Reliable structure-control coupling design optimization method

Abstract

The invention discloses a reliability structure-control coupling design optimization method, and particularly relates to the technical field of electromechanical equipment optimization, and the method comprises the steps: building a mathematical model for electromechanical equipment deterministic structure-control coupling design optimization, and solving to obtain optimal structure physical design parameters; fixing the optimal control variable, and performing reliability analysis on the optimal structure physical design parameters to obtain In-MPP points and constraint function values in an index circle; the initial penalty coefficient is used as a starting point in subsequent iteration, and the penalty coefficient is updated in combination with the change of the target function value and the satisfaction change of the constraint function at the In-MPP point; and in the iteration process, calculating a translation vector of an inequality constraint function, constructing and solving a decoupled deterministic structure-control coupling design problem in combination with a penalty coefficient, and repeating the steps to finally obtain a convergent design scheme meeting the reliability requirement. According to the method, the reliability of an intermediate result in the optimization process is improved, the convergence efficiency is improved, and the application range of the reliability structure-control coupling design optimization method is expanded.

Description

Technical Field

[0001] This invention relates to the field of electromechanical equipment optimization technology, specifically to a design optimization method for reliability structure-control coupling. Background Technology

[0002] Modern electromechanical equipment is mostly a complex large system, generally involving disciplines including structure, fluid dynamics, heat transfer, electromagnetics, and control. Its design can be viewed as a multidisciplinary design optimization problem. For example, the design of a wind turbine requires simultaneous consideration of structure, aerodynamics, electromagnetics, and control. Traditional multidisciplinary design optimization methods mainly focus on the design of structural parameters, neglecting the coupling between static structural parameters and dynamic control design in the overall system performance, thus failing to obtain the optimal solution at the system level.

[0003] The structure-control coupling design method focuses on the coupling relationship between static structural parameters and dynamic control strategies. It designs static structural parameters and control strategies through iterative sequences, optimizes static structural parameters in the outer loop while designing the corresponding control strategy in the inner loop, or treats the design of structural physical parameters and control strategies as a single optimization problem to be solved holistically. The structure-control coupling design method has been widely applied, improving the design performance of electromechanical equipment systems.

[0004] However, the structure-control coupling design method, as a deterministic design optimization method, cannot handle the multi-source uncertainties that occur during the production of equipment components and the operation of equipment. Electromechanical equipment has a high failure risk during operation, and its reliability is difficult to predict and guarantee.

[0005] On the other hand, reliability-based design optimization methods, including Reliability-Based Design Optimization (RBDO) and time-variant RBDO (t-RBDO), only consider the impact of uncertainties in structural or physical parameters on system performance and constraints. They do not involve the design of dynamic control strategies and cannot be applied in the context of structure-control coupling design.

[0006] Currently, research on design methods that consider the impact of design variable uncertainties under the structure-control coupling context is still in its early stages. Among these, methods based on the traditional Sequential Optimization and Reliability Assessment (SORA) framework assume the feasible region near the index circle is continuous and ignore the impact of control variable variations on reliability analysis, thus severely limiting the range of problems that can be solved. Methods based on generalized polynomial chaos (gPC) expansion and Monte Carlo simulation require multiple simulations, resulting in low efficiency. Therefore, how to optimize the reliability design of electromechanical equipment under the structure-control coupling context remains a challenging problem. Summary of the Invention

[0007] To address the aforementioned shortcomings of existing technologies, this invention improves upon the traditional SORA framework applicable to RBDO problems, extending it to structure-control coupled design optimization problems considering reliability. This provides a novel reliability-based structure-control coupled design optimization method. This method proposes a translation vector calculation method for discontinuous feasible regions within the fit index circle, while simultaneously limiting the deviation of control variables obtained from two adjacent deterministic optimization problems. This ensures the effectiveness of the translation vector obtained from the previous reliability analysis in guiding the current deterministic optimization design.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a design optimization method for reliability structure-control coupling, the method comprising:

[0009] A mathematical model for the deterministic structure-control coupling design optimization of electromechanical equipment is established and an objective function is defined to obtain the optimal structural physical design parameters, control variables, and objective function values. Then, the optimal control variables are fixed in the standard normal space, and a reliability analysis is performed on the optimal structural physical design parameters to obtain the corresponding objective function, the maximum possible point within the index circle, and the constraint function values.

[0010] In subsequent iterations, starting from the initial penalty coefficient, and combining the changes in the objective function value and the satisfaction change index of a single constraint function at the In-MPP point, the update index is calculated and the penalty coefficient is updated.

[0011] During the iteration process, the translation vector of the inequality constraint function is first calculated in the standard normal space. Combined with the updated penalty coefficient, the decoupled equivalent deterministic structure-control coupling design problem is constructed and solved to obtain the current optimal parameters. Then, the optimal control variables are fixed to perform reliability analysis to obtain the In-MPP point and constraint function values. If the constraints are satisfied and the change in the objective function is less than the set value, the iteration stops and the optimal result is output.

[0012] Preferably, based on the physical model and application scenario of the electromechanical equipment, a mathematical model for reliability structure-control coupling design optimization is established, ignoring the uncertainties of all variables, and the deterministic structure-control coupling design optimization problem is solved. The objective function is as follows:

[0013] ;

[0014] in, For the structural physical design parameters of electromechanical equipment, For state variables at discrete time points The matrix formed by the values, For control variables at discrete time points A matrix composed of the values ​​of , It is the number of discrete points. For endpoint-type objective function terms (Mayer terms), This is an integral objective function term (Lagrange term). For integral weights, To solve the differential matrix in the pseudospectral method for this type of problem, For the first Inequality constraint functions, The number of inequality constraint functions. For equality constraints, This is the function on the right-hand side of the state equation. and These are the state variables at the start and end points, respectively. and These represent the initial time and the terminal time, respectively. From this, the optimal physical design parameters for the electromechanical equipment structure, without considering the influence of deterministic factors, are obtained. Optimal control variables and objective function value .

[0015] Preferably, initialize model parameters, including the maximum number of model iterations. The objective function changes convergence setpoint between two adjacent iterations. The penalty coefficient of the objective function in the initial deterministic structure-control coupled design optimization problem. .

[0016] Preferably, in the standard normal space In this process, the optimal control variable is fixed. Optimal physical design parameters for electromechanical equipment structure The objective function for the reliability analysis problem is as follows:

[0017] ;

[0018] Among them, the standard normal space The formula is derived from Rosenblatt's transformation formula, as follows:

[0019] ;

[0020] in, It is the first A random electromechanical equipment structural design variable The cumulative distribution function, It is the inverse cumulative distribution function of the standard normal distribution. The number of random variables is used to obtain the In-MPP points within the indicator circle. and the corresponding constraint function values .

[0021] Preferably, the initial penalty coefficient is In subsequent iterations, an update index for the penalty coefficient of the objective function is calculated, and the penalty coefficient is updated according to the index. This indicator comprehensively evaluates changes in the objective function value. The change in the function value of the inequality constraint function at the maximum probability point In-MPP in reliability analysis The penalty coefficient update formula is as follows, where This represents the current iteration number. :

[0022] When the penalty coefficient update indicator is greater than or equal to +1, the penalty coefficient is halved;

[0023] ;

[0024] When the updated metric equals -3, the penalty coefficient is doubled.

[0025] ;

[0026] In other cases, the penalty coefficient remains unchanged;

[0027] ;

[0028] If the current objective function value Compared to the previous objective function value If it is better, then the change in the objective function value is indicated by the marker. If the value is +1, then -1; otherwise, 0. The formula is as follows:

[0029] ;

[0030] If the single constraint function value of the In-MPP point If the constraint satisfaction is better than before, then the change index of a single constraint function value is... If it's worse, record it as +1; if it's worse, record it as -1; otherwise, record it as 0. The formula is as follows:

[0031] ;

[0032] in, ;in For the first A constraint function, It represents the relative change in the function value of the constraint function at the In-MPP point between two consecutive constraints. This is the correction amount for the constraint function value near zero when solving for this relative change; if the problem has multiple constraint functions, the index of each individual constraint function value is summed. Simultaneously, the overall index of the constraint function is truncated when it exceeds +2 or falls below -2 to prevent the penalty coefficient update index from becoming more biased towards the constraint function index. This also applies to the function value change index of the inequality constraint function in In-MPP. The calculation formula is as follows:

[0033] .

[0034] Preferably, in the standard normal space of the reliability analysis problem In the middle, connect the coordinate zero point and the In-MPP point obtained from the reliability analysis. And extend it to the target indicator circle. Determine the direction of the translation vector and use the target index degree As the translation distance, calculate the translation vector of each inequality constraint function. The formula is as follows:

[0035] ;

[0036] in, It is the first A random structure design variable The inverse cumulative distribution function, The cumulative distribution function of the standard normal distribution. To correspond to the intersection points of the target index circles in the original design variable space, The optimal structural physical design parameters are obtained for the deterministic design problem.

[0037] Preferably, based on the desired translation vector Updated penalty coefficient The degree of deviation of the control variables in the objective function between two adjacent iterations. To apply penalties, construct the decoupled equivalent deterministic structure-control coupling design problem, as shown in the following formula:

[0038] ;

[0039] in, It is a matrix consisting of the values ​​of the control variables at each discrete point. and Let be the mean of the random state variable and the value of MPP at discrete time points, respectively. The function values ​​at each discrete time point The vector formed It is a matrix composed of the values ​​of the equality constraint functions at discrete time points. To solve the differential matrix in the pseudospectral method for the optimal control problem, It is a matrix composed of the function values ​​on the right-hand side of the state equation at each discrete point. Given the inequality constraint function, solve the problem to obtain the current optimal structural physical design parameters. Optimal control variables and objective function value .

[0040] Preferably, the above-mentioned optimal control variables are fixed in the standard normal space. For optimal structural physical design parameters The following formula is used for reliability analysis:

[0041] ;

[0042] Obtain In-MPP points within the indicator circle and the corresponding constraint function values .

[0043] Preferably, the constraint function value of the In-MPP point obtained in the reliability analysis is used to determine the constraint function value. Do the constraints meet? Simultaneously, it determines whether the change in the objective function of the deterministic structure-control coupled design optimization problem is less than a set value. When all the above conditions are met, stop the iteration and output the optimal structural physical design parameters. Optimal control variables If the convergence condition does not converge, then... Then, start the next iteration, recalculate the penalty coefficient, update the index, update the penalty coefficient, calculate the translation vector, solve the deterministic design optimization problem after decoupling, and determine the convergence condition until the convergence condition is met.

[0044] This invention extends the SORA framework from the traditional RBDO problem to the solution of the reliability structure-control coupled design optimization problem, solving two technical bottlenecks:

[0045] 1. The reliability assessment conclusions during the intermediate process became invalid due to excessive deviations between two consecutive control variables;

[0046] 2. The discontinuity of the feasible region within the index circle near the mean of the random design variables causes distortion of the translation direction of the translation vector in the original SORA framework;

[0047] Compared with existing technologies, this invention penalizes the deviation values ​​of adjacent control variables in the objective function of the decoupled deterministic structure-control coupled design optimization problem, limiting the optimization range of the current control variable to the effective range of the previous reliability analysis conclusion. This improves the reliability of intermediate results during the optimization process and enhances convergence efficiency. Furthermore, this invention proposes the concept of In-MPP points within the index circle and, based on this, proposes a new method for calculating translation vectors, adapting to the case of discontinuous feasible regions within the index circle. Therefore, this invention expands the application scope of the reliability structure-control coupled design optimization method and improves the convergence efficiency of the design optimization process. Attached Figure Description

[0048] Figure 1 A schematic diagram of a quarter-inch vehicle active suspension and a helical compression spring provided by the present invention;

[0049] Figure 2 An iterative process diagram of the control variables provided for this invention;

[0050] Figure 3 The constraint function provided for this invention The Monte Carlo simulation results are shown in the figure.

[0051] Figure 4 The constraint function provided for this invention The Monte Carlo simulation results are shown in the figure.

[0052] Figure 5 The constraint function provided for this invention The Monte Carlo simulation results are shown in the figure.

[0053] Figure 6 Monte Carlo simulation results of static constraints provided for this invention;

[0054] Figure 7A comparison diagram of the effects of the deterministic collaborative design method provided by this invention and the embodiments of the method proposed by this invention;

[0055] Figure 8 A flowchart provided for this invention. Detailed Implementation

[0056] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0058] like Figure 8 As shown, this invention proposes a design optimization method for reliability structure-control coupling, comprising the following steps:

[0059] Step 1: Solve the deterministic structure-control coupled design optimization problem

[0060] Based on the physical model and application scenario of the electromechanical equipment, a mathematical model for reliability structure-control coupling design optimization is established. Ignoring the uncertainties of all variables, the deterministic structure-control coupling design optimization problem is solved, with the objective function as follows:

[0061]

[0062] in, For the structural physical design parameters of electromechanical equipment, For state variables at discrete time points The matrix formed by the values, For control variables at discrete time points A matrix composed of the values ​​of , It is the number of discrete points. For endpoint-type objective function terms (Mayer terms), This is an integral objective function term (Lagrange term). For integral weights, To solve the differential matrix in the pseudospectral method for this type of problem, For the first Inequality constraint functions, The number of inequality constraint functions. For equality constraints, This is the function on the right-hand side of the state equation. and These are the state variables at the start and end points, respectively. and These represent the initial time and the terminal time, respectively. From this, the optimal physical design parameters for the electromechanical equipment structure, without considering the influence of deterministic factors, are obtained. Optimal control variables and objective function value ;

[0063] Step 2: Initialize algorithm parameters

[0064] Initialize model parameters, including the maximum number of model iterations. The objective function changes convergence setpoint between two adjacent iterations. The penalty coefficient of the objective function in the initial deterministic structure-control coupled design optimization problem. ;

[0065] Step 3: Perform reliability analysis

[0066] In standard normal space In this process, the optimal control variable is fixed. Optimal physical design parameters for electromechanical equipment structure The objective function for the reliability analysis problem is as follows:

[0067] ;

[0068] Among them, the standard normal space The formula is derived from Rosenblatt's transformation formula, as follows:

[0069] ;

[0070] in, It is the first A random electromechanical equipment structural design variable The cumulative distribution function, It is the inverse cumulative distribution function of the standard normal distribution. It is the number of random variables, from which the InnerMost Probable Point (In-MPP) within the indicator circle is obtained. and the corresponding constraint function values ;

[0071] Step 4: Set / update the penalty coefficient of the objective function in the deterministic optimization problem

[0072] The initial penalty coefficient is In subsequent iterations, an update index for the penalty coefficient of the objective function is calculated, and the penalty coefficient is updated according to the index. This indicator comprehensively evaluates changes in the objective function value. The change in the function value of the inequality constraint function at the maximum probability point In-MPP in reliability analysis The penalty coefficient update formula is as follows, where This represents the current iteration number. :

[0073] When the penalty coefficient update indicator is greater than or equal to +1, the penalty coefficient is halved;

[0074] ;

[0075] When the updated metric equals -3, the penalty coefficient is doubled.

[0076] ;

[0077] In other cases, the penalty coefficient remains unchanged;

[0078] ;

[0079] If the current objective function value Compared to the previous objective function value If it is better, then the change in the objective function value is indicated by the marker. If the value is +1, then -1; otherwise, 0. The formula is as follows:

[0080] ;

[0081] If the single constraint function value of the In-MPP point If the constraint satisfaction is better than before, then the change index of a single constraint function value is... If it's worse, record it as +1; if it's worse, record it as -1; otherwise, record it as 0. The formula is as follows:

[0082] ;

[0083] in, ;in For the first A constraint function, It represents the relative change in the function value of the constraint function at the In-MPP point between two consecutive constraints. This is the correction amount for the constraint function value near zero when solving for this relative change; if the problem has multiple constraint functions, the index of each individual constraint function value is summed. Simultaneously, the overall index of the constraint function is truncated when it exceeds +2 or falls below -2 to prevent the penalty coefficient update index from becoming more biased towards the constraint function index. This also applies to the function value change index of the inequality constraint function in In-MPP. The calculation formula is as follows:

[0084] ;

[0085] Step 5: Calculate the translation vector of the inequality constraint function.

[0086] In the standard normal space of reliability analysis problems In the middle, connect the coordinate zero point and the In-MPP point obtained from the reliability analysis in step three. And extend it to the target indicator circle. Determine the direction of the translation vector and use the target index degree As the translation distance, calculate the translation vector of each inequality constraint function. The formula is as follows:

[0087] ;

[0088] in, It is the first A random structure design variable The inverse cumulative distribution function, The cumulative distribution function of the standard normal distribution. To correspond to the intersection points of the target index circles in the original design variable space, These are the optimal structural physical design parameters for the deterministic design problem obtained in the first step.

[0089] Step 6: Solve the deterministic structure-control coupling design problem after translation.

[0090] Based on the required translation vector Updated penalty coefficient The degree of deviation of the control variables in the objective function between two adjacent iterations. To apply penalties, construct the decoupled equivalent deterministic structure-control coupling design problem, as shown in the following formula:

[0091] ;

[0092] in, It is a matrix consisting of the values ​​of the control variables at each discrete point. and Let be the mean of the random state variable and the value of MPP at discrete time points, respectively. The function values ​​at each discrete time point The vector formed It is a matrix composed of the values ​​of the equality constraint functions at discrete time points. To solve the differential matrix in the pseudospectral method for the optimal control problem, It is a matrix composed of the function values ​​on the right-hand side of the state equation at each discrete point. Let be the inequality constraint function. Solving this problem yields the current optimal structural physical design parameters. Optimal control variables and objective function value ;

[0093] Step 7: Perform reliability analysis

[0094] In the standard normal space, the above optimal control variables are fixed. For optimal structural physical design parameters The following formula is used for reliability analysis:

[0095] ;

[0096] Obtain In-MPP points within the indicator circle and the corresponding constraint function values ;

[0097] Step 8: Determine if the convergence condition is met.

[0098] Determine the constraint function value of the In-MPP point obtained in the reliability analysis. Do the constraints meet? Simultaneously, it determines whether the change in the objective function of the deterministic structure-control coupled design optimization problem is less than a set value. When all the above conditions are met, stop the iteration and output the optimal structural physical design parameters. Optimal control variables If the convergence condition does not converge, then... Then return to step four.

[0099] Example 1: Reliability Structure-Control Coupling Design of Vehicle Active Suspension

[0100] Figure 1 This is a diagram showing a quarter of the vehicle's active suspension and coil compression springs. and They are spring-loaded mass and unspring-loaded mass, respectively. , and These represent the vertical positions of the sprung mass, the unsprung mass, and the road surface excitation, respectively. In the model of a helical compression spring, the helix diameter... Wire diameter and the number of valid laps For structural design variables, the helix diameter is... Wire diameter The design variables are random normal distributions, with standard deviations of respectively. and Valid number of laps This is simplified to continuous deterministic design variables. The design optimization objective considered in the example is to ensure that the constraints meet probabilistic requirements while reducing the force required by the force generator and maximizing driving comfort and vehicle handling. The four states of the vehicle's active suspension in the example are wheel hop. unsprung mass vertical velocity Suspension clearance and the vertical velocity of the sprung mass The control variable is the force generated by the force generator, and the system state equation is as follows:

[0101] ;

[0102] This implementation requires consideration of nine constraints:

[0103] 1. Wheel hop must be less than tire compression, expressed as: Among them, tire compression ;

[0104] 2. The helix ratio of the spring should not be too small, as expressed as: ;

[0105] 3. The helix ratio of the spring should not be too large, as expressed as: ;

[0106] 4. The free length of the spring cannot exceed the specified cavity length, expressed as: ;

[0107] 5. A spring needs to be protected from buckling, as shown below: ;

[0108] 6. The outer diameter of the spring must not exceed the set value to prevent interference with other vehicle components, as indicated by: ;

[0109] 7. The maximum shear stress of a spring must be less than the shear yield strength of the material, expressed as: ,in Ultimate tensile strength 0.65 times, the maximum shear stress of the spring is The spring is at the height of tension. Axial force at the location for .Notice Let be the free length of the spring, from the formula Determined; Spring stiffness is determined by the formula Sure;

[0110] 8. Dynamic length of the spring A value greater than the spring's tension height is expressed as: , where dynamic length , It is the initial spring deflection under the weight of one-quarter of the vehicle's sprung mass, approximately... ;

[0111] 9. Dynamic length of a spring Less than the free length of the spring, denoted as .

[0112] In this embodiment, the target reliability of each constraint is set to Terminal time set to .

[0113] Step 1: Solve the deterministic structure-control coupling design optimization problem. The optimization model is as follows:

[0114] ;

[0115] Where the initial state value ,get objective function value and the optimal control variable curve .

[0116] Step 2: Initialize relevant algorithm parameters, including the maximum number of algorithm iterations. The relative change in the objective function between two adjacent iterations convergence setpoint Initial penalty coefficient .

[0117] Step 3: Fix the above optimal control variables A reliability analysis was performed on the optimal structural physical design parameters. The reliability analysis model is as follows:

[0118] ;

[0119] in, The initial value is , Based on the deterministic optimal control variables obtained in the first step The simulation results are obtained. In this embodiment, even with uncertainties... and Under the influence of constraints and Since the constraints are always 100% satisfied, they are not analyzed during the reliability analysis phase. Therefore, the maximum possible points within the index circles of each constraint function are obtained as follows: In-MPP1=[0.0805,0.0129], In-MPP3=[0.0810,0.0130], In-MPP4=[0.0786,0.0146], In-MPP5=[0.0746,0.0138], In-MPP7=[0.0746,0.0136], In-MPP8=[0.0809,0.0145], In-MPP9=[0.0764,0.0145], and the corresponding function values ​​are... , , , , , and .

[0120] Step 4: Set / update the penalty coefficient of the objective function in the deterministic optimization problem:

[0121] The initial penalty coefficient is set to .

[0122] Step 5: Calculate the translation vector of the inequality constraint function:

[0123] Connect the coordinate zero point and the In-MPP point obtained from the reliability analysis, and extend it to the target index circle to determine the direction of the translation vector. Using the target index degree as the translation distance, calculate the translation vector of each inequality constraint function. The calculation formula is as follows:

[0124] , ;

[0125] in, It is the inverse cumulative distribution function of the physical design parameters of the j-th uncertain structure. It is the standard cumulative distribution function. Therefore, we get... , , , , , , .

[0126] Step 6: Solve the deterministic structure-control coupling design problem after translation:

[0127] Based on the required translation vector ~ Updated penalty coefficient The decoupled equivalent deterministic structure-control coupling design problem is constructed, and the model is as follows:

[0128] ; ;

[0129] in Solve this problem to obtain the current optimal structural physical design parameters. =0.0759, =0.0128, optimal control variable curve The objective function value is 98.6622.

[0130] Step 7: Perform a reliability analysis.

[0131] Fix the above optimal control variables The reliability analysis of the optimal structural physical design parameters is performed, and the mathematical model is as follows:

[0132] ;

[0133] Thus, the In-MPP points within the index circle are obtained as follows: In-MPP1=[0.0738,0.0136], In-MPP3=[0.0783,0.0121], In-MPP4=[0.0759,0.0137], In-MPP5=[0.0719,0.0129], In-MPP7=[0.0719,0.0128], In-MPP8=[0.0791,0.0134], and In-MPP9=[0.0738,0.0136], with corresponding function values. , , , , , and .

[0134] Step 8: Determine if the convergence condition is met:

[0135] because If the convergence condition is not met, the iteration continues. .

[0136] Step 9: Return to step 4 and update the penalty coefficient of the objective function in the deterministic optimization problem.

[0137] because ,but Simultaneously calculated Update penalty coefficient .

[0138] Steps four through eight above are continued until the convergence condition of step eight is met. The iterative process is shown in the table below:

[0139] iterations 1 0.0786 0.0137 18.4692 89.1612 34.696% 100% 99.999% 2 2.5e-4 0.0759 0.0128 17.6177 98.6622 67.830% 100% 100% 3 2.5e-4 0.0753 0.0124 17.4205 89.9320 45.387% 100% 100% 4 1.25e-4 0.0759 0.0117 17.7284 96.9643 98.103% 100% 100% 5 1.25e-4 0.0755 0.0120 17.5134 89.8650 48.069% 100% 100% 6 1.25e-4 0.0759 0.0110 17.8018 96.2222 99.799% 100% 100% 7 1.25e-4 0.0759 0.0116 17.5859 90.1508 48.563% 100% 100% 8 1.25e-4 0.0759 0.0114 17.8620 95.7713 99.924% 100% 100% 9 1.25e-4 0.0759 0.0095 17.9442 94.7899 99.972% 99.928% 100% 10 1.25e-4 0.0759 0.0095 17.9433 94.6591 99.900% 99.934% 100% 11 6.25e-5 0.0759 0.0095 17.9438 94.6014 99.921% 99.934% 100%

[0140] The mean value of the structural design parameters for the reliability structure-control coupled design optimization problem is finally obtained as follows: =0.0759, =0.0095, =17.9438, the iterative process of the control variable is as follows Figure 2 As shown.

[0141] For the final solution, 100,000 Monte Carlo simulations were performed to verify it, obtaining the Monte Carlo simulation results for each constraint function, where the constraints... , , For dynamic constraints (corresponding to respectively) Figures 3-5 The remaining 6 are static constraints (corresponding to...) Figure 6 In , , , , , ).

[0142] The deterministic collaborative design method and the position trajectory of the sprung mass block obtained by the method proposed in this invention are also given, such as Figure 7 As shown.

[0143] In this embodiment, the traditional SORA framework and the present invention are compared, using dynamic constraints. , , Monte Carlo simulations were performed to verify the satisfaction probability, and it was found that the solution obtained in this invention can meet the requirements of the safety probability. The traditional SORA framework solves This approach fails to meet the requirements for safety probability. It should also be noted that the traditional SORA framework did not converge in this embodiment; the table below shows its results at the 21st iteration, while the present invention converged at the 11th iteration, demonstrating higher convergence efficiency. The above comparison shows that, in solving reliability-based structure-control coupling design optimization problems, the present invention outperforms the traditional SORA framework in both convergence efficiency and the degree to which the final result satisfies the constraint safety probability.

[0144] Deterministic Coordination Design 0.0786 0.0137 18.4692 89.1612 34.696% 100% 99.999% Traditional SORA 0.0759 0.0085 18.0443 94.2175 99.992% 50.099% 100% This invention 0.0759 0.0095 17.9438 94.6014 99.921% 99.934% 100%

[0145] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A design optimization method for reliability structure-control coupling, characterized in that: The methods include: A mathematical model for the deterministic structure-control coupling design optimization of electromechanical equipment is established and an objective function is defined to obtain the optimal structural physical design parameters, control variables and objective function values; Then, fix the optimal control variables in the standard normal space, perform reliability analysis on the optimal structural physical design parameters, and obtain the corresponding objective function, the maximum possible point inside the index circle, and the constraint function value; In subsequent iterations, starting from the initial penalty coefficient, and combining the changes in the objective function value and the satisfaction change index of a single constraint function at the In-MPP point, the update index is calculated and the penalty coefficient is updated. During the iteration process, the translation vector of the inequality constraint function is first calculated in the standard normal space. Combined with the updated penalty coefficient, the decoupled equivalent deterministic structure-control coupling design problem is constructed and solved to obtain the current optimal parameters. Then, the optimal control variables are fixed to perform reliability analysis to obtain the In-MPP point and constraint function values. If the constraints are satisfied and the change in the objective function is less than the set value, the iteration stops and the optimal result is output.

2. The design optimization method for a reliability structure-control coupling according to claim 1, characterized in that: Based on the physical model and application scenario of the electromechanical equipment, a mathematical model for reliability structure-control coupling design optimization is established. Ignoring the uncertainties of all variables, the deterministic structure-control coupling design optimization problem is solved, with the objective function as follows: ； in, For the structural physical design parameters of electromechanical equipment, For state variables at discrete time points The matrix formed by the values, For control variables at discrete time points A matrix composed of the values ​​of , It is the number of discrete points. For endpoint-type objective function terms, i.e., Mayer terms, This is an integral objective function term, specifically a Lagrange term. For integral weights, To solve the differential matrix in the pseudospectral method for this type of problem, For the first Inequality constraint functions, The number of inequality constraint functions. For equality constraints, This is the function on the right-hand side of the state equation; and These are the state variables at the start and end points, respectively. and These are the initial time and the terminal time, respectively; from this, the optimal physical design parameters for the electromechanical equipment structure, without considering the influence of deterministic factors, are obtained. Optimal control variables and objective function value .

3. The design optimization method for a reliability structure-control coupling according to claim 2, characterized in that: Initialize model parameters, including the maximum number of model iterations. The objective function changes convergence setpoint between two adjacent iterations. The penalty coefficient of the objective function in the initial deterministic structure-control coupled design optimization problem. .

4. The design optimization method for a reliability structure-control coupling according to claim 3, characterized in that: In standard normal space In this process, the optimal control variable is fixed. Optimal physical design parameters for electromechanical equipment structure The objective function for the reliability analysis problem is as follows: ； Among them, the standard normal space The formula is derived from Rosenblatt's transformation formula, as follows: ； in, It is the first A random electromechanical equipment structural design variable The cumulative distribution function, It is the inverse cumulative distribution function of the standard normal distribution. The number of random variables is used to obtain the In-MPP points within the indicator circle. and the corresponding constraint function values .

5. The design optimization method for a reliability structure-control coupling according to claim 4, characterized in that: The initial penalty coefficient is In subsequent iterations, an update index for the penalty coefficient of the objective function is calculated, and the penalty coefficient is updated according to the index. This indicator comprehensively evaluates changes in the objective function value. The change in the function value of the inequality constraint function at the maximum probability point In-MPP in reliability analysis The penalty coefficient update formula is as follows, where This represents the current iteration number. : When the penalty coefficient update indicator is greater than or equal to +1, the penalty coefficient is halved; ； When the updated metric equals -3, the penalty coefficient is doubled. ； In other cases, the penalty coefficient remains unchanged; ； If the current objective function value Compared to the previous objective function value If it is better, then the change in the objective function value is indicated by the marker. If the value is +1, then -1; otherwise, 0. The formula is as follows: ； If the single constraint function value of the In-MPP point If the constraint satisfaction is better than before, then the change index of a single constraint function value is... If it's worse, record it as +1; if it's worse, record it as -1; otherwise, record it as 0. The formula is as follows: ； in, ; in For the first A constraint function, It represents the relative change in the function value of the constraint function at the In-MPP point between two consecutive constraints. This is the correction amount for the constraint function value near zero when solving for this relative change; if the problem has multiple constraint functions, the index of each individual constraint function value is summed. Simultaneously, the overall index of the constraint function is truncated when it exceeds +2 or falls below -2 to prevent the penalty coefficient update index from becoming more biased towards the constraint function index. This also applies to the function value change index of the inequality constraint function in In-MPP. The calculation formula is as follows: 。 6. The design optimization method for a reliability structure-control coupling according to claim 5, characterized in that: In the standard normal space of reliability analysis problems In the middle, connect the coordinate zero point and the In-MPP point obtained from the reliability analysis. And extend it to the target indicator circle. Determine the direction of the translation vector and use the target index degree As the translation distance, calculate the translation vector of each inequality constraint function. The formula is as follows: ； in, It is the first A random structure design variable The inverse cumulative distribution function, The cumulative distribution function of the standard normal distribution. To correspond to the intersection points of the target index circles in the original design variable space, The optimal structural physical design parameters are obtained for the deterministic design problem.

7. The design optimization method for a reliability structure-control coupling according to claim 6, characterized in that: Based on the required translation vector Updated penalty coefficient The degree of deviation of the control variables in the objective function between two adjacent iterations. To apply penalties, construct the decoupled equivalent deterministic structure-control coupling design problem, as shown in the following formula: ； in, It is a matrix consisting of the values ​​of the control variables at each discrete point. and Let be the mean of the random state variable and the value of MPP at discrete time points, respectively. The function values ​​at each discrete time point The vector formed It is a matrix composed of the values ​​of the equality constraint functions at discrete time points. To solve the differential matrix in the pseudospectral method for the optimal control problem, It is a matrix composed of the function values ​​on the right-hand side of the state equation at each discrete point. Given the inequality constraint function, solve the problem to obtain the current optimal structural physical design parameters. Optimal control variables and objective function value .

8. The design optimization method for a reliability structure-control coupling according to claim 7, characterized in that: In the standard normal space, the above optimal control variables are fixed. For optimal structural physical design parameters The following formula is used for reliability analysis: ； Obtain In-MPP points within the indicator circle and the corresponding constraint function values .

9. The design optimization method for a reliability structure-control coupling according to claim 8, characterized in that: Determine the constraint function value of the In-MPP point obtained in the reliability analysis. Do the constraints meet? Simultaneously, it determines whether the change in the objective function of the deterministic structure-control coupled design optimization problem is less than a set value. When all the above conditions are met, stop the iteration and output the optimal structural physical design parameters. Optimal control variables ; If the convergence condition does not converge, then Then, start the next iteration, recalculate the penalty coefficient, update the index, update the penalty coefficient, calculate the translation vector, solve the deterministic design optimization problem after decoupling, and determine the convergence condition until the convergence condition is met.

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