Sequential Condition Diagnosis for Centrifugal Pump System Using Fuzzy Neural Network

Transcription

1 eural Informaton Processng Letters and Revews Vol., o. 3, March 007 LETTER Sequental Condton Dagnoss for Centrfugal Pump System Usng Fuzzy eural etwork Huaqng Wang and Peng Chen Department of Envronmental Scence & Technology, Me Unversty 577 Kurmamachya-cho, Tsu-cty, Me-Pref, , Japan Emal: Correspondng author: Tel & Fax: (Submtted on January 6, 007) Abstract Ths paper proposed a sequental dagnoss method usng fuzzy neural network called partally-lnearzed neural network (P), by whch the fault types of rotatng machnery can be precsely and effectvely dstngushed at an early stage on the bass of the possbltes of symptom parameters. The non-dmensonal symptom parameters (PS) n tme doman are defned for reflectng the features of tme sgnals measured for the fault dagnoss of rotatng machnery. The synthetc detecton ndex (SDI) s also proposed to evaluate the senstvty of SPs for detectng faults. The practcal example of condton dagnoss for detectng and dstngushng fault states of a centrfugal pump system, such as cavtaton, mpeller damage and unbalance whch often occur n a centrfugal pump system, are shown to verfy the effcency of the method proposed n ths paper. Keywords Sequental Dagnoss, Partally-lnearzed eural etwork, Symptom Parameter, Centrfugal Pump, Rotatng Machnery. Introducton In the feld of machnery dagnoss, vbraton sgnals are often used for detecton of mechancal fault and dscrmnaton of fault types. Machnery dagnoss depends largely on the feature analyss of vbraton sgnals measured for condton dagnoss, so t s mportant that the feature of the sgnal should be senstvely extracted when fault occurs at the state change of a machne. However, the feature extracton for the fault dagnoss s dffcult snce the vbraton sgnals measured at a pont of the machne often contans strong nose [-3]. In most cases of condton dagnoss for plant rotatng machnery, nformaton for dstngushng faults s ambguous because defnte relatonshps between symptoms and fault types cannot be easly dentfed [4]. The man reasons can be explaned as follows: () It s dffcult to dentfy the symptom parameters for dagnoss by whch all fault types can be dstngushed perfectly. () In an early stage of a fault, the effect of nose n the sgnal measured for the dagnoss s so strong that the symptom of the fault s not evdent. Furthermore, although many method of condton dagnoss for rotatng machnery usng neural networks () have been reported by many studes, they almost dealt wth the dscrmnaton of fault types [5-0]. The problems of the condton dagnoss usng conventonal are that the can not reflect the possblty grades of the ambguous dagnoss problems, and t wll never converge when the symptom parameters nputted n the st layer have the same values n dfferent states []. Based on the above reasons, n order to mprove the effcency of fault dagnoss and dstngush fault types at an early stage, ths paper proposes a sequental dagnoss method for rotatng machnery usng fuzzy neural network by whch the state of machnery can be automatcally udged on the bass of the possblty grades of normal and each abnormal state. Snce the relatonshp between the values of the symptom parameters and fault types s ambguous due to the effect of nose n the tme sgnals, we use the partally-lnearzed neural network to solve the ambguous problem of the fault dagnoss. on-dmensonal symptom parameters (SP) n tme doman are defned to reflect the features of tme sgnal measured for the fault dagnoss of rotatng machnery. The synthetc detecton ndex (SDI) s also proposed to evaluate the senstvty of SPs for detectng and 4

2 Sequental Condton Dagnoss for Centrfugal Pump System Huaqng Wang and Peng Chen (a) The experment system of pump (b) The equpment of centrfugal pump on feld Fgure. The centrfugal pump system for the condton dagnoss dstngushng faults. In ths paper, practcal example of fault dagnoss of a centrfugal pump system wll verfy that the method s effectve. The method proposed n ths paper can also be appled to other type of rotatng machnery.. Centrfugal Pump System for Fault Dagnoss The centrfugal pump system for the condton dagnoss s shown n Fgure. The states to be dagnosed for the centrfugal pump system are normal state, cavtaton, mpeller damage and unbalance. Cavtaton phenomenon s one of the sources of nstablty n a centrfugal pump. Cavtaton can cause more undesrable effects, such as deteroraton of the hydraulc performance (drop n head-capacty and effcency curves), damage of the pump by pttng and eroson and structure vbraton and resultng nose []. To prevent the occurrence of the cavtaton, we have to detect t at early stage of cavtaton phenomenon from the vbraton sgnal of a pump system. There were sx accelerometers used to measure vbraton sgnals for the detecton of faults. The locatons of the sensors are shown n Fgure. Two sensors were put at the pump nlet, another two at the pump outlet and one sensor at the motor and pump housng respectvely. The samplng frequency of sgnal measurement s 50 khz, and the samplng tme s 0s. The vbraton sgnals n each state shown n Fgure 3, are measured at a constant speed (3000rpm) and constant flow rate (9m 3 /h) of water. Low-pass flter wth 500Hz cut-off frequency s used to cancel the nose. The vbraton sgnals measured n each state after fltraton are shown n Fgure on-dmensonal symptom parameter (SP) Fgure. The locaton of the sensors 3. Symptom Parameters for Fault Dagnoss Many symptom parameters have been defned n the pattern recognton feld [3]. Here, 0 of nondmensonal symptom parameters (SPs) n tme doman, commonly used for the fault dagnoss of plant 4

3 eural Informaton Processng Letters and Revews Vol., o. 3, March 007 Fgure 3. Orgnal sgnals measured n each state. (a) ormal state, (b) Cavtaton state, (c) Impeller damage, (d) Impeller unbalance Fgure 4. Sgnals after fltraton. (a) ormal state, (b) Cavtaton state, (c) Impeller damage, (d) Impeller unbalance machnery, are consdered. Here, σ p = (Rate of varaton). () x abs σ = ( x x) ( ) (Standard devaton) () = x x = x = abs = x = 3 p x x) = 4 p3 x x) = (Mean value) (3) (Absolute mean value) (4) 3 = ( σ (Skewness) (5) 4 = ( σ (Kurtoss) (6) p 4 = x p x abs (7) p 5 = xmax x (8) p p6 = σ p x p (9) p7 = σ L x L (0) p8 = x σ () = 9 = x σ = p () 43

4 Sequental Condton Dagnoss for Centrfugal Pump System Huaqng Wang and Peng Chen where x p s the average of peak values of log( x + ) =! p 0 = (3) log( σ ) x (=~), x max s the average of 0 peak values (from top peak value to tenth value) of x (=~), σ p s the standard devaton of peak values of x (=~), and x L and σ L are the average and standard devaton of the valley values of x (=~), respectvely. The sgnals are normalzed by followng formula before the SPs are calculated, x ' μx' x = (4) σ x' Here, x ' s the sgnal after fltraton, μ and x' σ are the mean and standard devaton of x' x ', respectvely. 3. Senstvty evaluaton of symptom parameter The qualty of a symptom parameter (SP), whch wll be used to dstngush two states, such as normal or abnormal state, s derved n the followng way. Supposng that x and x are the SP values calculated from the sgnals measured n state and state respectvely, and they conform respectvely to the normal dstrbutons ( μ, σ ) and ( μ, σ ). Here, μ andσ are the average and the standard devaton of the SP. The larger the value of x x s, the hgher the senstvty of dstngushng the two states by the SP s. Because z = x x s conform to the normal dstrbuton ( μ μ, σ + σ ), we have the densty functon about z [4]. { z ( μ μ)} f ( z) = exp (5) π ( σ + ) ( σ + σ ) σ Here, μ μ (we can obtan the same concluson when μ μ ). The probablty of x < x can be calculated by the followng formula: = 0 0 f z) P ( dz (6) Here, -P 0 s called Dstncton Rate (DR). Wth the substtuton ( μ μ) u = z (7) σ + σ to formula (5) and (6), the P 0 can be obtaned by P0 = DI u exp( ) du π (8) Here, DI (Dstncton Index) s calculated by μ μ x x DI = or = (9) σ + σ σ + σ It s obvous that the larger the value of DI, the larger the value of "Dstncton Rate (DR=-P 0 )" wll be, and therefore, the better the SP wll be. So DI can be used as the ndex of the qualty to evaluate the dstngushng senstvty of SP. If the number of symptom parameters used for dagnoss s M, the synthetc detecton ndex (SDI) s defned as follows. SDI = M = DI. (0) 44

5 eural Informaton Processng Letters and Revews Vol., o. 3, March 007 Fgure 5. Flow chart of sequental dagnoss for pump 4. Sequental Dagnoss for Centrfugal Pump System In order to dstngush faults effectvely, a sequental dagnoss method s proposed as shown n Fgure 5. The nference of the sequental dagnoss s follows. Table shows the DIs of SPs (p and p ) for each step to dstngush the two knds of state respectvely. Snce all of those DIs are larger than.4, all of the detecton rates (DR) are larger than 99%. Table. DI of SPs for Each Step (a) For the frst step (b) For the second step (c) For the thrd and fourth step C D U D U U p p p p p p In the frst step, f the possblty grades of normal state () and abnormal state (A) are g and g A, respectvely, and g > g A, then the state s udged as normal state (), else proceed to the next step. In the second step, f the possblty grades of cavtaton (C) and another fault (A) are g C and g A, respectvely, and g C > g A, then the state s udged as cavtaton (C), else proceed to the next step. In the thrd step, f the possblty grades of mpeller damage (D) and another fault are g D and g A, respectvely, and g D > g A, then the state s udged as mpeller damage (D), else proceed to the next step. In the fourth step, f the possblty grades of unbalance (U) and another fault are g U and g UA, respectvely, and g U > g UA, then the state s udged as unbalance (U), else t wll be udged as unknown abnormal state (UA). In ths paper, two best SPs p and p, are selected by formula (9) for each state of the sequental dagnoss respectvely. The selecton results of the SPs are p 6 and p 9 : for the frst step to dstngush normal state from abnormal states; p and p 7 : for the second step to dstngush cavtaton from other abnormal states; p 9 and p 0 : for the thrd step to dstngush mpeller damage from other abnormal states; p 9 and p 0 : for the fourth step to dstngush unbalance from unknown state. The tranng data for the learnng of fuzzy neural network can be obtaned by the values of SP calculated by the vbraton sgnal measured n each state. If the p and p are selected for dstngushng state k from another state, and ther mean value and standard devaton are p k, p k and s k, s k respectvely, the tranng data for dstngushng state k form another state are calculated as follows. If pk sk < p < pk + s and p k k s k < p < p k + s k, then the state s udged as state k wth 00% possblty, else the state s udged as another state. Accordng to the method obtanng tranng data as stated above, Fgure 6, Fgure 7, Fgure 8 and Fgure 9, show the tranng data for dstngushng normal state, cavtaton, mpeller damage, unbalance and unknown state respectvely. These tranng data wll be used for the learnng of the fuzzy neural network. 45

6 Sequental Condton Dagnoss for Centrfugal Pump System Huaqng Wang and Peng Chen Fgure 6. Tranng data for dstngushng normal state from abnormal state Fgure 7. Tranng data for dstngushng cavtaton from another fault Fgure 8. Tranng data for dstngushng mpeller damage from another fault Fgure 9. Tranng data for dstngushng unbalance from another unknown fault 5. Fuzzy eural etwork for the Dagnoss and Verfcaton 5. Partally-lnearzed neural network (P) In the case of a conventonal neural network () bult for pattern recognton n fault dagnoss, the factors entered nto the nput (st) layer of the network are several features or symptom parameters. Each unt n the last layer exclusvely outputs two values ( or 0) for expressng categores of pattern (or state) [5-7]. Though the value between 0 and may appear n the output layer when executng a learnt, t s dffcult to accurately explan the meanng of the value as a result of the pattern recognton or condton dagnoss. For explanng ths fact, Fgure 0 shows a smple example for dentfyng possblty of state (β) wth one symptom parameter p. If an has learnt the values of tranng data shown by pont, t wll output non-lnear values shown by. In 46

7 eural Informaton Processng Letters and Revews Vol., o. 3, March 007 Possblty of state ( ß) :Learnt ponts :Outputted value by convetonal 00% :Outputted value by P 80% 60% 40% 0% Value of symptom parameter p The case of non-lnear (Conventonal ) p β Learnng 0% Dagnoss 80% Learnng 3 40% Dagnoss 4 0% Learnng 5 60% Thecaseoflnear (P) p β Learnng 0% Dagnoss 30% Learnng 3 40% Dagnoss 4 50% Learnng 5 60% Fgure 0. A smple example for comparng between and P order to mprove the absurd phenomenon, we partally lnearzed the non-lnear part n the, and call t partally-lnearzed neural network (P) [8]. In Fgure 0, the P output the lnear values shown by accordng to the learnt ponts shown by. The P s appled to dagnose rotatng machnery, and t s explaned as follows. The neuron numbers of m-th layer of a s m. The set ) (, ) X ( = { X } expresses the pattern nputted to the st layer and the set ( M ) ( M, k) X = { X } s the tranng data for the last layer (M-th layer). Here, = to P, = to, k = to M, and, (, ) X : The value nputted to the -th neuron n the nput ( st ) layer, ( M, k ) X : The output value of k-th neuron n the output (M-th) layer. () (M ) Even f the converge by learnng X and X, t cannot adequately deal wth the ambguous ()* (M )* (M )* relatonshp between new X and X, whch have not been learned. In order to predct X accordng to ()* the probablty dstrbuton of X, partally lnear nterpolaton of the s ntroduced as Fgure, we called t "Partally-lnearzed eural etwork (P)". () (M ) In the whch has converged by the data X and X, the symbols are used as follows. m ( m, t) X : The value of t-th neuron n the hdden (m-th) layer; t = to m ( m ) W : The weght between the u-th neuron n the m-th layer and the v-th neuron n the (m+)-th layer; uv to M ; u = to ; v = to = m m+, )* If all of these values are remembered by computer, when new values ( u (, u) (, u)* (, u) X ( X < X < X ) are + nputted to the frst layer, the predcted value of v-th neuron (v= to m ) n the (m+)-th layer (m= to M-) wll estmated by X m ( m) ( m, u) ( m, u) ( m+, v) ( m+, v) { Wuv ( X + X )}( X + X ) ( m+, ν ) ( m+, ν ) μ= 0 = X + () m ( m) ( m, u) ( m, u) Wuv ( X + X ) μ= 0 In the above way, the sgmod functon s partally lnearzed as shown n Fgure. If a functon must be learned, the P wll learn the ponts ndcated by the symbols shown n Fgure. When new data (s ', s ') are nput nto the converged P, the values ndcted by the symbols correspondng to the data (s ', s ') wll be quckly dentfed as P e. Thus, the P can be used to deal wth ambguous dagnoss problems. The new data (s ', s ') nputted nto the converged P, whch are not learned by the P for recognton, must satsfy the followng condton, s < s ' < s and s < s < s () (mn) (max) (mn) ' (max) 47

8 Sequental Condton Dagnoss for Centrfugal Pump System Huaqng Wang and Peng Chen Fgure. The partal lnearzaton of the sgmod functon P S P e S ' c a d b e S ' S Here, s (mn), s (mn) and s (max) been learned by the P. Therefore, n ths paper the verfy values of SPs ( k, must satsfy the followng condton, k(mn) Fgure. Interpolaton by the P, s (max) are the mnmum and maxmum value of s and s, whch have * k(max) * p and k(mn) * p ) nput to the P for dstngushng the state * P < P < P and P < P < P (3) k(max) Here, p k (mn), p k (mn) and p k (max), p k (max) are the mnmum and maxmum values of p and p respectvely. Fgure 3 shows Ps bult for the fault dagnoss of a centrfugal pump system on the bass algorthm of sequental dagnoss shown n Fgure 5. Fgure 3. P for the fault dagnoss of a centrfugal pump system 5. Dagnoss and verfcaton The tranng data for the P learnng are show n Fgure 6, Fgure 7, Fgure 8 and Fgure 9. The P are quckly convergent when learnng the tranng data. We sued the data measured n each known state, whch has not been learned by the P to verfy the dagnostc capablty of the P. Examples of fault dagnoss by the learnt P show n Table, 3, 4 and 5. In the cases of the verfcatons, the data nput to the learned P have 48

9 eural Informaton Processng Letters and Revews Vol., o. 3, March 007 not been traned, and the P correctly and quckly udged the states (: normal state, C: cavtaton, D: mpeller damage, U: unbalance, A: another fault, UA: unknown abnormal state), whch are expressed by the possbltes g, g C, g D, g U, g A and g UA. Accordng to the test results, the probablty grades output by the P show the correct udgment n each state. Therefore, the P can precsely dstngush the type of pump system fault on the bass of the possblty dstrbutons of symptom parameters. Table. Verfcaton Results for the Frst Step Table 3. Verfcaton Results for the Second Step p 6 p 9 g g A Judge p p 7 g C g A Judge C C C A A A A A A Table 4. Verfcaton Results for the Thrd Step Table 5. Verfcaton Results for the Fourth Step p 9 p 0 g D g A Judge p 9 p 0 g U g UA Judge D U D U D U A UA A UA A UA 6. Conclusons In order to mprove the effcency of the condton dagnoss for plant rotatng machnery and dstngushng fault types at an early stage, ths paper proposed a sequental dagnoss method for rotatng machnery usng fuzzy neural network by whch the state of machnery can be automatcally udged on the bass of the possblty grades of normal and each abnormal state. Snce the relatonshp between the values of the symptom parameters and fault types s ambguous due to the effect of nose n the tme sgnals, the partally-lnearzed neural network (P) as a fuzzy neural network and the possblty grade were appled to solve the ambguous problem of the condton dagnoss. on-dmensonal symptom parameters (SP) n tme doman were defned, whch can reflect the characterstcs of tme sgnal measured for the fault dagnoss of rotatng machnery. The synthetc detecton ndex (SDI) was also proposed to evaluate the senstvty of SPs for detectng and dstngushng faults. The practcal example of dagnoss of a centrfugal pump system for detectng and dstngushng fault states, such as cavtaton, mpeller damage and unbalance whch often occur n pump, were shown to verfy the effcency of the method proposed n ths paper. The method proposed n ths paper can also be appled to other type of rotatng machnery. References [] B. Lu, S.-F. Lng, On the selecton of nformatve wavelets for machnery dagnoss, Mechancal Systems and Sgnal Processng, Vol. 3,o., pp. 45-6, 999. [] L. Jng, Q. Langsheng, Feature extracton based on morlet wavelet and ts applcaton for mechancal fault dagnoss, Journal of Sound and Vbraton, Vol. 34, o., pp , 000. [3] Q.B. Zhu, Gear fault dagnoss system based on wavelet neural networks, Dynamcs of Contnuous Dscrete and Impulsve Systems-seres A-Mathematcal Analyss, Vol. 3: pp , Part Suppl S,

10 Sequental Condton Dagnoss for Centrfugal Pump System Huaqng Wang and Peng Chen [4] H. Matuyama, Dagnoss Algorthm, Journal of JSPE, Vol.75, o.3, pp.35-37, 99. [5] B. Samanta, K. R. Al-Balush, Artfcal neural network based fault dagnostcs of rollng element bearngs usng tme-doman features, Mechancal Systems and Sgnal Processng, Vol. 7, o., pp , 003. [6] A. C. McCormck and A. K. and, Real-tme classfcaton of the rotatng shaft loadng condtons usng artfcal neural networks, IEEE Transactons on eural etworks, Vol. 8, pp , 997. [7] B. Samanta, K. R. Al-Balush, S. A. Al-Aram, Artfcal neural networks and genetc algorthm for bearng fault detecton, Soft Comput, Vol. 0, o. 3, pp. 64-7, 006. [8] R. Q. L, J. Chen, X. Wu, Fault dagnoss of rotatng machnery usng knowledge-based fuzzy neural network, Appl. Math. Mech-Engl., Vol. 7, o., pp , 006. [9] V. Schetnn, J. Schult, Learnng polynomal networks for classfcaton of clncal electroencephalograms, Soft Comput, Vol. 0, o. 4, pp , 006. [0] R.M. Fang, Fault dagnoss of nducton machne usng artfcal neural network and support vector machne, Dynamcs of Contnuous Dscrete and Impulsve Systems-seres A-Mathematcal Analyss, Vol. 3: Part Suppl. S, 006. [] C. Bshop, M. I, eural etworks for Pattern Recognton, Oxford Unversty Press, 995 [] M. Cudna, Detecton of cavtaton phenomenon centrfugal pump usng audble sound, Mechancal Systems and Sgnal Processng, Vol. 7, o. 6, pp , 003. [3] K. Fkunaga, Introducton to Statstcal Pattern Recognton, Academc Press, 97. [4] J. S. Bendat, Probablty Functon for Random Processes: Predcton of Peak, Fatgue Damage, and Catastrophc Falure, ASA Report CR-33 (969) [5] M. Tao, Y.L, and J. Fang, Study on vacuum system fault dagnoss based on fuzzy neural network, Dynamcs of Contnuous Dscrete and Impulsve Systems-seres B-Applcatons & Algorthms, Vol.3: pp. 9-96, Part Suppl. S, 006. [6] A. Saxena and A. Saad, Evolvng an artfcal neural network classfer for condton montorng of rotatng mechancal systems, Appled Soft Computng, Vol. 7, o. : pp , 007. [7] H. Su and K.T. Chong, Inducton machne condton montorng usng neural network modelng, IEEE Transactons on Industral Electroncs, Vol. 54, o. : pp. 4-49, 007. [8] P. Chen, X. Lang and T. Yamamoto, Rough sets and partally-lnearzed neural network for structural fault dagnoss of rotatng machnery, Advances n eural etworks-is 004, PT Lecture ote n Computer Scence 374: , Sprnger, 004. Huaqng Wang receved a B.S. degree and a M.S. degree from Beng Unversty of Chemcal Technology, Chna n 995 and 00. From 995 to 005, He was a teacher of School of Mechancal & Electrcal Engneerng, Beng Unversty of Chemcal Technology. He s currently a doctoral course student of the Department of Envronmental Scence & Technology, Me Unversty, Japan. Hs research nterest ncludes fault dagnoss of rotatng plant machnery and sgnal processng. Peng Chen graduated from the doctoral course of the Kyushu Unversty n 990, and currently a professor of the Department of Envronmental Scence & Technology, Me Unversty, Japan. Hs research nterest ncludes condton dagnoss of plant machnery, nformaton processng and sgnal processng. (Home page: 50