Lamb波损伤成像中的频散补偿方法研究
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摘要
Lamb波是一种板类结构中的超声导波，具有传播距离远并对结构内部和表面损伤均敏感的优点，所以广泛应用于结构健康监测中。然而，Lamb波存在多模和频散特性。即使对于单模式的监测信号，频散效应也使其波包发生扩展和变形，幅值随之减小，这种现象会随着传播距离的增大表现得越明显，严重降低了传感信号的分辨率和信噪比。本文主要研究了Lamb波的单模式产生方法和频散补偿方法，并用于提高成像分辨率。主要研究工作包括以下几个方面：
（1）对基于PZT的Lamb波激励、传播和传感过程进行了力学建模，得到不同激励方式下的传感信号解析表达式，理论分析了Lamb波的多模特性，并在不同结构中进行了实验研究；建立了Lamb波传感模型，理论研究了不同频散特性对传感信号的影响情况，进行了数值验证。
（2）基于Lamb波力学建模结果，对比研究了频率调节和双面激励这两种单模式激励方法；在铝板中进行了一维近邻多损伤监测，考察了双面激励方法提高Lamb波监测分辨率的能力；理论分析了延迟叠加成像原理，并研究了基于复小波变换的信号包络提取方法；提出利用双面激励来提高延迟叠加成像的分辨率，在铝板中进行了实验验证。
（3）分别研究了非频散信号构建（ND-SC）和时间－距离域映射（TDDM）两种基于理论波数曲线的频散补偿方法，分别给出了基于宽带激励或窄带激励的ND-SC和TDDM实现过程。对利用阶跃激励获取结构脉冲响应进行了实验研究。提出了基于ND-SC和TDDM的高分辨率损伤成像方法，在铝板中进行了实验验证。
（4）针对ND-SC和TDDM扰乱信号频谱以及需要绝对波数曲线的问题，分别研究了线性频散信号构建（LD-SC）方法和改进的时间－距离域映射（ITDDM）方法。研究了Lamb波相对波数曲线的测量方法，证明了基于相对波数测量曲线的LD-SC和ITDDM的可行性。提出了基于LD-SC和ITDDM的高分辨率损伤成像方法，分别在铝板和材料参数未知的玻璃纤维复合材料板中进行了实验验证。
（5）理论和实验研究了时间反转（TR）对Lamb波信号的自动频散补偿作用。针对传统TR方法消除补偿波包时间信息以及TR物理操作复杂的问题，提出了虚拟时间反转（VTR）方法。VTR方法中，采用换元激励和接收机制（CERM）代替固定激励和接收机制（FERM）以保留信号时间信息，并通过信号运算虚拟进行基于CERM的TR操作。给出了基于阶跃激励的VTR实现过程，提出了基于VTR的高分辨率损伤成像方法。分别在铝板、玻璃纤维复合材料板以及碳纤维复合材料板中进行了实验研究。
Lamb waves, a kind of guided ultrasonic waves in plate-like structures, are widely used instructural health monitoring (SHM), because of the ability of long-distance transmission and highsensitivity to both the surface and the internal defects. However, Lamb waves have multi-mode anddispersion characteristics. Even for the single-mode signals, the wavepackets can spread out in timeand space with their envelopes deformed and amplitudes decreased, due to the dispersion effect. Theeffect will become more serious with longer traveling distance, resulting in extremely poorerresolution and signal-to-noise-rate (SNR) for sensor signals. In the dissertation, the single modegeneration and dispersion compensation methods are studied and adopted to improve the damageimaging resolution. The main works are as follows:
(1) After mechanical modeling for the procedure of Lamb wave exciting, propagating andreceiving with PZT wafers, the analytical expressions of the sensor signals under different excitationmanners are derived. The multi-mode characteristic of Lamb waves is then analyzed and validated byexperiments in different structures. Moreover, the sensing modal of Lamb waves is also established.The effects of different dispersion relations on sensor signals are theoretically and numericallyinvestigated.
(2) With the mechanical modeling results, two single mode generation methods, frequencytuning and double-side excitation, are compared. To prove the ability of double-side excitation ofimproving Lamb wave monitoring resolution, the one-dimension localization for adjacent multipledamages is carried out in an aluminum plate. Hereafter, the delay-and-sum imaging theory is studiedtogether with signal envelope extraction method using complex wavelet transform. Double-sideexcitation is then used to enhance the delay-and-sum imaging resolution and its efficiency isexperimentally verified.
(3) Two dispersion removal methods based on theoretical wavenumber curves, i.e.,non-dispersive signal construction (ND-SC) and time-to-distance domain mapping (TDDM) areresearched. The implement procedures of these two approaches are also discussed consideringbroadband or narrowband excitation. The method to estimate the structural impulse responses withstep pulse excitation is experimentally studied. The high-resolution imaging methods based onND-SC and TDDM are developed and validated.
(4) To solve the problems of seriously distorbing the signal spectra and requiring absolute wavenumber curves in ND-SC and TDDM, linear-dispersive signal construction (LD-SC) andimproved TDDM (ITDDM) methods are studied, respectively. The method of measuring the relativewavenumber curve is introduced and the feasibility of using LD-SC and ITDDM with relativewavenumber curves is testified. The methods of LD-SC and ITDDM are then applied to improve theimaging resolution in both the aluminum plate and the glass-fiber composite plate with unknownmaterial parameters.
(5) Automatically compensating dispersion effect in Lamb wave signals through time reversal(TR) is analyzed. To overcome the problems that traditional TR method eliminates propagation timeof Lamb waves and its procedure is complicated, a virtual time reversal (VTR) method is developed.In VTR, changing-element exciting and receiving mechanism (CERM) rather than fixed exciting andreceiving mechanism (FERM) is adopted for time information reservation. Furthermore, the physicalmanipulations of CERM-based TR are replaced by signal operations. The VTR realization under steppulse excitation is discussed. The high-resolution imaging method based on VTR is introduced. Toverify the proposed imaging method, the experiments are arranged in an aluminum plate, a glass-fibercomposite plate and a carbon-fiber composite plate, respectively.
（1）对基于PZT的Lamb波激励、传播和传感过程进行了力学建模，得到不同激励方式下的传感信号解析表达式，理论分析了Lamb波的多模特性，并在不同结构中进行了实验研究；建立了Lamb波传感模型，理论研究了不同频散特性对传感信号的影响情况，进行了数值验证。
（2）基于Lamb波力学建模结果，对比研究了频率调节和双面激励这两种单模式激励方法；在铝板中进行了一维近邻多损伤监测，考察了双面激励方法提高Lamb波监测分辨率的能力；理论分析了延迟叠加成像原理，并研究了基于复小波变换的信号包络提取方法；提出利用双面激励来提高延迟叠加成像的分辨率，在铝板中进行了实验验证。
（3）分别研究了非频散信号构建（ND-SC）和时间－距离域映射（TDDM）两种基于理论波数曲线的频散补偿方法，分别给出了基于宽带激励或窄带激励的ND-SC和TDDM实现过程。对利用阶跃激励获取结构脉冲响应进行了实验研究。提出了基于ND-SC和TDDM的高分辨率损伤成像方法，在铝板中进行了实验验证。
（4）针对ND-SC和TDDM扰乱信号频谱以及需要绝对波数曲线的问题，分别研究了线性频散信号构建（LD-SC）方法和改进的时间－距离域映射（ITDDM）方法。研究了Lamb波相对波数曲线的测量方法，证明了基于相对波数测量曲线的LD-SC和ITDDM的可行性。提出了基于LD-SC和ITDDM的高分辨率损伤成像方法，分别在铝板和材料参数未知的玻璃纤维复合材料板中进行了实验验证。
（5）理论和实验研究了时间反转（TR）对Lamb波信号的自动频散补偿作用。针对传统TR方法消除补偿波包时间信息以及TR物理操作复杂的问题，提出了虚拟时间反转（VTR）方法。VTR方法中，采用换元激励和接收机制（CERM）代替固定激励和接收机制（FERM）以保留信号时间信息，并通过信号运算虚拟进行基于CERM的TR操作。给出了基于阶跃激励的VTR实现过程，提出了基于VTR的高分辨率损伤成像方法。分别在铝板、玻璃纤维复合材料板以及碳纤维复合材料板中进行了实验研究。
Lamb waves, a kind of guided ultrasonic waves in plate-like structures, are widely used instructural health monitoring (SHM), because of the ability of long-distance transmission and highsensitivity to both the surface and the internal defects. However, Lamb waves have multi-mode anddispersion characteristics. Even for the single-mode signals, the wavepackets can spread out in timeand space with their envelopes deformed and amplitudes decreased, due to the dispersion effect. Theeffect will become more serious with longer traveling distance, resulting in extremely poorerresolution and signal-to-noise-rate (SNR) for sensor signals. In the dissertation, the single modegeneration and dispersion compensation methods are studied and adopted to improve the damageimaging resolution. The main works are as follows:
(1) After mechanical modeling for the procedure of Lamb wave exciting, propagating andreceiving with PZT wafers, the analytical expressions of the sensor signals under different excitationmanners are derived. The multi-mode characteristic of Lamb waves is then analyzed and validated byexperiments in different structures. Moreover, the sensing modal of Lamb waves is also established.The effects of different dispersion relations on sensor signals are theoretically and numericallyinvestigated.
(2) With the mechanical modeling results, two single mode generation methods, frequencytuning and double-side excitation, are compared. To prove the ability of double-side excitation ofimproving Lamb wave monitoring resolution, the one-dimension localization for adjacent multipledamages is carried out in an aluminum plate. Hereafter, the delay-and-sum imaging theory is studiedtogether with signal envelope extraction method using complex wavelet transform. Double-sideexcitation is then used to enhance the delay-and-sum imaging resolution and its efficiency isexperimentally verified.
(3) Two dispersion removal methods based on theoretical wavenumber curves, i.e.,non-dispersive signal construction (ND-SC) and time-to-distance domain mapping (TDDM) areresearched. The implement procedures of these two approaches are also discussed consideringbroadband or narrowband excitation. The method to estimate the structural impulse responses withstep pulse excitation is experimentally studied. The high-resolution imaging methods based onND-SC and TDDM are developed and validated.
(4) To solve the problems of seriously distorbing the signal spectra and requiring absolute wavenumber curves in ND-SC and TDDM, linear-dispersive signal construction (LD-SC) andimproved TDDM (ITDDM) methods are studied, respectively. The method of measuring the relativewavenumber curve is introduced and the feasibility of using LD-SC and ITDDM with relativewavenumber curves is testified. The methods of LD-SC and ITDDM are then applied to improve theimaging resolution in both the aluminum plate and the glass-fiber composite plate with unknownmaterial parameters.
(5) Automatically compensating dispersion effect in Lamb wave signals through time reversal(TR) is analyzed. To overcome the problems that traditional TR method eliminates propagation timeof Lamb waves and its procedure is complicated, a virtual time reversal (VTR) method is developed.In VTR, changing-element exciting and receiving mechanism (CERM) rather than fixed exciting andreceiving mechanism (FERM) is adopted for time information reservation. Furthermore, the physicalmanipulations of CERM-based TR are replaced by signal operations. The VTR realization under steppulse excitation is discussed. The high-resolution imaging method based on VTR is introduced. Toverify the proposed imaging method, the experiments are arranged in an aluminum plate, a glass-fibercomposite plate and a carbon-fiber composite plate, respectively.
引文
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