A method for online identification of dynamic loads based on interference observers

Abstract

This invention provides an online dynamic load identification method based on a disturbance observer. First, a structural state-space equation is established based on the mass matrix, damping matrix, and stiffness matrix of the linearly loaded structure. Then, the state-space equation of the loaded structure is compared and combined with the model equations in the control domain to design and determine the form and parameters of the disturbance observer characterized by the state-space equation parameters of the system model. This observer is then applied to the real-time online identification of external dynamic loads on the structure. By observing the difference between the actual output response and the estimated output response of the system in real time, the observer gain k is gradually adjusted until the estimated value approximates the actual input dynamic load. This method eliminates the need for complex design and extensive calculations, enabling accurate real-time identification of random dynamic loads on single-point / multi-point linearly loaded structures. It solves the problems of large solution errors and slow computation caused by matrix inversion operations in existing dynamic load identification technologies.

Description

Technical Field

[0001] This invention belongs to the field of dynamic load identification technology, specifically relating to an online dynamic load identification method based on an interference observer. Background Technology

[0002] Currently, in engineering fields such as aerospace and bridge construction, accurate acquisition of structural dynamic load information is the foundation and prerequisite for carrying out strength design and health monitoring. In recent years, modern engineering structures have been developing towards larger scale, greater complexity, and greater intelligence, and the forms of dynamic loads have also become increasingly diversified. To ensure the reliability of structural design, designers need to accurately know the amplitude and duration of impact loads acting on the structure in order to effectively reduce or even eliminate the adverse effects of impact loads on the structure. This has led to dynamic load identification technology playing an increasingly important role in more and more fields.

[0003] Dynamic load identification falls under the category of the second type of inverse problem in structural dynamics. The difficulty in determining the external dynamic loads borne by a structure under actual operating conditions lies in the fact that most dynamic loads exhibit characteristics such as non-stationarity in the time domain, broadband behavior in the frequency domain, and spatial distribution. These factors can all lead to the dynamic load localization problem being underdetermined or ill-determined. To address this problem, researchers have proposed numerous methods, including direct inversion methods, regularization methods, Kalman filtering methods, and AI-based dynamic load identification methods.

[0004] However, most of these methods require matrix inversion during implementation, which results in poor recognition accuracy and low computational efficiency. When identifying dynamic loads on large and complex structures, they cannot achieve fast, real-time, and accurate recognition. Summary of the Invention

[0005] Due to the non-stationarity in the time domain, broadband nature in the frequency domain, and spatial distribution of dynamic loads, modeling the inverse dynamic model of dynamic loads is difficult. Existing dynamic load identification methods involve complex solutions, resulting in poor identification accuracy, low efficiency, and an inability to achieve real-time online identification. We have found that the representation of a class of systems commonly used in control theory is similar to the state-space equations of linear loaded structures in structural dynamics. Therefore, we connect the state-space equations of dynamic systems with the model equations in control theory. Based on this, we designed a disturbance observer characterized by relevant parameters of the state-space equations of linear loaded structures and applied it to the real-time online identification of external dynamic loads on structures. This solves the problems of large solution errors and slow computation caused by matrix inversion operations in existing dynamic load identification technologies. Therefore, this invention proposes an online dynamic load identification method based on a disturbance observer.

[0006] To achieve the above objectives, the technical solution provided by this invention is:

[0007] A method for online identification of dynamic loads based on an interference observer, characterized by the following steps:

[0008] Step 1: Obtain the mass matrix M, damping matrix C, and stiffness matrix K of the linearly loaded structure;

[0009] Step 2: Based on the mass matrix M, damping matrix C, and stiffness matrix K obtained in Step 1, calculate the system matrix A, input matrix B, output matrix C, and direct transmission matrix D of the loaded structure, and establish the state-space equations of the linear loaded structure.

[0010] Among them, the system matrix Input matrix Output matrix C = [IO], direct transmission matrix D = O; z(t) is the system state vector, F(t) is the external dynamic load to be identified, and I is the identity matrix;

[0011] Step 3: Introduce a disturbance observer. Based on the state-space equations of the linearly loaded structure, construct the disturbance observer model in the following form:

[0012]

[0013] Where m represents the internal state of the observer. Let x = z(t) be the estimated value of the external dynamic load, z be the state vector of the system, and l(x) be the gain function of the disturbance observer.

[0014] The interference observer function is p(x) = k[OI]z(t), where k is the observer gain and k > 0;

[0015] Step 4: Conduct a preliminary experiment on the observer model obtained in Step 3. Input a vibration response, adjust the observer gain k, and when the estimated external dynamic load value... When the convergence reaches the external dynamic load F(t) to be identified, the value of the observer gain k is determined, and an interference observer model suitable for a linearly loaded structure is obtained.

[0016] Step 5: Obtain a disturbance observer model suitable for linearly loaded structures. Input the system state vector of the linearly loaded structure under load. Identify the external loads on a linearly loaded structure.

[0017] Furthermore, the specific method for constructing the disturbance observer model equation based on the state-space equation of the linear loaded structure in step 3 is as follows:

[0018] A class of available parameter system models in the field of reference control and the introduced interference observer model In the form of the linear loaded structure state space equation obtained in step 2, x = z(t) is taken as the state vector of the system, f(x) = Ax = Az(t), g2(x) = B, the disturbance vector d is the external dynamic load F(t) to be identified, and h(x) = Cx = Cz(t).

[0019] Since there is no control part in the linear system, g1(x)u=0;

[0020] The disturbance observer model equation, characterized by the parameters of the state-space equation of the linearly loaded structure, is then obtained as follows:

[0021]

[0022] Furthermore, in step 4, the process of obtaining the value of the observer gain k is as follows: given a value of k, observe the estimated value of the external dynamic load output by the observer model. If the convergence reaches the external dynamic load F(t) to be identified, and if not, adjust the given value of k until the output external dynamic load estimate is reached. The convergence is to the external dynamic load F(t) to be identified.

[0023] Furthermore, in step 3, an interference observer model is constructed in the Simulink Function module.

[0024] The advantages of this invention are:

[0025] 1. This invention applies the interference observer used in the control field to the field of dynamic load identification, effectively solving the bottleneck problem in the prior art that multi-point dynamic loads cannot be identified online. By observing the difference between the actual output response of the system and the nominal system output response in real time, the actual input dynamic load of the system is gradually adjusted and approximated according to the time step, thereby realizing accurate real-time identification of single-point / multi-point random dynamic loads.

[0026] 2. This invention determines the form and parameters of the interference sensor through the state-space equation of the loaded structure. Without the need for complex method design, the external load on the structure can be identified online by applying the real-time vibration response of the structure directly using the structural system parameters.

[0027] 3. In the process of online identification of dynamic loads of structural systems using an interference observer, the present invention eliminates the need for matrix inversion, thereby avoiding the accuracy loss and time consumption of matrix inversion calculation, and greatly improving the accuracy and efficiency of dynamic load identification. Attached Figure Description

[0028] Figure 1 This is a flowchart of the method of the present invention;

[0029] Figure 2 This is a schematic diagram of the discrete system structure in Embodiment 1 of this application;

[0030] Figure 3 This is the result of single-point random load identification in Embodiment 1 of this application;

[0031] Figure 4 This is the time history of the multi-point load in Embodiment 1 of this application;

[0032] Figure 5 This describes the three-degree-of-freedom displacement vibration response under multi-point load in Embodiment 1 of this application.

[0033] Figure 6 This is the three-degree-of-freedom velocity vibration response under multi-point load in Embodiment 1 of this application;

[0034] Figure 7 This is the load identification result of mass block 1 under multi-point random load in Embodiment 1 of this application;

[0035] Figure 8 This is the load identification result of mass block 2 under multi-point random load in Embodiment 1 of this application;

[0036] Figure 9 This is the load identification result of mass block 3 under multi-point random load in Embodiment 1 of this application;

[0037] Figure 10 This is a schematic diagram of the fixed beam model structure in Embodiment 2 of this application;

[0038] Figure 11 This is a schematic diagram of the finite element model of the fixed beam in Embodiment 2 of this application;

[0039] Figure 12 This is the result of single-point random load identification in Embodiment 2 of this application (truncated at 0.5 seconds);

[0040] Figure 13 This is the result of single-point random load identification in Embodiment 2 of this application (truncated at 0.1 seconds);

[0041] Figure 14 The load identification results of each point on the fixed beam under multi-point random load in Embodiment 2 of this application are (points 1, 2, 9, and 10 are selected). Detailed Implementation

[0042] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0043] In the field of control, consider a class of system model equations that can be expressed in terms of parameters:

[0044]

[0045] Where x is the state vector, u is the control input vector, d is the disturbance vector, and y is the output vector.

[0046] A disturbance observer is introduced to estimate the unknown disturbance d in the system model equation (1). The disturbance observer takes the form of:

[0047]

[0048] Where m represents the internal state of the observer. Let p(x) be the disturbance estimation vector, and p(x) be the disturbance observer function. The disturbance observer gain function l(x) is defined as follows:

[0049]

[0050] The perturbation estimation error is defined as follows: Assume the disturbance d is a constant value within one computation cycle, or in other words, the disturbance is slowly varying relative to the observer's iteration rate. Combining equations (1), (2), and (3), the rate of change of the disturbance estimation error is obtained as follows:

[0051]

[0052] Define l(x)g2(x)=λ, where λ is the gain matrix of the disturbance observer, which is a positive definite matrix with eigenvalues ​​much greater than 0. At this point, When the eigenvalue of λ is larger The faster the eigenvalues ​​of λ converge to 0, the faster the estimation error of the disturbance observer will converge to the smallest neighborhood of 0 in a very short time. This ensures that the disturbance observer based on equation (2) can accurately estimate external disturbances. It can converge to a very small neighborhood of d, thus enabling the identification of external disturbances.

[0053] Therefore, in the dynamic load identification problem, we deduce the magnitude of the dynamic load input of the system from the system's response (displacement, velocity, acceleration, etc.). More specifically, considering that the representation of the above system (1) is similar to the state-space equations used in structural dynamics, we introduce it into the field of dynamic load identification through state-space equations.

[0054] A method for online identification of dynamic loads in a linear system based on an interference observer includes the following steps:

[0055] Step 1: Obtain the mass matrix M, damping matrix C, and stiffness matrix K of the linear system.

[0056] Step 2: Based on the mass matrix M, damping matrix C, and stiffness matrix K obtained in Step 1, calculate the system matrix A, input matrix B, output matrix C, and direct transmission matrix D of the loaded structure, and establish the state-space equation of the linear system structure.

[0057] Typically, the differential equations of motion of a system can be transformed into state-space equations using the state-space method, thereby allowing the time-domain response of the vibration system to be solved. Displacement and velocity on each degree of freedom are defined as components of the system's state variables. For simplicity, and without affecting the essence of the problem, zero initial conditions are assumed, i.e., the initial values ​​of the state variables are 0. The system's state equations and output equations are shown below.

[0058]

[0059] Among them, the system matrix Input matrix Output matrix C = [IO], direct transmission matrix D = O; z(t) is the system state vector, F(t) is the external dynamic load, and I is the identity matrix. Let y(t) be the system state vector, and y(t) be the system output vector. Then F(t) = [f(t) O]. T The external load on the system.

[0060] Step 3: Compare the forms of formula (5) and formula (1), take x = z(t) as the state vector of the system, f(x) = Ax = Az(t), g2(x) = B; the disturbance vector d in formula (1) can be considered as the external dynamic load F(t) to be identified. Since there is no control part in the system in the dynamic load identification problem, the term g1(x)u in formula (1) is zero. Since the direct transmission matrix D is a zero matrix, h(x) = Cx = Cz(t). Thus, the state space equation of the system is linked with the model equation of the control domain. Based on this, the form of the disturbance observer characterized by the state space equation parameters of the system model can be obtained as follows:

[0061]

[0062] Where x = z(t) is the system's state vector, m is the observer's internal state, and F(t) = [f(t) O] T The external load on the system is p(x) = k[OI]z(t), where the parameter k is the observer gain, k > 0, and can be adjusted according to the needs of dynamic load identification.

[0063] at this time, Then λ=l(x)g2(x)=k[OI]B=k[M -1 The rate of change of the disturbance estimation error in equation (4) can be expressed as follows: When k > 0, the error of the disturbance observer asymptotically converges to 0, which is the estimated value of the external load on the structure. It asymptotically converges to the true value of the external load, F(t).

[0064] Step 4: Conduct a preliminary experiment on the observer model obtained in Step 3. Input a vibration response, adjust the observer gain k, and when the estimated external dynamic load value... When the convergence reaches the external dynamic load F(t) to be identified, the value of the observer gain k is obtained. Specifically, given a value of k, the estimated external dynamic load output by the observer model is observed. If the convergence reaches the external dynamic load F(t) to be identified, and if not, adjust the given value of k until the output external dynamic load estimate is reached. The convergence is to the external dynamic load F(t) to be identified.

[0065] Step 5: Input the system state vector of the linear loaded structure into the disturbance observer model obtained in Step 4. Online identification yields the external loads on a linearly loaded structure.

[0066] In this embodiment, the interference observer model of formula (6) is constructed in the Function module of Simulink, and its input structure is the system state vector when it is under load. External dynamic load estimates output by the observer model The curve converges to the curve of the external dynamic load F(t) to be identified, thus obtaining the external load F(t).

[0067] The following uses a multi-degree-of-freedom discrete system and a fixed beam structure as examples to illustrate the process and effect of dynamic load identification using the method of this invention.

[0068] Example 1: Taking a multi-degree-of-freedom discrete system as the research object.

[0069] In practical engineering vibration problems, the vibrating structures are often quite complex. To facilitate the fundamental study of the method, the actual vibration system is often abstracted into a simplified dynamic model while meeting engineering requirements. Practical engineering structures are typically continuous elastic bodies with an infinite number of degrees of freedom. With appropriate mechanical simplification, they can often be reduced to multi-degree-of-freedom vibration systems. Multi-degree-of-freedom vibration systems refer to vibration systems with a finite number of degrees of freedom. The vibration theory of discrete lumped-parameter multi-degree-of-freedom systems is also fundamental to solving engineering vibration problems. Therefore, in Example 1, a three-degree-of-freedom discrete vibration system is used to derive and verify the feasibility and effectiveness of the dynamic load identification method based on an interference observer in this invention.

[0070] A real-world vibration system, under the condition of meeting engineering requirements, can be simplified into a discrete lumped parameter system dynamic model described by three factors: mass, elasticity, and damping. Newton's laws are then applied to establish its vibration equations. According to vibration theory, the motion of an n-degree-of-freedom system can be represented by n independent coordinates, and the vibration motion of the system can be described by n quadratic differential equations, expressed using matrix vibration differential equations as follows:

[0071]

[0072] Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix of order n×n, respectively, f(t) is the excitation force matrix, and x is the displacement response matrix of the system.

[0073] This embodiment uses a three-degree-of-freedom lumped parameter vibration system, the structure of which is as follows: Figure 2 As shown, the system includes mass blocks m1, m2, and m3. In this three-degree-of-freedom lumped-parameter vibration system, each mass has a mass of 2 kg, a damping coefficient of 10 kN / m, and a spring stiffness coefficient of 4000 kN / m.

[0074] Step 1: Establish the dynamic equations of the system using Newton's second law. The mass matrix, damping matrix, and stiffness matrix of the system can be obtained as follows:

[0075]

[0076]

[0077]

[0078] Step 2: Calculate the system matrix of the structure from the mass matrix M, damping matrix C, and stiffness matrix K obtained in Step 1. Input matrix Given the output matrix C = [IO] and the direct transfer matrix D = O, establish its state-space equation. in

[0079]

[0080]

[0081]

[0082]

[0083] Step 3: Obtain the disturbance observer design parameters suitable for this model from the parameters of the structural state-space equations obtained in Step 2. The disturbance observer form characterized by the state-space equation parameters of the system model is designed as follows:

[0084]

[0085] For linear multi-degree-of-freedom discrete systems, given g2(x) = B, a disturbance observer function p(x) = k[OI]z(t) can be designed. Here, parameter k is the observer gain, which is set to 100 in this embodiment. Satisfying k > 0 allows the interference observer error to asymptotically converge to 0, i.e., the estimated value of the external load on the structure. It can converge asymptotically to the true value of the external load F(t).

[0086] Step 4: The disturbance observer model built in the Simulink Function module is used to identify the external loads on the three-degree-of-freedom discrete system.

[0087] Identification of single-point loads:

[0088] A random load excitation is applied to the mass block of the discrete system. The random load excitation is a deterministic sample of a white noise signal covering the third-order natural frequencies of the three-degree-of-freedom discrete system. It is obtained by passing a white noise signal through a bandpass filter with a bandwidth of 1-20Hz, resulting in a random load signal with a frequency range of 1-20Hz. Simultaneously, the vibration displacement and velocity responses in the three degrees of freedom are acquired.

[0089] The obtained vibration displacement and velocity response As known information input, the disturbance observer designed earlier is used to identify the external load F(t) on the system, and the results are as follows. Figure 3 As shown, the solid blue line represents the actual dynamic load to be identified, and the dashed red line represents the dynamic load identified by the interference observer. It can be seen that the two curves overlap quite accurately. Under noise-free simulation conditions, the magnitude and time history of the external load on the multi-degree-of-freedom discrete system can be identified well in real time.

[0090] Identification of multi-point loads:

[0091] Three different random load excitations are applied to the three mass blocks of the discrete system. The random load excitation at each degree of freedom is a deterministic sample of a white noise signal covering the third-order natural frequency of the three-degree-of-freedom discrete system. This sample is obtained by passing a white noise signal through a bandpass filter with a bandwidth of 1-20Hz, resulting in a random load signal with a frequency range of 1-20Hz. Figure 4 As shown. Simultaneously, the vibration displacement and velocity responses in three degrees of freedom are obtained, as follows: Figure 5 , 6 As shown.

[0092] The obtained vibration displacement and velocity response Using known information as input, a well-designed interference observer can be applied to identify the multi-point external loads F(t) acting on the system, achieving excellent identification results, such as... Figure 7-9 As shown, the solid blue line represents the dynamic load to be identified, and the dashed red line represents the dynamic load identified by the interference observer. The time history curves of the dynamic loads for each degree of freedom can be found to match the actual dynamic load time history curves.

[0093] Example 2: Taking a fixed-support beam structure as the research object.

[0094] Beam structures are fundamental components in dynamics research, characterized primarily by bending deformation, and are commonly used in practical engineering. For low-frequency vibrations of slender beams, shear deformation and rotation of the beam cross-section about the neutral axis can usually be neglected; this beam model is called the Euler-Bernoulli beam. Its theory is simple and easy to use, and in most cases, it can provide analytical solutions or relatively accurate approximate solutions, making it the most common beam structure in practical engineering. The beam structure dynamics analysis in this embodiment uses the Euler-Bernoulli beam model, which is a beam with a uniform cross-section made of homogeneous material, with fixed supports at both ends as the boundary condition. Figure 10 As shown. Its length L = 0.62m, width W = 0.03m, height H = 0.004m, elastic modulus E = 62GPa, Poisson's ratio μ = 0.3, and density ρ = 2700kg / m³. 3 .

[0095] Step 1: Based on the geometric and material parameters of the fixed beam described above, establish a finite element model of the fixed beam in finite element software, such as... Figure 11 As shown, 10 nodes are evenly arranged along the span of the beam, and the mass matrix M, damping matrix C and stiffness matrix K of the beam structure are extracted from the finite element software through finite element simulation.

[0096] Step 2: Calculate the system matrix A, input matrix B, output matrix C, and direct transmission matrix D of the structure from the mass matrix, damping matrix, stiffness matrix M, C, and K obtained in Step 1, and establish its state-space equations.

[0097] Step 3: Obtain the design parameters of the disturbance observer applicable to the model from the parameters of the structural state space equation obtained in Step 2, and construct a disturbance observer applicable to dynamic load identification of the beam model.

[0098] Step 4: Use the designed interference observer to identify the load on the structure.

[0099] Single-point load identification:

[0100] A random load excitation is applied to the structure at node 1. The random load excitation is a deterministic sample of white noise signal covering the first four natural frequencies of the fixed beam structure. It is obtained by passing a white noise signal through a bandpass filter with a bandwidth of 1-500Hz, resulting in a random load signal with a frequency range of 1-500Hz. At the same time, the vibration displacement and velocity response at each node are obtained through the state-space equations of the fixed beam model.

[0101] The obtained vibration displacement and velocity response As known information input, the interference observer designed in step 3 is used to identify the external load F(t) on the system, and the result is as follows. Figure 12 , 13 As shown, Figure 12 The recognition results were captured for 2-2.5 seconds. Figure 13 The identification results were captured for 2-2.1 seconds, which made the details of the identified load clearer. The blue curve represents the actual dynamic load to be identified, and the red curve represents the dynamic load identified by the interference observer. The two curves overlap well, indicating that the online dynamic load identification method based on the interference observer also performs well in identifying high-frequency random loads. It can accurately identify the time history of external loads online and has broad application prospects.

[0102] Identifying multi-point loads:

[0103] Random load excitation was applied at 10 measuring points on the fixed beam. The random load excitation at each degree of freedom was a deterministic sample of a white noise signal covering the first four natural frequencies of the fixed beam. This random load signal, with a frequency range of 1-500Hz, was obtained by passing a white noise signal through a bandpass filter with a bandwidth of 1-500Hz. The vibration displacement and velocity responses at the 10 measuring points were also acquired.

[0104] The obtained vibration displacement and velocity response Using known information as input, a well-designed interference observer can be applied to identify the multi-point external loads F(t) acting on the system, achieving excellent identification results, such as... Figure 14 As shown, the blue line represents the actual dynamic load to be identified, and the red line represents the dynamic load identified by the interference observer. The time history curves of the identified dynamic loads for each degree of freedom almost completely overlap with the time history curves of the actual applied dynamic loads.

[0105] 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 scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for online identification of dynamic load based on disturbance observer, characterized in that, Includes the following steps: Step 1: Obtain the mass matrix M, damping matrix C, and stiffness matrix K of the linearly loaded structure; Step 2, according to the mass matrix M, the damping matrix C and the stiffness matrix K obtained in step 1, the system matrix A, the input matrix B, the output matrix C and the direct transmission matrix D of the loaded structure are calculated to establish the linear loaded structure state space equation where the system matrix input matrix Output matrix C = [I0], direct transmission matrix D = 0; z(t) is the system state vector, F(t) is the external dynamic load to be identified, and I is the unit matrix; Step 3: Introduce a disturbance observer. Based on the state-space equations of the linearly loaded structure, construct the disturbance observer model in the following form: where m is the internal state of the observer, is the external dynamic load estimate, x = z(t) is the state vector of the system, l(x) is the disturbance observer gain function, The interference observer function is p(x) = k[OI]z(t), where k is the observer gain and k > 0; Step 4: Conduct a preliminary experiment using the observer model obtained in Step 3. Input a vibration response, adjust the observer gain k, and when the estimated external dynamic load value... When the convergence reaches the external dynamic load F(t) to be identified, the value of the observer gain k is determined, and an interference observer model suitable for a linearly loaded structure is obtained. Step 5: Input the system state vector of the linear loaded structure into the disturbance observer model obtained in Step 4. Identify the external loads on a linearly loaded structure.

2. The online dynamic load identification method according to claim 1, characterized in that, The specific method for obtaining the disturbance observer model equation based on the linear loaded structure state space equation in step 3 is as follows: A class of available parameter system models in the field of reference control and the introduced interference observer model In the form of the linear loaded structure state space equation obtained in step 2, x = z(t) is taken as the state vector of the system, f(x) = Ax = Az(t), g2(x) = B, the disturbance vector d is the external dynamic load F(t) to be identified, and h(x) = Cx = Cz(t). Since there is no control part in the linear system, g1(x)u=0; The disturbance observer model equation, characterized by the parameters of the state-space equation of the linearly loaded structure, is then obtained as follows:

3. The online dynamic load identification method according to claim 1, characterized in that, In step 4, the process of determining the value of the observer gain k is as follows: given a value of k, observe the estimated external dynamic load output by the observer model. If the convergence reaches the external dynamic load F(t) to be identified, and if not, adjust the given value of k until the output external dynamic load estimate is reached. The convergence is to the external dynamic load F(t) to be identified.

4. The online dynamic load identification method according to claim 1, characterized in that, In step 3, an interference observer model is constructed in the Function module of Simulink.

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