非平稳信号处理方法的改进及在地震工程中的应用研究
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摘要
自上世纪八十年代以来,信号处理进入了前所未有的快速发展期,新兴的理论和方法不断涌现。作为普遍的基础理论和应用工具,信号处理同其他学科交叉融合的趋势日益明显,并在许多应用领域由不同的信号处理方法形成了传统的优势地位。但非平稳信号处理仍是目前所面临的重要问题之一,其难点在于如何协调好精度和分辨率这一对矛盾。
在土木工程和地震工程中,振动信号处理是信号处理技术最典型的应用之一,其主要目的即是从信号中尽可能地提取完备的、具有实际物理意义的信息以满足科研和应用的需要。然而,现实中的信号大多是非线性、非平稳的,并且数据长度有限,这使得分析处理此类信号成为一项复杂的工作。特别地,地震动和结构响应是地震工程中两种常见的振动信号形式,由于两者及其对应的系统(结构)的特性存在一定的差异,使得与之密切相关的两方面应用——地震动输入研究和结构损伤识别又对信号处理提出了不同的要求。
在地震动输入研究方面,人们已经认识到除传统三要素外强度和频率非平稳特性同样是地震动的重要特性,而瞬时谱被认为是描述上述非平稳特性的有效的概念。虽然已有不少信号处理方法被用于地震动的瞬时谱估计,但一直未能解决好精度和分辨率的矛盾,而在此基础上的地震动瞬时谱的模型化研究则更是空白。因此,寻求有效的信号处理方法用于地震动瞬时谱的模型化研究,是结构抗震设计和分析对地震动输入研究提出的迫切需求。
在结构损伤识别方面,基于振动的损伤识别在过去十年里一直是研究热点,针对已有方法的不足,研究者在相继提出一些改进措施的同时,近年来也逐渐将注意力集中到通过结构振动信号完备信息的提取来实现结构损伤识别,这些研究为基于振动的结构损伤识别提供了一个新思路。显然,要实现这一思路就要求信号处理方法能够高效、实时地从结构振动(反应)信号中提取完备信息,并能据此对结构的性能(状态)做出准确的评判和推断。
为此,本文对非平稳信号处理方法及其在地震动非平稳特性和结构损伤识别中的应用展开了研究,主要工作和取得的创新成果可归纳为以下三个方面: 1.非平稳信号处理方法
首先,提出了三种改进的参数化方法,不仅解决了现有方法难以协调好精度和分辨率这一对矛盾的难题,而且也为地震动瞬时谱的模型化研究奠定了基础;其次,提出了基于EMD和VARMA模型的改进方法,由该方法所得Hilbert谱不仅更具物理意义而且分辨率和可读性更好。
2.地震动的非平稳特性及仿真方法
采用两种强度包线模型研究了地震动强度非平稳特性,基于所收集的翔实的(5700余条)强震记录分析了强度包线参数的多维相关性及衰减规律,并给出了强度包线参数的设计取值建议;提出了指数衰减曲线形式的地震动瞬时频率模型,分析了瞬时频率参数的多维相关性及衰减规律,并给出了设计取值建议;提出了时频域彼此独立的函数乘积形式的地震动瞬时谱模型,为结构抗震设计和分析用地震动输入的选择提供了一个重要的参考指标,为同时考虑强度和频率非平稳特性的地震动仿真与合成奠定了基础;提出了基于改进信号处理方法及模型化瞬时谱的地震动合成与仿真方法,为结构抗震设计和分析提供了更合理的地震动输入。
3.结构损伤识别
基于振动信号完备信息提取的思路,提出了三种改进的结构损伤识别方法,由于改进方法采用了具有时变特性的损伤指标,因此不仅具有较好的适用性、敏感性和抗噪性,而且解决了现有常规方法无法对结构损伤(包括多处损伤)的发生时间、先后次序、严重程度及累积发展过程等细节进行描述的难题。
论文以信号处理为纽带,将地震动输入和结构损伤识别这两个地震工程中看似不相关的重要内容联系起来,研究成果不仅有利于地震动特性的全面认识,从而为结构抗震设计和分析提供更合理的输入,而且也为结构损伤识别提供了一条新途径。
最后,论文分析了目前研究的不足,并对今后的研究方向进行了展望。
Since 1980s, signal processing has entered into an unprecedented period of rapid development with the emergence of new theories and methods. As a fundamental theory and a universal tool, signal processing has more closely interpenetrated and combined with other disciplines than ever, and in many applications some traditional methods have established their overwhelming superiority. However, non-stationary signal processing is still an important issue, of which the difficulty is to make a reasonable tradeoff between the precision and resolution. Such a problem exists both in parametric and nonparametric methods.
Vibration signal processing is the most typical application in civil and earthquake engineering, of which the major purpose is to extract physically meaningful information from a signal as much as possible. While in the real world, signals are often nonlinear and non-stationary and their length is often very short, which makes the processing of such signals a difficult task. Especially, in earthquake engineering ground motions and structural responses are two familiar types of vibration signals. Due to the different characteristics of them and the associated systems, two related applications, i.e. earthquake ground motion and structural damage detection, have different requirements for signal processing.
Firstly, for earthquake ground motions the non-stationary properties in amplitude and frequency contents are also important properties besides the conventional properties of amplitude, frequency and duration, and instantaneous spectrum is regarded as a proper notion to describe such non-stationary properties. Though there are several methods available for instantaneous spectrum estimation, the contradiction between precision and resolution is not yet reconciled, and the modeling of instantaneous spectrum is even more rarely studied. In this context, to find a method for the study of modeling of instantaneous spectrum is an efficient way to fulfill the requirement for ground motions in structural seismic design and analysis.
Secondly, in structural damage detection vibration based methods have been the research focus during the past decade. To reduce the limitations of some existing methods, continuous efforts have given rise to some improved methods. In addition, some more recent research has shown that extracting physically meaningful information from vibration signals to detect structural damages may be the new trend, which undoubtedly requires some signal processing methods to extract useful information from vibration signals in an efficient and real-time manner through which the performance (state) of structures can be accurately evaluated.
For above reasons, improved signal processing methods and their applications in non-stationary properties of ground motions and structural damage detection are systematically studied in this thesis, and major works and research findings are summarized as follows:
1. Non-stationary signal processing methods
First, three improved parametric methods are proposed which not only perfectly reconciles the contradiction between precision and resolution but also provides a basis for the modeling of instantaneous spectrum of ground motions. Then, an EMD and VARMA model based method is also proposed which offers advantages in accuracy and frequency resolution and produces more physically meaningful and readable Hilbert spectrum.
2. Non-stationary properties and synthesis of ground motions
Two types of envelope models are used to study the non-stationary properties in intensity of ground motions. Based on the 5750 strong ground motion records collected, the multidimensional correlation and attenuation relations of envelope parameters are investigated and the recommendations of envelope parameters are put forward. An exponential decay model of instantaneous frequency is proposed and the multidimensional correlation and attenuation relations of model parameters are analyzed, then the recommendations of model parameters are set forth. A simplified model of instantaneous spectrum in the form of the product of independent functions in time and frequency domains is proposed, which not only produce a reference index for selecting reasonable ground motions for structural seismic design and analysis but also provides a basis for synthesis and simulation of ground motions allowing for the non-stationary properties in amplitude and frequency contents at the same time. Based on the improved signal processing methods and the instantaneous spectrum model, several methods for synthesis and simulation of ground motions are proposed, which can provide reasonable ground motions for structural seismic design and analysis.
3. Structural damage detection
In the sense of extracting complete information from vibration signals, three improved methods for structural damage detection are proposed. Since time varying damage indices are used in these improved methods, they have the advantage in applicability, sensitivity and robustness, and can detail the time sequence of occurrence, relative severity and cumulative process of structural damages at multiple locations in an efficient manner, which cannot be done by using the conventional damage detection methods.
In this thesis, signal processing is used as a link between earthquake ground motion and structural damage detection which are two unrelated but important research fields in earthquake engineering. The research findings presented here not only help to provide more reasonable ground motions for structural seismic design and analysis on the basis of a more comprehensive understanding of the properties of ground motions, but also provide a novel approach for structural damage detection which can be easily combined with other applications such as structural health monitoring and vibration control.
Finally, the weakness of the present study is briefly discussed and some recommendations for future research are provided.
在土木工程和地震工程中,振动信号处理是信号处理技术最典型的应用之一,其主要目的即是从信号中尽可能地提取完备的、具有实际物理意义的信息以满足科研和应用的需要。然而,现实中的信号大多是非线性、非平稳的,并且数据长度有限,这使得分析处理此类信号成为一项复杂的工作。特别地,地震动和结构响应是地震工程中两种常见的振动信号形式,由于两者及其对应的系统(结构)的特性存在一定的差异,使得与之密切相关的两方面应用——地震动输入研究和结构损伤识别又对信号处理提出了不同的要求。
在地震动输入研究方面,人们已经认识到除传统三要素外强度和频率非平稳特性同样是地震动的重要特性,而瞬时谱被认为是描述上述非平稳特性的有效的概念。虽然已有不少信号处理方法被用于地震动的瞬时谱估计,但一直未能解决好精度和分辨率的矛盾,而在此基础上的地震动瞬时谱的模型化研究则更是空白。因此,寻求有效的信号处理方法用于地震动瞬时谱的模型化研究,是结构抗震设计和分析对地震动输入研究提出的迫切需求。
在结构损伤识别方面,基于振动的损伤识别在过去十年里一直是研究热点,针对已有方法的不足,研究者在相继提出一些改进措施的同时,近年来也逐渐将注意力集中到通过结构振动信号完备信息的提取来实现结构损伤识别,这些研究为基于振动的结构损伤识别提供了一个新思路。显然,要实现这一思路就要求信号处理方法能够高效、实时地从结构振动(反应)信号中提取完备信息,并能据此对结构的性能(状态)做出准确的评判和推断。
为此,本文对非平稳信号处理方法及其在地震动非平稳特性和结构损伤识别中的应用展开了研究,主要工作和取得的创新成果可归纳为以下三个方面: 1.非平稳信号处理方法
首先,提出了三种改进的参数化方法,不仅解决了现有方法难以协调好精度和分辨率这一对矛盾的难题,而且也为地震动瞬时谱的模型化研究奠定了基础;其次,提出了基于EMD和VARMA模型的改进方法,由该方法所得Hilbert谱不仅更具物理意义而且分辨率和可读性更好。
2.地震动的非平稳特性及仿真方法
采用两种强度包线模型研究了地震动强度非平稳特性,基于所收集的翔实的(5700余条)强震记录分析了强度包线参数的多维相关性及衰减规律,并给出了强度包线参数的设计取值建议;提出了指数衰减曲线形式的地震动瞬时频率模型,分析了瞬时频率参数的多维相关性及衰减规律,并给出了设计取值建议;提出了时频域彼此独立的函数乘积形式的地震动瞬时谱模型,为结构抗震设计和分析用地震动输入的选择提供了一个重要的参考指标,为同时考虑强度和频率非平稳特性的地震动仿真与合成奠定了基础;提出了基于改进信号处理方法及模型化瞬时谱的地震动合成与仿真方法,为结构抗震设计和分析提供了更合理的地震动输入。
3.结构损伤识别
基于振动信号完备信息提取的思路,提出了三种改进的结构损伤识别方法,由于改进方法采用了具有时变特性的损伤指标,因此不仅具有较好的适用性、敏感性和抗噪性,而且解决了现有常规方法无法对结构损伤(包括多处损伤)的发生时间、先后次序、严重程度及累积发展过程等细节进行描述的难题。
论文以信号处理为纽带,将地震动输入和结构损伤识别这两个地震工程中看似不相关的重要内容联系起来,研究成果不仅有利于地震动特性的全面认识,从而为结构抗震设计和分析提供更合理的输入,而且也为结构损伤识别提供了一条新途径。
最后,论文分析了目前研究的不足,并对今后的研究方向进行了展望。
Since 1980s, signal processing has entered into an unprecedented period of rapid development with the emergence of new theories and methods. As a fundamental theory and a universal tool, signal processing has more closely interpenetrated and combined with other disciplines than ever, and in many applications some traditional methods have established their overwhelming superiority. However, non-stationary signal processing is still an important issue, of which the difficulty is to make a reasonable tradeoff between the precision and resolution. Such a problem exists both in parametric and nonparametric methods.
Vibration signal processing is the most typical application in civil and earthquake engineering, of which the major purpose is to extract physically meaningful information from a signal as much as possible. While in the real world, signals are often nonlinear and non-stationary and their length is often very short, which makes the processing of such signals a difficult task. Especially, in earthquake engineering ground motions and structural responses are two familiar types of vibration signals. Due to the different characteristics of them and the associated systems, two related applications, i.e. earthquake ground motion and structural damage detection, have different requirements for signal processing.
Firstly, for earthquake ground motions the non-stationary properties in amplitude and frequency contents are also important properties besides the conventional properties of amplitude, frequency and duration, and instantaneous spectrum is regarded as a proper notion to describe such non-stationary properties. Though there are several methods available for instantaneous spectrum estimation, the contradiction between precision and resolution is not yet reconciled, and the modeling of instantaneous spectrum is even more rarely studied. In this context, to find a method for the study of modeling of instantaneous spectrum is an efficient way to fulfill the requirement for ground motions in structural seismic design and analysis.
Secondly, in structural damage detection vibration based methods have been the research focus during the past decade. To reduce the limitations of some existing methods, continuous efforts have given rise to some improved methods. In addition, some more recent research has shown that extracting physically meaningful information from vibration signals to detect structural damages may be the new trend, which undoubtedly requires some signal processing methods to extract useful information from vibration signals in an efficient and real-time manner through which the performance (state) of structures can be accurately evaluated.
For above reasons, improved signal processing methods and their applications in non-stationary properties of ground motions and structural damage detection are systematically studied in this thesis, and major works and research findings are summarized as follows:
1. Non-stationary signal processing methods
First, three improved parametric methods are proposed which not only perfectly reconciles the contradiction between precision and resolution but also provides a basis for the modeling of instantaneous spectrum of ground motions. Then, an EMD and VARMA model based method is also proposed which offers advantages in accuracy and frequency resolution and produces more physically meaningful and readable Hilbert spectrum.
2. Non-stationary properties and synthesis of ground motions
Two types of envelope models are used to study the non-stationary properties in intensity of ground motions. Based on the 5750 strong ground motion records collected, the multidimensional correlation and attenuation relations of envelope parameters are investigated and the recommendations of envelope parameters are put forward. An exponential decay model of instantaneous frequency is proposed and the multidimensional correlation and attenuation relations of model parameters are analyzed, then the recommendations of model parameters are set forth. A simplified model of instantaneous spectrum in the form of the product of independent functions in time and frequency domains is proposed, which not only produce a reference index for selecting reasonable ground motions for structural seismic design and analysis but also provides a basis for synthesis and simulation of ground motions allowing for the non-stationary properties in amplitude and frequency contents at the same time. Based on the improved signal processing methods and the instantaneous spectrum model, several methods for synthesis and simulation of ground motions are proposed, which can provide reasonable ground motions for structural seismic design and analysis.
3. Structural damage detection
In the sense of extracting complete information from vibration signals, three improved methods for structural damage detection are proposed. Since time varying damage indices are used in these improved methods, they have the advantage in applicability, sensitivity and robustness, and can detail the time sequence of occurrence, relative severity and cumulative process of structural damages at multiple locations in an efficient manner, which cannot be done by using the conventional damage detection methods.
In this thesis, signal processing is used as a link between earthquake ground motion and structural damage detection which are two unrelated but important research fields in earthquake engineering. The research findings presented here not only help to provide more reasonable ground motions for structural seismic design and analysis on the basis of a more comprehensive understanding of the properties of ground motions, but also provide a novel approach for structural damage detection which can be easily combined with other applications such as structural health monitoring and vibration control.
Finally, the weakness of the present study is briefly discussed and some recommendations for future research are provided.
引文
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