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FBG是一种反射式的光纤光栅,通过改变光纤芯区折射率,产生小的周期性调制而形成的,在前向传输和反向传输模式之前进行耦合,并且只能在这两种情况下进行耦合[15-18]。如图 1所示,当一束宽光谱激光经过光纤布喇格光栅时,被光栅反射回某一单色光λB,其它光通过光纤布喇格光栅透射过去,反射光的中心波长λB与光栅的折射率变化周期Λ和有效折射率neff的关系表达式如下:
$ {\lambda _B} = 2{n_{{\rm{eff}}}}\mathit{\Lambda } $
(1) 当光纤光栅受到轴向应力时,会引起弹光效应和轴向应变,进而会改变光纤Bragg光栅的周期和折射率,使反射光中心波长λB发生漂移,通过中心波长的漂移量就可以检测出环境应力的变化量,这就是用光纤Bragg光栅测应力测试的基本原理[19-21]。
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BP神经网络是一种多层的前馈网络系统,具有非常强大的非线性逼近能力。神经网络的训练过程中首先网络输入神经元的激活值将信息从输入层经隐藏层传递给输出层,输出层的各神经元期望输出值对应输入层的神经元信息[22]。然后,按预先设定的学习目标和减少误差的原则,通过反馈的误差值对输入层到隐藏层和隐藏层到输出层的连接权值和阈值进行修正。将冲击定位识别参量作为系统输入,FBG传感器的响应信号作为输出,输入信号前向传递,输出误差信号反向传播,进行重复训练,从而实现对碳纤维复合材料性能的初步定位检测。BP神经网络典型的拓扑结构如图 2所示。
图中, X1, X2, …,Xn是BP神经网络的输入层;H1, H2, …, Hr是隐藏层;Y1, Y2, …, Ym是神经网络的输出层;Wij和aj分别为输入层和隐藏层之间的连接权值和阈值;Wjk和ak分别为隐藏层和输出层之间的连接权值和阈值。
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当小钢球对冲击区域进行冲击时,碳纤维复合材料层合板受到小钢球的冲击上下振动,产生冲击应力波,应力波在复合材料层合板中传递时具有一定的波速,其距离位置越近,应力波到达的速度就越快,FBG传感器响应的时间就越短,因此冲击应力波的传递和时间有关,各光纤光栅传感器分别用于获取冲击后反映其所在位置应变的时域信号特征数据。应力波的曲线变化类似于正弦波,以小钢球冲击A1区采集的FBG1传感信号为例,其应力波变化如图 6所示。
利用插值拟合的方式对小钢球引起的冲击振荡信号的起始周期进行离散傅里叶拟合法进行拟合,以A13区采集的FBG传感信号为例,其起始周期应变时域放大图和拟合图如图 7所示。依次记录各FBG传感器的时域峰值响应时刻,分别为T1, T2, T3, T4,由于拟合峰对应的响应时刻的随机性大,不可通过寻峰算法直接找出T1, T2, T3, T4的值作为冲击定位参量,本实验中利用拟合出的时间差ΔTi作为冲击定位识别参量,将其作为BP神经网络的输入信号,结合BP神经网络算法实现碳纤维复合材料的参数化定位。时间差ΔTi计算方式如下:
$ \Delta {T_i} = {T_i} - {T_0}, (i = 1, 2, 3, 4) $
(2) 式中, Ti为FBGi的起始响应峰值所对应的时刻坐标;T0为碳纤维复合材料层合板冲击响应的起始响应时刻;ΔTi为各FBG传感器的冲击响应时间差。
利用小钢球对划定的16个区域的中心点依次进行冲击,将采集到的FBG传感器时域响应信号作为训练样本,通过MATLAB搭建的BP神经网络系统对复合材料层合板的冲击区域进行判定和预报。由实验过程可知,作为BP神经网络冲击定位监测系统的FBG响应传感器有4个,分别为FBG1, FBG2, FBG3和FBG4,所采集到的冲击定位识别参量分别为ΔT1, ΔT2, ΔT3和ΔT4,因此搭建的BP神经网络输入层神经元有4个,期望得到冲击点坐标,所以输出信号有2个,即冲击定位坐标(x, y)。小钢球对每个冲击位置重复冲击3次,16个冲击区域,共48个实验样本,选择单隐藏层,其隐藏节点为5个,设置附加动量因子Q=0.9,学习率η=0.0001。各FBG传感器所采集到的实验样本如表 1所示。
表 1 Training sample and test sample of impact location identification parameter
impact position frequency ΔT1/ms ΔT2/ms ΔT3/ms ΔT4/ms impact coordinates (x, y) training samples A1 1 0.333 0.451 0.646 0.469 (10, 10) 2 0.314 0.519 0.723 0.539 3 0.372 0.438 0.804 0.448 A2 1 0.332 0.381 0.823 0.413 (30, 10) 2 0.382 0.524 0.633 0.383 3 0.372 0.613 0.532 0.513 A3 1 0.382 0.632 0.544 0.254 (50, 10) 2 0.251 0.633 0.582 0.253 3 0.253 0.614 0.748 0.375 A4 1 0.532 0.754 0.628 0.381 (70, 10) 2 0.514 0.882 0.873 0.284 3 0.432 0.624 0.636 0.238 A5 1 0.251 0.632 0.521 0.132 (70, 30) 2 0.381 0.623 0.386 0.127 3 0.462 0.634 0.382 0.134 A6 1 0.251 0.532 0.373 0.249 (50, 30) 2 0.372 0.631 0.493 0.254 3 0.387 0.637 0.501 0.256 A7 1 0.248 0.513 0.632 0.382 (30, 30) 2 0.253 0.866 0.752 0.374 3 0.381 0.634 0.562 0.252 A8 1 0.248 0.372 0.634 0.521 (10, 30) 2 0.242 0.48 0.564 0.628 3 0.254 0.508 0.636 0.376 A9 1 0.501 0.487 0.139 0.386 (70, 50) 2 0.528 0.504 0.132 0.378 3 0.626 0.617 0.324 0.254 A10 1 0.486 0.582 0.376 0.259 (50, 50) 2 0.503 0.516 0.382 0.254 3 0.624 0.636 0.354 0.248 A11 1 0.382 0.406 0.743 0.736 (30, 50) 2 0.376 0.483 0.752 0.746 3 0.381 0.501 0.734 0.728 A12 1 0.251 0.384 0.388 0.632 (10, 50) 2 0.333 0.253 0.374 0.743 3 0.282 0.296 0.382 0.684 A13 1 0.752 0.256 0.128 0.372 (70, 70) 2 0.749 0.382 0.134 0.464 3 0.738 0.282 0.136 0.406 A14 1 0.632 0.501 0.383 0.463 (50, 70) 2 0.506 0.483 0.386 0.253 3 0.732 0.389 0.364 0.249 A15 1 0.532 0.124 0.258 0.753 (30, 70) 2 0.503 0.154 0.253 0.756 3 0.497 0.196 0.256 0.628 A16 1 0.253 0.236 0.258 0.384 (10, 70) 2 0.301 0.376 0.503 0.376 3 0.256 0.372 0.254 0.502 test samples A2 0.334 0.382 0.817 0.406 (30, 10) A5 0.286 0.618 0.482 0.148 (70, 30) A14 0.608 0.484 0.382 0.243 (50, 70) A15 0.502 0.148 0.254 0.686 (30, 70) 随机选中4个冲击区域对搭建的BP神经网络系统进行测试,分别为A2, A5, A14, A15,对每个样本测试区域冲击一次,记录实验数据。通过MATLAB搭建的BP神经网络对冲击定位区域的训练样本进行训练,将期望值和预测值的坐标点利用图形进行输出,结果如图 8所示。
从图 8可以看出,预测输出位置和期望输出位置均在同一个网格区域内,证明利用BP神经网络系统对基于FBG传感器的智能复合材料进行定位监测,能够准确预测小钢球的冲击位置,然后对期望位置和预测位置的横纵坐标的绝对误差进行求解,图形输出如图 9所示。
由图 9中的数据点可知,期望值和预测值的横纵坐标的同比例缩小误差范围在0mm~8mm之间,小于冲击识别区域(0,10),与待测复合材料层合板总长度比值小于0.1,完全可以精准地预测小钢球冲击点的位置,实现利用BP神经网络算法对复合材料层合板进行冲击定位识别。
基于BP算法和FBG传感的复合材料冲击定位检测技术
Composite material impact location detection technology based on BP algorithm and FBG sensing
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摘要: 复合材料在服役过程中易受到外部的低能量冲击, 造成不可见损伤, 为了监测复合材料健康状况, 将光纤布喇格光栅(FBG)传感网络粘贴布置于碳纤维复合材料表面, 采用基于反向传播(BP)神经网络系统的智能复合材料冲击定位识别技术, 获取FBG传感的时域信号响应值, 从而进行了复合材料冲击位置的预判。结果表明, BP神经网络算法具有非线性逼近能力强、容错率高和自适应能力强等优点, 可以实现复合材料层合板的参数化识别定位, 且预测结果与待测复合材料层合板总长度比值小于0.1。该FBG传感系统可为智能化复合材料冲击损伤自调整和自修复能力提供更准确的信息。Abstract: The composite material is susceptible to external low-energy impact which causes invisible damage during service. In order to achieve the purpose of monitoring the health of the composite material, the fiber Bragg grating (FBG) sensor network was pasted and arranged on the surface of the carbon fiber composite material. The intelligent composite material impact location recognition technology based on the back propagation (BP) neural network system was used to obtain the time-domain signal response value of the FBG sensor to predict the impact position of the composite material. The results show that the BP neural network algorithm has the advantages of strong nonlinear approximation ability, high fault tolerance and strong adaptive ability. It can realize the parameterized identification and positioning of composite laminates, and the ratio of the prediction results to the total length of the composite laminates to be tested less than 0.1. The FBG sensing system provides more accurate information for the self-adjustment and self-repair capabilities of intelligent composite materials.
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表 1 Training sample and test sample of impact location identification parameter
impact position frequency ΔT1/ms ΔT2/ms ΔT3/ms ΔT4/ms impact coordinates (x, y) training samples A1 1 0.333 0.451 0.646 0.469 (10, 10) 2 0.314 0.519 0.723 0.539 3 0.372 0.438 0.804 0.448 A2 1 0.332 0.381 0.823 0.413 (30, 10) 2 0.382 0.524 0.633 0.383 3 0.372 0.613 0.532 0.513 A3 1 0.382 0.632 0.544 0.254 (50, 10) 2 0.251 0.633 0.582 0.253 3 0.253 0.614 0.748 0.375 A4 1 0.532 0.754 0.628 0.381 (70, 10) 2 0.514 0.882 0.873 0.284 3 0.432 0.624 0.636 0.238 A5 1 0.251 0.632 0.521 0.132 (70, 30) 2 0.381 0.623 0.386 0.127 3 0.462 0.634 0.382 0.134 A6 1 0.251 0.532 0.373 0.249 (50, 30) 2 0.372 0.631 0.493 0.254 3 0.387 0.637 0.501 0.256 A7 1 0.248 0.513 0.632 0.382 (30, 30) 2 0.253 0.866 0.752 0.374 3 0.381 0.634 0.562 0.252 A8 1 0.248 0.372 0.634 0.521 (10, 30) 2 0.242 0.48 0.564 0.628 3 0.254 0.508 0.636 0.376 A9 1 0.501 0.487 0.139 0.386 (70, 50) 2 0.528 0.504 0.132 0.378 3 0.626 0.617 0.324 0.254 A10 1 0.486 0.582 0.376 0.259 (50, 50) 2 0.503 0.516 0.382 0.254 3 0.624 0.636 0.354 0.248 A11 1 0.382 0.406 0.743 0.736 (30, 50) 2 0.376 0.483 0.752 0.746 3 0.381 0.501 0.734 0.728 A12 1 0.251 0.384 0.388 0.632 (10, 50) 2 0.333 0.253 0.374 0.743 3 0.282 0.296 0.382 0.684 A13 1 0.752 0.256 0.128 0.372 (70, 70) 2 0.749 0.382 0.134 0.464 3 0.738 0.282 0.136 0.406 A14 1 0.632 0.501 0.383 0.463 (50, 70) 2 0.506 0.483 0.386 0.253 3 0.732 0.389 0.364 0.249 A15 1 0.532 0.124 0.258 0.753 (30, 70) 2 0.503 0.154 0.253 0.756 3 0.497 0.196 0.256 0.628 A16 1 0.253 0.236 0.258 0.384 (10, 70) 2 0.301 0.376 0.503 0.376 3 0.256 0.372 0.254 0.502 test samples A2 0.334 0.382 0.817 0.406 (30, 10) A5 0.286 0.618 0.482 0.148 (70, 30) A14 0.608 0.484 0.382 0.243 (50, 70) A15 0.502 0.148 0.254 0.686 (30, 70) -
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