Ship stern structure deformation monitoring method and system, storage medium and electronic equipment

Abstract

The invention provides a ship stern structure deformation monitoring method and system, a storage medium and electronic equipment. The method comprises the following steps: acquiring measurement data of a ship, wherein the measurement data comprises a first response parameter of a stern structure of the ship, a rigid body motion parameter of the whole ship and a main engine rotating speed of a propulsion shafting of the ship; separating a rigid body motion component caused by the rigid body motion parameter to the first response parameter from the measurement data to obtain a second response parameter of the stern structure; determining a modal parameter of the stern structure based on the second response parameter; the modal parameters represent dynamic vibration characteristics of the stern structure; based on the modal parameters of the stern structure, determining the vibration type of the stern structure; determining a target coupling mode related to propulsion shafting excitation based on a frequency matching relationship between the main engine rotating speed and the mode parameters and the vibration type; and determining the fatigue damage cumulant of the stern structure in different host rotation speed intervals based on the target coupling mode, and obtaining a deformation monitoring result of the stern structure.

Description

Technical Field

[0001] This application relates to the field of shipbuilding technology, and in particular to a method and electronic equipment for monitoring deformation of the stern structure of a ship. Background Technology

[0002] During navigation, the torsional vibration of the propulsion shafting is transmitted to the stern structure through the stern tube and bearing housing, causing the stern structure to bear complex dynamic loads over a long period. Existing ship vibration monitoring mainly focuses on measuring parameters such as torque and speed of the shafting itself, lacking continuous monitoring methods for the actual dynamic response of the stern structure under different operating conditions. This makes it difficult to accurately assess the cumulative fatigue damage of the stern structure over long-term operation, resulting in damage such as cracks in critical parts such as the stern bearing housing and steering gear room often being discovered only after significant expansion, affecting the safe operation of the ship. Summary of the Invention

[0003] In view of this, this application provides a method and electronic device for monitoring the deformation of the stern structure of a ship.

[0004] According to a first aspect of this application, a method for monitoring the deformation of a ship's stern structure is provided, comprising: acquiring measurement data of the ship, the measurement data including a first response parameter of the ship's stern structure, rigid body motion parameters of the ship as a whole, and the main engine speed of the ship's propulsion shafting; the first response parameter is obtained based on measurements taken at at least one measurement point located at a key position on the stern structure; separating the rigid body motion component caused by the rigid body motion parameters to the first response parameter from the measurement data to obtain a second response parameter of the stern structure; determining modal parameters of the stern structure based on the second response parameter; the modal parameters characterizing the dynamic vibration characteristics of the stern structure; determining the vibration type of the stern structure based on the modal parameters of the stern structure; determining the target coupled mode related to the propulsion shafting excitation based on the frequency matching relationship between the main engine speed and the modal parameters, and the vibration type; and determining the cumulative fatigue damage of the stern structure in different main engine speed ranges based on the target coupled mode to obtain the deformation monitoring result of the stern structure.

[0005] The second aspect of this application provides a ship stern structure deformation monitoring system, comprising: an acquisition module for acquiring measurement data of the ship, the measurement data including a first response parameter of the stern structure, rigid body motion parameters of the ship as a whole, and the main engine speed of the ship's propulsion shafting; the first response parameter is obtained based on measurements taken at at least one measurement point located at a key position on the stern structure; a calculation module for separating the rigid body motion component caused by the rigid body motion parameters to the first response parameter from the measurement data to obtain a second response parameter of the stern structure; a first determination module for determining modal parameters of the stern structure based on the second response parameter; the modal parameters characterize the dynamic vibration characteristics of the stern structure; a second determination module for determining the vibration type of the stern structure based on the modal parameters of the stern structure; a third determination module for determining the target coupled mode related to the propulsion shafting excitation based on the frequency matching relationship between the main engine speed and the modal parameters, and the vibration type; and a generation module for determining the cumulative fatigue damage of the stern structure in different main engine speed ranges based on the target coupled mode to obtain the stern structure deformation monitoring result.

[0006] A third aspect of this application provides an electronic device comprising: one or more processors; and a memory for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0007] A fourth aspect of this application provides a computer-readable storage medium storing computer-executable instructions that, when executed, implement the method described above.

[0008] By adopting the technical solution of this application, the response parameters of the stern structure can be continuously acquired during the normal operation of the ship. By separating the rigid body motion components, a second response parameter that truly reflects the elastic deformation of the stern structure can be obtained. Based on the modal parameters and vibration type information extracted from the second response parameter, and combined with the frequency matching relationship between the main engine speed and the modal parameters, the target coupled mode directly related to the excitation of the propulsion shaft system can be identified, thereby achieving an accurate assessment of the cumulative fatigue damage of the stern structure under different main engine speed ranges. Attached Figure Description

[0009] The above and other objects, features and advantages of this application will become clearer from the following description of embodiments with reference to the accompanying drawings, in which: Figure 1 A flowchart illustrating a method for monitoring deformation of a ship's stern structure provided in an embodiment of this application is shown below; Figure 2 This application discloses a ship stern structure deformation monitoring system. Figure 3This is a block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0010] The embodiments of this application will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of this application. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of this application for ease of explanation. However, it will be apparent that one or more embodiments may be implemented without these specific details. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0011] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0012] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0013] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0014] Figure 1 A flowchart illustrating a method for monitoring deformation of a ship's stern structure provided in an embodiment of this application is shown.

[0015] like Figure 1 As shown, the method for monitoring deformation of the stern structure of a ship may specifically include the following operations.

[0016] Operation S210 acquires measurement data of the ship, including the first response parameters of the ship's stern structure, the rigid body motion parameters of the ship as a whole, and the main engine speed of the ship's propulsion shaft system; the first response parameters are obtained based on measurements taken at at least one measurement point located at a key position on the stern structure. Operation S220 separates the rigid body motion component caused by the rigid body motion parameters to the first response parameter from the measurement data to obtain the second response parameter of the stern structure; Operation S230 determines the modal parameters of the stern structure based on the second response parameters; the modal parameters characterize the dynamic vibration characteristics of the stern structure; Operation S240 determines the vibration type of the stern structure based on the modal parameters of the stern structure; By operating S250, based on the frequency matching relationship between the main engine speed and modal parameters, as well as the vibration type, the target coupled modes related to the propulsion shaft system excitation are determined; By operating S260, the cumulative fatigue damage of the stern structure under different main engine speed ranges is determined based on the target coupled mode, and the deformation monitoring results of the stern structure are obtained.

[0017] In operation S210, the measurement data refers to the physical quantity measurement values ​​used to reflect the dynamic response characteristics of the ship's stern structure and operating conditions. It can be understood as a set of multi-source heterogeneous data collected in real time by sensors or monitoring equipment.

[0018] Optionally, the measurement data may include the first response parameters of the stern structure of the ship, the rigid body motion parameters of the ship as a whole, and the main engine speed of the ship's propulsion shafting.

[0019] The first response parameter refers to the dynamic physical response measurement value of the stern structure under the actual operating conditions of the ship. It can be understood as the original measurement signal reflecting the vibration or deformation state of the stern structure under the combined action of propulsion shaft excitation and overall hull motion.

[0020] Exemplarily, the first response parameter includes, but is not limited to, at least one of acceleration, displacement, velocity, and strain. In one embodiment, the first response parameter is a triaxial acceleration value measured by an accelerometer located at a key measurement point on the stern structure. In another embodiment, the first response parameter is a strain value measured by a strain sensor located at a key measurement point on the stern structure. In yet another embodiment, the first response parameter includes both acceleration and strain.

[0021] It should be noted that the first response parameter is obtained based on measurements taken at at least one measurement point located at a critical position on the stern structure. Here, a critical position refers to a spatial location within the stern structure that is sensitive to the torsional vibration energy transfer of the propulsion shaft system, prone to fatigue damage, or representative of the overall structural vibration characteristics. There can be one or more measurement points; when multiple measurement points are set, a distributed measurement array can be formed in space to obtain the spatial deformation mode information of the stern structure.

[0022] Similarly, the rigid body motion parameters of a ship as a whole refer to the physical quantities that characterize the six-degree-of-freedom motion state of the ship as a whole rigid body in the marine environment. They can be understood as the measured values ​​that describe the overall attitude changes of the ship under the action of waves, such as pitching, rolling, heave, and swaying. They are used to separate the rigid body motion components caused by the overall hull motion from the overall response of the stern structure.

[0023] For example, the rigid body motion parameters of the ship as a whole include, but are not limited to, at least one of linear acceleration, angular velocity, angular acceleration, attitude angle, and displacement. In one embodiment, the rigid body motion parameters are measured by an inertial measurement unit installed at a specific reference position on the ship, including three-axis acceleration, three-axis angular velocity, and three-axis angular acceleration.

[0024] Similarly, the main engine speed of a ship's propulsion shafting refers to the number of revolutions of the propulsion engine crankshaft or output shaft per unit time. It can be understood as a basic operating parameter characterizing the speed of rotation of the propulsion shafting, used to calculate the basic frequency of the periodic excitation generated by the propulsion shafting and to determine the operating condition range of the ship.

[0025] For example, the main engine speed is measured in revolutions per minute (rpm) and is obtained through a speed sensor in the main engine control system or a speed measurement device in the shafting monitoring system. The measured main engine speed varies with the ship's navigation conditions, corresponding to different speed values ​​at different speeds or loads.

[0026] In operation S220, the second response parameter of the stern structure refers to the relative elastic deformation response of the stern structure obtained after deducting the influence of the overall rigid body motion of the ship from the first response parameter. It can be understood as a net response signal that only reflects the vibration characteristics of the stern structure itself and does not include the overall hull motion component.

[0027] It should be noted that during actual ship navigation, the first response parameters measured at the measurement points on the stern structure are actually a superposition of two motion components: one is the response generated by the rigid body motion of the hull as a whole, and the other is the response generated by the elastic deformation of the stern structure itself. Since the rigid body motion component typically has a large amplitude, it can mask the true elastic vibration characteristics of the stern structure, making it impossible to accurately identify key parameters such as the natural frequencies and mode shapes of the stern structure. Therefore, it is necessary to separate the rigid body motion component from the first response parameters to obtain a second response parameter that truly reflects the dynamic characteristics of the stern structure.

[0028] In one feasible implementation, the spatial position vector of the measurement point relative to the measurement position of the rigid body motion parameters can be used as input. Combined with the linear acceleration, angular velocity and angular acceleration of the entire ship, the acceleration component caused by the motion of the entire ship at each measurement point is calculated according to the rigid body kinematics formula. Then, the calculated rigid body motion component is subtracted from the first response parameter to obtain the second response parameter.

[0029] In another feasible implementation, signal processing methods can be used to separate the rigid body motion components. Specifically, taking advantage of the fact that the frequency characteristics of rigid body motion parameters are usually located in the low-frequency range, frequency domain analysis is performed on the first response parameter to identify and filter out low-frequency components related to the frequency components of the rigid body motion parameters, while retaining the mid-to-high frequency components reflecting the elastic vibration of the stern structure as the second response parameter.

[0030] In operation S230, modal parameters refer to a set of physical quantities that describe the inherent vibration characteristics of the stern structure. They can be understood as characteristic parameters that characterize the essential properties of the stern structure under different vibration modes, such as frequency, mode shape, and damping.

[0031] It should be noted that during actual ship operation, the stern structure is subjected to the combined effects of periodic excitation from the propulsion shaft system and random excitation from waves. When the excitation frequency is close to a certain modal frequency of the stern structure, resonance can occur, leading to excessive dynamic stress and fatigue damage accumulation in the stern structure. Therefore, it is necessary to determine whether there is a risk of resonance under actual operating conditions by examining the modal parameters.

[0032] For example, modal parameters include, but are not limited to, at least one of modal frequency, mode shape, and modal damping ratio. The modal frequency reflects the natural frequencies of each mode of the stern structure, the mode shape reflects the deformation pattern of the stern structure under each mode, and the modal damping ratio reflects the energy dissipation characteristics of the stern structure.

[0033] In one feasible implementation, a fast Fourier transform can be performed on the second response parameter to obtain the frequency domain response function. The peak frequencies in the frequency domain response function are identified to determine the frequency of each mode. The damping ratio of each mode is calculated using the half-power bandwidth method. The mode shape is reconstructed based on the amplitude and phase information of the frequency domain response function at each mode frequency.

[0034] In another feasible implementation, wavelet transform can be performed on the second response parameter to obtain the time-frequency distribution characteristics of the signal, and the instantaneous frequency and instantaneous amplitude that change with time can be extracted from the time-frequency diagram to identify the modal parameters under non-stationary conditions.

[0035] In operation S240, vibration type refers to the type of vibration mode exhibited by the stern structure under actual working conditions. It can be understood as a classification reflecting different vibration mechanisms of the stern structure based on modal parameter characteristics.

[0036] It should be noted that in actual ship operation, abnormal vibrations in the stern structure may be caused by various physical factors. Therefore, it is necessary to accurately determine the vibration type through modal parameter characteristics to provide a basis for subsequent targeted vibration reduction design or maintenance measures.

[0037] For example, the vibration types include, but are not limited to, bending vibration of the stern structure, torsional vibration of the stern structure, local vibration of the stern structure, and coupled vibration of the stern structure and the propulsion shaft system.

[0038] In one feasible implementation, the spatial distribution of each mode shape can be analyzed. When the mode shape exhibits an overall up-and-down swinging characteristic and the amplitude of the measuring point is distributed in a gradient along the longitudinal direction of the stern, it is determined to be bending vibration. When the mode shape exhibits a left-right torsional swinging characteristic and the measuring point exhibits anti-phase vibration at a laterally symmetrical position in the stern, it is determined to be torsional vibration. When the mode shape only exhibits significant amplitude in a local area of ​​the stern while the amplitude in other areas is extremely small, it is determined to be local vibration.

[0039] In another feasible implementation, the operating speed of the propulsion shaft system and its excitation frequencies of each order can be obtained. The identified modal frequencies are compared with characteristic excitation frequencies such as the propeller blade passing frequency and the shaft system torsional vibration frequency. When a certain modal frequency is close to the propeller blade passing frequency, it is determined to be bending or torsional vibration of the propeller excitation based on the mode shape of that order. When a certain modal frequency is close to the shaft system torsional vibration frequency, it is determined to be the coupled vibration of the stern structure and the propulsion shaft system.

[0040] In operation S250, the frequency matching relationship between the main engine speed and the modal parameters refers to the degree of closeness or correspondence between the excitation frequencies of each order generated by the main engine speed and the modal frequencies of the stern structure. It can be understood as a correlation index that quantitatively characterizes the resonance risk between the excitation frequency and the natural frequency, and is used to screen out the stern structure modes that may be coupled with the propulsion shaft system.

[0041] For example, the frequency matching relationship between the main engine speed and the modal parameters can be the frequency ratio of the excitation frequency to the modal frequency, the frequency difference between the excitation frequency and the modal frequency, or the determination result that the excitation frequency falls within the modal frequency resonance bandwidth range. For instance, when the main engine speed is 120 rpm, the corresponding shaft frequency is 2 Hz. If the propeller has four blades, the blade passing frequency is 8 Hz. When a certain modal frequency is identified as 7.8 Hz, the frequency difference is only 0.2 Hz, and the frequency ratio is 0.975, indicating that there is a high degree of matching between this modal and the blade passing frequency.

[0042] Because stern structures typically exhibit multiple modes, not all modes cause engineering problems. Significant coupled vibrations and abnormal stern vibrations only occur when the natural frequency of a certain mode is close to the excitation frequency of the propulsion shaft system, and the vibration type of that mode matches the excitation characteristics.

[0043] Based on the frequency matching relationship and vibration type mentioned above, the target coupling mode related to the propulsion shaft excitation can be determined. The target coupling mode refers to the specific mode that couples with the propulsion shaft excitation frequency under actual operating conditions and dominates the abnormal vibration of the stern. It can be understood as the key mode that causes the coupling vibration problem between the stern structure and the propulsion shaft, selected from all the identified modes.

[0044] In one feasible implementation, the excitation frequencies of each order of the propulsion shaft system, including shaft frequency, blade passage frequency, and shaft torsional vibration frequency, can be calculated based on the main engine rotation speed. Each excitation frequency is compared with the identified modal frequencies one by one. When the frequency difference between a certain modal frequency and a certain excitation frequency is less than a preset threshold or the frequency ratio falls within a preset range, it is initially determined that there is a frequency matching relationship between that modal. Further verification is performed in conjunction with the vibration type of that modal. For example, when the excitation frequency is the blade passage frequency, if the corresponding mode shape is bending vibration or torsional vibration, then that modal is determined to be the target coupled mode. If the corresponding mode shape is only local vibration, then that mode is excluded.

[0045] In operation S260, the cumulative fatigue damage refers to the cumulative value of the fatigue damage caused by the stern structure under cyclic stress under the target coupled modal excitation.

[0046] Because the main engine speed varies frequently with sailing conditions, the excitation characteristics of the propulsion shaft system differ across different speed ranges, resulting in variations in the vibration response level of the stern structure. When the main engine speed causes the excitation frequency to approach the target coupling mode frequency, the amplitude of the dynamic stress generated in the stern structure increases significantly, and the rate of fatigue damage accumulation accelerates. Conversely, in speed ranges far from the resonance zone, the dynamic stress level is lower, and fatigue damage accumulation is slower. The fatigue damage of the stern structure is the superposition result of damage accumulation across different speed ranges.

[0047] In one feasible implementation, the commonly used speed range of the main unit can be divided into several speed intervals. For each speed interval, the dynamic stress time history of key positions of the stern structure is calculated based on the modal frequency and mode shape of the target coupled mode. The number of cycles under each stress level is counted using the rainflow counting method. Combined with the SN curve of the stern structure material, the cumulative fatigue damage in that speed interval is calculated. The cumulative fatigue damage of each speed interval is weighted and summed, with the weighting coefficient being the proportion of the actual running time of each speed interval, to obtain the total cumulative fatigue damage of the stern structure. When the total cumulative fatigue damage exceeds a preset threshold, it is determined that the stern structure has a risk of fatigue damage, and the corresponding deformation monitoring results are output.

[0048] By adopting the technical solution of this application, the response parameters of the stern structure can be continuously acquired during the normal operation of the ship. By separating the rigid body motion components, a second response parameter that truly reflects the elastic deformation of the stern structure can be obtained. Based on the modal parameters and vibration type information extracted from the second response parameter, and combined with the frequency matching relationship between the main engine speed and the modal parameters, the target coupled mode directly related to the excitation of the propulsion shaft system can be identified, thereby achieving an accurate assessment of the cumulative fatigue damage of the stern structure under different main engine speed ranges.

[0049] Furthermore, the technical solution of this application establishes a complete link from monitoring the actual dynamic response of the stern structure to quantitative assessment of fatigue damage. It solves the technical problem in the prior art of lacking continuous monitoring of the actual dynamic response of the stern structure under different operating conditions and the difficulty in accurately assessing the accumulation of fatigue damage. It can detect potential risks in a timely manner before the cracks and other damage in key parts such as the stern bearing housing and steering gear compartments significantly expand.

[0050] Based on the above embodiments, as an optional embodiment, in order to more accurately separate the influence of the overall rigid body motion of the ship from the first response parameter and obtain the second response parameter that only reflects the elastic deformation of the stern structure itself, this embodiment further limits the separation process of the rigid body motion component in operation S220.

[0051] Optionally, the key locations include at least one of the following: the stern bearing housing location, the stern longitudinal girder location, and the steering gear compartment bulkhead location; the rigid body motion parameters include the reference point linear acceleration, angular velocity, and angular acceleration of the entire ship; based on the above, the above operation S220 may also include the following operations.

[0052] Operation S310 separates the rigid body motion components caused by the rigid body motion parameters to the first response parameters from the measurement data, obtaining the second response parameters of the stern structure, including: Operate S320 to determine the spatial positional relationship of each measurement point relative to the measurement position of the rigid body motion parameters; Using S330, based on the overall ship's linear acceleration, angular velocity, angular acceleration, and spatial positional relationships, calculate the rigid body motion components at each measurement point; Operation S340 subtracts the rigid body motion component from the first response parameters to obtain the second response parameters.

[0053] In operation S310, the spatial position relationship refers to the spatial geometric position vector of each measurement point in the local coordinate system of the stern structure relative to the measurement position of the rigid body motion parameters. It can be understood as the three-dimensional coordinate difference that characterizes the distance and orientation between the measurement point and the measurement position of the rigid body motion parameters.

[0054] For example, the rigid body motion parameters are measured at a reference point where the inertial measurement unit is installed. This reference point is typically selected at a relatively stable support location on the stern structure, such as a fixed frame near the mid-section inside the steering gear compartment. The spatial relationship between each measurement point and this reference point can be obtained from the stern structure layout drawings or a 3D model, including the coordinate differences of the measurement points relative to the reference point in the longitudinal, lateral, and vertical directions.

[0055] Specifically, when the measuring point is set at the stern bearing housing, the spatial relationship between the measuring point and the reference point is mainly reflected in the difference in longitudinal distance and vertical height. Since the stern bearing housing is usually located aft and lower at the stern, its longitudinal coordinate is negative relative to the reference point, and its vertical coordinate is lower relative to the reference point. When the measuring point is set at the stern longitudinal girder, since the stern longitudinal girder is distributed longitudinally along the hull, the difference in longitudinal distance between the measuring point and the reference point at different rib positions is different, and the difference in longitudinal distance between the measuring point and the reference point is larger the closer the stern longitudinal girder is to the stern end. When the measuring point is set at the steering gear compartment bulkhead, if the bulkhead is longitudinal, the difference in lateral distance between the measuring point and the reference point is larger, and if the bulkhead is transverse, the difference in longitudinal distance between the measuring point and the reference point is larger.

[0056] In operation S320, the rigid body motion component refers to the motion response that should occur at each measurement point when the stern structure is assumed to be a rigid body moving with the ship as a whole. It can be understood as the theoretical motion component caused by the translation and rotation of the ship as a whole, without including the elastic deformation of the structure.

[0057] It should be noted that, according to the principles of rigid body kinematics, when a ship as a whole undergoes six degrees of freedom motion, the motion of any measurement point on the stern structure can be decomposed into three parts: the translation of the reference point, the tangential motion generated by the rotation about the reference point, and the centripetal motion generated by the angular velocity. Using the known linear acceleration, angular velocity, and angular acceleration of the reference point, combined with the spatial positional relationship of the measurement point relative to the reference point, the rigid body motion components of each measurement point can be calculated according to the rigid body kinematics formulas.

[0058] In another feasible implementation, a local coordinate system for the stern structure can be established. The linear acceleration, angular velocity, and angular acceleration of the reference point can be decomposed into components along the coordinate axes. The spatial positional relationship of the measurement point relative to the reference point can be represented as the coordinate differences in the three directions. The rigid body acceleration components in each coordinate direction can be calculated according to the rigid body kinematics formula, and combined to obtain the rigid body motion component vector of the measurement point in the three-axis directions. For example, for a measurement point located at the stern bearing housing, since the longitudinal and vertical distances from the reference point are large, the angular acceleration caused by the ship's pitching motion will produce a large vertical tangential acceleration component at this measurement point, and the angular acceleration caused by the rolling motion will produce a large lateral tangential acceleration component at this measurement point. For a measurement point located at the bulkhead of the steering gear compartment, since the lateral distance from the reference point may be large, the angular acceleration caused by the ship's rolling motion will produce a large vertical tangential acceleration component at this measurement point.

[0059] In operation S330, when the first response parameter is an acceleration parameter, the rigid body motion acceleration component in the corresponding direction is directly subtracted from the first response parameter; when the first response parameter is a strain parameter, the rigid body motion component can be converted into the equivalent strain value at the corresponding position before subtraction; when multiple types of first response parameters are collected simultaneously, the corresponding subtraction operation is performed on each type of parameter. For the measurement point set at the stern girder, since the stern girder will generate a large rigid body motion acceleration with the overall hull under the ship's roll and pitch motions, the second response parameter obtained after subtracting the rigid body motion component can more accurately reflect the bending vibration response of the stern girder under the torsional vibration excitation of the propulsion shaft; for the measurement point set at the rudder compartment bulkhead, the second response parameter obtained after subtracting the rigid body motion component can more accurately reflect the local vibration response of the rudder compartment bulkhead on the propulsion shaft torsional vibration transmission path.

[0060] By adopting the embodiments of this application, it is possible to accurately calculate the acceleration components caused by the rigid body motion of the ship at key locations such as the stern bearing seat, stern longitudinal girder, and steering gear compartment bulkhead, based on the spatial positional relationship of each measurement point relative to the reference point, when there is a large overall motion in the actual operation of the ship. The rigid body motion component is then accurately subtracted from the measured first response parameter to obtain a second response parameter that only reflects the elastic deformation characteristics of the stern structure itself.

[0061] Based on the above embodiments, as an optional embodiment, in order to accurately extract the modal characteristic parameters of the stern structure from the second response parameters after removing the influence of rigid body motion, and to identify the inherent vibration characteristics of the stern structure under actual working conditions, this embodiment further defines the modal parameter identification process in operation S230. Specifically, operation S230 may also include the following operations.

[0062] Operation S410 performs time-frequency analysis on the second response parameter to obtain the frequency response characteristics of the stern structure; the frequency response characteristics characterize the vibration energy distribution of the stern structure in the frequency domain; Operate S420 to identify resonance peaks based on frequency response characteristics; the resonance peaks correspond to the natural vibration frequencies of the stern structure; Operate S430 to extract the modal parameters corresponding to each resonance peak; the modal parameters include at least one of natural frequency, damping ratio and mode shape; wherein, the natural frequency characterizes the vibration frequency of the stern structure under a specific vibration mode; the damping ratio characterizes the vibration energy dissipation capability of the stern structure; and the mode shape characterizes the spatial deformation mode of the stern structure at a specific natural frequency.

[0063] In operation S410, time-frequency analysis refers to the mathematical processing of converting the second response parameter signal in the time domain to the frequency domain for analysis. It can be understood as converting the time history of the response signal into the correspondence between frequency components and amplitude through Fourier transform or other frequency domain conversion methods.

[0064] It should be noted that the frequency response characteristics can be represented as a frequency-amplitude curve, with the horizontal axis representing frequency and the vertical axis representing the response amplitude or power spectral density. This curve visually reflects the vibration intensity of the stern structure in each frequency range. When a certain frequency approaches the natural frequency of the stern structure, a significant peak in the vibration amplitude will appear near that frequency due to resonance.

[0065] In one feasible implementation, a fast Fourier transform can be performed on the second response parameter to convert the time-domain acceleration signal into a frequency-domain amplitude spectrum. The frequency response characteristics of the stern structure within the effective frequency range can be observed through the amplitude spectrum curve to identify frequency components with larger amplitudes.

[0066] For example, suppose that after rigid body subtraction is completed, the discrete-time sequence of the second response parameters of the stern structure at M measurement points is as follows:

[0067] In the formula, The discrete sampling time of the second response parameter is indicated by M; M represents the number of measurement points.

[0068] Perform DFT on the second response parameter at each measurement point i:

[0069] In the formula, k represents the frequency index. This represents the discrete frequency corresponding to the k-th frequency index.

[0070] To characterize the overall vibration energy distribution of the stern structure in the frequency domain, the spectral energy at all measurement points can be superimposed or averaged, and the frequency response characteristics can be defined as follows:

[0071] In operation S420, the resonance peak refers to the frequency point in the frequency response characteristic curve where the amplitude or power spectral density shows a significant peak. It can be understood as the frequency position where the vibration energy of the stern structure is concentrated, corresponding to the natural vibration frequency of the stern structure when resonance occurs at that frequency.

[0072] It should be noted that the identification of resonance peaks can be achieved through peak detection algorithms, which specifically include setting an amplitude threshold to exclude noise peaks, setting a peak width to distinguish adjacent modes, and calculating peak prominence to determine peak significance. Stern structures typically have multiple natural frequencies, so multiple resonance peaks may appear in the frequency response characteristic curve, each corresponding to a different order of natural vibration modes.

[0073] For example, for the stern structure, the first resonance peak corresponding to the overall bending vibration mode may be identified in the low-frequency range; several resonance peaks corresponding to the local plate frame vibration mode or torsional vibration mode may be identified in the mid-frequency range; and higher-order resonance peaks corresponding to the complex combined vibration modes of the stern structure may be identified in the higher-frequency range. The resonance peaks in different frequency ranges reflect the inherent vibration characteristics of the stern structure under different vibration modes. The low-order modes usually correspond to large-scale overall deformation, while the high-order modes usually correspond to small-scale local deformation.

[0074] For example, in In the curve, resonance peaks are determined by finding local maxima. A set of frequency indices can be defined to satisfy: for The maximum value in its local neighborhood, and ≥ .

[0075] In the formula, K represents the number of resonance peaks; This represents the energy threshold used to remove noise peaks.

[0076] The estimated natural vibration frequency corresponding to each resonance peak is defined as:

[0077] In operation S430, modal parameter extraction refers to the quantitative calculation of characteristic parameters of the stern structure vibration characteristics from the identified resonance peaks. It can be understood as extracting physical quantities such as natural frequency, damping ratio and mode shape from frequency response characteristics or time domain response signals through modal parameter identification algorithms to describe the dynamic characteristics of the vibration system.

[0078] It should be noted that the natural frequency can be obtained directly from the frequency value corresponding to the resonance peak, the damping ratio can be calculated by the half-power bandwidth method or the peak amplitude method of the resonance peak, and the mode shape can be obtained by analyzing the response amplitude and phase relationship of multiple measurement points at the same natural frequency.

[0079] In one feasible implementation, the peak picking method can be used to extract modal parameters. The frequency corresponding to the resonance peak is directly used as the natural frequency. The damping ratio is calculated by the ratio of the frequency difference corresponding to the amplitude on both sides of the resonance peak dropping to a certain proportion of the peak value to the natural frequency. The mode shape vector is constructed by the proportional relationship of the response amplitude of each measurement point at the natural frequency.

[0080] In another feasible implementation, advanced modal parameter identification algorithms such as frequency domain decomposition or random subspace identification can be used to simultaneously identify multi-order modal parameters based on the second response parameters of multiple measurement points. This method can handle cases with dense modes or large damping, and improve the accuracy and stability of modal parameter identification.

[0081] For example, the extracted modal parameters may include: the first mode corresponds to the overall vertical bending deformation, with its natural frequency in the low-frequency range and a relatively small damping ratio; the second mode corresponds to the horizontal torsional deformation, with its natural frequency in the mid-frequency range and a relatively large damping ratio; the third mode corresponds to the combined mode of local bending deformation of the stern longitudinal girder and lateral vibration of the steering gear compartment bulkhead, with its natural frequency in the mid-frequency range, and the mode shape exhibits the characteristic of larger vibration amplitude in local areas and smaller vibration amplitude in other areas. By comparing the amplitude ratio and phase relationship of different measurement points under each mode, the spatial deformation mode of the stern structure at different natural frequencies can be accurately described.

[0082] For example, for each resonance peak, a small frequency range is selected in its vicinity: ; in, >0 represents the local fitting bandwidth.

[0083] Within the interval, assuming the stern structure can be dominated by a single-degree-of-freedom damped oscillator in this frequency band, its amplitude-frequency characteristics can be approximated by the following form:

[0084] in, This represents the angular natural frequency of the p-th mode; This represents the damping ratio of the p-th mode; This represents the complex amplitude parameter related to the modal intensity.

[0085] Least squares fitting can be used to... exist Fitting the observations within Form, that is:

[0086] Near the frequency corresponding to the p-th order resonance peak, the spectrum of each measurement point is sampled to construct a multi-point frequency response vector:

[0087] To eliminate the influence of the overall scale, the vector can be normalized, and the mode shape vector of the p-th order can be defined as follows:

[0088] in, This represents the relative response amplitude and phase of the p-th mode at the i-th measurement point.

[0089] By adopting the embodiments of this application, frequency response characteristics can be obtained by performing time-frequency analysis on the second response parameters, the resonance peaks where the vibration energy of the stern structure is concentrated can be clearly identified in the frequency domain, and modal parameters such as natural frequency, damping ratio and mode shape can be quantitatively extracted from each resonance peak, thereby accurately obtaining the inherent vibration characteristics of the stern structure under actual working conditions.

[0090] Based on the above embodiments, as an optional embodiment, in order to accurately determine the vibration mechanism type corresponding to each mode from the identified multi-mode parameters and distinguish different vibration modes such as bending-dominant, torsional-dominant, and bending-torsional coupling, the above operation S240 may further include the following operations.

[0091] Operate S510 to determine the mode shapes in each modal parameter; each modal parameter corresponds to a resonance peak. Operate the S520 to analyze the deformation characteristics of each mode shape in the spatial distribution of the measurement points; Operation S530 determines the vibration type corresponding to each mode based on deformation characteristics; the vibration type includes at least one of bending vibration, torsional vibration and coupled vibration; wherein, bending vibration characterizes the vibration type in which the stern structure undergoes lateral flexural deformation; torsional vibration characterizes the vibration type in which the stern structure undergoes torsional deformation around the longitudinal axis; coupled vibration characterizes the vibration type in which the stern structure undergoes both bending and torsional deformation simultaneously.

[0092] In operation S510, the mode shape refers to the spatial distribution pattern of relative displacement or acceleration at each measurement point of the stern structure at a certain natural frequency. It can be understood as a set of vectors describing the overall deformation pattern of the stern structure under a specific mode.

[0093] It should be noted that, following the above operations, multiple resonance peaks and corresponding modal parameters of the stern structure have been identified. Each modal parameter includes the natural frequency, damping ratio, and mode shape of that mode. The mode shape is composed of the response amplitude and phase at each measurement point at that natural frequency, and after normalization, it forms a feature vector describing the spatial deformation mode.

[0094] For example, for the p-th mode, its mode shape can be represented as an M-dimensional complex vector or a real vector, where the i-th component of the vector corresponds to the relative response amplitude and phase information of the i-th measurement point under that mode. When the measurement points are arranged at different spatial locations of the stern structure, the spatial distribution characteristics of the mode shape vector can reflect whether the stern structure undergoes overall bending, torsion around the axis, or a coupling deformation mode at that natural frequency.

[0095] In the operation of S520, deformation characteristics refer to the geometric change law of the mode shape in the spatial distribution of the stern structure. It can be understood as extracting spatial characteristic quantities that can characterize the vibration mode category by analyzing the amplitude, phase relationship and distribution trend of the modal response at each measurement point.

[0096] In one feasible implementation, the modal relationship of the measuring points at symmetrical positions on the port and starboard sides can be observed along the transverse direction of the stern structure. When the modal response amplitudes of the symmetrical measuring points on the port and starboard sides are close and the phases are consistent, it indicates that the modal exhibits a symmetrical distribution characteristic in the transverse direction. When the modal response phases of the symmetrical measuring points on the port and starboard sides are opposite or the amplitudes differ significantly, it indicates that the modal exhibits an antisymmetric distribution characteristic in the transverse direction.

[0097] In another feasible implementation, the modal vibration trend of different longitudinal measurement points can be observed along the longitudinal direction of the stern structure. When the modal response amplitude shows a gradient distribution or a wave-like distribution along the longitudinal direction, it indicates that the mode has longitudinal bending deformation characteristics. When the modal response amplitude of the measurement points at different distances from the longitudinal central axis on the same cross section increases linearly with the increase of distance, it indicates that the section has torsional angle variation characteristics around the longitudinal axis.

[0098] For example, let the set of symmetrical measurement point pairs on the port and starboard sides be {(Lm, Rm)}, m = 1, 2, ..., Ns, where Lm is the port side measurement point index in the m-th pair, and Rm is the starboard side measurement point index in the m-th pair. For the p-th mode shape, the transverse symmetry index can be defined as the amplitude average of the sum of the responses of each symmetrical measurement point pair, and the transverse antisymmetry index can be defined as the amplitude average of the difference in the responses of each symmetrical measurement point pair. When the symmetry index is significantly greater than the antisymmetry index, the mode shape exhibits a symmetrical distribution in the transverse direction; when the antisymmetry index is significantly greater than the symmetry index, the mode shape exhibits an antisymmetric distribution in the transverse direction.

[0099] In operation S530, the vibration type is determined based on the extracted deformation features for classification.

[0100] Specifically, when the mode shapes of a certain mode exhibit a symmetrical distribution in the transverse direction and show typical bending waveform changes in the longitudinal direction, while the amplitude of the measurement point response mainly reflects vertical or transverse displacement components, and the torsional characteristics around the longitudinal axis are weak, this mode is identified as bending vibration. This vibration type reflects that the stern structure mainly undergoes transverse flexural deformation at this natural frequency, similar to the bending vibration mode of a beam.

[0101] Specifically, when the mode shape of a certain mode exhibits an antisymmetric distribution in the transverse direction, meaning that the response phases of measuring points at symmetrical positions on the port and starboard sides are opposite, and the response amplitude of measuring points within the same cross section increases with increasing distance from the longitudinal central axis, it indicates that the section mainly undergoes angular changes around the longitudinal axis, while the overall longitudinal bending characteristics are weak. In this case, the mode is identified as torsional vibration. This vibration type reflects the torsional deformation of the stern structure around the longitudinal axis at this natural frequency, similar to the torsional vibration mode of a shaft.

[0102] Specifically, when a certain mode exhibits both significant transverse or longitudinal bending waveform distribution and obvious antisymmetric characteristics in the transverse direction, meaning that bending and torsional deformations coexist in space and their amplitudes are not negligible, this mode is classified as coupled vibration. This vibration type reflects that the stern structure undergoes both bending and torsional deformations simultaneously at this natural frequency, with the two deformation modes coupling with each other.

[0103] In one feasible implementation, bending characteristic thresholds and torsional characteristic thresholds can be set. By comparing the magnitudes of the lateral symmetry index, antisymmetry index, and longitudinal bending gradient index with the corresponding thresholds, the vibration type corresponding to each mode can be automatically determined according to preset judgment rules. For example, when the lateral symmetry index is greater than the bending characteristic threshold and the antisymmetry index is less than the torsional characteristic threshold, it is determined to be bending vibration; when the antisymmetry index is greater than the torsional characteristic threshold and the symmetry index is less than the bending characteristic threshold, it is determined to be torsional vibration; when both the symmetry index and the antisymmetry index are at a moderate level or both exceed their respective thresholds, it is determined to be coupled vibration.

[0104] By adopting the embodiments of this application, based on the identified mode shapes, the vibration type corresponding to each mode can be accurately determined as bending vibration, torsional vibration, or coupled vibration by analyzing the symmetry, antisymmetry, and deformation gradient characteristics of the spatial distribution of measurement points in different directions. This provides a mode shape-level judgment basis for subsequently screening out the target coupled modes related to the torsional vibration excitation of the propulsion shaft system by combining the matching relationship between the main engine speed and the modal frequency.

[0105] Based on the above embodiments, as an optional embodiment, in order to screen out the dangerous modes from the identified multi-modes that pose a resonance risk with the rotational excitation of the propulsion shaft system and can cause abnormal vibrations in the stern structure, a correlation between the main engine speed condition and the vibration response of the stern structure is established. The above operation S250 may further include the following operations.

[0106] Operator S610 calculates the main engine operating fundamental frequency based on the main engine rotation speed; the main engine operating fundamental frequency characterizes the basic frequency of the propulsion shaft rotational motion. Operate S620 to determine multiple excitation orders of the propulsion shaft system; the excitation order is an integer multiple of the main engine's operating fundamental frequency, corresponding to the periodic excitation frequency generated by the propulsion shaft system during rotation; Operate S630 to calculate the frequency deviation between the natural frequency of each modal parameter and the frequency of each excitation order for each modal parameter; Operate S640 to determine whether the frequency deviation is less than the preset frequency matching threshold; if the frequency deviation is less than the frequency matching threshold and the vibration type of the corresponding mode is torsional vibration or coupled vibration, then the mode of the corresponding order is determined as the target coupled mode.

[0107] In the operation of S610, the operating base frequency of the main unit refers to the frequency at which the output shaft of the propulsion main unit completes a rotation cycle per unit time. It can be understood as the most basic frequency component of the rotational motion of the propulsion shaft system.

[0108] It should be noted that the main engine speed is usually measured in revolutions per minute (rpm), while the frequency used in frequency domain analysis is measured in Hertz (Hz), and there is a conversion relationship between the two. The main engine operating fundamental frequency is equal to the main engine speed divided by 60, and this frequency corresponds to the excitation frequency generated by the propulsion shaft per revolution.

[0109] In the operation of S620, the excitation order refers to the excitation frequency generated by the propulsion shaft system during rotation that is an integer multiple of the base frequency of the main engine. It can be understood as the higher-order excitation components caused by periodic factors such as the number of propeller blades, shaft imbalance, and gear meshing.

[0110] It should be noted that during rotation, the propulsion shaft system generates excitation not only at the fundamental frequency of the main engine but also at frequencies that are integer multiples of the fundamental frequency. For propellers, the blade passage frequency is several times the fundamental frequency; for gear transmission systems, the meshing frequency is several times the fundamental frequency; and for shaft torsional vibration, the torsional vibration frequencies are usually close to integer multiples of the fundamental frequency. These integer multiples of frequencies are collectively referred to as excitation orders.

[0111] For example, the excitation order may include at least one of the shaft frequency, blade passage frequency, gear meshing frequency, and shaft torsional vibration frequency. Depending on the ship type and propulsion system characteristics, it is usually necessary to consider the frequency components of multiple excitation orders.

[0112] In operation S630, frequency deviation refers to the absolute value of the difference between the natural frequency of a certain mode of the stern structure and the excitation frequency of a certain mode of the propulsion shaft system. It can be understood as a numerical value that quantifies the degree of closeness between the natural frequency and the excitation frequency of the mode.

[0113] In one feasible implementation, for each modal parameter, the absolute value of the difference between the natural frequency of the modal and the frequencies of all considered excitation orders can be calculated one by one to obtain the set of frequency deviations between the modal and each excitation order. The minimum frequency deviation is selected as the evaluation index of the frequency matching degree between the modal and the propulsion shaft system excitation.

[0114] In operation S640, the frequency matching threshold refers to the critical value of frequency deviation that determines whether there is a risk of resonance between the modal natural frequency and the excitation frequency. It can be understood as the criterion that the excitation frequency falls within the modal resonance bandwidth when the frequency deviation is less than the threshold.

[0115] It should be noted that even if the modal natural frequency and the excitation frequency do not completely coincide, a significant resonant amplification effect will still occur when they are sufficiently close. The setting of the frequency matching threshold needs to comprehensively consider the modal damping ratio, excitation intensity, and allowable response amplification factor. Modes with smaller damping ratios correspond to narrower resonant bandwidths and require smaller frequency matching thresholds; modes with larger damping ratios correspond to wider resonant bandwidths and can be set with larger frequency matching thresholds.

[0116] In one feasible implementation, the frequency matching threshold can be set as a preset percentage of the natural frequency, thereby allowing the frequency matching threshold to adaptively adjust with the magnitude of the natural frequency. In another feasible implementation, the resonant bandwidth can be calculated based on the modal damping ratio, and a preset proportion of the resonant bandwidth can be used as the frequency matching threshold, thus ensuring that the frequency matching determination matches the actual resonant characteristics of the mode.

[0117] It should be noted that frequency matching alone is insufficient to determine whether a mode will cause abnormal vibration in the stern structure; a comprehensive assessment is also necessary, taking into account the vibration type of the mode. When a certain mode matches the excitation frequency of the propulsion shaft system, but the vibration type of this mode is bending vibration, the torsional excitation of the propulsion shaft system mainly causes torque in the torsional direction, and its excitation effect on the bending mode is limited, resulting in a typically small response amplitude for this mode. However, when the vibration type of the mode is torsional vibration or coupled vibration, the torsional excitation of the propulsion shaft system can effectively excite this mode, leading to significant torsional deformation or bending-torsional coupled deformation in the stern structure, causing abnormal vibration and fatigue damage accumulation.

[0118] Therefore, based on the premise that the frequency deviation meets the matching condition, the vibration type of the corresponding mode is further determined. Only when the vibration type is torsional vibration or coupled vibration is the mode identified as the target coupled mode. This set of target coupled modes is the focus of subsequent fatigue damage assessment and identification of dangerous speed ranges.

[0119] By adopting the embodiments of this application, the excitation frequencies of each order of the propulsion shaft system can be calculated based on the main engine speed. By comparing the deviations between the natural frequencies of each modal of the stern structure and the excitation frequencies, and combining the modal vibration type information, the target coupled modes that have a frequency matching relationship with the torsional vibration excitation of the propulsion shaft system and can be effectively excited can be accurately screened. This provides an accurate modal screening basis for subsequent evaluation of the fatigue damage accumulation of the stern structure in different speed ranges based on the target coupled modes.

[0120] Based on the above embodiments, as an optional embodiment, in order to quantitatively assess the cumulative fatigue damage of the stern structure under different main engine speed conditions and identify the dangerous speed range leading to structural fatigue, the above operation S260 may further include the following operations.

[0121] By operating S710, the operating range of the main unit's speed is divided into multiple speed intervals; Operating S720, strain response time history data at key locations of the stern structure are extracted for each speed range; the strain response time history data characterizes the sequence of strain measurements at key locations over time within that speed range. Operate S730 to identify strain cycle characteristics in strain response time history data and count the number of cycles corresponding to each strain amplitude to obtain statistical results; Operating S740, based on statistical results and combined with preset material fatigue characteristic curves, calculates the cumulative fatigue damage corresponding to each speed range; the material fatigue characteristic curves characterize the fatigue life characteristics of the stern structure material under different stress amplitudes; By operating the S750, fatigue damage accumulation and fatigue damage accumulation rate are used to generate stern structure deformation monitoring results.

[0122] In the operation of S710, the speed range refers to several speed segments obtained by dividing the operating range of the host speed according to a preset interval. It can be understood as discretizing a continuous speed range into multiple sub-intervals in order to evaluate fatigue damage characteristics in segments.

[0123] It should be noted that the main engine speed covers a wide range from idle to maximum speed during operation. The excitation frequency of the propulsion shaft system varies at different speeds, resulting in differences in the vibration response characteristics of the stern structure. Dividing the speed range into multiple intervals allows for separate analysis of the strain response characteristics and fatigue damage accumulation of the stern structure within each speed range.

[0124] In one feasible implementation, the operating range can be divided into equal intervals according to a fixed rotational speed interval.

[0125] In another feasible implementation, based on the natural frequency and excitation order relationship of the target coupled mode, a denser rotational speed interval can be set near the rotational speed at which resonance is expected to occur, and a sparser rotational speed interval can be set in the region far from the resonance rotational speed, thereby reducing the amount of computation while ensuring the resolution of the dangerous area.

[0126] In the operation of S720, strain response time history data refers to the sequence of strain measurement values ​​continuously collected by the strain sensor within a specific speed range as a function of time. It can be understood as a discrete time sequence reflecting the dynamic deformation process of the stern structure under that speed condition.

[0127] In one feasible implementation, strain response data can be acquired in real time during the actual operation of the ship by using strain sensors deployed at key locations. The strain sensors can be of various types, such as resistance strain gauges, fiber optic grating sensors, or piezoelectric thin-film sensors, selected based on the environmental conditions at the measurement point, accuracy requirements, and cost factors.

[0128] In another feasible implementation, strain response time history data can be calculated based on a numerical simulation model of the stern structure. Specifically, excitation loads of the propulsion shaft system corresponding to the rotational speed range are applied in the finite element model, transient dynamic analysis is performed, and the strain response at key locations as a function of time is calculated.

[0129] In operation S730, strain cyclic characteristics refer to the strain amplitude and its variation law reflected in the strain response time history data. It can be understood as a cyclic load characteristic quantity that describes how the strain changes back and forth within a certain amplitude range.

[0130] It should be noted that fatigue damage originates from the cumulative cyclic plastic deformation of materials under alternating stress. The amplitude of strain cycles and the number of cycles are key parameters for fatigue damage assessment. The larger the strain amplitude, the greater the damage caused by a single cycle; the more cycles, the greater the cumulative damage.

[0131] In one feasible implementation, rainflow counting can be used to process strain response time history data. Rainflow counting is a widely adopted international standard method for counting fatigue load cycles. Its basic principle is to simulate the flow of rainwater along the strain time history curve and identify strain cycles through specific flow rules. Specifically, rainflow counting uses each peak and trough in the strain time history as a potential cycle starting point, and determines which peak-trough combinations constitute a complete strain cycle according to predetermined rainflow rules. For each identified strain cycle, its strain amplitude is calculated, defined as half the difference between the maximum and minimum strain values ​​in the cycle, and the average strain value of that cycle is recorded. The number of cycles corresponding to each strain amplitude level is statistically analyzed to form a statistical distribution of strain amplitude versus number of cycles.

[0132] In another feasible implementation, either peak counting or range counting can be used for cycle identification. Peak counting treats each local maximum value in the strain time history as one cycle, and the cycle amplitude is equal to the difference between the peak value and the previous valley value; range counting treats the range between adjacent peaks and valleys in the strain time history as one cycle.

[0133] In operation S740, the material fatigue characteristic curve refers to the characteristic relationship curve describing the number of fatigue cycles that a material can withstand under different stress amplitudes. It can be understood as the constitutive relationship reflecting the material's fatigue resistance.

[0134] It should be noted that material fatigue characteristic curves are typically obtained through material fatigue testing. In this test, a cyclic load with a constant stress amplitude is applied to a standard specimen, and the number of cycles at which fatigue failure occurs is recorded. Multiple sets of tests are conducted for different stress amplitude levels to obtain the correlation between stress amplitude and fatigue life. This relationship is usually expressed as a logarithmic relationship between stress amplitude and fatigue life, appearing as an approximately straight line in a logarithmic coordinate system, known as the SN curve, where S represents the stress amplitude and N represents the number of fatigue life cycles. The SN curve shows that the larger the stress amplitude, the fewer cycles the material can withstand; after the stress amplitude decreases to a certain level, the material can withstand an infinite number of cycles without fatigue failure; this stress amplitude is called the fatigue limit.

[0135] In one feasible implementation, the linear cumulative damage theory can be used to calculate the cumulative fatigue damage. Also known as Miner's rule, this is the most commonly used damage accumulation criterion in fatigue analysis. The basic assumption of this theory is that fatigue damage generated under different stress amplitudes can be linearly superimposed, and fatigue failure occurs when the total damage accumulates to a critical value. Specifically, the actual number of cycles corresponding to each strain amplitude is calculated as a ratio to the allowable number of cycles given by the material fatigue characteristic curve at that strain amplitude, yielding the partial damage degree at each strain amplitude level. The partial damage degree represents the actual fatigue life consumed at that strain amplitude level, numerically equal to the actual number of cycles divided by the allowable number of cycles. The partial damage degrees of all strain amplitude levels are summed to obtain the total cumulative fatigue damage for that rotational speed range.

[0136] The cumulative fatigue damage is a dimensionless parameter ranging from 0 to 1. A cumulative fatigue damage of 0 indicates that the structure has not experienced any fatigue damage and is in a brand-new state; a cumulative fatigue damage of 1 indicates that the fatigue life of the structure has been completely exhausted, and fatigue failure will theoretically occur. In engineering practice, considering the uncertainty of the calculation model, the dispersion of material properties, and safety margin requirements, the allowable value of the cumulative fatigue damage is usually set to a value less than 1. When the cumulative fatigue damage reaches the allowable value, the structure needs to be inspected, repaired, or replaced.

[0137] In the operation of S750, the fatigue damage accumulation rate refers to the growth rate of the accumulated fatigue damage per unit time or unit running time. It can be understood as a rate index that characterizes how fast fatigue damage develops in the stern structure within a specific speed range.

[0138] It should be noted that the same cumulative fatigue damage may correspond to different operating durations in different speed ranges. While the total cumulative fatigue damage in a certain speed range may be small, if the actual operating time in that range is short, its fatigue damage accumulation rate may be high, indicating that the structural fatigue life is being consumed rapidly per unit time in that speed range. Conversely, while the total cumulative fatigue damage in a certain speed range may be large, if that range is operated continuously for a long period, its fatigue damage accumulation rate may be low, indicating that that speed range is relatively safe. The fatigue damage accumulation rate can more accurately reflect the degree of danger in each speed range and is an important indicator for identifying dangerous speed ranges.

[0139] A high rate of fatigue damage accumulation at specific speeds indicates that the stern structure experiences severe vibration, frequent strain cycles, and large amplitudes at these speeds, leading to rapid depletion of fatigue life over extended periods. This high damage rate typically corresponds to a situation where the propulsion shaft excitation frequency resonates or nearly resonates with the natural frequency of the coupling mode of the stern structure. This significantly amplifies structural vibrations and dramatically increases the strain response amplitude, resulting in rapid accumulation of fatigue damage. Once these critical speed ranges are identified, appropriate operational control measures should be implemented, such as avoiding prolonged operation within these ranges, quickly navigating through them, and adjusting engine speed by changing ship speed or propeller pitch to avoid these ranges, in order to extend the fatigue life of the stern structure.

[0140] In one feasible implementation, the cumulative fatigue damage in each speed range can be divided by the actual operating time of that speed range to obtain the cumulative fatigue damage rate for that speed range. The actual operating time can be obtained from ship operation records, main engine operation logs, or data acquisition systems.

[0141] For example, the stern structure deformation monitoring results may include at least one of the following: cumulative fatigue damage value for each speed range, cumulative fatigue damage rate value, critical speed range identifier, and predicted remaining fatigue life of the stern structure.

[0142] By adopting the embodiments of this application, the operating range of the main engine speed can be divided into multiple intervals. For each speed interval, strain response data of key positions of the stern structure can be extracted. Through strain cycle statistics and fatigue damage calculation, the cumulative amount and rate of fatigue damage in each speed interval can be quantitatively evaluated, and the deformation monitoring results of the stern structure can be generated. This provides a scientific basis for identifying dangerous speed intervals, optimizing the main engine operation strategy, and extending the fatigue life of the stern structure.

[0143] Based on the above embodiments, as an optional embodiment, the above method may further include the following operations.

[0144] Operate S760 to determine the fatigue damage accumulation rate for each speed range; the fatigue damage accumulation rate characterizes the amount of fatigue damage accumulated per unit time. When the fatigue damage accumulation rate exceeds the preset damage rate threshold, the corresponding speed range is marked as a dangerous speed range by operating S770. Operate S780 to generate warning information based on the cumulative fatigue damage in each speed range and the identification results of the dangerous speed range.

[0145] In operation S760, the fatigue damage accumulation rate is determined by dividing the accumulated fatigue damage in each speed range by the actual operating time of that speed range. The actual operating time can be extracted from the ship's main engine operation record system. The fatigue damage accumulation rate reflects the rate at which the fatigue life of the stern structure is consumed at a specific speed.

[0146] In operation S770, the damage rate threshold refers to the critical value for determining whether a speed range constitutes a risk of fatigue damage. In one feasible implementation, the average cumulative fatigue life of the stern structure can be divided by the total number of operating hours corresponding to the expected service life to obtain the average fatigue damage rate; this average rate can then be multiplied by a safety factor to obtain the damage rate threshold. In another feasible implementation, speed ranges whose cumulative fatigue damage rate exceeds a preset percentile of the rate distribution across all speed ranges can be marked as dangerous speed ranges.

[0147] In operation S780, the prompt information may include at least one of the following: the specific range of the dangerous speed range, the ranking of the cumulative fatigue damage in each speed range, the operation recommendations for the dangerous speed range, and the prediction of the remaining fatigue life of the stern structure. The operation recommendations can set different operation strategies according to the level of danger, such as "prohibit long-term operation", "limit operation time", or "enhance monitoring".

[0148] like Figure 2 As shown, Figure 2 This application discloses a ship stern structure deformation monitoring system. The ship stern structure deformation monitoring system includes: The system comprises the following modules: an acquisition module for acquiring measurement data of the ship, including first response parameters of the stern structure, rigid body motion parameters of the ship as a whole, and main engine speed of the propulsion shafting; the first response parameters are obtained based on measurements taken at at least one measurement point located at a key position on the stern structure; a calculation module for separating the rigid body motion components caused by the rigid body motion parameters to the first response parameters from the measurement data to obtain second response parameters of the stern structure; a first determination module for determining modal parameters of the stern structure based on the second response parameters; modal parameters characterize the dynamic vibration characteristics of the stern structure; a second determination module for determining the vibration type of the stern structure based on the modal parameters of the stern structure; a third determination module for determining the target coupled modes related to the propulsion shafting excitation based on the frequency matching relationship between the main engine speed and the modal parameters, and the vibration type; and a generation module for determining the cumulative fatigue damage of the stern structure in different main engine speed ranges based on the target coupled modes to obtain the deformation monitoring results of the stern structure.

[0149] According to an embodiment of this application, the calculation module is further configured to determine the spatial positional relationship of each measurement point relative to the measurement position of the rigid body motion parameters; calculate the rigid body motion components of each measurement point based on the reference point linear acceleration, angular velocity, and angular acceleration of the entire ship and the spatial positional relationship; subtract the rigid body motion components from the first response parameters to obtain the second response parameters. According to an embodiment of this application, the first determining module is further configured to perform time-frequency analysis on the second response parameters to obtain the frequency response characteristics of the stern structure; the frequency response characteristics characterize the vibration energy distribution of the stern structure in the frequency domain; identify resonance peaks based on the frequency response characteristics; the resonance peaks correspond to the natural vibration frequencies of the stern structure; extract the modal parameters corresponding to each resonance peak; the modal parameters include at least one of natural frequency, damping ratio, and mode shape; wherein, the natural frequency characterizes the vibration frequency of the stern structure under a specific vibration mode; the damping ratio characterizes the vibration energy dissipation capability of the stern structure; and the mode shape characterizes the spatial deformation mode of the stern structure at a specific natural frequency.

[0150] According to an embodiment of this application, the second determining module is further configured to determine the mode shape in each modal parameter; each modal parameter corresponds to a resonance peak; analyze the deformation characteristics of each mode shape in the spatial distribution of the measurement points; determine the vibration type corresponding to each mode based on the deformation characteristics; the vibration type includes at least one of bending vibration, torsional vibration and coupled vibration; wherein, bending vibration characterizes the vibration type in which the stern structure undergoes lateral flexural deformation; torsional vibration characterizes the vibration type in which the stern structure undergoes torsional deformation around the longitudinal axis; coupled vibration characterizes the vibration type in which the stern structure undergoes both bending and torsional deformation simultaneously.

[0151] According to an embodiment of this application, the third determining module is further configured to calculate the host operating fundamental frequency based on the host rotation speed; the host operating fundamental frequency characterizes the basic frequency of the propulsion shaft system's rotational motion; determine multiple excitation orders of the propulsion shaft system; the excitation order is an integer multiple of the host operating fundamental frequency, corresponding to the periodic excitation frequency generated by the propulsion shaft system during rotation; for each modal parameter, calculate the frequency deviation between the natural frequency of the modal parameter and the frequency of each excitation order; determine whether the frequency deviation is less than a preset frequency matching threshold; if the frequency deviation is less than the frequency matching threshold, and the vibration type of the corresponding mode is torsional vibration or coupled vibration, then the mode of the corresponding order is determined as the target coupled mode.

[0152] According to an embodiment of this application, the generation module is further configured to divide the operating range of the main engine speed into multiple speed ranges; for each speed range, extract strain response time history data at key locations of the stern structure; the strain response time history data characterizes the strain measurement value sequence of the key location changing with time within the speed range; identify the strain cycle characteristics in the strain response time history data and count the number of cycles corresponding to each strain amplitude to obtain statistical results; based on the statistical results and combined with a preset material fatigue characteristic curve, calculate the cumulative fatigue damage corresponding to each speed range; the material fatigue characteristic curve characterizes the fatigue life characteristics of the stern structure material under different stress amplitudes; and generate stern structure deformation monitoring results based on the cumulative fatigue damage and fatigue damage accumulation rate of each speed range.

[0153] According to an embodiment of this application, the generation module is further configured to determine the fatigue damage accumulation rate of each speed range; the fatigue damage accumulation rate characterizes the amount of fatigue damage accumulated per unit time; when the fatigue damage accumulation rate exceeds a preset damage rate threshold, the corresponding speed range is marked as a dangerous speed range; based on the amount of fatigue damage accumulation in each speed range and the identification result of the dangerous speed range, a prompt message is generated.

[0154] Figure 3 This is a block diagram of an electronic device provided in an embodiment of this application. Figure 3 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0155] like Figure 3 As shown, an electronic device according to an embodiment of this application includes a processor 301, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 302 or a program loaded from a memory 308 into a random access memory (RAM) 303. The processor 301 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 301 may also include onboard memory for caching purposes. The processor 301 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of this application.

[0156] RAM 303 stores various programs and data required for the operation of the electronic device. Processor 301, ROM 302, and RAM 303 are interconnected via bus 304. Processor 301 executes various operations of the method flow according to embodiments of this application by executing programs in ROM 302 and / or RAM 303. It should be noted that the programs may also be stored in one or more memories other than ROM 302 and RAM 303. Processor 301 may also execute various operations of the method flow according to embodiments of this application by executing programs stored in said one or more memories.

[0157] According to embodiments of this application, the electronic device may further include an input / output (I / O) interface 306, and an input / output (I / O) interface 304 is also connected to a bus 304. The electronic device may also include one or more of the following components connected to the input / output (I / O) interface 304: an input device 306 including a keyboard, mouse, etc.; an output device 307 including a cathode ray tube (CRT), liquid crystal display (LCD), display screen, etc., and a speaker, etc.; a memory 308 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN card, modem, etc. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the input / output (I / O) interface 304 as needed. A removable medium 311, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 310 as needed so that computer programs read from it can be installed into the memory 308 as needed.

[0158] According to embodiments of this application, the method flow according to embodiments of this application can be implemented as a computer software program. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowchart. In such embodiments, the computer program can be downloaded and installed from a network via communication section 309, and / or installed from removable medium 311. When the computer program is executed by processor 301, it performs the functions defined in the system of embodiments of this application. According to embodiments of this application, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0159] This application also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this application.

[0160] According to embodiments of this application, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0161] For example, according to embodiments of this application, a computer-readable storage medium may include the ROM 302 and / or RAM 303 described above and / or one or more memories other than ROM 302 and RAM 303.

[0162] Embodiments of this application also include a computer program product comprising a computer program containing program code for performing the methods provided in the embodiments of this application. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the methods provided in the embodiments of this application.

[0163] When the computer program is executed by the processor 301, it performs the functions defined in the system / apparatus of this application embodiment. According to the embodiments of this application, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0164] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via communication section 309, and / or installed from removable medium 311. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0165] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Those skilled in the art will understand that the features recited in the various embodiments and / or claims of this application can be combined and / or combined in various ways, even if such combinations or combinations are not expressly stated in this application. In particular, the various embodiments and / or features described in the claims of this application may be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application.

[0166] The embodiments of this application have been described above. However, these embodiments are merely illustrative and not intended to limit the scope of this application. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of this application is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this application, and all such substitutions and modifications should fall within the scope of this application.

Claims

1. A method for monitoring deformation of a ship's stern structure, characterized in that, include: Acquire measurement data of the ship, the measurement data including a first response parameter of the stern structure of the ship, rigid body motion parameters of the ship as a whole, and main engine speed of the ship's propulsion shaft system; the first response parameter is obtained based on at least one measurement point set at a key position on the stern structure; The rigid body motion component caused by the rigid body motion parameter to the first response parameter is separated from the measurement data to obtain the second response parameter of the stern structure; The modal parameters of the stern structure are determined based on the second response parameters; the modal parameters characterize the dynamic vibration characteristics of the stern structure. Based on the modal parameters of the stern structure, the vibration type of the stern structure is determined; Based on the frequency matching relationship between the main engine rotation speed and the modal parameters, and the vibration type, the target coupled mode related to the propulsion shaft system excitation is determined; Based on the target coupling mode, the cumulative fatigue damage of the stern structure under different main engine speed ranges is determined, and the deformation monitoring results of the stern structure are obtained.

2. The method according to claim 1, wherein the key locations include at least one of the following: stern bearing housing location, stern longitudinal girder location, and steering gear compartment bulkhead location; the rigid body motion parameters include the reference point linear acceleration, angular velocity, and angular acceleration of the entire ship; The step of separating the rigid body motion component caused by the rigid body motion parameter to the first response parameter from the measurement data to obtain the second response parameter of the stern structure includes: Determine the spatial positional relationship of each measurement point relative to the measurement position of the rigid body motion parameters; Based on the reference point linear acceleration, angular velocity, and angular acceleration of the entire ship, as well as the spatial positional relationship, calculate the rigid body motion components of each measurement point; The second response parameter is obtained by subtracting the rigid body motion component from the first response parameter.

3. The method according to claim 1, characterized in that, Determining the modal parameters of the stern structure based on the second response parameter includes: Time-frequency analysis is performed on the second response parameter to obtain the frequency response characteristics of the stern structure; the frequency response characteristics characterize the vibration energy distribution of the stern structure in the frequency domain; Resonance peaks are identified based on the frequency response characteristics; the resonance peaks correspond to the natural vibration frequencies of the stern structure. Extract the modal parameters corresponding to each resonance peak; the modal parameters include at least one of natural frequency, damping ratio, and mode shape; Wherein, the natural frequency characterizes the vibration frequency of the stern structure under a specific vibration mode; the damping ratio characterizes the vibration energy dissipation capability of the stern structure; and the mode shape characterizes the spatial deformation mode of the stern structure at a specific natural frequency.

4. The method according to claim 3, characterized in that, The vibration type of the stern structure is determined based on the modal parameters of the stern structure. Determine the mode shapes in each of the modal parameters; each modal parameter corresponds to a specific resonance peak. Analyze the deformation characteristics of each mode shape in the spatial distribution of the measurement points; Based on the deformation characteristics, the vibration type corresponding to each mode is determined; the vibration type includes at least one of bending vibration, torsional vibration, and coupled vibration. Wherein, the bending vibration characterizes the vibration type in which the stern structure undergoes lateral flexural deformation; the torsional vibration characterizes the vibration type in which the stern structure undergoes torsional deformation around the longitudinal axis; and the coupled vibration characterizes the vibration type in which the stern structure undergoes both bending and torsional deformation simultaneously.

5. The method according to claim 4, characterized in that, The determination of the target coupled mode related to the propulsion shaft system excitation based on the frequency matching relationship between the main engine rotation speed and the modal parameters, and the vibration type, includes: The operating fundamental frequency of the main engine is calculated based on the main engine rotation speed; the operating fundamental frequency of the main engine represents the basic frequency of the rotational motion of the propulsion shaft system. Multiple excitation orders are determined for the propulsion shaft system; the excitation order is an integer multiple of the base frequency of the main engine, corresponding to the periodic excitation frequency generated by the propulsion shaft system during rotation; For each modal parameter, the frequency deviation between the natural frequency of the modal parameter and the frequency of each excitation order is calculated; Determine whether the frequency deviation is less than a preset frequency matching threshold; If the frequency deviation is less than the frequency matching threshold, and the vibration type of the corresponding mode is the torsional vibration or the coupled vibration, then the mode of the corresponding order is determined as the target coupled mode.

6. The method according to claim 1, characterized in that, The determination of the cumulative fatigue damage of the stern structure under different engine speed ranges based on the target coupled mode, and the obtaining of the deformation monitoring results of the stern structure, includes: The operating range of the host machine's rotation speed is divided into multiple rotation speed intervals; For each of the aforementioned rotational speed ranges, strain response time history data at key locations of the stern structure are extracted; the strain response time history data characterizes the sequence of strain measurements at the key locations over time within that rotational speed range. The strain cycle characteristics in the strain response time history data are identified, and the number of cycles corresponding to each strain amplitude is counted to obtain statistical results; Based on the statistical results and combined with the preset material fatigue characteristic curve, the cumulative fatigue damage corresponding to each rotational speed range is calculated; the material fatigue characteristic curve characterizes the fatigue life characteristics of the stern structure material under different stress amplitudes. Based on the cumulative fatigue damage and the cumulative fatigue damage rate in each of the aforementioned speed ranges, the deformation monitoring results of the stern structure are generated.

7. The method according to claim 6, characterized in that, The method further includes: Determine the fatigue damage accumulation rate for each of the aforementioned rotational speed ranges; the fatigue damage accumulation rate characterizes the amount of fatigue damage accumulated per unit time. When the fatigue damage accumulation rate exceeds a preset damage rate threshold, the corresponding speed range is marked as a dangerous speed range. Based on the cumulative fatigue damage in each of the aforementioned speed ranges and the identification results of the dangerous speed ranges, a warning message is generated.

8. A ship stern structure deformation monitoring system, characterized in that, include: The acquisition module is used to acquire measurement data of the ship, including a first response parameter of the stern structure of the ship, rigid body motion parameters of the ship as a whole, and main engine speed of the ship's propulsion shaft system; the first response parameter is obtained based on at least one measurement point set at a key position on the stern structure; The calculation module is used to separate the rigid body motion component caused by the rigid body motion parameter to the first response parameter from the measurement data, and obtain the second response parameter of the stern structure; The first determining module is used to determine the modal parameters of the stern structure based on the second response parameters; The modal parameters characterize the dynamic vibration characteristics of the stern structure; The second determining module is used to determine the vibration type of the stern structure based on the modal parameters of the stern structure; The third determining module is used to determine the target coupled mode related to the propulsion shaft system excitation based on the frequency matching relationship between the host rotation speed and the modal parameters, as well as the vibration type. The generation module is used to determine the cumulative fatigue damage of the stern structure under different engine speed ranges based on the target coupling mode, and to obtain the deformation monitoring results of the stern structure.

9. An electronic device, comprising: One or more processors; Memory, used to store one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1 to 7.

10. A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform the method of any one of claims 1 to 7.

Images