Ship propulsion shafting vertical vibration data acquisition method and state analysis method

Abstract

The application provides a ship propulsion shafting vertical vibration data acquisition method and a state analysis method. The ship propulsion shafting vertical vibration data acquisition method comprises the following steps: acquiring a motion video of a propulsion shafting through a camera arranged in a cabin, converting the motion video into a vibration image combination; pre-processing the vibration image, acquiring a region of interest, performing threshold segmentation and binarization processing on the region of interest image once, acquiring the barycentric coordinates of the label of the processed image, and the region of interest containing an artificial label and a shafting vibration maximum range; and calculating the vibration data of a single vibration image based on the barycentric coordinates of the processed image. The application selects a camera as a vibration monitoring sensor, combines an artificial label with an image processing analysis technology to realize extraction of shafting vibration data, reduces the influence of environmental noise and vibration on the accuracy of data acquisition, and further accurately analyzes the running state of the shafting.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ship engineering, in particular, especially relates to a ship propulsion shafting vertical vibration data acquisition method and state analysis method. BACKGROUND

[0002] The construction and development of intelligent engine room can effectively improve the intelligent degree of ship, further improve the work efficiency of ship personnel, and reduce the probability of occurrence of dangerous accidents of ship sailing at sea. The ship propulsion system is responsible for the transmission of ship power, and is an important part of the intelligent engine room power device. The dynamic characteristics directly affect the sailing performance of the ship, and are the focus of attention and research. The propulsion shafting is the core unit of the propulsion system, and is an essential part of the transmission of ship propulsion torque and thrust. Its running state directly affects the operating conditions and running conditions of the ship, and even affects the service life of the ship. Health state monitoring and diagnosis of the shafting is one of the keys to ensure the efficient and intelligent operation of the ship.

[0003] The ship propulsion shafting has the following characteristics compared with other large rotating machinery.

[0004] 1. The physical structure is large, the span and diameter of the shafting gradually increase with the increase of the tonnage of the ship, and the overall rigidity is affected to a certain extent.

[0005] 2. The shafting is a rotating machinery, and there is a certain offset between the rotation center of the shaft and its geometric center during the working process.

[0006] 3. There are many components and the structure is complex, and it is affected by multiple excitation forces such as the excitation force of diesel engine, gravity, and excitation force of propeller. Therefore, there is a certain difference in the vibration condition of each position of the shafting during operation.

[0007] The vibration signal of the propulsion shafting during operation is an important research object of the health detection of the ship engine room, and is a key monitoring factor to ensure the efficient and stable operation of the shafting. Through processing and analysis, the rich operation information of the shafting can be effectively obtained, the working condition of the shafting can be perceived and judged, and the overall running state of the ship can be analyzed and predicted, thereby reducing the occurrence of dangerous accidents of the ship at sea.

[0008] The amplitude and energy of the noise interference will far exceed the vibration fault impact signal due to the strong background noise interference of the ship, the complex transmission path and the influence of signal acquisition, transmission and attenuation, etc. The analysis of the vibration signal is to extract the effective main features from the vibration signal of the system equipment by using a reasonable analysis and processing method. The analysis and processing method of the vibration signal is now mainly divided into three categories of time domain, frequency domain and time-frequency domain. However, whether the time domain analysis, the frequency domain analysis or the time-frequency domain analysis of the vibration signal, the purpose is to find the abnormal data in the vibration signal, and to realize the extraction of the characteristic information contained in the vibration signal and the related diagnosis and analysis.

[0009] Now the commonly used vibration signal sensor of the shaft system is mainly a single fixed point electric measurement type, such as a displacement sensor and an acceleration sensor fixed at the bearing. The vibration signal of a single point may not show the overall running condition of the shaft system with large span, and there is a certain limitation. SUMMARY

[0010] In view of the deficiencies of the prior art, the present application provides a ship propulsion shafting vertical vibration data acquisition method and state analysis method. The camera is selected as the vibration monitoring sensor, and the artificial label and image processing analysis technology are combined to realize the extraction of the shafting vibration data, thereby reducing the influence of environmental noise and vibration on the accuracy of data acquisition.

[0011] The technical means adopted by the present application are as follows:

[0012] A ship propulsion shafting vertical vibration data acquisition method comprises the following steps:

[0013] A camera arranged in the engine room is used to acquire the motion video of the propulsion shafting, and the motion video is converted into a vibration image group;

[0014] The vibration image is preprocessed to acquire a region of interest, the region of interest image is subjected to threshold segmentation and binarization processing once, the center of gravity coordinates of the label of the processed image are acquired, and the region of interest contains an artificial label and a maximum range of shafting vibration;

[0015] The vibration data of a single vibration image are calculated based on the center of gravity coordinates of the processed image according to the following formula:

[0016]

[0017] Wherein, d p is the vibration data of the pth image, K f is a proportional factor, (x center , y center ) is the center of gravity coordinates of the label, (x s , y s) is preset.

[0018] Further, before acquiring the motion video of the propulsion shafting, the method further comprises:

[0019] The long-strip rectangular visual artificial label is arranged around the surface of the rotating shaft along a direction perpendicular to the axis of the propulsion shafting.

[0020] The camera is calibrated by using the Zhang Zhengyou camera calibration method.

[0021] Further, the center coordinates of the label are calculated according to the following formula:

[0022]

[0023]

[0024] wherein (x center , y center ) represents the center coordinates of the label, g(x i , y j ) represents the pixel value of the i-th row and the j-th column of the binary image, x i represents the coordinate of the i-th row of the binary image, and y j represents the coordinate of the j-th row of the binary image, and the size of the binary image is m s × n.

[0025] The application further discloses a ship propulsion shafting vertical vibration state analysis method, comprising the following steps:

[0026] The ship propulsion shafting vertical vibration data is acquired based on the ship propulsion shafting vertical vibration data acquisition method.

[0027] The ship propulsion shafting vertical vibration data is processed to obtain a principal component feature matrix, and the processing process comprises standardization processing, dynamic matrix reconstruction processing, kernel principal component analysis processing and eigenvalue screening processing.

[0028] The square prediction error of the vibration data is calculated based on the principal component feature matrix, the calculated square prediction error is compared with a square prediction error control limit, and a ship propulsion shafting vertical vibration state analysis result is output according to the comparison result, and the square prediction error control limit is obtained offline by training historical vibration data in normal operation.

[0029] Further, the square prediction error of the vibration data is calculated according to the following formula:

[0030]

[0031] wherein SPE represents the square prediction error of the vibration data, This represents the mapping data of the original data, where N represents the number of sequences of dynamically reconstructed data, typically the number of rows in the data, and p. * The number of principal elements in the mapped data matrix is ​​calculated using the principal element cumulative contribution rate method.

[0032] Furthermore, based on the comparison results, the output of the vertical vibration state analysis results of the ship's propulsion shafting includes:

[0033] A fault alarm is triggered when the calculated square prediction error exceeds the square prediction error control limit; otherwise, the vertical vibration of the ship's propulsion shaft system is normal.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] 1. This invention extracts shaft vibration data from a ship's propulsion system based on a visual sensor. Because visual measurement has a wider range, it enables multi-point health monitoring of the shaft system, resulting in better monitoring performance. Furthermore, since the camera is a non-contact sensor, it is less affected by the vibration of the monitored target, is easy to deploy, and is less affected by environmental factors such as electromagnetic fields.

[0036] 2. This invention analyzes the detected multidimensional vibration data of the shaft system based on a dynamic analysis model. While acquiring the dynamic characteristics of the data, it can also effectively reduce the dimensionality of data analysis, reduce the difficulty of fault diagnosis analysis, and further improve the accuracy of subsequent fault diagnosis. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a method for acquiring vertical vibration data of a ship propulsion shaft system in Example 1.

[0039] Figure 2 This is a flowchart of a method for analyzing the vertical vibration state of a ship propulsion shaft system in Example 2.

[0040] Figure 3 This is a flowchart of the fault detection method for vertical vibration state of ship propulsion shafting in Example 2. Detailed Implementation

[0041] In the following, the technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application in order to make the technical personnel in the technical field better understand the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by the ordinary technical personnel in the technical field without creative labor should belong to the scope of protection of the present application.

[0042] It should be noted that the terms "first", "second", and the like in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device that includes a series of steps or units does not have to be limited to those steps or units clearly listed, but can include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0043] Embodiment 1

[0044] As Figure 1 shown, the present application provides a ship propulsion shafting vertical vibration data acquisition method. Based on the method, vibration signal extraction can be realized, effective processing of monitoring video can be realized, and shafting multi-point vibration information can be quickly and accurately acquired. Mainly includes video processing steps, image preprocessing steps, image analysis steps and vibration information extraction steps.

[0045] Before the video processing step, shooting preparation is needed. In order to reduce the difficulty of image analysis and further improve the accuracy of image analysis, two groups of condition preparation, label selection and camera calibration, are needed before video shooting.

[0046] 1) Label selection

[0047] In order to fully exert the precision of camera measurement, appropriate visual artificial label can be selected. Common label types include linear, circular, rectangular, triangular and other special shapes. The existence of artificial label is to better select the image analysis area, reduce the complexity of image processing, and provide more accurate analysis target for subsequent algorithm analysis. The shaft vibration information in the application is closely related to the shaft rotation. The label is attached to the surface of the shaft and moves with the shaft. When a circular or triangular label is selected, the label will be empty during visual monitoring. There is no label pattern in the monitoring video, which will affect the subsequent visual algorithm analysis and calculation. In order to reduce the empty period of label rotation, a long rectangular label is selected, which is arranged vertically to the axis and attached to the surface of the shaft. During the rotation of the shaft system, the label shape captured by the camera is a rectangular strip, and there is no empty time. The motion state of each point of the shaft system can be monitored, and the overall monitoring of the rotation motion state of the shaft system can be realized.

[0048] 2) Camera calibration

[0049] Although the consumer camera lens has developed at a faster speed with the progress of industrial technology in recent years, the field of view (FOV) of low-cost and lightweight cameras may cause deviation between the detected image and the ideal image. During the detection process, the photographed image of the measured target in the video has a certain distortion, which affects the accuracy of dynamic displacement measurement. From this point of view, camera calibration is a crucial link in eliminating geometric distortion in the image and accurately measuring physical displacement. Zhang Zhengyou camera calibration method is a commonly used calibration method based on calibration target. It captures the image of known geometric points by using a checkerboard pattern, estimates the camera intrinsic matrix from different angles, including camera focal length, lens axis offset, principal point, skew and lens distortion characteristics, and completes the calibration and calibration of the monitoring camera by using the relationship between the photographed picture and the real object.

[0050] First, the video is acquired and processed. The motion video of the propulsion shaft system is acquired by the camera arranged in the cabin and transmitted to the computer end for storage. The video is composed of multiple pictures. In order to meet the analysis requirements of the subsequent visual processing algorithm, the photographed video needs to be converted into pictures. The application uses Matlab software to write programs to complete the simple processing of the video and convert it into pictures saved in a specific folder.

[0051] Then, the image is preprocessed, including selecting the region of interest, threshold segmentation, binarization, and extracting the center of gravity of the label in the image. Specifically:

[0052] 1) Image ROI region selection

[0053] In the collected shafting motion video pictures, the proportion of the label area in each picture is small relative to the whole picture. If the whole picture is processed, a large amount of computing resources will be wasted and the computing time will be increased. In order to more conveniently process the picture, the partial area of the picture can be extracted for separate analysis and processing. The selected area is a region of interest (ROI) in image processing, and the area should contain the maximum range of shaft vibration and the artificial label.

[0054] 2) Threshold segmentation

[0055] Since the monitoring target has different absorption and refraction rates for light, the main performance on the image is that the pixel gray scale of the object is different. According to this principle, a certain threshold gray scale can be determined, and the artificial marking area and the background area in the image are separated through the size of the threshold. In order to quickly obtain the information of the artificial label, image segmentation is needed. In the present application, the artificial marking is of the same type, and the monitoring target does not change. Therefore, a single threshold segmentation method can be used.

[0056] The threshold can be selected by the human eye observation method, and the most suitable threshold can be screened out through continuous updating and judgment. Machine vision monitoring of shaft vibration is a continuous process, and multiple images per second need to be processed. Therefore, the maximum inter-class variance threshold segmentation method (Qtsu) is selected. This method is a commonly used threshold segmentation method, and its basic principle is to select the optimal threshold to maximize the pixel inter-class variance between the background and the target. The greater the variance, the greater the difference between the background and the target. Therefore, the variance determines the misclassification condition. The specific principle is as follows:

[0057] Suppose the number of pixels of the image is N p , the gray scale range is [0, L g , and the number of gray scale i is n i . The probability of the occurrence of the gray scale is

[0058]

[0059] Let the threshold of the monitored image be T s , T s divides the image into two classes: R0 and R1, where the pixel gray scale value range of R0 is [0, T s -1], and the pixel gray scale value range of R1 is [T s , L g ]. The average of the image gray scale is

[0060]

[0061] The average of the two divided areas is

[0062]

[0063] wherein

[0064]

[0065] According to the above formula, we can deduce

[0066] μ = w0μ0+ w1μ1 (5)

[0067] Further, the expression of the inter-class variance is

[0068]

[0069] Threshold T s ∈ [0, L g ], by constantly taking the value, to ensure that the maximum σ 2 value, the solution is the best threshold.

[0070] 3) Image binarization

[0071] Image binarization is to convert the image pixel gray data into 0 value representing black or 255 value representing white, and to differentiate the image according to different optimal threshold, the image changes from color to black and white, further reducing image analysis calculation. Assuming that the monitoring image is f(x i ,y j ), wherein x i represents the coordinates of the i-th row of the image, y j is the coordinates of the j-th row of the image, and the optimal threshold T s of the image is obtained by using Qtsu method, and the binary image g(x i ,y j ) is obtained by operation

[0072]

[0073] 4) Sub-pixel image barycenter method

[0074] In order to improve the accuracy of visual detection and reduce the measurement error of the equipment, the sub-pixel barycenter method is used to analyze the image. The binary artificial label area of m s ×n pixel range is analyzed and calculated by using the formula, and the barycenter coordinates (x center ,y center ) of the label can be obtained.

[0075]

[0076] In the formula, x i represents the coordinates of the i-th row of the image, y j is the coordinates of the j-th row of the image, and g(x iy j represents the pixel value of the i-th row and j-th column of the image, g(x i ,y j Generally, g(x

[0077] Then, the vibration signal is calculated.

[0078] Like other monitoring sensors, the purpose of measuring vibration by using machine vision method is to obtain vibration data of the monitoring target. In order to capture the vibration signal in the video image, the relationship between the pixel coordinates and the physical coordinates needs to be established first, and then the pixel points of the image and the Cartesian coordinate system can be combined to plan and analyze the captured image, and finally the scaling coefficient between the picture pixels and the physical distance (usually in millimeters / pixel) is obtained by calculation.

[0079] Suppose the scaling factor K f is calculated as shown below

[0080]

[0081] K f represents the actual size of a single pixel point, l Z and l F represent the actual distance and the number of image pixels respectively, and the vibration data of the monitoring shafting is inferred according to the scaling factor obtained

[0082]

[0083] where x center and y center are the pixel coordinates of the shafting label, and x s and y s are the pixel coordinates of the shafting reference point set by human beings, and the motion condition of the shafting can be calculated by the formula. The present application mainly studies the vertical vibration of the shafting, so the change amount of the horizontal coordinate is 0.

[0084] Example 2

[0085] Based on the above embodiment 1, the embodiment provides a ship propulsion shafting vertical vibration state analysis method. The multi-dimensional vibration signal obtained by the visual analysis method is closely related to the shafting motion state, and has certain dynamic characteristics. Direct processing and modeling cannot reflect the dynamic operation characteristics of the sample. In order to obtain the dynamics of system data and improve the accuracy of system fault diagnosis, the original data needs to be analyzed and processed. At the same time, due to the existence of the center of gravity of the shafting, the vibration conditions of each point of the shafting will have certain differences in the rotating process, so the obtained multi-element vibration signals are not related to each other, which are linearly independent data groups. In order to reduce the influence of data dynamic characteristics and nonlinearity on the analysis results, the redundant information in data analysis is proposed, and a dynamic analysis model based on dynamic theory and kernel principal component analysis method is constructed. This model applies dynamic theory to construct an augmented matrix, and uses KPCA to process and analyze the constructed multi-dimensional dynamic matrix. While obtaining the dynamic characteristics of system data, the non-linear characteristics between data can also be extracted, redundant data can be reduced, and the accuracy and diagnosis precision of system fault diagnosis can be further improved. The specific process is shown in Figures 2-3 . Specifically, it includes

[0086] 1) Assuming that m labels are made on the shafting, the obtained shafting vertical vibration data contains m label variables, N D data values, then the initial vibration data X is

[0087]

[0088] where x i (i=1,2,...,N D ) is an m-column vector, and the data X is expanded by using dynamic theory to construct an augmented matrix

[0089]

[0090] In the formula, m dimensional observation data at time t, and l is the lag time factor. When l=0, the newly constructed dynamic data is strictly linearly related to the original data. When l gradually increases, new linear and nonlinear dynamic relationships are formed. When l changes, the parallel analysis method can be used to obtain the new dynamic relationship,

[0091]

[0092] In the formula, r n is a relationship function, which is a cyclic function to obtain a suitable l value. r=m(l+1), when l=0, the initial r=m(l+1)=m, and through cyclic calculation until r n ≤0, the lag time l is obtained, and the augmented matrix is constructed. N=N D -l. DKPCA(Dynamic Kernel Principal Component Analysis) in the construction of good augmented matrix, using KPCA data analysis.

[0093] 2) using KPCA on the reconstruction data nonlinear mapping, which will be from Φ: χ k → H k , x→ Φ(x), assuming that in the reconstruction space inside a point in the center, then it will be derived

[0094]

[0095] For the data after mapping can be expressed by its covariance matrix in the feature space of the probability density of multi-dimensional random variables, while the covariance matrix E to its corresponding eigenvalues and eigenvectors, can be obtained

[0096] Ep k = λ k p k , k = 1, 2, 3,..., N (15)

[0097] The expression of the eigenvector p k can be derived as follows

[0098]

[0099] The eigenvector p k is the correlation of the weighted coefficient in the mapping space.

[0100] From formula (15) and (16) can be obtained:

[0101]

[0102] In order to simplify the calculation, here we introduce a radial kernel function K, the kernel function expression is K = <Φ(x i ), Φ(x j )> = Φ(x i ) Φ(x j ) T The selection of kernel function generally has linear kernel function, polynomial kernel function and radial basis kernel function, combined with the nonlinear characteristics of the obtained propulsion shaft vibration data, select the Gaussian kernel function as the mapping function. The expression formula of the kernel function is introduced into formula (15), which can be obtained Using the introduced kernel function can be obtained K 2 α k = NKλ k αk Both sides simplify and obtain

[0103]

[0104] To obtain the average value within the center of the high-dimensional space, satisfying the input vector expression of formula (14), the Gaussian kernel function is centered to obtain the central kernel matrix. I is the identity matrix, with a size of N×N. Using... Replace K for relevant calculations.

[0105] Kernel principal component analysis is based on the weighting coefficient α k The calculation is performed so that the k-th principal component has eigenvector p in the feature space H. k The mapping value on

[0106]

[0107] When the input data x changes, the output data t k This will also result in corresponding changes, leading to the mapping data matrix T. N ∈R N×N This enables mapping analysis of nonlinear data.

[0108] 3) To reduce the difficulty of calculation and analysis, the cumulative variance method is used to filter the data and obtain a low-dimensional principal component feature matrix.

[0109]

[0110] p * The number of principal elements, σ, is calculated using the Cumulative Contribution Value (CPV) method. 0 The selection criterion for principal component contribution rate is generally 85%. This is determined by the retained principal component p... * Construct p * 3D matrix

[0111] 4) Squared prediction error is used SPE This indicates that it describes the error between each sampling and the statistical model in terms of the trend of change, representing the measurement of changes in external data of the model. The calculation method is as follows:

[0112] Using the acquired The principal component matrix is ​​used to calculate the SPE of the vibration data to diagnose the motion condition of the shaft system. The calculation formula is shown below.

[0113]

[0114] The SPE obtained from the training data is analyzed using the confidence level (CL) method to obtain the control limits SPE of the SPE data. lim.

[0115] 5) SPE statistics and original data points one-to-one correspondence, generally considered in the control limit above the statistics is abnormal data points, in the fault diagnosis, using the relevant parameters of the off-line modeling to analyze the real-time data, calculate the SPE t data, the control limit SPE lim and real-time data SPE t data comparison and analysis, to realize the analysis and diagnosis of the working condition of the propulsion shafting.

[0116] Through the reconstruction of the matrix to obtain the dynamic characteristics between the data, improve the accuracy of fault diagnosis. And using KPCA to realize the nonlinear transformation of data, while reducing the feature redundancy, simplifying the analysis difficulty of the problem, improving the analysis efficiency.

[0117] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for acquiring vertical vibration data of a ship's propulsion shafting, characterized in that, Includes the following steps: The motion video of the propulsion shaft system is acquired by cameras installed in the cabin, and the motion video is converted into a combination of vibration images; The vibration image is preprocessed to obtain the region of interest (ROI). The ROI image is then subjected to thresholding and binarization to obtain the centroid coordinates of the label in the processed image. The ROI includes the artificial label and the maximum range of shaft vibration. The centroid coordinates of the label are calculated as follows: in, Indicates the center coordinates of the label. Represents the binarized image. Line 1 Column pixel values, Represents the binarized image. The coordinates of the row This is the binarized image of the th The coordinates of the row, the size of the binarized image is ; Based on the centroid coordinates of the processed image, the vibration data of a single vibration image is calculated according to the following formula: in, For the vibration data of the p-th vibration image, As a scaling factor, The centroid coordinates of the label. These are the preset coordinates of the axis reference points.

2. The method for acquiring vertical vibration data of a ship propulsion shafting system according to claim 1, characterized in that, Before acquiring the motion video of the propulsion shaft system, the following is also included: Long, rectangular visual artificial labels are arranged around the surface of the rotating shaft in a direction perpendicular to the axis of the propulsion shaft system; The camera was calibrated using Zhang Zhengyou's camera calibration method.

3. A method for analyzing the vertical vibration state of a ship's propulsion shafting, characterized in that, Includes the following steps: The method for acquiring vertical vibration data of ship propulsion shafting as described in claim 1 is used to collect vertical vibration data of ship propulsion shafting. The vertical vibration data of the ship's propulsion shaft system is processed to obtain the principal component feature matrix. The processing includes standardization, dynamic matrix reconstruction, kernel principal component analysis, and eigenvalue filtering. The squared prediction error of the vibration data is calculated based on the principal component feature matrix. The calculated squared prediction error is compared with the squared prediction error control limit. The vertical vibration state analysis result of the ship propulsion shaft system is output according to the comparison result. The squared prediction error control limit is obtained offline training based on the historical vibration data of normal operation.

4. The method for analyzing the vertical vibration state of a ship propulsion shafting system according to claim 3, characterized in that, The squared prediction error of the vibration data is calculated as follows: in, This represents the squared prediction error of the vibration data. Mapping data representing the original data This represents the number of sequences of data after dynamic reconstruction, typically the number of rows in the data. The number of principal elements in the mapped data matrix is ​​calculated using the principal element cumulative contribution rate method.

5. The method for analyzing the vertical vibration state of a ship's propulsion shafting according to claim 3, characterized in that, Based on the comparison results, the output of the vertical vibration state analysis results of the ship's propulsion shafting system includes: A fault alarm is triggered when the calculated square prediction error exceeds the square prediction error control limit; otherwise, the vertical vibration of the ship's propulsion shaft system is normal.

Images