35 Sustainable Marine Structures | Volume 02 | Issue 02 | July 2020 Distributed under creative commons license 4.0 DOI: https://doi.org/10.36956/sms.v2i2.330 Sustainable Marine Structures http://ojs.nassg.org/index.php/sms ARTICLE New Method for Building Vector of Diagnostic Signs to Classify Technical States of Marine Diesel Engine by Torsional Vibrations on Shaft-Line Do Duc Luu1* Cao Duc Hanh1 Nguyen Xuan Tru2 1. Vietnam Maritime University, Hai Phong, Vietnam 2. Naval Technical Institute, Hai Phong, Vietnam ARTICLE INFO ABSTRACT Article history Received: 24 March 2021 Accepted: 9 April 2021 Published Online: 15 April 2021 Vector of diagnostic signs (VDS) using torsional vibration (TV) signal on the main propulsion plant (MPP) is the vector of z maxima (or minima) values of the TV signal in accordance with the cylinder firing orders. The technical states of the marine diesel engine (MDE) include R= z+1 classes and are presented in z-dimensional space coordinate of VDS. The presentation of Dk, k=1÷R using z diagnostic signs (Vi, i=1÷z) is nonfigurative and quite complicated. This paper aims to develop a new method for converting VDS from z-dimensional to 2-dimensional space (two-axes) based on the firing orders of the diesel cylinders, as an equivalent geometrical sign of the all diagnostic signs. The proposed model is useful for presenting a technical state Dk in two-dimensional space (x, y) for better visualization. The paper verifies the simulation of the classification illustration of the 7–state classes for the MDE 6S46- MCC, installed on the motor vessel (MV) 34000DWT, using the new above mentioned method. The seven technical state classes (for 6-cylinder MDE, z=6) are drawn separately and visually in the Descartes. The received results are valuable to improve smart diagnostic system for analyzing normal/misfire states of cylinders in operation regimes. Keywords: Two-dimensional vector of diagnostic signs of torsional vibration signal New model of VDS for misfiring diagnostics of MDE Vi s i o n d i a g n o s t i c s o f M D E b y t o r s i o n a l vibration signal 1. Introduction The TV signal (TVS) contains much important infor- mation about the misfiring / normal working conditions of every cylinder in the multi-cylinder marine diesel engine (MDE) [1]. The characteristics of the TVS identifying in time or frequency domains are used to estimate the tech- nical states of the diagnostic object (DO) and called diag- nostic signs. In the works [1, 2, 4], the VDS are formed from the maxi- ma (VA) or minima (VB) of the TVS correspondence with firing order of each cylinder. The size of the VDS is equal to the number of cylinders in the DO. The z-dimensional VDS are used for classifying the technical states (normal / misfiring conditions) of every DME cylinder, in this case DO is 6 cylinder MDE type 6S46 MCC-7 of MAN-BW *Corresponding Author: Do Duc Luu, Vietnam Maritime University, Hai Phong, Vietnam; Email: luudd@vimaru.edu.vn 36 Sustainable Marine Structures | Volume 02 | Issue 02 | July 2020 Distributed under creative commons license 4.0 manufactory. It’s hardly to illustrate every technical state Dk, k=1÷R in z-dimensional space V= [V1…Vz] of the VDS (V=VA or V=VB; VA= [VA1... VAz] or VB= [VB1... VBz]) because imagining mathematic models in the multi-dimensional space is quite complicated. In many cases, the illustration of Dk (V1, V2 … Vz) is divided in to a number of a pair of two-dimensional space (Vi, Vj); i ≠j, i=1÷z; j=1÷z [4]. To overcome the above-mentioned presentation incon- venience, the authors convert VDS from z-dimensional to 2-dimensional space. From there, the diagnosis and identi- fication processes could be solved in a more visualization way and easily applied in real-world diagnostic problems. 2. Research Method 2.1 Modeling New Two –dimensional VDS from VA or VB Let us assume that the TV signals are simulated (or measured) in a working cycle of MDE containing z cyl- inders. The signal normally has a number of samples, N=1024 or 2048. The signal is divided in to z parts, and every part has Nc = [N/z] samples. In the part in accor- dance with firing order of every cylinder, we find the maximal and minimal values. We conduct the VA and VB vector of the diagnostic signs from these values. The firing order of every cylinder is given in the MDE technical documents, such as the 6S 46MCC shows the order [6]: 1-5-3-4-2-6. The parameter features (VAm, VBm) of mth –cylinder are de-phased αm (degree) in ac- cordance with the first cylinder (two-stroke diesel engine): α1=0; α5= 60 o; α3= 120 o; α4= 180 o; α2= 240 o; α6= 300 o or in radian: α1=0; α5= π/3; α3= 2π/3; α4= π; α2= 4π/3; α6= 5π/3. In generally, we conduct the de-phase vector of the working cylinders α: α = [0, α2…αz], (radian) (1) The new diagnostic vectors VN are calculated as fol- low: z z x i=1 i=1 VN = V(i)cos( (i) VN = V(i)sin( (i)); ) y α α∑ ∑ (2) Where, V= [V (1), V (2) … V (z)], and V=VA or V=VB. Every class Dk is written by two reference parameters: the mean vector µk and the covariance matrix Kk in accor- dance with the two-dimensional VDS VN= (VNx, VNy), k=1÷R. Illustration of the cylinder working conditions in the Descartes (VNx,VNy). The z –cylinder MDE is classified into R =(z+1) tech- nical classes Dk as above mentioned for diagnostics of the normal or misfiring state of cylinder in accordance with the Rules for Classification and Construction of Sea-going Ships [7]. The block scheme for building the new VDS VN (VNx, VNy) and illustrating the R states via the 2-dimensional space is shown in Figure 1. Figure 1. Block scheme for building new VDS in two-di- mensional space VN(x, y) DoE –Design of Experiments, CF –Vector of the z fir- ing coefficients, MDE as a DO; VA, VB –vector of diag- nostic signs (z elements of maxima or minima);VN –new vector of two equivalent elements in two-dimensional space (x,y) In measuring process, we supposed that the revolution n (rpm) and the Load Index (LI) are fixed. However, the real measured signal has some random components and measuring errors. Therefore, we conducted the measuring process ten repeated times with random noises, and the measurement device error is ±5%. This ±5% is bigger than almost thresholds of precise measuring devices in the market today [4]. The main controlling parameters of the technical states of all cylinders are firing coefficients, which are written in the form of vector CF = [Cf (1)… Cf (z)]. The real fir- ing processes are random and for diagnostics model, we assume that firing coefficient Cf (k) is varied with ±5% in accordance with the mean value. In the case of normal working, the Cf = [0.9, 1.0], and with the misfiring state, Cf = [0.0, 0.1]. For every cylinder there are three levels of one firing regime to be examined. The design of experiments has Nn revolution regimes, for example nmean = 75 rpm, the ∆N=5%.75 =3.75. We would carry out the numerical experiments at Nd = {71÷ 79} (rpm), for example at the nmean = 75 rpm, Nd = 9 ex- periments. The design of experiments has R= (z+1) technical state classes. Thus, we conduct Ns = 3 z experiments for every revolution regime. For example, z=6, Ns = 729. The total number of experiments of the DoE is N=Nd*Ns. Let us assume z =6, and we conduct each revolution 10 times (in accordance with the real measur- ing repeat times, Nd =10), the total N is 10* 729 =7290 (experiments). After building database from the measured (simulated) TVS, the authors analyze TVS to find the VA or VB, and DOI: https://doi.org/10.36956/sms.v2i2.330 37 Sustainable Marine Structures | Volume 02 | Issue 02 | July 2020 Distributed under creative commons license 4.0 finally to draw the new VN-database for the R= (z+1) = 7 states. The VN–database is drawn visually in the two-dimensional (VNx, VNy) axes, in accordance with Equation (2). To diagnose the misfire of any cylinder in the multi-cyl- inder MDE by classification methodology we have to make the new standard diagnostic characteristics and new diagnostic classifier using the new vector of diagnostic signs VN(x, y). 2.2 Modeling Standard Characteristics of MDE on the New VDS VN(x,y) The technical states of MDE are grouped in to R=z+1 classes, written with the symbol Dk, k=1…R. Every class has the called referenced (standard) characteristic to iden- tify one with other [1]: (3) The covariance matrix Kk is calculated. (4) 2.3 Diagnostics Classification of MDE on the New VDS VN(x,y) The current considered state Dc is presented in the simi- lar form with Equation (3) in the following [1, 4]: (5) The solution of the diagnosis is finding minimum of Mahalanobis distance dck from distance set: (6) The Mahalanobis distance between two classes “c” and “k” is defined below. (7) Where, Kck – compound covariance matrix of the two matrixes Kc and Kk. 3. Cases Study: Building the Two-dimension- al VDS for Diagnosing the 6S46 MCC The MDE type 6S46 MCC is installed on the general cargo motor vessel with 34000 DWT (MV 34000 DWT). The TVS of the ship MPP are conducted and supposed to DNV (register) approve by HuDong manufactory [6]. The method and software for automatic torsional vibration calculation (SATVC) are developed at Vietnam Maritime University [0, 5] for this MPP on LabView platform. The SATVC has the features to automatically calculate one of the 7 normal/ misfiring states of the 6 cylinders with rev- olution regimes N= [0.4, 1.2] NMCR, where NMCR -max- imal continuous rate (rpm) and in this case of MV 34000 DWT, NMCR =129 rpm. For diagnosing technical states normal / misfiring, the diagnostic revolution regimes have to be far from reso- 　　　　 (a)　　　　　　　　　　　　　　　　　　　　　　　(b) Figure. 2 Illustrating the seven classes of the MDE 6S46MCC on MV 34000 DWT via new two-dimensional space (VNx, VNy) in accordance with VDS VA (a) and VB (b) DOI: https://doi.org/10.36956/sms.v2i2.330 38 Sustainable Marine Structures | Volume 02 | Issue 02 | July 2020 Distributed under creative commons license 4.0 nance revolution ranges of the torsional vibrations of the MPP because in the resonance or near–resonance revolu- tions the TVS are quite excited and too large. Therefore we have to calculate the freedom TV for the MPP. Table 1. Freedom resonances of the MPP on the MV 34000 DWT The resonances of the first and second modes of the MPP on the MV 34000 DWT are also defined by the SAT- VC, especially by the freedom torsional vibration module. The results of the freedom TVs are shown below[3,4]: n01=337.16 rpm; n02= 1436.02 rpm. The revolutions of the DME on the MV 34000 DWT at the interval [52, 155] rpm are resonances that are shown in Table 1. The interval Nd = [71, 80] is selected for diagnostic revolution regimes. The two-dimensional illustrations of the seven techni- cal normal or misfiring conditions in cylinders of the DO are shown in Figure 2 using the simulation software which is developed in LabView by authors. Figure 2(a) shows that when using the maxima VA of the TVS, the pairs of state classes: (D0 and D4), (D2 and D4), and (D6 and D2) couldn’t be separated fully in new two-dimensional VNA (VNAx, VNAy). However, Figure 2(b) shows that using the minima VB of the TVS, the pairs of state classes are very well separated in the new two-dimensional VNB (VNBx, VNBy) 4. Conclusions Using the new method for building two-dimensional VDS has the advantages in classifying R technical states of MDE. The authors applied the new approach for diag- nosing the technical sates in the two -axes Descartes (VNx and VNy) using the maxima and minima VDS of the shaft- line TVS. The results show that the minima VDS produc- es the better classification performance than the maxima VDS. References [1] Do Duc Luu: Dynamics and diagnostics of marine diesel engine by vibration technique. Publisher “Transport”, Ha Noi (2009). [2] Do Duc Luu, et all (2020): Regressive models for condition diagnosing marine diesel engine by tor- sional vibrations on propulsion shaft-line. Interna- tional Journal of Modern Physis B. ISSN 02179849. (5 pages). © World Scientific Publishing Company. DOI: https://doi.org/10.1142/S0217979220401268. [3] Do Duc Luu and Cao Duc Hanh (2021). Automatic Calculation of Torsional Vibrations on Marine Propul- sion Plant Using Marine Two-Stroke Diesel Engine: Algorithms and Software. Journal of The Institution of Engineers (India): Series C. ISSN 2250-0545 Volume 102 Number 1. pp. 51-58. https://doi.org/10.1007/s40032-020-00626-y. [4] Do Duc Luu, Cao Duc Hanh, et al. (2021): Smart diagnostics for marine diesel engines using tor- sional vibrations signals on the ship propulsion shaft – line. Naval Engineer Journal. ISSN: 0028- 1425. March 2021| No 133-1. pp. 143-153 https:// w w w. i n g e n t a c o n n e c t . c o m / c o n t e n t o n e / a s n e / nej/2021/00000133/00000001/art00026. [5] Luong Cong Nho, Do Duc Luu, et al.: Researching, building simulation of main propulsion plant and main switch-board on the marine cargo ship. Nation- al Independent Project on Science and Technology with ID. DTDL.CN-14/15 carried out in Vietnam Maritime University, Hai Phong (2015 -2019). [6] Hudong heavy machinery Co. Ltd: Torsional Vibra- tion Calculation Report DE 6S46MC–C7860 kW @ 129 r/min 34,000 DWT. PhaRung Shipyard. DNV Approved 2007. [7] Russian Maritime Register of Shipping, Edit 2014: Rules for Classification and Construction of Sea-go- ing Ships. Saint-Petecbuarg, Russian (2014). Abbreviation list CF Vector of firing coefficients DO Diagnostic object DoE Design of Experiments DWT Dead weigh tonnage MDE Marine diesel engine MPP Main propulsion plant MV Motor vessel SATVC Software for automatic torsional vibration calculation TV Torsional vibration TVS Torsional vibration signal VDS Vector of diagnostic signs VN New vector of two equivalent elements DOI: https://doi.org/10.36956/sms.v2i2.330