble, but subject to a hdden trouble that f the ncorrect number of redundant unts s added, t may fnd t mpossble to satsfy all the system constrants (system cost, system volume, system weght and system relablty). Facng ths trouble, ths paper follows the concept of satsfacton to buld a system redundancy optmzaton model, n order to guarantee the maxmzaton of system relablty. Meanwhle, ths can keep the system wthn the range of other constrants, so as to acheve the most satsfyng effect of redundancy optmzaton. After combnng Table III and Table IV, a redundancy optmzaton model subject to four factors, namely, system 326

5 Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 relablty constrant, system volume constrant, system weght constrant and system cost constrant, s establshed based on the mssons and structure of the submarne free-runnng model system. The model s as follows: max F P V m C P, P s s f( P) 0, P s 1, 48000xA 22000xB 32000xC 500xD 500xE 800xF 300xG f( V) 0, 48000xA 22000xB 32000xC 500xD 500xE 800xF 300xG , 45xA 15xB 5xC xd xe 0.5xF 0.5xG 200 f( m) 0, 45xA 15xB 5xC xd xe 0.5xF 0.5xG 200 1, 20xA 8xB 2xC xd xe 3xF 4xG 90 f( C) C0 C,20xA 8xB 2xC xd xe 3xF 4xG (3) Equpment to Be Optmzed TABLE V: RELIABILITY OPTIMIZATION OF THE SUBMARINE FREE-RUNNING MODEL SYSTEM Prelmnary Desgn Techncal Improvement Redundancy Optmzaton AC servo drve 4 DC servo drve 4 DC servo drve 4 Water tank 4 Torque controller 1 Torque controller 1 45L water tank ballast 1 100L water tank ballast 1 100L water tank ballast acoustc postonng devce acoustc postonng devce acoustc postonng devce 30 Batteres 1 Batteres 1 Batteres 2 Hgh-pressure gas cylnder 1 Hgh-pressure gas cylnder 1 Hgh-pressure gas cylnder 2 Water pump 1 Water pump 1 Water pump 3 Water supply controller 1 Water supply controller 1 Water supply controller 5 Dranage controller 1 Dranage controller 1 Dranage controller 4 Exhaust controller 1 Exhaust controller 1 Exhaust controller 2 Pressure 1 Pressure 1 Pressure 2 Descrpton: In Equaton (3), the value of the comprehensve optmum F s between [0, 1], n whch 0 stands for dssatsfacton and 1 stands for the hghest satsfacton. Thus, f the value of the target functon F s closer to 1, the effect of optmzaton s more satsfyng. f (p), f (p), f (V), f (m), and f (C), are the sngle-objectve optmal functons for four constrants. If relablty satsfes the requrements, t s the fnal relablty. If t fals to satsfy the requrements, the optmal value s 0, and the optmal value of other constrants wthn the specfed range s 1, or t s 0. The weght coeffcents of constrants (P, V, m, C) are , , and , respectvely. The value s between [0, 1], and the sum of the weght coeffcents of all factors must be 1. The weghts of factors can be determned by employng the AHP method [11]. 3) Partcle swarm optmzaton algorthm There are lots of algorthms for ntellgent optmzaton. Ths paper employs the partcle swarm optmzaton algorthm sutable for solvng the problems n engneerng desgn to calculate the relablty of the system after redundancy optmzaton. Ths algorthm s featured by good adaptablty to varables and good ablty of global optmzaton. The partcle swarms wth 20 partcles and 7 partcles are selected. It has 100 evolutonary generatons and acceleraton constants c1=1.4 and c2=1.4. The algorthm obtans the optmzaton results after 100 random computatons. The Fg. 5 presents the teratve dagram after optmzaton. Obvously, the comprehensve satsfacton s stablzed at after 38 teratons. The results of parallel redundancy relablty optmzaton for the submarne free-runnng model test system are as follows: 1 for equpment A, 1 for equpment B, 4 for equpment C, 3 for equpment D, 1 for equpment E, 1 for equpment F and 2 for equpment G; system relablty s degree of optmzaton 优化度 Iteratve optmzaton results 优化结果迭代图 迭代次数 Iteraton Count Fg. 5. Dagram of optmzaton structure. IV. RESULT The optmzaton results reveal that the submarne free-runnng model test system mproves ts relablty of to after techncal mprovement and redundancy optmzaton subject to volume, weght and cost constrants. The fnal relablty satsfes the requrement for 0.995(llustraton n Table V). Ths proves that relablty optmzaton s feasble and effectve for the submarne free-runnng model system. V. CONCLUSION Ths paper carres out the relablty optmzaton desgn of 327

6 Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 free-runnng model subject to the parallel desgn condtons. In the practcal process, submarne free-runnng model test system s more and more complcated, so we wll further take nto account vote redundancy and standby redundancy, etc. n the future. REFERENCES [1] M. Alam and M. S. Ubad, Ttatve relablty evaluaton of reparable phased-msson systems usng Markova approach, Transactons on Relablty, vol. 35, no. 5, pp , 1986 [2] W. Kuo, V. R. Prasad, F. A. Tllman, and C. L. Hwang, Optmzaton Relablty Desgn: Basc and Clncal, Bejng: Scence Press, [3] J. Yu, T. Hu, and J. J. Yang, Relablty parallel redundancy optmzaton model of phased-msson systems, Fre Control & Command Control, vol. 18, pp , 2011,. [4] J. Yu, T. Hu, and J. J. Yang. Relablty redundancy optmzaton model of phased msson systems based on desrablty functon, Fre Control & Command Control, vol. 37, pp , [5] S. P. Chew, S. J. Dunnett, and J. D. Andrews, Phased msson modellng of systems wth mantenance-free operatng perods usng smulated Petr nets, Relablty Engneerng and System Safety, vol. 93, pp ,2008. [6] GJB450A, General Requrements for Equpment Relablty, Bejng: Natonal Defense Industry Press, 1990 [7] S. K. Zeng,T. D. Zhao, and J. G. Zhang, A Course of System Relablty Desgn Analyss, Bejng: Behang Unversty Press, 2001 [8] S. Y. Wang, Falure Mode and Effect Analyss (FMEA), Guangzhou: Zhongshan Unversty Press, [9] S.. Zhou and Z. Q. Wang, Calculaton of Warshp System Redundancy Optmzaton Based on Relablty, Chna Water Transport, vol. 2, pp , [10] S. Q. Lu, Relablty Optmzaton Desgn of Submarne Free-runnng Model System, Naval Unversty of Engneerng, Wuhan, Chna, [11] J. Yu, Study on Relablty Redundancy Optmzaton of Phased Msson System, Naval Unversty of Engneerng, Wuhan, Chna, J. J. Yang was born n Chna n He receved hs Ph.D. n system engneerng from Navy Unversty of Engneerng, Wu Han, Chna n Dr. Yang s currently an assocate professor of Department of Management Scence at Naval Unversty of Engneerng. He has performed and drected research on the development and applcaton of relablty analyses of complex systems. W. J. L was born n Chna n She s currently a postgraduate student n management scence and engneerng, Navy Unversty of Engneerng, Wu Han, Chna. 328