CN116796636A - RBFN-based positive dynamic analysis method and system containing sliding friction mechanism - Google Patents
RBFN-based positive dynamic analysis method and system containing sliding friction mechanism Download PDFInfo
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Abstract
The application provides a positive dynamic analysis method and a system of a sliding friction mechanism based on RBFN, wherein the method comprises the following steps: step S1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial valuesValue x i , =1, 2, …, step S2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system to solve the accurate acceleration containing the sliding friction mechanismStep S3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model; step S4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized; step S5: real-time simulation of mechanism dynamics of related friction with constraint force is realized based on quick solution of positive dynamics of the mechanism with sliding friction.
Description
Technical Field
The application relates to the fields of robots and engineering machinery, in particular to a RBFN-based positive dynamic analysis method and system for a sliding friction mechanism, and more particularly relates to control, online dynamic prediction and real-time semi-physical simulation of a heavy-load mechanism, a parallel mechanism and the like containing friction related to constraint force.
Background
The dynamic analysis of the mechanism reveals the quantitative relation between the stress and the movement of the mechanism, and has important significance for the design, control and optimization of the mechanism. In the prior art, two joint friction modeling modes are respectively joint friction irrelevant to constraint force and joint friction relevant to constraint force, wherein the joint friction is commonly found in industrial mechanical arms, robots and the like supported by rolling bearings, the joint friction is commonly found in parallel mechanisms and engineering machinery and the like with spherical hinges, and the problems that the mechanism dynamics of the parallel mechanisms and the engineering machinery and the like with the spherical hinges are high in solving difficulty and overlong in analysis are mainly solved.
Regarding a mechanism containing constraint force irrelevant friction, the section book et al uses constraint force irrelevant Stribeck friction to carry out forward-reverse dynamics modeling on a six-degree-of-freedom serial mechanical arm, and the influence of joint friction on the dynamic behavior of the mechanism is revealed; liu Dongyu et al uses three joint friction models irrelevant to constraint force to identify the joint friction moment of the mechanical arm on the Tiangong No. two, and good identification accuracy is obtained; liu Guanghui et al established a constraint force independent coulomb-cubic curve friction model, accurately described joint friction of a 6-degree-of-freedom industrial robot, and used in parameter identification and force control; he Yimin et al obtained a low-speed Stribeck friction model independent of the restraining force based on measured data for a six-degree-of-freedom serial mechanical arm. As can be seen from the existing researches, joint friction irrelevant to constraint force is usually used in a scene of low load and the use of a rolling bearing as joint support, and a forward dynamics equation can be simplified into a set of ordinary differential equations, so that the solving difficulty is low.
However, constraint-independent joint friction is not universal. Wang Gengxiang et al dynamically model a 4-SPS/CU parallel mechanism with a sliding spherical hinge by using Newton-Euler method in combination with joint friction related to constraint force, and analyze the rule of influence of friction force on driving force of the mechanism through numerical calculation; zhang Yanfei et al use Lagrangian equation to model dynamics of a 3-RPS parallel robot with sliding spherical hinges, using constraint-related friction; guo Feng et al uses the friction related to constraint force to carry on the dynamics modeling to the polishing robot of five degrees of freedom, consider the friction of ball joint, universal joint and ball screw at the same time; the sliding revolute pair was modeled using constraint force related friction, and a dynamic model of a planar four-bar mechanism was obtained that takes into account clearance and friction. Therefore, the mechanism with the sliding joint is generally dynamically modeled using constraint force-related friction, and is often used in a parallel mechanism including a spherical pair, a heavy-duty mechanism using the sliding joint, and the like.
Research has been done to simplify the mechanism dynamics, such as natural orthogonal complement theory for decoupling of tandem mechanisms, and the widely applicable newton-euler method in generalized coordinate form. However, these efforts are difficult to generalize to situations with binding force related friction. In fact, the constraint force cannot be simplified due to the friction related to the constraint force, so that a mechanical dynamics equation is changed into a semi-explicit differential-algebraic equation, the number of equations is greatly increased, and the problem of solving in real time is solved.
Accordingly, there are certain limitations in the prior art, including: some studies have not considered the influence of the restraining force on the friction force, because they have focused on electrically driven robots supported by rolling bearings with low loads. In parallel mechanisms comprising spherical hinges and heavy-duty mechanisms comprising sliding friction joints, the methods used in the above-mentioned studies are not applicable; still other studies consider the effect of restraining forces on friction, but their kinetic calculations are performed by solving a large number of kinetic equations, which are difficult to solve in real time.
According to the application, the dynamic equation set is simplified through RBFN, the differential-algebraic equation set containing the dynamics of the sliding friction mechanism is converted into the nonlinear very differential equation set, so that the number of unknown intermediate variables of the problem is greatly reduced, and the speed of numerical calculation is improved, thereby being applied to hardware with high real-time requirements in ring simulation and other applications.
Disclosure of Invention
Aiming at the defects in the prior art, the application aims to provide a RBFN-based positive dynamic analysis method and system for a sliding friction mechanism.
The application provides a positive dynamic analysis method of a sliding friction mechanism based on RBFN, which comprises the following steps:
step S1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial values x i ，i＝1,2，...，n；
Step S2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system,solving for accurate acceleration including sliding friction mechanism
Step S3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model;
step S4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized;
step S5: realizing real-time simulation of mechanism dynamics of related friction with constraint force based on quick solution of positive dynamics of the mechanism with sliding friction;
the agent model is a positive dynamic equation containing a sliding friction mechanism through a numerical fitting mode.
Preferably, the step S2 employs:
wherein h represents a radial basis function network, and the current radial basis function network is a nonlinear function; q the number of the groups of the group,F a respectively representing generalized coordinates, generalized speed and main power of the mechanism; ω represents radial basis function network parameters.
Preferably, the proxy model employs:
h(x)＝(h 1 (x) h 2 (x)…h f (x)) T
wherein, psi is i Representing nonlinear functions, i is the subscript of the different nonlinear functions, taking i=1, 2An amount of; mu (mu) i The weight value of each nonlinear basis function is expressed and is a parameter to be optimized; x represents the input of the RBFN,the mechanism consists of generalized coordinates, generalized speed and main power of the mechanism; w (w) i The linear transformation is input and is a parameter to be optimized; b i Representing the input offset, which is the parameter to be optimized; beta represents a constant, which is a parameter to be optimized.
Preferably, the loss function employs:
preferably, the training process of the proxy model is expressed as an unconstrained optimization process:
preferably, the step S4 employs: the trained agent model is used as an original mechanism positive mechanics system, and the quick solution of the mechanism positive mechanics is realized through the numerical solution of a normal differential equation.
The application provides a positive dynamic analysis system containing a sliding friction mechanism based on RBFN, which comprises the following components:
module M1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial values x i ，i＝1,2，...，n ；
Module M2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system to solve the accurate acceleration containing the sliding friction mechanism
Module M3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model;
module M4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized;
module M5: realizing real-time simulation of mechanism dynamics of related friction with constraint force based on quick solution of positive dynamics of the mechanism with sliding friction;
the agent model is a positive dynamic equation containing a sliding friction mechanism through a numerical fitting mode.
Preferably, the module M2 employs:
wherein h represents a radial basis function network, and the current radial basis function network is a nonlinear function; q the number of the groups of the group,F a respectively representing generalized coordinates, generalized speed and main power of the mechanism; ω represents radial basis function network parameters.
Preferably, the proxy model employs:
h(x)＝(h 1 (x) h 2 (x)…h f (x)) T
wherein, psi is i Representing nonlinear functions, i being subscripts of different nonlinear functions, taking i=1, 2..m, m representing the number of nonlinear basis functions in the RBFN; mu (mu) i The weight value of each nonlinear basis function is expressed and is a parameter to be optimized; x represents the input of the RBFN,consisting of generalized coordinates of the mechanism, generalized speed and main power to which the mechanism is subjected；w i The linear transformation is input and is a parameter to be optimized; b i Representing the input offset, which is the parameter to be optimized; beta represents a constant, which is a parameter to be optimized;
the loss function employs:
the training process of the proxy model is expressed as an unconstrained optimization process:
preferably, the module M4 employs: the trained agent model is used as an original mechanism positive mechanics system, and the quick solution of the mechanism positive mechanics is realized through the numerical solution of a normal differential equation.
Compared with the prior art, the application has the following beneficial effects: the method for simplifying the forward dynamics problem of the friction mechanism with the constraint force by using the proxy model realizes the technical effects of high precision and large-scale simplification of the dynamics problem of the original complex mechanism by using the technical characteristics of the data-driven proxy model, greatly reduces the required calculation amount on the premise of small influence on the precision, improves the calculation efficiency, provides a real-time calculation basic technology for the dynamics problem of the mechanism with the sliding spherical hinge and the heavy-duty mechanism with the sliding friction pair, and greatly reduces the calculation force requirement for solving the dynamics problem of the mechanism with the sliding friction pair in real time.
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Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
fig. 1 is a schematic diagram of a general organization under investigation.
FIG. 2 is a schematic diagram of a single hidden layer neural network as a proxy model.
FIG. 3 is a schematic diagram of a single hidden layer neural network as a proxy model.
Detailed Description
The present application will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present application, but are not intended to limit the application in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present application.
Example 1
The application provides a positive dynamic analysis method of a sliding friction mechanism based on RBFN, as shown in figure 3, comprising the following steps:
step S1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial values x i ，i＝1，2，...，n；
Step S2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system to solve the accurate acceleration containing the sliding friction mechanism
Step S3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model;
step S4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized;
step S5: realizing real-time simulation of mechanism dynamics of related friction with constraint force based on quick solution of positive dynamics of the mechanism with sliding friction;
the agent model is a positive dynamic equation containing a sliding friction mechanism through a numerical fitting mode.
The mechanism is a space link mechanism which is composed of p moving components and is driven in a non-redundant mode, the degree of freedom of the space link mechanism is f, the space link mechanism is articulated through sliding friction joints, and gaps and component deformation at the joints are ignored. Regardless of under-actuated or redundant constraints, each degree of freedom in the mechanism corresponds to a group of actuators that can output primary power, together with f groups of actuators.
As shown in fig. 1, the system of the base frame is denoted as ozz. The space link mechanism is required to be split into a serial mechanism part and a parallel mechanism part (only one of the serial mechanism part and the parallel mechanism part can be included), the motion of each actuator of the serial mechanism part is independent, and the generalized coordinates can be directly selected as the motion parameters (such as translational displacement of a piston rod or rotation angle of an output shaft) of the actuators; the movement of each hydraulic actuator of the parallel mechanism part may not be independent, and the optional terminal movable platform system O e X e Y e Z e Relative to parallel mechanism base system O p X p Y p Z p The position of (2) is taken as the generalized coordinates, so that the generalized coordinates are equal in number and degree of freedom and are independent, and geometric constraint does not exist between the generalized coordinates. The generalized coordinates of the mechanism may be expressed as
q＝(q 1 q 2 …q f ) T
(1)
The satellite origin of each component is set at the centroid. For each moving component i, the position of the component i can be determined by the translation vector r of the component follower system relative to the OXYZ system i And a rotation tensor S i To express:
r i ＝(x i y i z i ) T ，S i (α i ，β i ，γ i )，i＝1,2，…，p
(2)
the coordinates expressed by the coordinates of the member are:
u＝(x 1 y 1 z 1 x 2 …α p β p γ p ) T
(3)
in a mechanism containing constraint-related friction, forward dynamics is given a kinematic initial value q 0 ，And main power F a Solving for mechanism motion +.>
The forward dynamics of the mechanism can be written as:
wherein, the liquid crystal display device comprises a liquid crystal display device,is a generalized inertia matrix: j is a mechanical jacobian matrix obtained by mechanical kinematic analysis. Since both equations contain friction terms related to the constraint force, the constraint force F is unknown r Coupling, therefore equation (4) is a set of semi-explicit differential-algebraic equations. The main reason for the high difficulty of solving forward dynamics of friction mechanism is that generalized acceleration +.>Not easily explicitly written as motion state q, < >>And main power F a Is not easily written in the form of a normal differential equation. When solving, the two formulas in (4) are needed to be solved at the same time, and generally, the solution is difficult to solve by an implicit numerical format, the calculation amount is high in requirement, and the method is difficult to be used in calculation tasks with high real-time requirement. Therefore, a dynamic rapid solving method based on RBFN is proposed.
RBFN (radial basis function network), can be regarded as a nonlinear function h
RBFN is an approximation of the ordinary differential equation built into the dynamics system (4), which is essentially a fit to a nonlinear function, interpolating only over the range of values of the parameters. Although errors can be generated, the method can bypass the solution of a differential-algebraic equation with considerable calculated quantity when solving the mechanism dynamics including the related friction of the constraint force, and improves the speed of numerical calculation.
Recording deviceThe reasonable value range of the working space, the running speed of the mechanism and the main power is +.>By a series of randomly obtained initial values +.>The substitution dynamics system (4) carries out accurate calculation to obtain a large number of numerical calculation results +.>For training the parameter omega in RBFN, a continuous nonlinear function h is obtained as the error decreases continuously during the training process.
Since the set of generalized coordinates selected at the time of establishment of the previous coordinates are independent of each other, the RBFN can be divided into f independent functions
h(x)＝(h 1 (x) h 2 (x) …h f (x)) T
(6)
The whole RBFN is thus made up of f independent sets of functions. The following describes RBFN kth dimension h k Is established. Equation (7) exhibits an expression of the kth dimension of RBFN.
Wherein the nonlinear function is a Gaussian radial basis function, i.eThe RBFN is structured such that an input x is first mapped into an m-dimensional feature by a linear mapping w,the m nonlinear functions are applied to the m features, respectively, and the final output is represented as a set of nonlinear functions ψ i Is a sum of a linear combination of (c) and a constant beta. As shown in fig. 2
Wherein w is i 、b i μ, β are all optimizable parameters. The agent model realizes high-precision simplification of the positive dynamic problem of the friction mechanism by a data driving and fitting approximation method.
The training set is an ordered pair of n groups of input and acceleration accurate solutions obtained by randomly generating initial values and substituting the initial values into a dynamics system calculationFor n groups of data in the training set, the kth dimension proxy model h in (7) k Generating n sets of outputs and creating a loss function using the sum of squares of all output errors
The training process of the agent model (7) can be written as the following unconstrained optimization problem
L to w i ，b i Both the first and second derivatives of μ, β exist, so for the unconstrained optimization problem (9), a BFGS quasi-newton method with quadratic convergence is used for solving. After each iteration step, substituting the verification set data into the loss function (8) to verify the training effect of the proxy model, and stopping optimization after the loss function value cannot be reduced after continuous multiple iterations, so that the proxy model training is completed. The proxy model is used as a global approximation of the original dynamics problem in a reasonable interval, so that retraining is not needed as long as the original dynamics problem parameters are not changed.
Finally, the agent model is used for replacing the original dynamics problem, and the positive dynamics problem can be simplified into a normal differential equation
The proposed method for simplifying the forward dynamics problem of the friction mechanism related to the binding force by using the agent model greatly reduces the required calculation amount on the premise of small influence on precision, improves the calculation efficiency, provides a real-time analysis basic method for the dynamics problem of the mechanism containing the spherical hinge and the heavy-duty mechanism containing the sliding friction pair, and particularly can be applied to semi-physical simulation considering the dynamics of the mechanism in the design and verification of the controller containing the spherical hinge parallel mechanism and the engineering mechanical mechanism, thereby protecting the mechanism.
The application provides a positive dynamic analysis system containing a sliding friction mechanism based on RBFN, which comprises:
module M1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial values x i ，i＝1,2，...，n；
Module M2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system to solve the accurate acceleration containing the sliding friction mechanism
Module M3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model;
module M4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized;
module M5: realizing real-time simulation of mechanism dynamics of related friction with constraint force based on quick solution of positive dynamics of the mechanism with sliding friction;
the agent model is a positive dynamic equation containing a sliding friction mechanism through a numerical fitting mode.
The mechanism is a space link mechanism which is composed of p moving components and is driven in a non-redundant mode, the degree of freedom of the space link mechanism is f, the space link mechanism is articulated through sliding friction joints, and gaps and component deformation at the joints are ignored. Regardless of under-actuated or redundant constraints, each degree of freedom in the mechanism corresponds to a group of actuators that can output primary power, together with f groups of actuators.
As shown in fig. 1, the system of the base frame is denoted as ozz. The space link mechanism is required to be split into a serial mechanism part and a parallel mechanism part (only one of the serial mechanism part and the parallel mechanism part can be included), the motion of each actuator of the serial mechanism part is independent, and the generalized coordinates can be directly selected as the motion parameters (such as translational displacement of a piston rod or rotation angle of an output shaft) of the actuators; the movement of each hydraulic actuator of the parallel mechanism part may not be independent, and the optional terminal movable platform system O e X e Y e Z e Relative to parallel mechanism base system O p X p Y p Z p The position of (2) is taken as the generalized coordinates, so that the generalized coordinates are equal in number and degree of freedom and are independent, and geometric constraint does not exist between the generalized coordinates. The generalized coordinates of the mechanism may be expressed as
q＝(q 1 q 2 …q f ) T
(1)
The satellite origin of each component is set at the centroid. For each moving component i, the position of the component i can be determined by the translation vector r of the component follower system relative to the OXYZ system i And a rotation tensor S i To express:
r i ＝(x i y i z i ) T ，S i (α i ，β i ，γ i )，i＝1,2，…，p
(2)
the coordinates expressed by the coordinates of the member are:
u＝(x 1 y 1 z 1 x 2 …α p β p γ p ) T
(3)
in mechanisms involving friction associated with binding forces, positive powerThe study is given by the initial value q of the kinematics 0 ，And main power F a Solving for the mechanism motion q, < >>
The forward dynamics of the mechanism can be written as:
wherein, the liquid crystal display device comprises a liquid crystal display device,is a generalized inertia matrix: j is a mechanical jacobian matrix obtained by mechanical kinematic analysis. Since both equations contain friction terms related to the constraint force, the constraint force F is unknown r Coupling, therefore equation (4) is a set of semi-explicit differential-algebraic equations. The main reason for the high difficulty of solving forward dynamics of friction mechanism is that generalized acceleration +.>Not easily explicitly written as motion state q, < >>And main power F a Is not easily written in the form of a normal differential equation. When solving, the two formulas in (4) are needed to be solved at the same time, and generally, the solution is difficult to solve by an implicit numerical format, the calculation amount is high in requirement, and the method is difficult to be used in calculation tasks with high real-time requirement. Therefore, a dynamic rapid solving method based on RBFN is proposed.
RBFN (radial basis function network), can be regarded as a nonlinear function h
RBFN is an approximation of the ordinary differential equation built into the dynamics system (4), which is essentially a fit to a nonlinear function, interpolating only over the range of values of the parameters. Although errors can be generated, the method can bypass the solution of a differential-algebraic equation with considerable calculated quantity when solving the mechanism dynamics including the related friction of the constraint force, and improves the speed of numerical calculation.
Recording deviceThe reasonable value range of the working space, the running speed of the mechanism and the main power is +.>By a series of randomly obtained initial values +.>The substitution dynamics system (4) carries out accurate calculation to obtain a large number of numerical calculation results +.>For training the parameter omega in RBFN, a continuous nonlinear function h is obtained as the error decreases continuously during the training process.
Since the set of generalized coordinates selected at the time of establishment of the previous coordinates are independent of each other, the RBFN can be divided into f independent functions
h(x)＝(h 1 (x) h 2 (x) …h f (x)) T
(6)
The whole RBFN is thus made up of f independent sets of functions. The following describes RBFN kth dimension h k Is established. Equation (7) presents an expression of the kth dimension of RBFN.
Wherein the nonlinear function is a Gaussian radial basis function, i.eThe RBFN is structured such that an input x is first mapped by a linear map w into m-dimensional features, m nonlinear functions are applied to the m features, respectively, and the final output is represented as a set of nonlinear functions ψ i Is a sum of a linear combination of (c) and a constant beta. As shown in fig. 2
Wherein w is i 、b i μ, β are all optimizable parameters. The agent model realizes high-precision simplification of the positive dynamic problem of the friction mechanism by a data driving and fitting approximation method.
The training set is an ordered pair of n groups of input and acceleration accurate solutions obtained by randomly generating initial values and substituting the initial values into a dynamics system calculationFor n groups of data in the training set, the kth dimension proxy model h in (7) k Generating n sets of outputs and creating a loss function using the sum of squares of all output errors
The training process of the agent model (7) can be written as the following unconstrained optimization problem
L to w i ，b i Both the first and second derivatives of μ, β exist, so for the unconstrained optimization problem (9), a BFGS quasi-newton method with quadratic convergence is used for solving. After each iteration step, substituting the verification set data into the loss function (8) to verify the training effect of the proxy model, and stopping optimization after the loss function value cannot be reduced after continuous multiple iterations, so that the proxy model training is completed. The proxy model is used as a global approximation of the original dynamics problem in a reasonable interval, so that retraining is not needed as long as the original dynamics problem parameters are not changed.
Finally, the agent model is used for replacing the original dynamics problem, and the positive dynamics problem can be simplified into a normal differential equation
The proposed method for simplifying the forward dynamics problem of the friction mechanism related to the binding force by using the agent model greatly reduces the required calculation amount on the premise of small influence on precision, improves the calculation efficiency, provides a real-time analysis basic method for the dynamics problem of the mechanism containing the spherical hinge and the heavy-duty mechanism containing the sliding friction pair, and particularly can be applied to semi-physical simulation considering the dynamics of the mechanism in the design and verification of the controller containing the spherical hinge parallel mechanism and the engineering mechanical mechanism, thereby protecting the mechanism.
Those skilled in the art will appreciate that the systems, apparatus, and their respective modules provided herein may be implemented entirely by logic programming of method steps such that the systems, apparatus, and their respective modules are implemented as logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc., in addition to the systems, apparatus, and their respective modules being implemented as pure computer readable program code. Therefore, the system, the apparatus, and the respective modules thereof provided by the present application may be regarded as one hardware component, and the modules included therein for implementing various programs may also be regarded as structures within the hardware component; modules for implementing various functions may also be regarded as being either software programs for implementing the methods or structures within hardware components.
The foregoing describes specific embodiments of the present application. It is to be understood that the application is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the application. The embodiments of the application and the features of the embodiments may be combined with each other arbitrarily without conflict.
Claims (10)
1. The RBFN-based positive dynamic analysis method for the sliding friction mechanism is characterized by comprising the following steps of:
step S1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial values x i ,i＝1,2,…,n；
Step S2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system to solve the accurate acceleration containing the sliding friction mechanism
Step S3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model;
step S4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized;
step S5: realizing real-time simulation of mechanism dynamics of related friction with constraint force based on quick solution of positive dynamics of the mechanism with sliding friction;
the agent model is a positive dynamic equation containing a sliding friction mechanism through a numerical fitting mode.
2. The RBFN-based positive dynamic analysis method of the sliding friction-containing mechanism of claim 1, wherein said step S2 employs:
wherein h represents a radial basis function network, and the current radial basis function network is a nonlinear function; q the number of the groups of the group,F a respectively representing generalized coordinates, generalized speed and main power of the mechanism; ω represents radial basis function network parameters.
3. The RBFN-based sliding friction-containing mechanism positive kinetic analysis method of claim 1, wherein the proxy model employs:
wherein, psi is i Representing nonlinear functions, i is the subscript of different nonlinear functions, taking i=1, 2, …, m, m representing the number of nonlinear basis functions in the RBFN; mu (mu) i The weight value of each nonlinear basis function is expressed and is a parameter to be optimized; x represents the input of the RBFN,the mechanism consists of generalized coordinates, generalized speed and main power of the mechanism; w (w) i The linear transformation is input and is a parameter to be optimized; b i Representing the input offset, which is the parameter to be optimized; beta represents a constant, which is a parameter to be optimized.
4. The RBFN-based sliding friction-containing mechanism positive kinetic analysis method of claim 1, wherein the loss function employs:
5. the RBFN-based sliding friction mechanism-containing positive dynamic analysis method of claim 4, wherein the training process of the proxy model is expressed as an unconstrained optimization process:
6. the RBFN-based positive dynamic analysis method of the sliding friction-containing mechanism of claim 1, wherein said step S4 employs: the trained agent model is used as an original mechanism positive mechanics system, and the quick solution of the mechanism positive mechanics is realized through the numerical solution of a normal differential equation.
7. An RBFN-based positive dynamic analysis system with a sliding friction mechanism, comprising:
module M1: for dynamic system parameters containing sliding friction mechanismInitial value sampling is carried out to obtain n initial values x i ,i＝1,2,…,n；
Module M2: substituting the obtained initial value into a differential-algebraic equation of the positive dynamics of the original dynamics system to solve the accurate acceleration containing the sliding friction mechanism
Module M3: constructing a proxy model by using ordered pairs of initial and acceleration componentsTraining the proxy model until the loss function is minimum, and obtaining a trained proxy model;
module M4: based on the trained agent model, the quick solution of the positive dynamics of the sliding friction mechanism is realized;
module M5: realizing real-time simulation of mechanism dynamics of related friction with constraint force based on quick solution of positive dynamics of the mechanism with sliding friction;
the agent model is a positive dynamic equation containing a sliding friction mechanism through a numerical fitting mode.
8. The RBFN-based sliding friction-containing mechanism positive kinetic analysis system of claim 7, wherein the module M2 employs:
wherein h represents a radial basis function network, and the current radial basis function network is a nonlinear function; q the number of the groups of the group,F a respectively representing generalized coordinates, generalized speed and main power of the mechanism; ω represents radial basis function network parameters.
9. The RBFN-based sliding friction-containing mechanism positive kinetic analysis system of claim 7, wherein the proxy model employs:
wherein, psi is i Representing nonlinear functions, i is the subscript of different nonlinear functions, taking i=1, 2, …, m, m representing the number of nonlinear basis functions in the RBFN; mu (mu) i The weight value of each nonlinear basis function is expressed and is a parameter to be optimized; x represents the input of the RBFN,by generalized coordinates and generalized velocities of the mechanismsThe degree and the main power of the mechanism; w (w) i The linear transformation is input and is a parameter to be optimized; b i Representing the input offset, which is the parameter to be optimized; beta represents a constant, which is a parameter to be optimized;
the loss function employs:
the training process of the proxy model is expressed as an unconstrained optimization process:
10. the RBFN-based sliding friction-containing mechanism positive kinetic analysis system of claim 7, wherein the module M4 employs: the trained agent model is used as an original mechanism positive mechanics system, and the quick solution of the mechanism positive mechanics is realized through the numerical solution of a normal differential equation.
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