An active structure low-energy consumption geometric nonlinear optimization control method and system based on a differentiable structure analysis

Abstract

The application discloses a kind of active structure low-energy consumption geometric nonlinear optimization control method and system based on microstructure analysis, comprising: the active structure analysis model considering geometric nonlinearity is established, and the structural response is calculated;The structural analysis process is constructed as a differentiable computing process, and the nonlinear equilibrium analysis process of structure under the action of external load and actuator is expressed as a differentiable computing graph;Based on the differentiable computing process, the gradient information of the structural response about actuator control quantity is obtained;An optimization control model is constructed, with the actuation energy consumption as the objective function, and with the structural displacement and / or stress satisfying the preset constraint condition as the constraint;Based on the gradient information, the optimal actuator control quantity is obtained by using the gradient optimization algorithm;The active structure is controlled according to the optimal actuator control quantity, so that the structure meets the performance requirements and the actuation energy consumption is reduced.The application can significantly reduce the actuation energy consumption while ensuring the structural performance constraints, and improve the optimization solving efficiency.

Description

Technical Field

[0001] This invention relates to the fields of structural engineering and intelligent control technology, and in particular to an active structural low-energy geometric nonlinear optimization control method and system based on differentiable structural analysis. Background Technology

[0002] With the widespread application of long-span and lightweight structures in engineering, structural flexibility is constantly increasing, making them prone to large displacements and internal force responses under external loads. To improve structural performance, active structures, by arranging actuators within the structure to actively control its response, have become an important development direction in the field of structural engineering.

[0003] For example, Chinese patent document CN101174655A discloses a non-contact photoelectric actuator and device for flexible structure control; Chinese patent document CN108639383A discloses an intelligent flexible actuator based on a distributed flexible structure.

[0004] In active structural control, determining reasonable actuator control parameters while meeting structural performance requirements (such as displacement and stress constraints) is a crucial issue. Existing methods are mostly based on linear structural analysis, using analytical methods or simplified optimization models to determine the control strategy. However, for large-span or flexible structures, geometric nonlinear effects are significant, and linear analysis cannot accurately reflect the true structural response, thus affecting the control effect.

[0005] For geometrically nonlinear problems, existing research typically transforms the determination of the control variable into an optimization problem, which is then solved by repeatedly calling nonlinear structural analysis. However, due to the complexity of the nonlinear equilibrium process, the gradient of the structural response with respect to the control variable is difficult to obtain accurately. Existing methods often employ finite difference or derivative-free optimization algorithms, resulting in low computational efficiency and limited accuracy, especially when the number of actuators is large. Therefore, there is an urgent need for a method that can efficiently obtain gradient information and achieve low-energy-consumption optimization control while considering geometric nonlinearity. Summary of the Invention

[0006] This invention provides a low-energy-consumption geometric nonlinear optimization control method and system for active structures based on differentiable structure analysis, which can solve the problems of difficulty in gradient acquisition, low optimization efficiency and high energy consumption in active structure control under geometric nonlinear conditions in the prior art.

[0007] A low-energy-consumption geometrical nonlinear optimization control method for active structures based on differentiable structure analysis includes the following steps: (1) Establish an active structural analysis model that considers geometric nonlinearity and calculate the structural response; the active structure includes the structural body and actuators arranged in the structural body; (2) The structural analysis process is constructed as a differentiable computational process, and the nonlinear equilibrium analysis process of the structural body under external loads and actuators is represented as a differentiable computational diagram; (3) Based on the differentiable calculation process, obtain the gradient information of the structural response with respect to the actuator control quantity; (4) Construct an optimized control model with kinetic energy consumption as the objective function and the structural displacement and / or stress satisfying the preset constraint conditions as the constraint; (5) Based on the gradient information, the optimal actuator control quantity is obtained by using a gradient optimization algorithm; (6) Control the active structure according to the optimal actuator control quantity so that the structure meets the performance requirements and the actuation energy consumption is reduced.

[0008] This invention achieves high-precision gradient calculation of structural response with respect to actuator control quantity by constructing a differentiable computational form of the structural analysis process. This enables the use of efficient gradient optimization algorithms to solve for the optimal control strategy, thereby reducing actuation energy consumption and improving computational efficiency while satisfying structural performance constraints.

[0009] Furthermore, in step (1), the geometric nonlinearity includes nonlinear effects caused by large displacement, large deformation, or configuration changes.

[0010] Furthermore, in step (2), the differentiable calculation process includes constructing the unit internal force calculation, structural equilibrium solution and displacement update process in the nonlinear finite element analysis process into a differentiable calculation unit.

[0011] Furthermore, in step (3), the gradient information is obtained through an automatic differentiation method or an equivalent differentiable calculation method.

[0012] Furthermore, in step (4), the actuation energy consumption is calculated based on the relationship between the change in actuator length and the corresponding internal force, and a smooth function is used to approximate the non-smooth terms.

[0013] Furthermore, in step (4), the constraint conditions include one or more of the following: maximum structural displacement constraint, maximum component stress constraint, or target shape constraint.

[0014] Furthermore, in step (5), the gradient optimization algorithm includes the moving asymptote method, the sequential quadratic programming method, or other gradient-based optimization algorithms.

[0015] Furthermore, step (5) also includes normalizing the actuator control quantity and then performing inverse normalization after optimization to obtain the actual control quantity.

[0016] An active structure low-energy geometric nonlinear optimization control system based on differentiable structure analysis, used to implement the above-mentioned active structure low-energy geometric nonlinear optimization control method, includes: The structural analysis module is used to build an active structural analysis model that considers geometric nonlinearity and to calculate the structural response; The differentiable computation module is used to construct the structural analysis process as a differentiable computation process and obtain the gradient information of the structural response with respect to the actuator control quantity; The optimization control module is used to construct an optimization model with actuation energy consumption as the objective and structural performance constraints as the condition, and to solve for the optimal actuator control quantity based on the gradient information. The control execution module is used to regulate the active structure according to the optimal actuator control quantity.

[0017] Furthermore, the differentiable computation module is implemented based on automatic differentiation or equivalent differentiable computation mechanism; the optimization control module uses a gradient-based optimization algorithm to iteratively update the control quantity.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention achieves high-precision gradient calculation of the structural response to actuator control quantity under geometric nonlinear conditions by constructing a differentiable structural analysis process, thus avoiding the problem of low computational efficiency of traditional finite difference methods.

[0019] 2. This invention can effectively combine nonlinear structural analysis with gradient optimization methods, thereby reducing actuation energy consumption while satisfying structural displacement and stress constraints.

[0020] 3. This invention significantly reduces the number of calls to nonlinear structural analysis during the optimization process, improves overall computational efficiency, and is suitable for large-scale structures with a large number of actuators.

[0021] 4. This invention has good versatility and can be applied to control problems of different types of active structures, including morphological control, displacement control and internal force regulation and other application scenarios.

[0022] 5. This invention provides a feasible technical means for the efficient optimization control of complex engineering structures, and has good prospects for engineering applications. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating an embodiment of the present invention.

[0025] Figure 2 The active arched truss structure configuration and actuator arrangement are shown in Embodiment 1 of the present invention.

[0026] Figure 3 This is a comparison diagram of the deformation before and after the active arched truss structure was controlled in Embodiment 1 of the present invention.

[0027] Figure 4 The active simply supported truss structure configuration and actuator arrangement are shown in Embodiment 2 of the present invention.

[0028] Figure 5 This is a comparison diagram of the shape of the active simply supported truss structure before and after control in Embodiment 2 of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0031] like Figure 1 As shown, an active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis is proposed. The method utilizes the structure analysis module, differentiable computation module, optimization control module, and control execution module included in the system to perform the following steps: First, the initial model information of the active structure is obtained, the active structure being equipped with... m One actuator; initial nonlinear finite element analysis is performed based on external loads to obtain the initial displacement and initial element internal forces of the structure; the actuator command vector is initialized, the vector containing a predetermined actuator length change: ; To accurately capture the nonlinear structural response during the actuation process, the total actuator command will be... Classified as One incremental step: ; In the At each increment step, a small increment in actuator length is applied to the structure, and the equilibrium configuration is obtained by solving the following equation: ; in, ; Under the influence of external loads and actuator commands at the current increment step, the Newton-Raphson iterative method is used to solve the nonlinear equilibrium equations and continuously update the structural configuration. ; in Represents the tangent stiffness matrix. Indicates iterative index, This represents the internal force vector of the structure. Through the above iterative solution, the nodal displacement vectors of the structure's response at the current increment step are obtained. The nodal displacement vectors calculated at the current increment step, along with the actuator... The axial force and other state variables, as well as the processes of incremental driving, displacement calculation, and internal force calculation, are recorded as differentiable nodes in the dynamic calculation graph for subsequent gradient tracking. Repeat the above steps until completion. The calculation of each incremental step establishes a complete mapping relationship between actuator commands and structural responses.

[0032] After establishing the mapping relationship between actuator commands and structural responses, an optimal control objective function is constructed using actuator commands as design variables to comprehensively evaluate drive energy consumption and structural response. The objective function Essentially, it is a scalar function of actuator commands, which can be generalized to represent any system response quantity that depends on the input design variables, such as drive energy consumption, maximum nodal displacement, or maximum element stress.

[0033] Specifically, the drive energy consumption corresponds to the mechanical work done during the drive process; for any actuator In its first The incremental work at each increment step is derived from the axial force extracted at the current increment step. With length increment change The product of the two is negative to obtain the result; considering that recovered energy is usually not available in actual drive systems, only the contribution of positive work is considered when evaluating the drive energy consumption. To maintain the global continuity and differentiability of the dynamic calculation graph and avoid gradient breakage caused by non-differentiability at zero points, the Softplus function is used to smooth the incremental work, that is: the effective incremental work after smoothing is calculated as: ; The Softplus function is defined as follows: .

[0034] All actuators in The effective incremental work under each incremental step is accumulated to obtain the total driving energy consumption for objective function evaluation, and this energy accumulation process is integrated into the dynamic calculation graph.

[0035] Furthermore, to evaluate the performance constraints, directly calculating the maximum nodal displacement or maximum element stress has non-smooth characteristics, which would lead to an interruption of continuous gradient evaluation; in order to achieve globally continuous differentiable gradient evaluation, a minimum constant is introduced. A smooth approximation is performed using the Log-Sum-Exponential (LSE) function; the maximum nodal displacement after smoothing is... and maximum element stress They are represented as follows: ; in, Indicates the first i The node at the th K The final displacement under each incremental step; , indicating the first i Stress of each element This represents the cross-sectional area of ​​the corresponding unit. The LSE function is defined as follows: .

[0036] Based on the computational module constructed above, a specific optimization control model is built. This optimization problem aims to determine the optimal actuator control command, with minimizing the drive energy consumption as the primary objective, and with the maximum nodal displacement and maximum element stress meeting allowable limits as performance constraints. This optimization problem can be precisely formulated as: ; Subject to the following constraints: ; ; ; in, and These represent the lower and upper limits of the actuator length variation, respectively. The above energy consumption assessment and constraint assessment processes are all connected as differentiable nodes to the dynamic calculation graph to ensure the continuous differentiability of the entire process.

[0037] To improve the numerical conditions and convergence robustness of subsequent gradient-based optimization algorithms and eliminate the influence of different physical quantities on the gradient magnitude, the optimization control model is normalized before differentiation and optimization. First, the physical actuator length variation variable is mapped to the [0, 1] interval to obtain the normalized design variables. : ; in, This allows us to construct a normalized design variable vector: ; Secondly, to maintain the balance of gradient magnitudes during optimization, the objective function and performance constraints are normalized relative to a reference baseline value. The total drive energy consumption objective function is then normalized relative to the reference energy value. Convert to dimensionless form: ; Simultaneously, the maximum nodal displacement constraint and the maximum element stress constraint of the structure are respectively transformed into dimensionless relative limit forms: ; ; Through the above steps, the original optimization control problem is completely transformed into a problem using normalized variables. For the object to be solved, a dimensionless objective function is used. A standard numerical optimization model for optimizing objectives, but constrained by dimensionless boundaries and performance constraints.

[0038] In this model, design variables, objective functions, and constraint functions are all represented in normalized form, which improves the numerical stability of gradient-based optimization and facilitates efficient numerical implementation. Within this framework, the state variables required for evaluating the objective function and constraints, such as operating energy consumption, structural nodal displacements, and element stresses, are all obtained through the differentiable nonlinear analysis recorded in the aforementioned dynamic computation graph.

[0039] Through this differentiable nonlinear analysis, the backward differentiation algorithm (AD) is used to calculate the objective function's effect on the physical actuator command along the dynamic computation graph. Sensitivity: ; After extracting the physical gradients, since the optimization model has been transformed into a normalized form, the required sensitivity will be automatically propagated further through the variable normalization mapping relationship. According to the chain rule, the automatic differentiation algorithm multiplies the physical gradients by the constant partial derivative matrix of the normalization mapping (i.e., the difference between the upper and lower limits of the actuator length change), thereby efficiently and accurately evaluating the final gradients of the objective function and constraint function with respect to the normalized design variable x.

[0040] Finally, the precise gradient information of the objective function and constraint function with respect to the normalized design variable x obtained above is input into the gradient-based numerical optimization algorithm; the design variable is continuously iterated and updated within the normalization space until the optimal normalized variable is obtained. Then The corresponding physical actuator instructions are converted back through inverse normalization mapping.

[0041] Example 1 Embodiment 1 of the present invention Figure 2 Let's take an arched truss as an example. A downward concentrated load of P = 1250 kN is applied to the top node of the left half span of the arched truss. The member is made of Q550 high-strength steel with a Young's modulus of 210 GPa and a stress limit of 550 MPa.

[0042] The specific implementation steps of this embodiment include: Step S101: Establish an active structural analysis model.

[0043] Based on the structural geometry, topological connections, material parameters, and actuator arrangement, an active structural analysis model considering geometric nonlinearity is established.

[0044] Step S102: Establish an optimal control mathematical model.

[0045] The control command of the actuator in the diagonal web member (i.e., the change in actuator length) is used as the optimization design variable, and the minimization of the actuator's operating energy consumption is used as the objective function. At the same time, dual constraints of displacement and stress are set: the maximum nodal displacement of the structure shall not exceed 1 / 300 of the span (i.e., 166.67 mm), and the maximum stress of all components shall not exceed 550 MPa.

[0046] Step S103: Construct a differentiable computational graph and perform nonlinear analysis.

[0047] A geometric nonlinear finite element analysis is performed on the state of the structure under the combined action of external loads and current actuator control variables. This nonlinear equilibrium iterative analysis process is transformed into a standard form supporting automatic differentiation (AD), and a differentiable computational graph based on a differentiable programming framework is established to achieve forward calculation tracing from actuator control variables to structural responses (displacement, stress), objective functions, and constraints.

[0048] Step S104: Perform automatic differential calculation to obtain the gradient.

[0049] Based on the aforementioned differentiable calculation process, backpropagation calculations are performed on the solution process of nonlinear equilibrium and the objective function and constraint function in the optimization model. This allows for the direct and accurate analysis of the gradient information of the structural response (nodal displacements, component stresses) and total kinetic energy consumption relative to the actuator control variables.

[0050] Step S105: Update the actuator design variables.

[0051] A gradient-based optimization algorithm (moving asymptote method MMA in this embodiment) is used to generate a new set of actuator control variable values ​​based on the high-precision gradient information calculated in step S104.

[0052] Step S106: Convergence judgment and execution control.

[0053] Check if the optimization process meets the termination condition. If it has not converged, return to step S103 and restart the nonlinear calculation and analysis with the updated actuator control quantity; if it has converged, output the final optimal actuator control strategy.

[0054] Based on this strategy, the active structure was driven and controlled, and the maximum nodal displacement of the structure in this embodiment was successfully controlled to approximately 163.76 mm (deformation comparison before and after control is as follows). Figure 3 As shown in the figure, the maximum component stress was reduced to 535.59 MPa, and the actuation energy consumption was only 859.97 kJ. Thus, the structural performance met the standards and the energy consumption was significantly reduced in only 32 finite element calculations and evaluations, with a calculation time of only 0.93 seconds.

[0055] For comparison, this embodiment further employs a non-gradient-based random search algorithm (particle swarm optimization) to calculate the problem, limiting the maximum number of finite element evaluations to 50,000. The results show that the control commands obtained by the particle swarm optimization algorithm after 50,000 finite element evaluations (computation time 421.32 seconds) still fail to meet the stress and displacement limits.

[0056] Example 2 Embodiment 2 of the present invention Figure 4 Taking a simply supported beam truss with a span of 20 meters as an example, this invention is illustrated in active structural shape control. The Young's modulus of the truss material is 210 GPa, and the allowable stress is 250 MPa. Unlike the previous embodiment, which focused on reducing energy consumption, this embodiment aims to move the structure precisely from its initial position to a preset target position via actuators.

[0057] The specific implementation steps of this embodiment include: Step S201: Establish an active structural analysis model that considers geometric nonlinearity.

[0058] Obtain the initial model information of the simply supported beam truss. In this embodiment, external loads are not considered, and the structural form is entirely driven by actuator commands. Actuators are arranged at the specified web members and chord members of the truss, and an active structural geometric nonlinear analysis model including the truss body and actuators is established.

[0059] Step S202: Construct an optimized control model.

[0060] Based on the shape control requirements of this embodiment, a mathematical optimization model is constructed that comprehensively considers shape and position deviations, driving energy consumption, and safety constraints. The goal of this embodiment is to control the nodes... a andb The vertical displacement is controlled at -1.5 m, and the node... c and d The vertical displacement is controlled at 2.5 m, so that the structure presents a sinusoidal shape.

[0061] Since pure shape control can lead to high energy consumption and stress exceeding limits, the optimized control model constructed in this step uses the weighted sum of shape control error and actuation energy consumption penalty term as the joint objective function, and uses the maximum element stress of all components not exceeding 250 MPa as the constraint condition.

[0062] Step S203: Construct the differentiable computation process of the structural response.

[0063] The nonlinear equilibrium analysis process of large geometric deformation of a simply supported beam truss under actuator drive, as well as the evaluation process of the objective function and constraint conditions constructed in step S202, are uniformly transformed into a standard form that supports automatic differentiation. The processes of incremental drive, displacement calculation, internal force calculation, and energy consumption accumulation are recorded as differentiable nodes in the dynamic calculation diagram.

[0064] Step S204: Obtain gradient information based on the differentiable calculation process.

[0065] The backward-mode automatic differentiation (AD) algorithm is employed to perform backward differentiation along the differentiable computation graph constructed in step S203. Since the optimization model is already defined, the system can directly and accurately analyze the gradient information of the aforementioned "joint objective function" and "stress constraint function" with respect to each actuator control variable.

[0066] Step S205: The optimal actuator control quantity is obtained by using a gradient optimization algorithm.

[0067] The precise gradient information obtained in step S204 is input into a gradient-based optimization algorithm (moving asymptote method MMA in this embodiment). Under the condition of satisfying the 250 MPa stress constraint, the actuator design variables are iteratively updated to minimize the joint objective function until the optimization converges, and the corresponding optimal actuator control quantity is solved.

[0068] Step S206: Control the active structure according to the optimal actuator control quantity.

[0069] The actuator in the simply supported beam truss is driven by the optimal control quantity obtained in step S205. For example... Figure 5 As shown, the controlled structure accurately achieved the preset sinusoidal target shape, while the maximum component stress was strictly controlled at 246.46 MPa, and the actuation energy consumption was significantly reduced to 175.13 kJ.

[0070] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for low-energy-consumption geometrical nonlinear optimization control of active structures based on differentiable structure analysis, characterized in that, Includes the following steps: (1) Establish an active structural analysis model that considers geometric nonlinearity and calculate the structural response; the active structure includes the structural body and actuators arranged in the structural body; (2) The structural analysis process is constructed as a differentiable computational process, and the nonlinear equilibrium analysis process of the structural body under external loads and actuators is represented as a differentiable computational diagram; (3) Based on the differentiable calculation process, obtain the gradient information of the structural response with respect to the actuator control quantity; (4) Construct an optimized control model with kinetic energy consumption as the objective function and the structural displacement and / or stress satisfying the preset constraint conditions as the constraint; (5) Based on the gradient information, the optimal actuator control quantity is obtained by using a gradient optimization algorithm; (6) Control the active structure according to the optimal actuator control quantity so that the structure meets the performance requirements and the actuation energy consumption is reduced.

2. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, In step (1), the geometric nonlinearity includes nonlinear effects caused by large displacement, large deformation or configuration change.

3. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, In step (2), the differentiable computation process includes constructing the unit internal force calculation, structural equilibrium solution and displacement update process in the nonlinear finite element analysis process into a differentiable computation unit.

4. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, In step (3), the gradient information is obtained by automatic differentiation or equivalent differentiable calculation.

5. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, In step (4), the actuation energy consumption is calculated based on the relationship between the change in actuator length and the corresponding internal force, and a smooth function is used to approximate the non-smooth terms.

6. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, In step (4), the constraints include one or more of the following: maximum structural displacement constraints, maximum component stress constraints, or target shape constraints.

7. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, In step (5), the gradient optimization algorithm includes the moving asymptote method, the sequential quadratic programming method, or other gradient-based optimization algorithms.

8. The active structure low-energy geometric nonlinear optimization control method based on differentiable structure analysis according to claim 1, characterized in that, Step (5) also includes normalizing the actuator control quantity and then performing inverse normalization after optimization to obtain the actual control quantity.

9. A low-energy-consumption geometrical nonlinear optimization control system for active structures based on differentiable structure analysis, used to implement the low-energy-consumption geometrical nonlinear optimization control method for active structures according to any one of claims 1 to 8, characterized in that, include: The structural analysis module is used to build an active structural analysis model that considers geometric nonlinearity and to calculate the structural response; The differentiable computation module is used to construct the structural analysis process as a differentiable computation process and obtain the gradient information of the structural response with respect to the actuator control quantity; The optimization control module is used to construct an optimization model with actuation energy consumption as the objective and structural performance constraints as the condition, and to solve for the optimal actuator control quantity based on the gradient information. The control execution module is used to regulate the active structure according to the optimal actuator control quantity.

10. The active structural low-energy geometric nonlinear optimization control system based on differentiable structure analysis according to claim 9, characterized in that, The differentiable computation module is implemented based on automatic differentiation or equivalent differentiable computation mechanism; the optimization control module uses a gradient-based optimization algorithm to iteratively update the control quantity.

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