CN110377965A - A kind of discrimination method of the flexible structure nonlinear characteristic containing hinge - Google Patents
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Abstract
本发明公开了一种含铰柔性结构非线性特征的辨识方法，包括如下步骤，对含铰柔性结构进行动力学试验，同时获取结构位移响应x、速度响应v、加速度响应a和外激励f；根据公式F＝f‑ma，计算结构的恢复力F，其中m为含铰柔性结构的质量；利用获得的三维数据{x，v，F}，作出恢复力F关于位移响应x和速度响应v的三维点集；采用自然邻域插值法对三维点集{x，v，F}进行插值并作出三维恢复力曲面；当速度为零时，提取位移与恢复力关系曲线，通过曲线拟合确定阻尼模型；当位移为零时，提取速度与恢复力关系曲线，通过曲线拟合确定刚度模型。本发明可准确识别含铰结构的复杂非线性模型，辨识结果可靠性高。
The invention discloses a method for identifying nonlinear characteristics of a hinged flexible structure, comprising the following steps of performing a dynamic test on the hinged flexible structure, and simultaneously obtaining the structural displacement response x, velocity response v, acceleration response a, and external excitation f; According to the formula F=f-ma, calculate the restoring force F of the structure, where m is the mass of the hinged flexible structure; use the obtained three-dimensional data {x, v, F} to calculate the restoring force F with respect to the displacement response x and the velocity response v The three-dimensional point set; use the natural neighborhood interpolation method to interpolate the three-dimensional point set {x, v, F} and make a three-dimensional restoring force surface; when the velocity is zero, extract the relationship curve between displacement and restoring force, and determine it by curve fitting Damping model; when the displacement is zero, the relationship curve between velocity and restoring force is extracted, and the stiffness model is determined by curve fitting. The invention can accurately identify the complex nonlinear model of the hinged structure, and the identification result has high reliability.
Description
技术领域technical field
本发明涉及，尤其涉及一种含铰柔性结构非线性特征的辨识方法。The invention relates, in particular, to a method for identifying nonlinear characteristics of hinged flexible structures.
背景技术Background technique
随着航天科技的发展，航天结构趋于大型化、柔性化和高精度化。由于运载技术的限制和大折展比的要求，航天器结构往往含有大量的铰链，例如太阳能帆板、伸展臂等结构的各部件间采用铰链连接的方式来实现折叠和展开功能。由于铰链结构中存在间隙，在外界激励下，结构产生碰撞和摩擦等非线性现象，导致结构表现出较强的非线性特性，影响结构和相关仪器的正常工作。With the development of aerospace science and technology, aerospace structures tend to be large, flexible and high-precision. Due to the limitation of carrying technology and the requirement of large folding ratio, the spacecraft structure often contains a large number of hinges, such as solar panels, extension arms and other structural components, which are hinged to realize folding and unfolding functions. Due to the existence of gaps in the hinge structure, under external excitation, the structure produces nonlinear phenomena such as collision and friction, resulting in strong nonlinear characteristics of the structure, which affects the normal operation of the structure and related instruments.
现有的技术，需要提前假设含铰结构的非线性特征模型，由此得到的辨识结果与实际情况不符，同时在实际的应用中存在局限性。The existing technology needs to assume the nonlinear characteristic model of the hinge structure in advance, and the identification results obtained from this are not consistent with the actual situation, and there are limitations in the actual application.
因此，亟待解决上述问题。Therefore, urgently need to solve the above-mentioned problem.
发明内容Contents of the invention
发明目的：本发明的目的是提供可解决在已知结构外激励和动响应的情况下无法准确辨识结构非线性特征的难题的一种含铰柔性结构非线性特征的辨识方法。Purpose of the invention: The purpose of the invention is to provide a method for identifying the nonlinear characteristics of hinged flexible structures that can solve the problem that the nonlinear characteristics of the structure cannot be accurately identified when the external excitation and dynamic response of the structure are known.
技术方案：为实现以上目的，本发明公开了一种含铰柔性结构非线性特征的辨识方法，包括如下步骤：Technical solution: To achieve the above objectives, the present invention discloses a method for identifying nonlinear characteristics of hinged flexible structures, which includes the following steps:
(1)对含铰柔性结构进行动力学试验，同时获取结构位移响应x、速度响应v、加速度响应a和外激励f；(1) Conduct dynamic tests on flexible structures with hinges, and obtain structural displacement response x, velocity response v, acceleration response a and external excitation f at the same time;
(2)根据公式F＝f-ma，计算结构的恢复力F，其中m为含铰柔性结构的质量；(2) Calculate the restoring force F of the structure according to the formula F=f-ma, where m is the mass of the hinged flexible structure;
(3)利用步骤(1)和(2)所获得的三维数据{x，v，F}，作出恢复力F关于位移响应x和速度响应v的三维点集；(3) Using the three-dimensional data {x, v, F} obtained in steps (1) and (2), make a three-dimensional point set of restoring force F about displacement response x and velocity response v;
(4)采用自然邻域插值法对三维点集{x，v，F}进行插值并作出三维恢复力曲面；(4) Use the natural neighborhood interpolation method to interpolate the three-dimensional point set {x, v, F} and make a three-dimensional restoring force surface;
(5)当速度为零时，提取位移与恢复力关系曲线，通过曲线拟合确定阻尼模型；当位移为零时，提取速度与恢复力关系曲线，通过曲线拟合确定刚度模型。(5) When the velocity is zero, the relationship curve between displacement and restoring force is extracted, and the damping model is determined by curve fitting; when the displacement is zero, the relationship curve between velocity and restoring force is extracted, and the stiffness model is determined by curve fitting.
其中，所述步骤(3)中x、v、F中的元素个数相同，且一一对应，即为同一时间点下含铰柔性结构的位移、速度和恢复力数据。Wherein, the number of elements in x, v, and F in the step (3) is the same, and they correspond one-to-one, that is, the displacement, velocity and restoring force data of the hinged flexible structure at the same time point.
优选的，所述步骤(3)中三维点集{x，v，F}在速度和位移坐标系内均匀分布。Preferably, in the step (3), the three-dimensional point set {x, v, F} is evenly distributed in the velocity and displacement coordinate system.
再者，所述步骤(4)中采用自然邻域插值法作出三维恢复力曲面包括如下步骤：Furthermore, adopting the natural neighborhood interpolation method in the described step (4) to make the three-dimensional restoring force curved surface includes the following steps:
(1)给定位移x和速度v的插值区间和步长，得到插值点；(1) Given the interpolation interval and step size of the displacement x and velocity v, the interpolation point is obtained;
(2)采用meshgrid函数得到插值点的位移x和速度v坐标；(2) Obtain the displacement x and velocity v coordinates of the interpolation point by using the meshgrid function;
(3)利用样本点的三维数据和插值点坐标，采用griddata函数中自然邻域插值法获得插值点的恢复力z坐标；(3) Utilize the three-dimensional data of the sample point and the coordinates of the interpolation point, adopt the natural neighborhood interpolation method in the griddata function to obtain the z coordinate of the restoring force of the interpolation point;
(4)利用mesh函数作出恢复力三维网格图。(4) Use the mesh function to make a three-dimensional mesh diagram of the restoring force.
进一步，所述步骤(1)中结构位移响应x通过激光位移计测得，速度响应v通过位移响应x微分得到，加速度响应a通过加速度计测得。Further, in the step (1), the structural displacement response x is measured by a laser displacement meter, the velocity response v is obtained by differentiating the displacement response x, and the acceleration response a is measured by an accelerometer.
再者，所述步骤(1)中结构位移响应x通过激光位移计测得，速度响应v通过加速度响应a积分得到，加速度响应a通过加速度计测得。Furthermore, in the step (1), the structural displacement response x is measured by a laser displacement meter, the velocity response v is obtained by integrating the acceleration response a, and the acceleration response a is measured by an accelerometer.
有益效果：与现有技术相比，本发明具有以下显著优点：本发明通过动力学试验获取结构位移响应、速度响应和结构恢复力，在不需要假设结构非线性特征的情况下，准确识别含铰结构的复杂非线性模型，数据易获取，受外界影响小，实施方便，辨识结果可靠性高。Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention obtains structural displacement response, velocity response and structural restoring force through dynamic tests, and accurately identifies The complex nonlinear model of the hinge structure, the data is easy to obtain, less affected by the outside world, easy to implement, and the identification results are highly reliable.
附图说明Description of drawings
图1为本发明中含铰柔性结构进行动力学试验的示意图；Fig. 1 is the schematic diagram that contains hinged flexible structure in the present invention and carries out dynamic test;
图2为本发明中采用自然邻域内插法拟合得到的恢复力曲面图；Fig. 2 adopts the restoring force curved surface diagram that natural neighborhood interpolation method fitting obtains among the present invention;
图3为本发明中位移与恢复力关系曲线；Fig. 3 is displacement and restoring force relationship curve among the present invention;
图4为本发明中速度与恢复力关系曲线。Fig. 4 is the relationship curve between speed and restoring force in the present invention.
具体实施方式Detailed ways
下面结合附图对本发明的技术方案作进一步说明。The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.
本发明提供的一种含铰柔性结构非线性特征的辨识方法原理如下：The principle of the identification method for the nonlinear characteristics of a hinged flexible structure provided by the present invention is as follows:
根据牛顿第二定律，系统的运动方程可表示为：According to Newton's second law, the equation of motion of the system can be expressed as:
式中，为系统的恢复力，是系统瞬时状态的函数，即速度和位移x的函数。恢复力中包含了结构的广义阻尼和广义刚度；m为结构质量；F为外激励。将恢复力与外激励和惯性力分离，则(1)式可改写为In the formula, is the restoring force of the system, which is a function of the instantaneous state of the system, that is, the velocity and a function of displacement x. The restoring force includes generalized damping and generalized stiffness of the structure; m is the mass of the structure; F is the external excitation. Separating the restoring force from the external excitation and inertial force, formula (1) can be rewritten as
假如结构质量m已知，外激励F和加速度已经测量得到，可以得知公式(2)中右边的表达式，进而f也可以得知。在动力学试验中，时域信号Δt离散采样得到的，则在第i个采样时刻，公式(2)改写为If the structural mass m is known, the external excitation F and the acceleration It has been measured, and the expression on the right side of the formula (2) can be known, and then f can also be known. In the dynamic experiment, the time-domain signal Δt is obtained by discrete sampling, then at the i-th sampling moment, the formula (2) is rewritten as
根据公式(3)，每个采样时刻的恢复力fi都可以得到。结构的位移响应通过激光位移计测得，速度响应通过位移响应微分得到，也可通过加速度响应直接积分得到，加速度响应通过加速度计测量得到，则每个采样时刻的三维数据点集前两个数据xi和表示该点在相平面中的投影，而第三个数据fi则表示该点的高度，由此可以构成离散分布的恢复力曲面。According to formula (3), the restoring force fi at each sampling moment can be obtained. The displacement response of the structure is measured by the laser displacement meter, the velocity response is obtained by differential displacement response, and can also be obtained by direct integration of acceleration response, which is obtained by accelerometer measurement, then the three-dimensional data point set at each sampling time The first two data xi and Indicates the projection of the point on the phase plane, and the third data f i indicates the height of the point, thus a discretely distributed restoring force surface can be formed.
本发明一种含铰柔性结构非线性特征的辨识方法，包括如下步骤：A method for identifying nonlinear characteristics of hinged flexible structures in the present invention comprises the following steps:
(1)对含铰柔性结构进行动力学试验，同时获取结构位移响应x、速度响应v、加速度响应a和外激励f；结构位移响应x通过激光位移计测得，速度响应v通过位移响应x微分得到，也可通过加速度响应a积分得到；加速度响应a通过加速度计测得。(1) Carry out dynamic tests on the flexible structure with hinges, and simultaneously obtain the structural displacement response x, velocity response v, acceleration response a and external excitation f; the structural displacement response x is measured by the laser displacement meter, and the velocity response v is measured by the displacement response x It can be obtained by differentiation, and can also be obtained by integrating the acceleration response a; the acceleration response a is measured by the accelerometer.
(2)根据公式F＝f-ma，计算结构的恢复力F，其中m为含铰柔性结构的质量；(2) Calculate the restoring force F of the structure according to the formula F=f-ma, where m is the mass of the hinged flexible structure;
(3)利用步骤(1)和(2)所获得的三维数据{x，v，F}，作出恢复力F关于位移响应x和速度响应v的三维点集；其中x、v、F中的元素个数相同，且一一对应，即为同一时间点下含铰柔性结构的位移、速度和恢复力数据，三维点集{x，v，F}在速度和位移坐标系内均匀分布；(3) Using the three-dimensional data {x, v, F} obtained in steps (1) and (2), make a three-dimensional point set of restoring force F with respect to displacement response x and velocity response v; where x, v, F The number of elements is the same, and there is one-to-one correspondence, that is, the displacement, velocity and restoring force data of the hinged flexible structure at the same time point, and the three-dimensional point set {x, v, F} is uniformly distributed in the velocity and displacement coordinate system;
(4)采用自然邻域插值法对三维点集{x，v，F}进行插值并作出三维恢复力曲面，采用自然邻域插值法作出三维恢复力曲面包括如下步骤：(4) Use the natural neighborhood interpolation method to interpolate the three-dimensional point set {x, v, F} and make a three-dimensional restoring force surface. Using the natural neighborhood interpolation method to make a three-dimensional restoring force surface includes the following steps:
(1)给定位移x和速度v的插值区间和步长，得到插值点；(1) Given the interpolation interval and step size of the displacement x and velocity v, the interpolation point is obtained;
(2)采用meshgrid函数得到插值点的位移x和速度v坐标；(2) Obtain the displacement x and velocity v coordinates of the interpolation point by using the meshgrid function;
(3)利用样本点的三维数据和插值点坐标，采用griddata函数中自然邻域插值法获得插值点的恢复力z坐标；(3) Utilize the three-dimensional data of the sample point and the coordinates of the interpolation point, adopt the natural neighborhood interpolation method in the griddata function to obtain the z coordinate of the restoring force of the interpolation point;
(4)利用mesh函数作出恢复力三维网格图；(4) Use the mesh function to make a three-dimensional mesh map of the restoring force;
(5)当速度为零时，提取位移与恢复力关系曲线，通过曲线拟合确定阻尼模型；当位移为零时，提取速度与恢复力关系曲线，通过曲线拟合确定刚度模型。(5) When the velocity is zero, the relationship curve between displacement and restoring force is extracted, and the damping model is determined by curve fitting; when the displacement is zero, the relationship curve between velocity and restoring force is extracted, and the stiffness model is determined by curve fitting.
下面以含铰柔性结构为试验对象进行非线性特征辨识来验证方法的可靠性。The reliability of the method is verified by nonlinear feature identification with hinged flexible structure as the test object.
首先，对图1所示含铰柔性结构进行动力学试验，获取三维数据点集{x,v,F}；其次，采用自然邻域插值法作出恢复力曲面，如图2所示；最后，恢复力曲面与速度为零平面的交线为位移-恢复力关系曲线，如图3所示，恢复力曲面与位移为零平面的交线为速度-恢复力关系曲线，如图4所示，通过拟合获取结构刚度参数K和阻尼参数c。结构的刚度和阻尼拟合结果如公式(4)和公式(5)所示First, the dynamic test is carried out on the hinged flexible structure shown in Fig. 1, and the three-dimensional data point set {x, v, F} is obtained; secondly, the restoring force surface is made by using the natural neighborhood interpolation method, as shown in Fig. 2; finally, The intersection line between the restoring force surface and the zero velocity plane is the displacement-restoring force relationship curve, as shown in Figure 3, and the intersection line between the restoring force surface and the zero displacement plane is the velocity-restoring force relationship curve, as shown in Figure 4, The structural stiffness parameter K and damping parameter c are obtained by fitting. The stiffness and damping fitting results of the structure are shown in formula (4) and formula (5)
结构中存在铰链间隙，该方法识别出结构的刚度表现出分段线性特征，与实际相符合。因此，该方法能够对含铰结构进行系统参数识别。There are hinge gaps in the structure, and the method identifies that the stiffness of the structure exhibits a piecewise linear characteristic, which is consistent with reality. Therefore, this method is capable of system parameter identification for hinged structures.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111259328A (en) * | 2020-01-16 | 2020-06-09 | 东南大学 | Method for detecting nonlinear characteristics of spacecraft structure driven by free vibration displacement response |
| CN112632694A (en) * | 2020-12-02 | 2021-04-09 | 东南大学 | Spacecraft structure nonlinear parameter hybrid identification method |
| CN112632694B (en) * | 2020-12-02 | 2024-09-03 | 东南大学 | Spacecraft structure nonlinear parameter hybrid identification method |
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