A non-parametric modeling method for ship propulsion shafting and its dynamic characteristics analysis method

Abstract

The invention provides a non-parametric modeling of a ship propulsion shaft system and an analysis method of its dynamic characteristics, belonging to the technical field of ship propulsion shaft system analysis. The method establishes a non-parametric dynamic model of the ship propulsion shaft system; various uncertainties in the operation process of the ship propulsion shaft system are added to the non-parametric dynamic model of the ship propulsion shaft system; a motion differential equation of the ship propulsion shaft system under the action of uncertainty is established; the Runge-Kutta method is used to obtain the dynamic response of the ship propulsion shaft system, the uncertainty of the output of the ship propulsion shaft system is simulated, and the dynamic characteristics of the ship propulsion shaft system are analyzed to obtain the vibration characteristics of the dynamic response under the conditions of data uncertainty and model uncertainty of the ship shaft system. The method reveals the uncertain operation state of the propulsion shaft system, provides a basis for the dynamic characteristics analysis of the propulsion shaft system, and also provides a new method for vibration monitoring and state evaluation of the propulsion shaft system.

Description

Technical Field

[0001] The present invention relates to the technical field of ship propulsion shaft system analysis, and in particular to a method for establishing a ship propulsion shaft system dynamics model containing uncertainty, which is a non-parametric dynamics modeling method, and a method for solving the ship propulsion shaft system motion differential equation and studying and analyzing the dynamic characteristics. Background Art

[0002] During the navigation of a ship, the propulsion shaft system will be affected by many dynamic nonlinear factors, such as hull deformation, wind and wave currents, bearing dynamic stiffness, etc. In the previous studies on the operation status and dynamic characteristics of the ship propulsion shaft system, the influence of these dynamic factors was mostly ignored. However, recent studies have shown that the influence of these dynamic factors often causes the actual operation status of the ship propulsion shaft system to have strong uncertainty. Therefore, establishing a dynamic model with uncertainty to analyze the dynamic characteristics of the ship propulsion shaft system has received increasing attention.

[0003] In recent decades, the method of describing the propulsion shafting system with dynamic models has developed rapidly, but there are still many problems. For example, the geometric dimensions, mechanical parameters, material properties, etc. of the propulsion shafting system will change with the changes in dynamic factors and cannot be accurately expressed, which will cause certain data uncertainties. Due to the complex structure of the ship propulsion shafting system, some irregularly shaped components such as bolts and meshing gears are difficult to describe with accurate mathematical models and can only be processed by some simplified methods, which will cause certain model uncertainties.

[0004] With the addition of data uncertainty and model uncertainty, the uncertainty of the model calculation output results will inevitably lead to uncertainty. The dynamic response of the propulsion shaft system output is random, nonlinear, and the operating state is also uncertain. These uncertainties will cause the dynamic response of the ship propulsion shaft system theoretically calculated to have a large deviation from the vibration signal of the actual ship test. It is difficult for theoretical calculations to accurately guide the state assessment and fault monitoring of the shaft system, and it is difficult to establish an accurate calculation model, and it is impossible to obtain a unified description of the model based on a single method. The existing technology lacks a method that simultaneously considers data uncertainty and model uncertainty to model and analyze dynamic characteristics. Therefore, there is an urgent need for a method that considers uncertainty to study the dynamic characteristics of the ship propulsion shaft system. Summary of the invention

[0005] According to the above-mentioned existing methods for calculating the dynamic response of the propulsion shaft system, it is difficult to accurately guide the state assessment and fault monitoring of the shaft system. Therefore, this patent proposes a non-parametric modeling method of a ship propulsion shaft system and an analysis method of its dynamic characteristics, which is characterized by comprising the following steps:

[0006] Establish a non-parametric dynamic model of the ship propulsion shaft system;

[0007] In the non-parametric dynamic model of the ship propulsion shaft system, various uncertainties in the operation process of the ship propulsion shaft system are added;

[0008] Establish the differential equation of motion of the ship propulsion shaft system under the action of uncertainty;

[0009] The Runge-Kutta method is used to obtain the dynamic response of the ship propulsion shaft system, simulate the uncertainty of the ship propulsion shaft system output, and analyze the dynamic characteristics of the ship propulsion shaft system to obtain the vibration characteristics of the dynamic response under the conditions of ship shaft system data uncertainty and model uncertainty.

[0010] Furthermore, the process of establishing the non-parametric dynamic model of the ship propulsion shaft system is as follows:

[0011] SG0 based on the mean value model of ship propulsion shaft system and random matrix + Ensemble, combining the maximum entropy principle and random matrix theory, using Lagrangian operators, derives the optimal probability density function expression;

[0012] By controlling the size of the divergence control parameter δ, the mass matrix of the ship propulsion shaft system is adjusted [ M ], stiffness matrix[ K ], damping matrix[ C ] by adding the uncertainty into the random sample matrix [M] of mass matrix, the random sample matrix [K] of stiffness matrix and the random sample matrix [C] of damping matrix, and a non-parametric dynamic model of ship propulsion shafting is established.

[0013] Furthermore, the uncertainties include: hull deformation, bearing stiffness changes, temperature changes and propeller excitation force changes.

[0014] Furthermore, the divergence control parameters are set to 0, 0.2, 0.5, and 0.8 respectively.

[0015] Furthermore, the mass matrix random sample matrix [ M ], Stiffness matrix random sample matrix [ K ], random sample matrix of damping matrix [ C ] are all produced by using a method for generating a random matrix in a non-parametric modeling method, wherein the method for generating a random matrix in the non-parametric modeling method comprises the following steps:

[0016] Assuming that the matrix [A], which is the mass, stiffness or damping matrix of the system, is an n×n random matrix and is symmetric and positive definite, its probability density function p[ A ] The following three conditions must be met:

[0017]

[0018] Where: is the space containing all positive definite symmetric real matrices; v = E{ln(det[A])}E is the mathematical expectation;

[0019] In order to make the constructed random matrix meet the above three conditions, it is necessary to establish the Lagrange function of the system through the maximum entropy principle, solve the Lagrange function, and obtain the probability density function of [A] after obtaining the optimal solution:

[0020]

[0021] Where [A] is a random matrix [ A ], c A is a positive constant, and its calculation formula is:

[0022]

[0023] In the formula, is the Gamma function, and λ is a parameter that has not yet been determined in the derivation process;

[0024] The variance of a random matrix [A] is expressed as:

[0025]

[0026] because

[0027]

[0028] Where: j, k represent the number of rows and columns of the matrix respectively;

[0029] By setting a divergence control parameter δ A , then, the formula for calculating λ is derived as:

[0030]

[0031] For an n-dimensional random system, the divergence control parameter δ controls the size of the uncertainty. A The larger the value, the smaller λ is; when λ is infinite, the variance σ of the random matrix jk and the divergence control parameter δ A tends to infinitesimal, and the random matrix [A] also tends to the mean matrix [ A ];

[0032] From the above analysis, we can see that the random matrix [ A The construction of ] is mainly related to the divergence control parameter δ A Related; by controlling the divergence control parameter δ A, for the mean matrix [ A ] to simulate and obtain the corresponding random matrix [A], and there are multiple random matrices; the mean matrix can be any positive definite symmetric real matrix [ A ], first perform Cholesky factorization on it, and then [ A ] is decomposed into the product of a lower triangular matrix and an upper triangular matrix:

[0033] [ A ]=[L A ] T [L A ] (8)

[0034] Where, L A is an upper triangular matrix in the real field;

[0035] Assume that λ is a positive integer, let m A =n-1+2λ, the random matrix [A] can be simulated by the following formula:

[0036]

[0037] Where U j is a set of vectors that satisfy the standard normal distribution and are independent of each other;

[0038] If λ is a non-positive integer, it is processed according to the following rules:

[0039] (3) For the random variables L on the off-diagonal line of the matrix [A] n,jj' (j<j′) has

[0040] L n,jj' =σ n U jj' (10)

[0041] In the formula, σ n =δ(n+1) -1 / 2 ,U jj' is a random variable that follows a standard normal distribution;

[0042] (4) For the random variable L on the diagonal of the matrix [A] n,jj' (j=j′), we have:

[0043]

[0044] Where v is a positive Gamma random variable. And the density function of the probability distribution of v is:

[0045]

[0046] Therefore, through the mean matrix [ A ]Get the random matrix samples of the system, the random matrix samples are distributed in a certain range and are controlled by the divergence control parameters; by adding the random matrix samples to the mean dynamics model, the random matrix model of the ship propulsion shaft system is obtained.

[0047] Furthermore, the mean matrix [A] is simulated using the Monte Carlo method.

[0048] Furthermore, the uncertainty includes the influence of the mass matrix, the stiffness matrix and the damping matrix on the dynamic response of the shaft system under the separate effects.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] The present invention is based on random matrix The ensemble is combined with the maximum entropy principle and the Lagrangian operator to derive the optimal probability density function expression. By controlling the divergence control parameter δ and adding uncertainty to the mass matrix [M], the stiffness matrix [K] and the damping matrix [C], a non-parametric dynamic model of the ship propulsion shaft system is established. Finally, the Runge-Kutta method is used to solve the corresponding dynamic equations of the non-parametric dynamic model and analyze its dynamic characteristics. In addition, based on the ship propulsion shaft system, the present invention introduces a non-parametric modeling method to establish a non-parametric dynamic model of the ship propulsion shaft system taking into account data uncertainty, model uncertainty and output uncertainty, analyzes the uncertainty of the model output, extracts the vibration characteristics of the propulsion shaft system dynamic response, and reveals the uncertain operating state of the propulsion shaft system, which provides a basis for the dynamic characteristics analysis of the propulsion shaft system and also provides a new method for vibration monitoring and state assessment of the propulsion shaft system. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0052] Figure 1 It is a flow chart of a method for non-parametric modeling of a ship propulsion shaft system and analysis of its dynamic characteristics according to the present invention;

[0053] Figure 2 This is a schematic diagram of a ship propulsion shafting test bench in an embodiment of the present invention;

[0054] Figure 3 is a mean dynamics model diagram of a ship propulsion shaft system in an embodiment of the present invention;

[0055] Figure 4 (a) is the ship propulsion shaft system in the embodiment of the present invention without considering the uncertainty factor, that is, the divergence control parameter δ M =δ C =δ K = 0, the time domain waveform of the ship shafting at the aft bearing;

[0056] Figure 4 (b) is the ship propulsion shaft system in the embodiment of the present invention without considering the uncertainty factor, that is, the divergence control parameter δ M =δ C =δ K = 0, the time-frequency spectrum of the ship shafting at the aft bearing;

[0057] Figure 4 (c) is the divergence control parameter δ of the ship propulsion shaft system in the embodiment of the present invention without considering the uncertainty factor. M =δ C =δ K = 0, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0058] Figure 5 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.2, time domain waveform of the ship shafting at the aft bearing;

[0059] Figure 5 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.2, the spectrum diagram of the ship shafting at the aft bearing;

[0060] Figure 5 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.2, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0061] Figure 6 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.5, the time domain waveform of the ship shafting at the aft bearing;

[0062] Figure 6 (b) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.5, the spectrum diagram of the ship shafting at the aft bearing;

[0063] Figure 6 (c) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.5, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0064] Figure 7 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.8, time domain waveform of the ship shafting at the aft bearing;

[0065] Figure 7 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.8, the spectrum diagram of the ship shafting at the aft bearing;

[0066] Figure 7 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.8, the axis trajectory diagram of the ship shaft system at the stern aft bearing.

[0067] Figure 8 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ C =δ K =0,δ M =0.5, the time domain waveform of the ship shafting at the aft bearing;

[0068] Figure 8 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ C =δ K =0,δ M =0.5, the spectrum diagram of the ship shafting at the aft bearing;

[0069] Figure 8(c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ C =δ K =0,δ M =0.5, the axis trajectory diagram of the ship shafting at the stern aft bearing.

[0070] Fig. 9 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ K =0,δ C =0.5, the time domain waveform of the ship shafting at the aft bearing;

[0071] Fig. 9 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ K =0,δ C =0.5, the spectrum diagram of the ship shafting at the aft bearing;

[0072] Fig. 9 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ K =0,δ C =0.5, the axis trajectory diagram of the ship shafting at the stern aft bearing.

[0073] Fig.10 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =0,δ K =0.5, the time domain waveform of the ship shafting at the aft bearing;

[0074] Fig.10 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =0,δ K =0.5, the spectrum diagram of the ship shafting at the aft bearing;

[0075] Fig.10 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =0,δ K =0.5, the axis trajectory diagram of the ship shafting at the stern aft bearing.

[0076] In the figure: 1. Motor; 2. Elastic coupling; 3. Intermediate bearing; 4. Shaft system; 5. Bearing position adjustment device; 6. Front stern bearing; 7. Rear stern bearing; 8. Three-axis acceleration sensor; 9. Counterweight plate. DETAILED DESCRIPTION

[0077] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0078] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0079] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, the numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be clear that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The technology, methods and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, methods and equipment should be regarded as part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0080] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. If not otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0081] The composition of the ship propulsion shaft system used in the present invention is as follows Figure 1 As shown, the ship propulsion shaft system includes a motor 1, an elastic coupling 2, an intermediate bearing 3, a shaft system 4, a bearing position adjustment device 5, a stern front bearing 6, a stern rear bearing 7, a three-axis acceleration sensor 8, and a counterweight plate 9;

[0082] The motor 1 is connected to one end of the elastic coupling 2, the other end of the elastic coupling 2 is connected to one end of the intermediate bearing 3, the other end of the intermediate bearing 3 is connected to one end of the shaft system 4, the other end of the shaft system 4 is connected to one end of the front stern bearing 6, the other end of the front stern bearing 6 is connected to one end of the rear stern bearing 7 through the shaft system, the other end of the rear stern bearing 7 is connected to one end of the three-axis acceleration sensor 8, and the other end of the three-axis acceleration sensor 8 is connected to the counterweight plate 9; the front stern bearing 6 is also connected to the bearing position adjustment device 5.

[0083] The present invention provides a method for non-parametric modeling of a ship propulsion shaft system and analysis of its dynamic characteristics, comprising the following steps:

[0084] S1. Combined with the structural characteristics of the ship propulsion shafting test bench, the ship propulsion shafting is simplified into a mean dynamics model of multiple concentrated masses. Based on the mean dynamics model, the excitation force in the model is determined, and various uncertainties in the operation of the ship propulsion shafting are added to the non-parametric dynamics model of the ship propulsion shafting; and the motion differential equation of the ship propulsion shafting under the action of uncertainty is established. Among them, the method for establishing the motion differential equation of the mean dynamics model is as follows:

[0085]

[0086] In the formula, [ M ]、[ C ]、[ K ] are the mass matrix, damping matrix and stiffness matrix of the mean value calculation model, and they are all n×n order positive definite symmetric real matrices. M ]From the actual ship propulsion shaft system, [ K ] can be obtained by the flexibility coefficient method, [ C ] can be generated by the proportional damping method: [ C ]=α[ M ]+β[ K ], α and β are proportional coefficients determined by experiments. [F x ]、[F y ] is the lateral and longitudinal excitation force on the system, generally considered: gravity G g , acting on the entire shaft, in a downward direction; unbalanced force F e =m i eω 2 , acting on each concentrated disk, the direction changes periodically, where m iis the mass of each concentrated disk, e is the mass eccentricity, ω is the angular velocity of rotation; the nonlinear oil film force F exerted on the shaft at the front bearing, intermediate bearing and stern bearing generally adopts the improved unsteady-state nonlinear oil film force model proposed in 1991 - Capone model.

[0087] S2: The Runge-Kutta method is used to obtain the dynamic response of the ship propulsion shaft system, simulate the uncertainty of the ship propulsion shaft system output, and analyze the dynamic characteristics of the ship propulsion shaft system to obtain the vibration characteristics of the dynamic response under the conditions of ship shaft system data uncertainty and model uncertainty.

[0088] Furthermore, the process of establishing the non-parametric dynamic model of the ship propulsion shaft system is as follows:

[0089] Based on the mean value model and random matrix of ship propulsion shaft system Ensemble, combining the maximum entropy principle and random matrix theory, using Lagrangian operators, derives the optimal probability density function expression;

[0090] By controlling the size of the divergence control parameter δ, the mass matrix of the ship propulsion shaft system is adjusted [ M ], stiffness matrix[ K ], damping matrix[ C ] by adding the uncertainty into the random sample matrix [M] of mass matrix, the random sample matrix [K] of stiffness matrix and the random sample matrix [C] of damping matrix, and a non-parametric dynamic model of ship propulsion shafting is established.

[0091] Furthermore, the uncertainty includes dynamic factors such as “hull deformation, bearing stiffness, temperature change, propeller excitation force”; further, the mass matrix random sample matrix [ M ], Stiffness matrix random sample matrix [ K ], random sample matrix of damping matrix [ C ] are all produced by using a method for generating a random matrix in a non-parametric modeling method, wherein the method for generating a random matrix in the non-parametric modeling method comprises the following steps:

[0092] 1 Assume that the matrix [A], which is the mass, stiffness or damping matrix of the system, is an n×n random matrix and is symmetric and positive definite, then its probability density function p is [A] The following three conditions must be met:

[0093]

[0094] Where: is the space containing all positive definite symmetric real matrices; v = E{ln(det[A])}, where E is the mathematical expectation.

[0095] 2 In order to make the constructed random matrix meet the above three conditions, it is necessary to establish the Lagrange function of the system through the maximum entropy principle. After that, the Lagrange function is solved and the optimal solution is obtained, and the probability density function of [A] can be obtained:

[0096]

[0097] Where [A] is a random matrix [ A ], c A is a positive constant, and its calculation formula is

[0098]

[0099] In the formula, is the Gamma function, and λ is a parameter that has not been determined in the derivation process.

[0100] The variance of a random matrix [A] can be expressed as:

[0101]

[0102] Where j is the number of matrix rows and k is the number of matrix columns.

[0103] because

[0104]

[0105] Where: j, k represent the number of rows and columns of the matrix respectively;

[0106] By setting a divergence control parameter δ A , then, we can deduce that the λ calculation formula is:

[0107]

[0108] From the above formula, we can see that for an n-dimensional random system, the divergence control parameter δ that controls the uncertainty size is A The larger the value, the smaller λ is; when λ is infinite, the variance σ of the random matrix jk and the divergence control parameter δ A tends to infinitesimal, and the random matrix [A] also tends to the mean matrix [ A ].

[0109] 3 From the above analysis, we can see that the construction of the random matrix [A] is mainly related to the divergence control parameter δ A By controlling the divergence control parameter δ A , for the average matrix [ A] can be simulated by Monte Carlo method, and the corresponding random matrix [A] can be obtained. In addition, there can be multiple random matrices. For any positive definite symmetric real matrix [ A ], first perform Cholesky factorization on it, and [ A ] is decomposed into the product of a lower triangular matrix and an upper triangular matrix:

[0110] [ A ]=[L A ] T [L A ] (8)

[0111] Where, L A is an upper triangular matrix in the real field.

[0112] Assume that λ is a positive integer, let m A =n-1+2λ, the random matrix [A] can be simulated by the following formula:

[0113]

[0114] Where U j is a set of vectors that satisfy the standard normal distribution and are independent of each other.

[0115] If λ is a non-positive integer, it is processed according to the following rules:

[0116] (5) For the random variables L on the off-diagonal line of the matrix [A] n,jj' (j<j′) has

[0117] L n,jj' =σ n U jj' (10)

[0118] In the formula, σ n =δ(n+1) -1 / 2 ,U jj' is a random variable that follows a standard normal distribution, U jj It is a random variable that obeys the standard normal distribution and can be randomly generated by MATLAB.

[0119] (6) For the random variable L on the diagonal of the matrix [A] n,jj' (j=j′), we have

[0120]

[0121] Where v is a positive Gamma random variable. And the density function of the probability distribution of v is

[0122]

[0123] Therefore, the mean matrix [ A ] get the random matrix samples of the system, which are distributed in a certain range and controlled by the divergence control parameter. By adding these random matrix samples to the mean dynamics model, the random matrix model of the system can be obtained.

[0124] Furthermore, based on the obtained random matrices [M], [C], and [K], combined with the above mean value model, a random matrix model is established, and its motion differential equation is in the form of:

[0125]

[0126] where [M], [C] and [K] are random matrices corresponding to the mean mass, damping and stiffness matrices, respectively, and are controlled by the divergence parameter δ M , δ C , δ K Determine the sample space of its random matrix. At this time, the dynamic model includes the vibration state of the ship shaft system including data uncertainty and model uncertainty, and then its vibration response characteristics can be studied.

[0127] The scheme and effects of the present invention are further described below through specific application examples.

[0128] In this embodiment, the specific parameters of the mean value model of the ship propulsion shaft system are: m1=5kg, m2=2.53kg, m3=2.78kg, m4=7.05kg, m5=9.05kg, m6=7.94kg, m7=15kg, c1=1050N·s / m, c2=2100N·s / m, c3=1050N·s / m, c4=2100N·s / m, c5=1050N·s / m, c6=2100N·s / m, c7=1050N·s / m, k1=3.1×108N / m, k2=7.8×106N / m, k3=3.42×105N / m, k4=3.9×106N / , where [ M ]=[m10 0 0 0 0; 0 m2 0 0 0 0; 0 0 m3 0 0 0 0; 0 0 0 m4 0 0 0; 0 0 0 0 m5 0 0; 0 0 0 0 0 0m6 0; 0 0 0 0 0 0 m7], [ C ]=[c1 0 0 0 0 0,0 c2 0 0 0 0,0 0 c3 0 0 0 0,0 0 0 c40 0 0,0 0 0 0 c5 0 0,0 0 0 0 0 c6 0,0 0 0 0 0 0 c7],[ K]=[k1 -k1 0 0 0 0 0, -k1 k1+k2 -k2 0 0 0 0; 0 -k2 2k2 -k2 0 0 0; 0 0 -k2 k2+k3 -k3 0 0; 0 0 0 -k3 2k3 -k3 0; 0 0 0 0 -k3 k3+k4 -k4; 0 0 0 0 0 -k4 k4]. Figure 2 This is a schematic diagram of a ship propulsion shafting test bench in an embodiment of the present invention; Figure 3 is a mean dynamic model diagram of the ship propulsion shaft system in the embodiment of the present invention; the mass divergence control parameter δ M , damping divergence control parameter δ C The control parameters of stiffness divergence are set to 0, 0.2, 0.5, and 0.8, and the uncertainty of mass matrix, stiffness matrix, and damping matrix are applied separately. A total of seven calculations are performed, and the number of samples each time is 10,000 (see Appendix Figures 4 to 10 Only one of them is randomly selected);

[0129] Figure 4 (a) is the ship propulsion shaft system in the embodiment of the present invention without considering the uncertainty factor, that is, the divergence control parameter δ M =δ C =δ K = 0, the time domain waveform of the ship shafting at the aft bearing; Figure 4 (b) is the ship propulsion shaft system in the embodiment of the present invention without considering the uncertainty factor, that is, the divergence control parameter δ M =δ C =δ K = 0, the time-frequency spectrum of the ship shafting at the aft bearing; Figure 4 (c) is the divergence control parameter δ of the ship propulsion shaft system in the embodiment of the present invention without considering the uncertainty factor. M =δ C =δ K = 0, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0130] Figure 5 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.2, time domain waveform of the ship shafting at the aft bearing; Figure 5 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.2, the spectrum diagram of the ship shafting at the aft bearing; Figure 5(c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.2, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0131] Figure 6 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.5, the time domain waveform of the ship shafting at the aft bearing; Figure 6 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.5, the spectrum diagram of the ship shafting at the aft bearing; Figure 6 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.5, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0132] Figure 7 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.8, time domain waveform of the ship shafting at the aft bearing; Figure 7 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.8, the spectrum diagram of the ship shafting at the aft bearing; Figure 7 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =δ K =0.8, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0133] Figure 8 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ C =δ K =0,δ M =0.5, the time domain waveform of the ship shafting at the aft bearing; Figure 6(b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ C =δ K =0,δ M =0.5, the spectrum diagram of the ship shafting at the aft bearing; Figure 6 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ C =δ K =0,δ M =0.5, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0134] Fig. 9 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ K =0,δ C =0.5, the time domain waveform of the ship shafting at the aft bearing; Figure 6 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ K =0,δ C =0.5, the spectrum diagram of the ship shafting at the aft bearing; Figure 6 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ K =0,δ C =0.5, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0135] Fig.10 (a) is the ship propulsion shaft system in the embodiment of the present invention, considering the uncertainty factor and the divergence control parameter δ M =δ C =0,δ K =0.5, the time domain waveform of the ship shafting at the aft bearing; Figure 6 (b) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =0,δ K =0.5, the spectrum diagram of the ship shafting at the aft bearing; Figure 6 (c) is the case where the ship propulsion shaft system in the embodiment of the present invention takes into account the uncertainty factor and the divergence control parameter δ M =δ C =0,δ K =0.5, the axis trajectory diagram of the ship shaft system at the stern rear bearing;

[0136] Each sample is taken from Figures 4 to 10 Just randomly select one of them;

[0137] This example is based on the consideration of the influence of uncertain factors. First, the divergence control parameters of mass, stiffness, and damping are set to 0. The time domain waveform, spectrum, and axis trajectory of the ship shafting at the stern bearing are as follows: Figure 4 As shown in (a), (b) and (c).

[0138] Secondly, the divergence control parameters of mass, stiffness and damping are 0.2, and the time domain waveform, spectrum and axis trajectory of the ship shafting at the stern bearing are drawn again, as shown in Figure 5 As shown in (a), (b) and (c).

[0139] Then the divergence control parameters of mass, stiffness and damping are set to 0.5, and the time domain waveform, spectrum and axis trajectory of the ship shafting at the stern bearing are drawn again, as shown in Figure 6 As shown in (a), (b) and (c).

[0140] Then the divergence control parameters of mass, stiffness and damping are set to 0.8, and the time domain waveform, spectrum and axis trajectory of the ship shafting at the stern bearing are drawn again, as shown in Figure 7 As shown in (a), (b) and (c).

[0141] Then the divergence control parameters of stiffness and damping are 0, and the divergence control parameter of mass is 0.5. The time domain waveform, spectrum and axis trajectory of the ship shafting at the stern bearing are drawn again, as shown in Figure 8 As shown in (a), (b) and (c).

[0142] Then the divergence control parameters of mass and stiffness are 0, and the divergence control parameter of damping is 0.5. The time domain waveform, spectrum and axis trajectory of the ship shafting at the stern bearing are drawn again, as shown in Fig. 9 As shown in (a), (b) and (c).

[0143] Then the divergence control parameters of damping and stiffness are 0, and the divergence control parameter of stiffness is 0.5. The time domain waveform, spectrum and axis trajectory of the ship shafting at the stern bearing are drawn again, as shown in Fig.10 As shown in (a), (b) and (c).

[0144] In the process of non-parametric modeling, 10,000 random samples are generated each time. Due to the large amount of data, after statistical analysis, these samples are randomly selected to calculate the dynamic response of the ship propulsion shaft system. Here, one random sample is randomly selected and the vibration response diagram of this embodiment is given.

[0145] In this example, the divergence control parameters are adjusted to simulate the strength of uncertainty. As can be seen from the figure, the time domain waveforms, spectra, and axis trajectories calculated for these samples show certain differences, such as Figure 5 Basic and Figure 4 The shapes of the time domain waveform, spectrum and axis trajectory of are slightly different. Its vibration response is a single sine curve in the time history, and no other frequency multiples are generated in the spectrum diagram, indicating that when the uncertainty of the system is small, the vibration response of the shaft system does not change much; Figure 6 Although the vibration response is still a periodic signal in the time history, it is no longer a single sine curve, and other signal components appear. From the spectrum, it can also be seen that there is a half-frequency component in the system vibration response, and the axis trajectory of the system has a double elliptical trajectory; when the uncertainty increases to a large extent, such as Figure 7 , the time domain waveform of the ship propulsion shaft system presents a double peak with unequal amplitudes. The amplitude of the half-frequency component in the spectrum diagram has increased compared with the previous one. The degree of disorder of the axis trajectory has increased, presenting multiple elliptical orbits, indicating that the uncertainty factor has caused the system to exhibit nonlinear behavior. This is due to the addition of uncertainty, which is reflected in the mass, stiffness, and damping matrices of the ship propulsion shaft system as a process of diverging from the mean matrix to the vicinity. The degree of divergence is controlled by the divergence control parameters. Therefore, the calculation results of these random samples also reflect the uncertainty of the output. The vibration response of each random sample is a possible operating state of the ship propulsion shaft system. Finally, according to Figure 8 , Fig. 9 , Fig.10 It can be analyzed that when uncertainty is applied to mass, damping and stiffness separately, the uncertainty in stiffness has a more obvious impact on the dynamic response of the shaft system when the same uncertainty is applied.

[0146] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for non-parametric modeling of a ship propulsion shaft system and analysis of its dynamic characteristics, characterized in that: Includes: includes the following steps: Establish a non-parametric dynamic model of the ship propulsion shaft system; In the non-parametric dynamic model of the ship propulsion shaft system, the uncertainty of the ship propulsion shaft system operation process is added; Establish the differential equation of motion of the ship propulsion shaft system under the action of uncertainty; The Runge-Kutta method is used to obtain the dynamic response of the ship propulsion shaft system, simulate the uncertainty of the ship propulsion shaft system output, and analyze the dynamic characteristics of the ship propulsion shaft system to obtain the vibration characteristics of the dynamic response under the conditions of ship shaft system data uncertainty and model uncertainty; The process of establishing the non-parametric dynamic model of the ship propulsion shaft system is as follows: SG0 based on the mean value model of ship propulsion shaft system and random matrix + Ensemble, combining the maximum entropy principle and random matrix theory, using Lagrangian operators, derives the optimal probability density function expression; By controlling the size of the divergence control parameter δ and adjusting the size of the uncertainty added to the mass matrix, stiffness matrix and damping matrix of the ship propulsion shaft system, the random sample matrix of the mass matrix, the random sample matrix of the stiffness matrix and the random sample matrix of the damping matrix are obtained, and a non-parametric dynamic model of the ship propulsion shaft system is established.

2. The method for non-parametric modeling of a ship propulsion shaft system and analysis of its dynamic characteristics according to claim 1, characterized in that: The uncertainties include: hull deformation, bearing stiffness changes, temperature changes and propeller excitation force changes.

3. The method for non-parametric modeling of a ship propulsion shaft system and analysis of its dynamic characteristics according to claim 1, characterized in that: The divergence control parameters are set to 0, 0.2, 0.5, and 0.8 respectively.

4. The method for non-parametric modeling of a ship propulsion shaft system and analysis of its dynamic characteristics according to claim 1, characterized in that: The uncertainty includes the influence of the mass matrix, the stiffness matrix and the damping matrix on the dynamic response of the shaft system under the separate effects.

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