Rigidity distribution optimization method based on elastic beam driving bionic fish body

Abstract

The invention discloses a rigidity distribution optimization method based on an elastic beam driving bionic fish body, and belongs to the field of underwater bionic robots. According to the method, the problem that the swimming performance of the bionic fish body is poor due to the fact that an existing method cannot achieve overall rigidity distribution optimization of the bionic fish body is solved. According to the method, a parameter vector composed of a characteristic size, an elastic modulus, a Poisson's ratio and a damping parameter is selected as an optimization variable, and a center line movement track is calculated through an elastic beam deformation track, a rigid fish head track, a tail peduncle track, a tail fin track and a middle beam deformation track on the two sides of a bionic fish body; the parameter vectors are iteratively searched and updated according to the midline motion trail and the rigidity distribution scheme, so that the optimization range is expanded from the tail to the whole bionic fish body, the flexibility and continuity of the full length of the fish body are realized, the obtained rigidity distribution optimization result is closer to the swimming mechanism of real fish, and the swimming performance of the bionic fish body is improved. The method can be applied to rigidity distribution optimization of the elastic beam driven bionic fish body.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of underwater bionic robots, and particularly relates to a stiffness distribution optimization method for a bionic fish body driven by elastic beams. BACKGROUND

[0002] Among various bionic fish driving mechanisms, the elastic beam driving mode, as a new scheme, has advantages such as compact structure, continuously adjustable driving waveform and few control parameters, and provides a new idea for the exploration, development and research of the ocean. The bionic fish of this type takes the muscle tissue on both sides of the fish body as the bionic object, constructs artificial muscles by arranging super-elastic beams on both sides and the tail of the fish body, and realizes the swimming of the fish body by the periodic bending deformation of the elastic beams.

[0003] However, the stiffness distribution of the elastic beam directly determines the fish body wave when the bionic fish swims, thereby affecting the swimming performance. Due to the strong nonlinear dynamic characteristics of the rigid-elastic-flow coupling of the driving system, it is difficult to optimize the stiffness distribution. At present, the stiffness optimization design method for the bionic fish of this driving mechanism mostly focuses on the optimization of the local stiffness distribution of the tail fin, and there is still a lack of overall stiffness distribution optimization method throughout the fish body, so the range of stiffness distribution optimization is limited, resulting in the overall stiffness distribution result showing the characteristics of localization, discretization and segmentation, and further resulting in the poor swimming performance of the bionic fish body. SUMMARY

[0004] The purpose of the present application is to solve the problem of poor swimming performance of the bionic fish body due to the inability of the existing method to realize the overall stiffness distribution optimization of the bionic fish body, and a stiffness distribution optimization method for a bionic fish body driven by elastic beams is proposed.

[0005] The technical scheme adopted by the present application to solve the above technical problem is: a stiffness distribution optimization method for a bionic fish body driven by elastic beams, which specifically comprises the following steps:

[0006] Step 1: establishing a dynamic model of a bionic fish body driven by elastic beams, the elastic beams being arranged on both sides of the fish body and at the tail of the bionic fish body, respectively;

[0007] Step 2: discretizing the elastic beams on both sides of the bionic fish body and the elastic beam at the keel of the bionic fish body into N segments along the longitudinal direction, respectively, and selecting a parameter vector for the stiffness distribution optimization of the elastic beams;

[0008] Step 3: optimizing the parameter vector in step 2 by using a stiffness distribution optimization algorithm, and designing the elastic beams according to the optimized parameter vector to realize the optimization of the stiffness distribution of the elastic beams.

[0009] Further, the parameters in the parameter vector in step 2 include characteristic size, elastic modulus, Poisson's ratio and damping parameter.

[0010] Furthermore, the specific process of step three is as follows:

[0011] Step 3.1: Initialize the maximum number of iterations. The initial number of individuals in the population is set to Initialize the coefficient of maximum change. ;

[0012] Step 3.2: Initialize the population. The initial value of each individual is , In this context, the value of each individual represents a set of parameter vector values.

[0013] Step 33: Initialize the number of iterations ;

[0014] Steps three and four: ... The first generation of the population The value of each individual Loaded into the dynamic model, calculation Corresponding midline trajectory ;

[0015] Step 35: Based on the trajectory of movement along the center line Calculate the first The first generation of the population The objective function value corresponding to each individual. Based on the calculated objective function value, the first... The best individual in the population ;

[0016] The first The best individual in the current generation (pbest) is compared with the historical best individual (gbest) in the population. The better individual between pbest and gbest is taken as the historical best individual after the overall population update. ;

[0017] Step 36: Update the change coefficient as follows Calculate the first The first generation of the population The speed of individuals and according to Judge the first The first generation of the population The speed of individuals Does it meet the following requirements: ;

[0018] If satisfied ,but Keep it unchanged, and then proceed to step three seven;

[0019] If not satisfied Then when At that time, The value is updated to ,when At that time, The value is updated to Then proceed to step three seven;

[0020] Step 37: Based on the speed of each individual , No. The best individual in the population The best individual in history after the overall population update Update the individual's value to get the first... The first generation of the population The value of each individual ;

[0021] Step 38, Judgment The first in Are the parameters satisfied? ,in, express The Middle The values ​​of the parameters, Indicates the first The minimum value of each parameter. Indicates the first The maximum value of each parameter;

[0022] If satisfied ,but The first in The values ​​of the parameters remain unchanged;

[0023] If not satisfied Then when At that time, The value is updated to ,when At that time, The value is updated to ;

[0024] Traversal After each parameter in the sequence, we obtain the first... The first generation of the population The final value of each individual ;

[0025] Step 39: Determine if the number of iterations is satisfied. ;

[0026] If satisfied Then the best historical individual of the entire population will be updated. The corresponding parameter vector is used as the final parameter vector;

[0027] If not satisfied Then let Return to steps three and four.

[0028] Furthermore, the specific process of steps three and four is as follows:

[0029] Step 3-41, place the first The first generation of the population The value of each individual The deformation trajectory of the elastic beam on the left side of the bionic fish body was calculated by loading it into the dynamic model. Deformation trajectory of the elastic beam on the right side of the bionic fish body The trajectory of the rigid fish head in the bionic fish body The trajectory of the caudal peduncle of the biomimetic fish body The trajectory of the tail fin of the biomimetic fish body The deformation trajectory of the central beam located at the keel of the bionic fish body ;

[0030] Step 342: Based on the trajectories obtained in Step 341, calculate the midline motion trajectory to obtain the midline motion trajectory of the bionic fish body. :

[0031]

[0032] in, It is an intermediate variable.

[0033] Furthermore, the deformation trajectories of the left elastic beam, the right elastic beam, and the central elastic beam located at the keel of the bionic fish body are all calculated using the target shooting method.

[0034] Furthermore, the trajectories of the rigid fish head, the tail fin, and the bionic fish body are all calculated using multi-rigid-body dynamics.

[0035] Furthermore, the deformation trajectory of the left elastic beam of the bionic fish body is specifically as follows:

[0036]

[0037] in, Indicates the total number of time steps; Indicates the first One time step; Indicates the first A segment of elastic beam; the first segment of the matrix The row indicates the first row. The deformation trajectory of the elastic beam at the nth time step; the matrix at the nth time step. Column represents the first The matrix describes the motion behavior of each elastic beam on the left side of the bionic fish body in the whole driving cycle.

[0038] Further, the change amount coefficient is:

[0039]

[0040] wherein, represents a floor function.

[0041] Further, the intermediate variable is:

[0042]

[0043] Preferably, the target function value is:

[0044]

[0045] wherein, represents fish body wave simulation, represents energy transmission efficiency, represents average propulsion force, , and are , and corresponding weights, and the weight values satisfy .

[0046] The beneficial effects of the present application are:

[0047] The present application selects a parameter vector composed of characteristic size, elastic modulus, Poisson's ratio and damping parameter as an optimization variable, calculates the centerline motion trajectory through the deformation trajectory of the elastic beams on both sides of the bionic fish body, the trajectory of the rigid fish head, the trajectory of the tail filament, the trajectory of the tail fin and the deformation trajectory of the middle beam, and then iteratively searches and updates the parameter vector according to the centerline motion trajectory and the stiffness distribution scheme, so that the optimization range is expanded from the tail to the whole bionic fish body, thereby realizing the flexibility and continuity of the whole fish body, making the obtained stiffness distribution optimization result closer to the swimming mechanism of real fish, improving the swimming performance of the bionic fish body, and the optimized parameter vector can be used to guide the structure design and manufacturing of the actual bionic fish. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is a flowchart of a stiffness distribution optimization method of a bionic fish body driven by an elastic beam according to the present application;

[0049] Figure 2 is a flowchart of the variable optimization process. DETAILED DESCRIPTION

[0050] Specific implementation one: combination Figure 1 The present embodiment is described. The rigidity distribution optimization method based on the elastic beam driven bionic fish body described in the embodiment specifically includes the following steps:

[0051] Step one, establish the rigid-elastic-flow coupling dynamics model of the bionic fish body driven by the elastic beam (the model established in the present invention is the model in the literature "A novel robotic fish based on elastic beam actuation mechanism"), the elastic beam is arranged on both sides of the bionic fish body and the keel of the bionic fish body respectively;

[0052] It should be noted that the dynamics model includes the geometric parameters, physical parameters, driving parameters and size and material parameters of the elastic beam of the bionic fish. The geometric parameters of the bionic fish include length, width, height and elastic beam mounting position; the physical parameters of the bionic fish include overall mass and inertia tensor; the driving parameters of the bionic fish include driving frequency, amplitude and phase; the size parameters of the elastic beam include length, cross-sectional shape, characteristic size (such as radius of circular cross-section or length, width of rectangular cross-section); the material parameters of the elastic beam include density, elastic modulus, Poisson's ratio and damping coefficient of the material;

[0053] Step two, the elastic beams on both sides of the bionic fish body and the elastic beam at the keel of the bionic fish body are respectively discretized into N segments along the longitudinal direction, and a parameter vector for elastic beam rigidity distribution optimization is selected;

[0054] The following takes the elastic beam at the keel of the bionic fish body as an example to explain the discretization process in detail as follows:

[0055] The elastic beam at the keel of the bionic fish body is segmented along the longitudinal direction, and the longitudinal length of each segmented elastic beam is equal. Then the elastic beams on both sides of the bionic fish body are segmented respectively;

[0056] In the present invention, some parameters that have a greater impact on rigidity distribution optimization are used to construct the parameter vector. Through the optimization design of the present invention, the rigidity distribution optimization effect can be guaranteed to the greatest extent while ensuring the rigidity distribution optimization efficiency. The parameters in the selected parameter vector in the present invention include characteristic size, elastic modulus, Poisson's ratio and damping parameter. The designed parameter vector is used to represent the equivalent stiffness of each beam, and each group of parameter vectors corresponds to a specific rigidity distribution scheme.

[0057] Step three, use the rigidity distribution optimization algorithm to optimize the parameter vector in step two, and design the elastic beam according to the optimized parameter vector to realize the optimization of the rigidity distribution of the elastic beam.

[0058] The stiffness distribution optimization algorithm is described in detail as follows: Figure 2 The stiffness distribution optimization algorithm is described in detail as follows:

[0059] Step three one, initialize the maximum iteration number as , initialize the number of individuals in the population as , and initialize the maximum change coefficient ;

[0060] Step three two, initialize the initial value of the th individual in the population as , , wherein the value of each individual respectively represents a group of parameter vector values;

[0061] Step three three, initialize the iteration number ;

[0062] Step three four, load the value of the th individual in the population of the th generation to the dynamics model, calculate the corresponding centerline trajectory , specifically: Step three four one, load the value of the th individual in the population of the

[0063] th generation to the dynamics model, calculate the deformation trajectory of the left elastic beam of the bionic fish body , the deformation trajectory of the right elastic beam of the bionic fish body , the trajectory of the rigid fish head of the bionic fish body , the trajectory of the caudal filament of the bionic fish body , the trajectory of the caudal fin of the bionic fish body , and the deformation trajectory of the center beam located at the keel of the bionic fish body ; The deformation trajectory of the left elastic beam of the bionic fish body, the deformation trajectory of the right elastic beam of the bionic fish body, and the deformation trajectory of the center beam located at the keel of the bionic fish are calculated by the shooting method.

[0064] The trajectory of the rigid fish head of the bionic fish body, the trajectory of the caudal filament of the bionic fish body, and the trajectory of the caudal fin of the bionic fish body are all calculated by multi-rigid body dynamics.

[0065] The trajectory of the rigid fish head of the bionic fish body, the trajectory of the caudal filament of the bionic fish body, and the trajectory of the caudal fin of the bionic fish body are all calculated by multi-rigid body dynamics.

[0066] ​​Since the head, tail fin, and caudal fin of the bionic fish are all rigid bodies, the trajectory of any point on them can be represented by linear algebra to represent the trajectory of all points on the rigid body. Therefore, it is not necessary to discretize the head, tail fin, and caudal fin of the bionic fish into N segments. In this invention, the head, tail fin, and caudal fin are discretized into 0.25×N segments.

[0067] The deformation trajectory of the elastic beam on the left side of the bionic fish body is related to the arc length and time. Taking the deformation trajectory of the elastic beam on the left side of the bionic fish body as an example, the specific deformation trajectory of the elastic beam on the left side of the bionic fish body is as follows:

[0068]

[0069] in, Indicates the total number of time steps; Indicates the first One time step; Indicates the first A segment of elastic beam; the first segment of the matrix The row indicates the first row. The deformation trajectory of the elastic beam at the nth time step; the matrix at the nth time step. Column represents the first The motion behavior of each segment of the elastic beam throughout the entire time step is described by a matrix, which represents the motion behavior of each segment of the elastic beam on the left side of the bionic fish body throughout the entire driving cycle.

[0070] The deformation trajectories of the elastic beam on the right and the elastic beam at the keel are similar to those of the elastic beam on the left.

[0071] Step 342: Based on the fish's structure, the deformation trajectory of the elastic beam is equivalently converted to the fish's size information, and the lateral line deformation is equivalent to the central axis. That is, the central axis motion trajectory is calculated based on the trajectories obtained in Step 341 to obtain the central axis motion trajectory of the biomimetic fish. :

[0072]

[0073] The intermediate variable for:

[0074]

[0075] Step 35: Based on the trajectory of movement along the center line Calculate the first The first generation of the population The objective function value corresponding to each individual. Based on the calculated objective function value, the first... The best individual in the population ;

[0076] The first The best individual pbest in the current generation is compared with the historical best individual gbest in the population (i.e., compared by the objective function value), and the better individual between pbest and gbest is taken as the historical best individual after the overall population update. The updated historical best individual will be used as the population's historical best individual in the next iteration.

[0077] Step 36: Update the change coefficient as follows Calculate the first The first generation of the population The speed of individuals and according to Judge the first The first generation of the population The speed of individuals Does it meet the following requirements: ;in, ;

[0078] If satisfied ,but Keep it unchanged, and then proceed to step three seven;

[0079] If not satisfied Then when At that time, The value is updated to ,when At that time, The value is updated to Then proceed to step three seven;

[0080] Step 37: Based on the speed of each individual , No. The best individual in the population The best individual in history after the overall population update Update the individual's value to get the first... The first generation of the population The value of each individual ;

[0081] Step 38, Judgment The first in Are the parameters satisfied? ,in, express The Middle The values ​​of the parameters, Indicates the first The minimum value of each parameter. Indicates the first The maximum value of each parameter;

[0082] If satisfied ,but The first in The values ​​of the parameters remain unchanged;

[0083] If not satisfied Then when At that time, The value is updated to ,when At that time, The value is updated to ;

[0084] Traversal After each parameter in the sequence, we obtain the first... The first generation of the population The final value of each individual ;

[0085] Step 39: Determine if the number of iterations is satisfied. ;

[0086] If satisfied Then the best historical individual of the entire population will be updated. The corresponding parameter vector is used as the final parameter vector;

[0087] If not satisfied Then let Return to steps three and four.

[0088] It should be noted that the method of this invention is applicable to various cruise drive frequencies of bionic fish. The following section discusses the movement trajectory based on the centerline. Calculate the first The first generation of the population individual The specific process of obtaining the corresponding objective function value will be explained in detail:

[0089] First, performance indicators need to be extracted based on the centerline motion trajectory. Then, these performance indicators are quantified into objective function values, which are used to evaluate the merits of the stiffness distribution scheme. The calculated performance indicators include, but are not limited to, fish wave simulation, energy transfer efficiency, and average propulsion force.

[0090] 1. Fish body wave simulation:

[0091] By calculating the average distance between the longitudinal displacement of the centerline of the biomimetic fish actuated by the elastic beam and the longitudinal displacement of the corresponding node of the theoretical fish body wave over all time steps, the quality of the fish body wave simulation can be evaluated.

[0092]

[0093] in, This represents a fish body wave simulation. express The Middle Line number The value of the column, express The number of columns (i.e.) The corresponding total number of segments, with each elastic beam corresponding to N segments (assuming the fish head, tail fin, and tail section are each 0.25 × N segments). express The corresponding standard value, express and The distance;

[0094] 2. Energy transfer efficiency:

[0095] Calculate the average instantaneous energy transfer efficiency across all time steps to assess the utilization rate of the driving energy that can be provided to the fish:

[0096]

[0097] in, Indicates energy transfer efficiency. Indicates the first The energy of the elastic beam at the keel under time step. Indicates the first The energy of the elastic beam at the keel under time step. Indicates the first The sum of the energies of all elastic beams at time step, Indicates the first The sum of the energies of all elastic beams at time step, initialized and All are 0.

[0098] 3. Average thrust (AVERT)

[0099] Calculate the average propulsion force of the bionic fish actuated by the elastic beam over all time steps to evaluate the effectiveness of the bionic fish's forward propulsion:

[0100]

[0101] in, Indicates average thrust. express The quality of the last paragraph express The final segment's velocity in the lateral direction, express The Middle The quality of the segment express The Middle The speed of the segment in the lateral direction.

[0102] When optimizing an algorithm with a single objective, fish wave simulation, energy transfer efficiency, or average propulsion force can be selected as the objective function. When optimizing an algorithm with multiple objectives, it is necessary to combine the various performance indicators into a comprehensive coupled objective function based on their weight values ​​for calculation.

[0103]

[0104] Wherein, the weight values ​​satisfy .

[0105] Preferred version of the present invention As the objective function value, it can effectively guarantee the effect of stiffness distribution optimization.

[0106] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for optimizing the stiffness distribution of an elastic beam driven bionic fish body, characterized in that, The method specifically comprises the following steps: Step one, establishing a dynamic model of the bionic fish body driven by elastic beams, the elastic beams being arranged on both sides of the bionic fish body and at the tail of the bionic fish body respectively; Step two, discretizing the elastic beams on both sides of the bionic fish body and the elastic beam at the keel of the bionic fish body into N segments along the longitudinal direction respectively, and selecting a parameter vector for optimization of the stiffness distribution of the elastic beams; Step three, optimizing the parameter vector in step two by using a stiffness distribution optimization algorithm, and designing the elastic beams according to the optimized parameter vector to realize optimization of the stiffness distribution of the elastic beams.

2. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 1, characterized in that, The parameters in the parameter vector in step two include characteristic dimensions, elastic modulus, Poisson's ratio and damping parameters.

3. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 2, characterized in that, The specific process of step three is as follows: Step three one, initialize the maximum iteration number as , initialize the number of individuals in the population as , and initialize the maximum change coefficient ; Step three two, initialize the initial value of the first individual in the population as , where the value of each individual respectively represents a set of parameter vector values; Step three, initialize iteration count ; Step three four, the value of the first individual in the population of descendants is loaded into the kinetic model, the corresponding median trajectory of motion is calculated ;​​​ Step three five, according to the middle line motion trajectory Calculate the target function value corresponding to the first individual in the first generation population, Calculate the target function value corresponding to the first individual in the first generation population, Calculate the target function value corresponding to the first individual in the first generation population, , according to the calculated target function value, obtain the optimal individual in the first generation population ; Calculate the target function value corresponding to the first individual in the first generation population, ; Calculate the target function value corresponding to the first individual in the first generation population, The best individual pbest in the population is compared with the historical best individual gbest in the population, and the better one of pbest and gbest is taken as the historical best individual after the population is updated The best individual pbest in the population is compared with the historical best individual gbest in the population, and the better one of pbest and gbest is taken as the historical best individual after the population is updated ; Step 36: Update the change coefficient as follows Calculate the first The first generation of the population The speed of individuals and according to Judge the first The first generation of the population The speed of individuals Does it meet the following requirements: ; If the condition is satisfied, then the process remains unchanged and step 37 is executed again. If not satisfied , then when , the value of is updated to , when , the value of is updated to ; and step three seven is executed again; Step three 7, updating the value of the individual according to the speed of each individual , the optimal individual in the population of the first generation , the optimal individual in the population of the first generation , the optimal individual in the population of the first generation , the optimal individual in the population of the first generation , the optimal individual in the population of the first generation , the optimal individual in the population of the first generation , the optimal individual in the population of the first generation Step three eight, judging whether the first parameter in satisfies , wherein represents the value of the first parameter in , represents the minimum value of the first parameter, and represents the maximum value of the first parameter. ​ If satisfied ,but The first in The values ​​of the parameters remain unchanged; If not satisfied , then when , the value of is updated to , when , the value of is updated to ; traverse After each parameter in the population of the final value of the ; Step three 39, judge whether the iteration number meets ; If the following condition is satisfied the updated historical best individual of the population as a whole the parameter vector corresponding to the updated historical best individual is taken as the final parameter vector; If not satisfied then let return to step 34.

4. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 3, characterized in that, The specific process of step three is as follows: Step 3-41, place the first The first generation of the population The value of each individual The deformation trajectory of the elastic beam on the left side of the bionic fish body was calculated by loading it into the dynamic model. Deformation trajectory of the elastic beam on the right side of the bionic fish body The trajectory of the rigid fish head in the bionic fish body The trajectory of the caudal peduncle of the biomimetic fish body The trajectory of the tail fin of the biomimetic fish body The deformation trajectory of the central beam located at the keel of the bionic fish body ; Step three four two, according to each trajectory obtained in step three four one, carry out the centerline motion trajectory folding, obtain the centerline motion trajectory of the bionic fish body : wherein is an intermediate variable.

5. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 4, characterized in that, The deformation trajectory of the left elastic beam of the bionic fish body, the deformation trajectory of the right elastic beam of the bionic fish body and the deformation trajectory of the middle elastic beam at the keel of the bionic fish body are all calculated by using the shooting method.

6. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 5, characterized in that, The trajectory of the rigid fish head of the bionic fish body, the trajectory of the caudal filament of the bionic fish body and the trajectory of the caudal fin of the bionic fish body are all calculated by using multi-rigid-body dynamics.

7. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 6, characterized in that, The deformation trajectory of the left elastic beam of the bionic fish body is specifically as follows: wherein, denotes the total number of time steps; denotes the time step number denotes the time step number denotes the time step number denotes the time step number denotes the time step number denotes the time step number denotes the time step number denotes the time step number denotes the motion behavior of the elastic beam at the time step number 8. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 7, characterized in that, The change amount coefficient is: wherein denotes a floor function.

9. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 8, characterized in that, The intermediate variable is: 。 10. The method for optimizing the stiffness distribution of a biomimetic fish body driven by an elastic beam according to claim 9, characterized in that, The target function value is as follows: in, This represents a fish body wave simulation. Indicates energy transfer efficiency. Indicates average thrust. , and They are respectively , and The corresponding weights, and the weight values ​​satisfy .

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