动载荷反演问题时域分析理论方法和实验研究
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摘要
准确地确定结构在运行过程中所受的动态载荷,是结构设计及其优化的一个重要方面。此外,动载荷的确定对结构健康监测、参数辨识、以及结构疲劳寿命估计,也具有重要意义。然而,在实际工程中结构所受动态载荷往往难以直接测量,如力传感器的引入会阻碍结构的工作路径,或改变结构的固有特性等等。在此背景下,载荷识别技术得以提出,也即根据结构部分测点得到的响应信息和结构动力学反演模型来估计结构所受的动态载荷。结构动态载荷识别技术在现代工程设计中有着广泛的应用前景,属于结构动力学反问题中的第二类反问题,而且具有学科交叉的特征,涉及到计算机仿真、动态测试技术以及反演问题求解技术等多种学科。本文对动态载荷反演问题开展了一些应用基础性研究,具体工作有以下几个方面：
首先总结了动态载荷反演问题研究发展现状,并对已有的动态载荷识别方法进行分析,指出当前动载荷识别方法仍存在的局限性,确定本文的研究思路为在时域内开展动态载荷反演问题分析理论和实验方面研究,重点讨论动载荷反演问题的不适定性、动载荷反演精细模型的建立、动载荷反演算法的稳定性、动载荷反演实验技术以及动载荷反演技术在工程中的应用等几方面。
将反演问题求解的正则化理论应用到动载荷反演问题中,提出了基于正则化技术的动态载荷反演问题的求解方法,来抑制测量噪声在载荷反演过程中产生的振荡,得到满足实际工程要求的稳定近似解。然而,正则化技术仅从数学角度来处理动载荷反演问题的不适定性,并不能完全消除模型误差和响应数据中的测量噪声带来的影响。因此,建立合适的动载荷反演模型成为亟需解决的问题。
提出了基于Markov参数精细计算的动态载荷识别方法,为避免递推迭代格式中动载荷反演问题求解误差累积,把整个时域过程离散展开,在状态空间建立了离散动力系统滑动平均模型,并用2N算法精细计算了系统模型的马尔科夫(Markov)参数矩阵,给出了Toeplitz矩阵形式的全局时域内多点分布动态载荷识别问题的载荷识别模型,最后采用正则化技术求解该载荷反演模型。
提出了基于线性空间逼近的动载荷反演问题参数化求解方法,通过对单一载荷基函数在时间和空间上多点逼近未知输入载荷,实现动态载荷识别的参数化,使得载荷反演问题转化为多点权系数求解问题。该方法可以有效地解决模态截断或建模不精确造成的求解误差问题,具有在时间和空间上配置逼近节点的灵活性,可以有效的利用两方面的约束信息提高识别精度。
提出了基于灵敏度分析的动态载荷识别方法,将结构输入载荷表示为一系列参数的形式,建立基于灵敏度分析的参数化反演模型,通过灵敏度迭代求解确定载荷输入参数来重构结构动态载荷。进一步推广上述方法提出了基于灵敏度矩阵精细计算的动态载荷识别技术。由于反演问题的特点,建立的动态载荷反演模型仍为不适定的,在求解过程中都需应用正则化技术来抑制测量噪声带来的不稳定性。
开展了动态载荷识别实验研究,根据提出的动载荷识别理论,设计了动态载荷识别试验,以悬臂梁结构和变截面梁结构为试验对象,验证了本文提出动态载荷识别方法的正确性和有效性。基于本文所建立的动载荷识别算法开发了动态载荷识别程序模块,并应用到高速运载工具在发射过程中的动态载荷识别。利用飞行器结构在发射和运行过程中得到的遥测响应数据,重构高速运载工具在运行过程中经受恶劣工况下的载荷,为高速运载工具的优化设计提供载荷设计依据。
Accurately knowledge of the dynamic force acting on the structure during its designated life can be very important components in the design of mechanical systems, from the spacecraft and processing plants to electronic circuits. Regardless of actual application or the underlying physics, the expected force plays a key role in the structural health monitoring, the determination of the system properties or parameters, and the fatigue life estimationof operating systems. Unfortunately, in many practical situations, it is difficult, if not impossible, to perform direct measurements or calculations of the external forces acting on vibrating structures. For example, if the force gauges are inserted into force transfer path to measure those dynamic forces directly, they may either alter the system properties or intrude the load path. Instead, the vibration responses can often be conveniently measured. In such cases, indirect estimating these dynamic forces by using measured vibration responses in some sort of inverse model is sometimes necessary, which means that unknown force is established as the solution to an inverse problem, based on the measured vibration responses. The dynamic force identification, as the second type inverse problem in structural dynamics, has some splendent prospects in the state-of-art engineering design, and is also related to a variety of disciplines such as the numerical simulation, the dynamic vibration test and the theory of inverse problem. In this thesis the issues of basic applications of the dynamic force identification are studied, and the specific research works are as follows.
Firstly, the force identification methods proposed by many researchers in the area of vibration and acoustics are reviewed, and the limitations of the current force identification methods are pointed out, and the idea of study on the force identification problem in the framework of theoretical and experimental study in time domain is established, and the interest areas in this thesis mainly focus on the ill-posedness of force identification problem, the foundation of precise force identification model, the stability of force identification algorithm, and the application of force identification technique.
In general, the inverse problem of force identification is ill-posed, i.e. an arbitrarily small perturbation of the measured responses can cause arbitrarily large perturbation of the solution. In order to deal with this issue, the regularization technique of the mathematical theory to solve the inverse problem is utilized in this thesis to single out a useful and stable solution. The regularization technique, however, is only to cope with the ill-posed problem from the mathematical view, and not to completely eliminate the influence of errors in force identification model and the white noise in the measured vibration responses. Thus the establishment of proper force identification model is worth being concerned.
In this thesis, three force identification models are established for the sake of reconstructing the input force of the structural systems. The force identification algorithm based on the precise computation for Markov parameters, is firstly presented to remove the numerical rounding errors of the dynamic force identification model, where a discrete moving average model of force identification is founded in state space, and the Markov parameter matrix is computed by the 2N type precise computation algorithm, and then the force identification model is recasted as Toeplitz matrix forms with a global multi-points distribution in time domain. The parameter estimation method for the force identification of the linear structural system is secondly proposed, in order to eliminate the effects of errors caused by the theoretical model or the truncated modal parameters in the experiment. The input force is expressed as a single base function, and the force identification problem is transformed into a problem of finding the parameters of the base function on the discrete time points. This force identification method is robust to improve the accuracy and the stability of the identified force. Finally, the force identification algorithm based on sensitivity analysis is proposed, where the input force is expressed as a series of parameters, and the sensitivity analysis method is used to iteratively update these parameters of input force in the inverse analysis. Furthermore, the sensitivity response matrix can be computed precisely when the input force is expressed as the harmonic functions. All these force identification methods presented in this thesis are still ill-posed, and the regularization process is necessary to suppress the fluctuations caused by the white noise in measured data.
Finally, three force estimation experiments, corresponding to the force identification methods, are implemented, in order to verify that these force identification methods are valid. The forces, applied on the cantilever beam and the variable section beam in laboratory, are successfully reconstructed by the presented force identification methods in this thesis. Furthermore, the force identification program modules are developed and applied to estimate the input force acting on the high-speed aircraft in the launching process. The time history of harsh loads applied on the space aircrafts, are reconstructed by the telemetry response data, in order to optimize the design of high-speed aircrafts.
首先总结了动态载荷反演问题研究发展现状,并对已有的动态载荷识别方法进行分析,指出当前动载荷识别方法仍存在的局限性,确定本文的研究思路为在时域内开展动态载荷反演问题分析理论和实验方面研究,重点讨论动载荷反演问题的不适定性、动载荷反演精细模型的建立、动载荷反演算法的稳定性、动载荷反演实验技术以及动载荷反演技术在工程中的应用等几方面。
将反演问题求解的正则化理论应用到动载荷反演问题中,提出了基于正则化技术的动态载荷反演问题的求解方法,来抑制测量噪声在载荷反演过程中产生的振荡,得到满足实际工程要求的稳定近似解。然而,正则化技术仅从数学角度来处理动载荷反演问题的不适定性,并不能完全消除模型误差和响应数据中的测量噪声带来的影响。因此,建立合适的动载荷反演模型成为亟需解决的问题。
提出了基于Markov参数精细计算的动态载荷识别方法,为避免递推迭代格式中动载荷反演问题求解误差累积,把整个时域过程离散展开,在状态空间建立了离散动力系统滑动平均模型,并用2N算法精细计算了系统模型的马尔科夫(Markov)参数矩阵,给出了Toeplitz矩阵形式的全局时域内多点分布动态载荷识别问题的载荷识别模型,最后采用正则化技术求解该载荷反演模型。
提出了基于线性空间逼近的动载荷反演问题参数化求解方法,通过对单一载荷基函数在时间和空间上多点逼近未知输入载荷,实现动态载荷识别的参数化,使得载荷反演问题转化为多点权系数求解问题。该方法可以有效地解决模态截断或建模不精确造成的求解误差问题,具有在时间和空间上配置逼近节点的灵活性,可以有效的利用两方面的约束信息提高识别精度。
提出了基于灵敏度分析的动态载荷识别方法,将结构输入载荷表示为一系列参数的形式,建立基于灵敏度分析的参数化反演模型,通过灵敏度迭代求解确定载荷输入参数来重构结构动态载荷。进一步推广上述方法提出了基于灵敏度矩阵精细计算的动态载荷识别技术。由于反演问题的特点,建立的动态载荷反演模型仍为不适定的,在求解过程中都需应用正则化技术来抑制测量噪声带来的不稳定性。
开展了动态载荷识别实验研究,根据提出的动载荷识别理论,设计了动态载荷识别试验,以悬臂梁结构和变截面梁结构为试验对象,验证了本文提出动态载荷识别方法的正确性和有效性。基于本文所建立的动载荷识别算法开发了动态载荷识别程序模块,并应用到高速运载工具在发射过程中的动态载荷识别。利用飞行器结构在发射和运行过程中得到的遥测响应数据,重构高速运载工具在运行过程中经受恶劣工况下的载荷,为高速运载工具的优化设计提供载荷设计依据。
Accurately knowledge of the dynamic force acting on the structure during its designated life can be very important components in the design of mechanical systems, from the spacecraft and processing plants to electronic circuits. Regardless of actual application or the underlying physics, the expected force plays a key role in the structural health monitoring, the determination of the system properties or parameters, and the fatigue life estimationof operating systems. Unfortunately, in many practical situations, it is difficult, if not impossible, to perform direct measurements or calculations of the external forces acting on vibrating structures. For example, if the force gauges are inserted into force transfer path to measure those dynamic forces directly, they may either alter the system properties or intrude the load path. Instead, the vibration responses can often be conveniently measured. In such cases, indirect estimating these dynamic forces by using measured vibration responses in some sort of inverse model is sometimes necessary, which means that unknown force is established as the solution to an inverse problem, based on the measured vibration responses. The dynamic force identification, as the second type inverse problem in structural dynamics, has some splendent prospects in the state-of-art engineering design, and is also related to a variety of disciplines such as the numerical simulation, the dynamic vibration test and the theory of inverse problem. In this thesis the issues of basic applications of the dynamic force identification are studied, and the specific research works are as follows.
Firstly, the force identification methods proposed by many researchers in the area of vibration and acoustics are reviewed, and the limitations of the current force identification methods are pointed out, and the idea of study on the force identification problem in the framework of theoretical and experimental study in time domain is established, and the interest areas in this thesis mainly focus on the ill-posedness of force identification problem, the foundation of precise force identification model, the stability of force identification algorithm, and the application of force identification technique.
In general, the inverse problem of force identification is ill-posed, i.e. an arbitrarily small perturbation of the measured responses can cause arbitrarily large perturbation of the solution. In order to deal with this issue, the regularization technique of the mathematical theory to solve the inverse problem is utilized in this thesis to single out a useful and stable solution. The regularization technique, however, is only to cope with the ill-posed problem from the mathematical view, and not to completely eliminate the influence of errors in force identification model and the white noise in the measured vibration responses. Thus the establishment of proper force identification model is worth being concerned.
In this thesis, three force identification models are established for the sake of reconstructing the input force of the structural systems. The force identification algorithm based on the precise computation for Markov parameters, is firstly presented to remove the numerical rounding errors of the dynamic force identification model, where a discrete moving average model of force identification is founded in state space, and the Markov parameter matrix is computed by the 2N type precise computation algorithm, and then the force identification model is recasted as Toeplitz matrix forms with a global multi-points distribution in time domain. The parameter estimation method for the force identification of the linear structural system is secondly proposed, in order to eliminate the effects of errors caused by the theoretical model or the truncated modal parameters in the experiment. The input force is expressed as a single base function, and the force identification problem is transformed into a problem of finding the parameters of the base function on the discrete time points. This force identification method is robust to improve the accuracy and the stability of the identified force. Finally, the force identification algorithm based on sensitivity analysis is proposed, where the input force is expressed as a series of parameters, and the sensitivity analysis method is used to iteratively update these parameters of input force in the inverse analysis. Furthermore, the sensitivity response matrix can be computed precisely when the input force is expressed as the harmonic functions. All these force identification methods presented in this thesis are still ill-posed, and the regularization process is necessary to suppress the fluctuations caused by the white noise in measured data.
Finally, three force estimation experiments, corresponding to the force identification methods, are implemented, in order to verify that these force identification methods are valid. The forces, applied on the cantilever beam and the variable section beam in laboratory, are successfully reconstructed by the presented force identification methods in this thesis. Furthermore, the force identification program modules are developed and applied to estimate the input force acting on the high-speed aircraft in the launching process. The time history of harsh loads applied on the space aircrafts, are reconstructed by the telemetry response data, in order to optimize the design of high-speed aircrafts.
引文
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