Force correction based on adaptive model to improve newton iteration hybrid test method

Abstract

The application relates to a force correction improved Newton iteration hybrid test method based on an adaptive model, relates to the application field of structure hybrid test technology, and solves the technical problems of slow iteration convergence and low precision caused by fixed force correction models in traditional structure hybrid tests. The application comprises the following steps: dividing an overall structure into numerical substructures and physical substructures, respectively modeling and establishing dynamics boundaries; carrying out a preliminary test to establish an equivalent model, performing the 0th and 1st iterations, collecting restoring forces and determining a symbol judgment function; starting from the 2nd iteration, performing normal iterations, and gradually integrating and calculating the restoring forces through an inner loop in each round; determining a force correction coefficient by using the difference between the restoring forces of two adjacent rounds; solving an improved Newton iteration format, updating displacement commands, loading the collected corrected restoring forces, and calculating the root mean square error of the restoring forces of two adjacent rounds; if the root mean square error is smaller than a tolerance, the iteration converges, and the method returns to step three and iterates until convergence. The application has a good application prospect in the field of engineering structure performance testing.

Description

Technical Field

[0001] This invention relates to the field of structural hybrid testing technology, specifically to a force-corrected improved Newton iterative hybrid testing method based on an adaptive model. Background Technology

[0002] Many areas in my country are located in high-risk earthquake zones, making the improvement of seismic resilience in major engineering projects an urgent need. Traditional structural testing methods (such as quasi-static tests and shaking table tests) have inherent limitations in terms of simulation accuracy, equipment constraints, and cost-effectiveness. Hybrid substructure testing, by combining physical experiments with numerical simulations, provides a feasible solution for testing large and complex structures; however, its core branch—real-time hybrid testing—faces challenges related to computational latency and system instability. While iterative hybrid testing methods developed to address these issues avoid computational delays, they introduce new problems such as numerous iterations and high testing costs. Therefore, developing an efficient iterative algorithm that optimizes convergence speed and reduces resource consumption has broad applicability.

[0003] Traditional iterative hybrid tests still suffer from bottlenecks such as low convergence efficiency, difficulty in repeatedly loading elasto-plastic test objects, and high cost of vulnerability assessment tests. How to conduct seismic vulnerability assessment of ductile structures using iterative hybrid tests faces significant challenges. Existing iterative methods primarily employ fixed-point iteration. Even hybrid tests using Newton iteration typically use the most common Newton-Raphson method, rather than the faster-converging and fewer-iteration-time improved Newton iteration. Under the same accuracy requirements, the improved Newton iteration method converges much faster than ordinary Newton iteration and fixed-point iteration. In other words, using the improved Newton iteration method until convergence requires far fewer iterations than ordinary Newton iteration and fixed-point iteration.

[0004] The existing force correction hybrid experimental method uses the restoring forces of the physical substructures from the first two iterations and fixed model parameters to build a restoring force correction model. However, since the model parameters used to calculate the restoring force correction value based on the difference between the first two iterations remain unchanged, errors exist in the calculated difference of the restoring force model. A force correction improved Newton iteration hybrid experimental method based on an adaptive model is proposed. This method replaces fixed-point iteration with improved Newton iteration. Compared to fixed-point iteration, improved Newton iteration achieves global convergence. Simultaneously, an adaptive model is set using adaptive model parameters and the errors from all iterations for restoring force correction calculation. The displacement calculated using a successive integration algorithm is used as the new loading command, thereby improving the iteration convergence speed and accuracy. Summary of the Invention

[0005] To address the technical problems of slow iterative convergence, low accuracy, and large deviations in the coupled responses of physical and numerical substructures caused by fixed force correction models in traditional structural hybrid experiments, this invention provides a force-corrected improved Newton iterative hybrid experimental method based on an adaptive model, comprising:

[0006] Step 1: First, define the engineering structure to be tested in the hybrid experiment as the overall structure. Select the components that need to be physically loaded from the overall structure as physical substructures. The remaining parts of the overall structure excluding the selected physical substructures are defined as numerical substructures. Establish numerical models of the numerical substructures and linear numerical models of the physical substructures respectively, and construct the dynamic boundary relationship between the two to provide a clear structural basis and interaction basis for subsequent iterative experiments.

[0007] Step 2: Based on the dynamic boundary relationship, the numerical model of the numerical substructure, and the linear numerical model of the physical substructure, preliminary preparation experiments are conducted, and an equivalent model of the physical substructure is established using historical test data. Then, rounds 0 and 1 are iterated sequentially: In round 0, an external load is input, the displacement is calculated through the numerical substructure model and transferred to the physical substructure for loading, and the restoring force of round 0 is collected; In round 1, the initial model parameters are set as force correction model parameters, the initial restoring force correction value is obtained by calling the restoring force calculation of round 0, the displacement command is output for loading, the restoring force of round 1 is collected, and the sign judgment function is determined by comparing the full-time reaction forces of the two rounds.

[0008] Step 3: Based on the sign judgment function, the restoring force in round 0 and the restoring force in round 1, start from round 2 and perform j normal iterations containing adaptive model parameters and restoring force correction values, j>2. In each normal iteration, first perform the inner loop stepwise integration calculation to obtain the physical substructure restoring force of each round.

[0009] Step 4: Calculate the difference in restoring force using the restoring force of the physical substructures of the two adjacent wheels, and determine the force correction coefficient;

[0010] Step 5: Combine the force correction coefficient with the adaptive model parameters to solve the improved Newton iteration formula, update the displacement command and pass it to the physical substructure loading, and collect the restoring force of the physical substructure after force correction in this round.

[0011] Step 6: Based on the restoring force of the physical substructure after force correction in the current round and the restoring force of the physical substructure after force correction in the previous round, calculate the root mean square error of the two. If the root mean square error is less than the preset tolerance, the experiment converges; otherwise, let j = j + 1, return to step 3 to continue normal iteration until the convergence condition is met.

[0012] Furthermore, the initial model parameter mentioned in step two is 0.8.

[0013] Furthermore, in step 2, the formula for the initial restoring force correction value is:

[0014]

[0015] in, This is the correction value calculated for the numerical substructure in the i-th step of the first round. These are the initial model parameters. The damping matrix of the physical substructure. The velocity of the physical substructure in the i-th step of the first round, calculated using the kinematic equations. The velocity of the physical substructure in the 0th round, i-th step, calculated using the kinematic equations. The stiffness matrix of the physical substructure. The displacement of the physical substructure in the first round, step i, is calculated using the kinematic equations. The displacement of the physical substructure in the 0th round and i-th step is calculated using the kinematic equations.

[0016] Furthermore, in step two, the sign judgment function Sign(β) is defined as follows: when β>0, Sign(β)=1; when β≤0, Sign(β)=-1, where β is a parameter related to the difference between the uncorrected restoring force in round 0 and the corrected restoring force in round 1.

[0017] Furthermore, in step three, the kinetic equation for the stepwise integration of the inner loop is:

[0018]

[0019] Wherein, the subscript E represents the physical substructure, N represents the numerical substructure, and i represents the integration step. , , These are the mass matrix, damping matrix, and stiffness matrix of the numerical substructure, respectively. The acceleration calculated for the numerical substructure in the j-th round at step i is... , The velocity and displacement of the numerical substructure in the j-th round and i-th step are calculated using kinematic equations. For the restoring force of the physical substructure in round j-1, For force correction factor, This is the correction value calculated for the numerical substructure in the j-th round at step i. Let be the external load in the j-th iteration.

[0020] Furthermore, in step five, the improved Newton iteration formula is:

[0021]

[0022] in, The improved Newton's iteration formula can only be used if this condition is met. The initial values ​​are the values ​​used in Newton's iterations. The iteration value is the value of Newton's iteration. Let h(x) be a scalar parameter, and h(x) be a nonlinear system of equations representing displacement. It is a Jacobian matrix.

[0023] The beneficial effects of this invention are as follows: By constructing an adaptive model to integrate the restoring force correction data from multiple iterations with the actual response of the physical substructure, optimizing the iterative logic of the force correction coefficient, and adopting a block-based improved Newton iteration formula, this invention significantly improves the iterative convergence speed and force correction accuracy of the structural hybrid test, effectively reduces the coupling deviation between the physical substructure and the numerical substructure, enhances the reliability and stability of the test results, and reduces the dependence on initial parameters. It is suitable for efficient and accurate testing of different types of engineering structures. Attached Figure Description

[0024] Figure 1 The flowchart shows the improved Newton-based iterative hybrid experimental method based on adaptive model force correction.

[0025] Figure 2 A schematic diagram of a hybrid trial iteration to improve the Newton-Raphson iteration algorithm;

[0026] Figure 3 A diagram illustrating the implementation of the improved Newton-Raphson iterative algorithm based on an adaptive model;

[0027] Figure 4 This is a schematic diagram of the improved Newton iterative hybrid test method based on adaptive model force correction (using the hybrid test of high-speed train anti-hunting vibration damper as the test substructure). Detailed Implementation

[0028] The technical solution of the present invention will be further described below with reference to embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention. In the following embodiments, process equipment or devices not specifically specified are all conventional equipment or devices in the art. Unless specifically specified, the technical means used in the embodiments of the present invention are all conventional means well known to those skilled in the art.

[0029] Example 1: A force-corrected improved Newton-based iterative hybrid experimental method based on an adaptive model, comprising:

[0030] Step 1: First, define the engineering structure to be tested in the hybrid experiment as the overall structure. Select the components that need to be physically loaded from the overall structure as physical substructures. The remaining parts of the overall structure excluding the selected physical substructures are defined as numerical substructures. Establish numerical models of the numerical substructures and linear numerical models of the physical substructures respectively, and construct the dynamic boundary relationship between the two to provide a clear structural basis and interaction basis for subsequent iterative experiments.

[0031] Step 2: Based on the dynamic boundary relationship, the numerical model of the numerical substructure, and the linear numerical model of the physical substructure, preliminary preparation experiments are conducted, and an equivalent model of the physical substructure is established using historical test data. Then, rounds 0 and 1 are iterated sequentially: In round 0, an external load is input, the displacement is calculated through the numerical substructure model and transferred to the physical substructure for loading, and the restoring force of round 0 is collected; In round 1, the initial model parameters are set as force correction model parameters, the initial restoring force correction value is obtained by calling the restoring force calculation of round 0, the displacement command is output for loading, the restoring force of round 1 is collected, and the sign judgment function is determined by comparing the full-time reaction forces of the two rounds.

[0032] Step 3: Based on the sign judgment function, the restoring force in round 0 and the restoring force in round 1, start from round 2 and perform j normal iterations containing adaptive model parameters and restoring force correction values, j>2. In each normal iteration, first perform the inner loop stepwise integration calculation to obtain the physical substructure restoring force of each round.

[0033] Step 4: Calculate the difference in restoring force using the restoring force of the physical substructures of the two adjacent wheels, and determine the force correction coefficient;

[0034] Step 5: Combine the force correction coefficient with the adaptive model parameters to solve the improved Newton iteration formula, update the displacement command and pass it to the physical substructure loading, and collect the restoring force of the physical substructure after force correction in this round.

[0035] Step 6: Based on the restoring force of the physical substructure after force correction in the current round and the restoring force of the physical substructure after force correction in the previous round, calculate the root mean square error of the two. If the root mean square error is less than the preset tolerance, the experiment converges; otherwise, let j = j + 1, return to step 3 to continue normal iteration until the convergence condition is met.

[0036] Specifically, in combination Figure 1As can be seen from the figure, the complete process logic of the hybrid experiment is presented. The core includes two major stages: initial iteration and normal iteration. First, the preliminary preparation is completed by establishing numerical and physical substructure models and constructing dynamic coupling relationships. Then, the 0th and 1st rounds of iteration are carried out in sequence. From the 2nd round onwards, normal iteration begins. The difference between the restoring forces of adjacent rounds is used to determine γ. The improved Newton iteration formula is solved by substituting the adaptive model parameters and the restoring force correction value. The displacement command is updated and the restoring force is collected. Finally, the root mean square error of the restoring force after two consecutive rounds of correction is used to determine convergence. If convergence is not achieved, the iteration is repeated.

[0037] Combination Figure 2 As can be seen, the diagram visually illustrates the core calculations and operations within a single iteration: initialization is performed first, followed by loading the physical specimen in the kth round, collecting displacement and restoring force signals from the first and kth rounds, obtaining the displacement signal for the (k+1)th round through numerical solution, and then judging the round and convergence. If the convergence condition is met, the process ends; otherwise, it returns to the relevant stage to continue iterating.

[0038] Combination Figure 3 It can be seen that, taking the external load as input, it integrates two key technologies: the improved Newton iteration algorithm and the physical sub-loading system; it sets up adaptive model parameter calculation and restoring force correction value calculation links for force correction optimization; structurally, it is divided into a numerical substructure (inner loop) and an iterative controller (outer loop). The outer loop has an iterative update mechanism of j=j+1 and is also associated with the relevant response parameters of the physical substructure, reflecting the key components and operating framework of the force correction improved Newton iteration hybrid experiment based on the adaptive model.

[0039] Furthermore, the initial model parameter mentioned in step two is 0.8.

[0040] Furthermore, in step 2, the formula for the initial restoring force correction value is:

[0041]

[0042] in, This is the correction value calculated for the numerical substructure in the i-th step of the first round. These are the initial model parameters. The damping matrix of the physical substructure. The velocity of the physical substructure in the i-th step of the first round, calculated using the kinematic equations. The velocity of the physical substructure in the 0th round, i-th step, calculated using the kinematic equations. The stiffness matrix of the physical substructure. The displacement of the physical substructure in the first round, step i, is calculated using the kinematic equations. The displacement of the physical substructure in the 0th round and i-th step is calculated using the kinematic equations.

[0043] Furthermore, in step two, the sign judgment function Sign(β) is defined as follows: when β>0, Sign(β)=1; when β≤0, Sign(β)=-1, where β is a parameter related to the difference between the uncorrected restoring force in round 0 and the corrected restoring force in round 1.

[0044] Furthermore, in step three, the kinetic equation for the stepwise integration of the inner loop is:

[0045]

[0046] Wherein, the subscript E represents the physical substructure, N represents the numerical substructure, and i represents the integration step. , , These are the mass matrix, damping matrix, and stiffness matrix of the numerical substructure, respectively. The acceleration calculated for the numerical substructure in the j-th round at step i is... , The velocity and displacement of the numerical substructure in the j-th round and i-th step are calculated using kinematic equations. For the restoring force of the physical substructure in round j-1, For force correction factor, This is the correction value calculated for the numerical substructure in the j-th round at step i. Let be the external load in the j-th iteration.

[0047] Furthermore, in step five, the improved Newton iteration formula is:

[0048]

[0049] in, The improved Newton's iteration formula can only be used if this condition is met. The initial values ​​are the values ​​used in Newton's iterations. The iteration value is the value of Newton's iteration. Let h(x) be a scalar parameter, and h(x) be a nonlinear system of equations representing displacement. It is a Jacobian matrix.

[0050] Specifically, the product of the adaptive model parameters and the restoring force correction value used in this invention As an adaptive model, the adaptive model parameters and the formula for the restoring force correction value are as follows:

[0051]

[0052]

[0053] Where n is the number of partitions in the physical substructure, and the subscripts c and m represent the calculated and measured values, respectively.

[0054] Example 2, combined with Figure 4 This embodiment uses an iterative hybrid test of a high-speed train anti-hunting vibration damper as an example to illustrate the basic principle of applying the present invention to conduct an improved Newton iterative hybrid test based on adaptive model correction. The implementation process is as follows:

[0055] The original structure consisted of a high-speed train and an uneven track. One of the carriages was selected as the test carriage, and one section of the anti-hunting vibration damper in that carriage was used as the test substructure for loading. The remaining part was used as the numerical substructure for simulation.

[0056] This embodiment is refined into two stages to conduct iterative hybrid tests, with the hybrid test of the high-speed train anti-hunting damper as the test substructure. The specific method steps are as follows:

[0057] Phase 1:

[0058] (1) A numerical model was established by taking one section of the carriage as the test substructure and the remaining part as the numerical substructure.

[0059] (2) Install the anti-hunting vibration damper on the actuator, and by setting different parameters of the numerical substructure and inputting different external excitations, carry out real-time mixed tests under different working conditions to collect the force-displacement relationship of the anti-hunting vibration damper under different working conditions and establish a database;

[0060] (3) Establish an equivalent model of the physical substructure using historical data. Conduct hybrid tests under pure numerical calculation as iterative prediction rounds. Input the iterative prediction results into the numerical substructure, perform stepwise integration calculations with adaptive model parameters to obtain the loading command of the anti-hunting damper, and pass it to the anti-hunting damper structure.

[0061] Phase Two:

[0062] (4) Perform full-time numerical calculations on the overall structural numerical model of the carriage to obtain the full-time response of the overall structure and the full-time displacement response of the anti-hunting damper;

[0063] (5) Apply full-time displacement loading to the anti-hunting vibration damper and collect the full-time reaction force;

[0064] (6) Calculate the difference in restoring force using the restoring force of the two adjacent anti-hunting shock absorbers, and determine the force correction coefficient γ;

[0065] (7) Use the obtained force correction coefficient and restoring force to solve the constructed improved Newton iterative formula to obtain the loading command required for the next round of anti-hunting vibration damper;

[0066] (8) Calculation and If the root mean square error is less than the tolerance, then the experiment converges and ends; otherwise, let... Return to the second stage (6).

[0067] pass Figure 4 As can be seen, in this embodiment, the physical shock absorber (experimental substructure) is connected to a numerical simulation loop containing a whole vehicle model (overall structure) through a servo loading system. Real-time information exchange is carried out using a data interaction center, and an algorithm based on an improved Newton's iterative formula is adopted. Through iterative calculation and force correction, the experimental response of the shock absorber is precisely matched with the simulation response of the whole vehicle system, thereby efficiently and accurately obtaining the dynamic performance of the shock absorber in the real vehicle system.

[0068] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A force-corrected improved Newton-based iterative hybrid experimental method based on an adaptive model, characterized in that, include: Step 1: First, define the engineering structure to be tested in the hybrid experiment as the overall structure. Select the components that need to be physically loaded from the overall structure as physical substructures. The remaining parts of the overall structure excluding the selected physical substructures are defined as numerical substructures. Establish numerical models of the numerical substructures and linear numerical models of the physical substructures respectively, and construct the dynamic boundary relationship between the two to provide a clear structural basis and interaction basis for subsequent iterative experiments. Step 2: Based on the dynamic boundary relationship, the numerical model of the numerical substructure, and the linear numerical model of the physical substructure, preliminary preparation experiments are conducted, and an equivalent model of the physical substructure is established using historical test data. Then, rounds 0 and 1 are iterated sequentially: In round 0, an external load is input, the displacement is calculated through the numerical substructure model and transferred to the physical substructure for loading, and the restoring force of round 0 is collected; In round 1, the initial model parameters are set as force correction model parameters, the initial restoring force correction value is obtained by calling the restoring force calculation of round 0, the displacement command is output for loading, the restoring force of round 1 is collected, and the sign judgment function is determined by comparing the full-time reaction forces of the two rounds. Step 3: Based on the sign judgment function, the restoring force in round 0 and the restoring force in round 1, start from round 2 and perform j normal iterations containing adaptive model parameters and restoring force correction values, j>2. In each normal iteration, first perform the inner loop stepwise integration calculation to obtain the physical substructure restoring force of each round. Step 4: Calculate the difference in restoring force using the restoring force of the physical substructures of the two adjacent wheels, and determine the force correction coefficient; Step 5: Combine the force correction coefficient with the adaptive model parameters to solve the improved Newton iteration formula, update the displacement command and pass it to the physical substructure loading, and collect the restoring force of the physical substructure after force correction in this round. Step 6: Based on the restoring force of the physical substructure after force correction in this round and the restoring force of the physical substructure after force correction in the previous round, calculate the root mean square error of the two. If the root mean square error is less than the preset tolerance, the test converges. Otherwise, let j = j + 1, return to step three and continue normal iteration until the convergence condition is met; In step five, the improved Newton iteration formula is: in, The improved Newton's iteration formula can only be used if this condition is met. The initial values ​​are the values ​​used in Newton's iterations. The iteration value is the value of Newton's iteration. Let h(x) be a scalar parameter, and h(x) be a nonlinear system of equations representing displacement. It is a Jacobian matrix.

2. The force-corrected improved Newton iterative hybrid experimental method based on an adaptive model according to claim 1, characterized in that, The initial model parameter mentioned in step two is 0.

8.

3. The force-corrected improved Newton iterative hybrid experimental method based on an adaptive model according to claim 1, characterized in that, In step 2, the formula for the initial restoring force correction value is: in, This is the correction value calculated for the numerical substructure in the i-th step of the first round. These are the initial model parameters. The damping matrix of the physical substructure. The velocity of the physical substructure in the i-th step of the first round, calculated using the kinematic equations. The velocity of the physical substructure in the 0th round, i-th step, calculated using the kinematic equations. The stiffness matrix of the physical substructure. The displacement of the physical substructure in the first round, step i, is calculated using the kinematic equations. The displacement of the physical substructure in the 0th round and i-th step is calculated using the kinematic equations.

4. The force-corrected improved Newton-based iterative hybrid experimental method based on an adaptive model according to claim 1, characterized in that, In step two, the sign judgment function Sign(β) is defined as follows: when β>0, Sign(β)=1; when β≤0, Sign(β)=-1, where β is a parameter related to the difference between the uncorrected restoring force in round 0 and the corrected restoring force in round 1.

5. The force-corrected improved Newton iterative hybrid experimental method based on an adaptive model according to claim 1, characterized in that, In step three, the kinetic equation for the stepwise integration of the inner loop is: Wherein, the subscript E represents the physical substructure, N represents the numerical substructure, and i represents the integration step. , , These are the mass matrix, damping matrix, and stiffness matrix of the numerical substructure, respectively. The acceleration calculated for the numerical substructure in the j-th round at step i is... , The velocity and displacement of the numerical substructure in the j-th round and i-th step are calculated using kinematic equations. For the restoring force of the physical substructure in round j-1, For force correction factor, This is the correction value calculated for the numerical substructure in the j-th round at step i. Let be the external load in the j-th iteration.

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