Non-contact Diagnosis of Cable Joint Insulation Deterioration Based on Deep Learning Surface Temperature
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摘要:
为提升电缆中间接头绝缘层劣化程度的现场诊断效率和准确度，提出一种基于表层温度自适应深度学习的接头绝缘劣化状态非接触式诊断方法。首先，对电缆接头及两端电缆的绝缘表层进行红外热成像，实现电缆接头中心两边多个对称区域的表层温度、接头两端电缆的表层温度的非接触式采集；其次，构建基于双隐层自编码极限学习机的深度学习网络，以挖掘表层温度数据内部深层次隐含特征，将提取的深度隐含特征作为随机森林诊断模型输入；然后，提出一种非线性动态自适应旋转角的量子旋转门以改进量子烟花算法的更新策略，并用于诊断模型参数优化；最后，结合接头表层红外温度和绝缘介质损耗角正切值构建数据集，对诊断模型进行训练和现场测试。实验结果表明，改进后的量子烟花算法可以较好地逼近全局最优解、收敛效率高，深度学习随机森林诊断模型具有较强的特征抽取和分类能力，参数优化后诊断模型的分类精度和稳定性得到有效提高，在小样本训练集条件下就能达到较好的诊断效果，可实现接头绝缘劣化状态的非接触式诊断。
Abstract:To improve the efficiency and accuracy of the field diagnosis of insulation layer deterioration of the cable intermediate joint, a non-contact diagnosis method based on adaptive deep learning of surface temperature is proposed. First, infrared thermal imaging was performed on the insulating surface of the cable joint and cables at both ends. The surface temperatures of multiple symmetric areas on both sides of the center of the cable joint and cables at both ends were collected without contact. Subsequently, a deep learning network based on a two-hidden autoencoder extreme learning machine was constructed to mine the deep hidden features in the surface temperature data. The extracted deep hidden features were used as input to the random forest diagnosis model. A quantum rotation gate with a nonlinear dynamic adaptive rotation angle was further proposed to improve the update strategy of the quantum firework algorithm and optimize the parameters of the diagnostic model. Finally, by combining the infrared temperature of the joint surface and loss angle tangent value of the insulating medium, a dataset was constructed to train and test the diagnostic model in the field. The experimental results show that the improved quantum fireworks algorithm can better approximate the global optimal solution and has high convergence efficiency. The deep learning random forest diagnostic model exhibited strong feature extraction and classification capabilities, whereby the classification accuracy and stability of the diagnostic model were effectively improved after parameter optimization, and better diagnostic results were achieved under the condition of a small sample training set. Therefore, noncontact diagnosis of joint insulation deterioration is achievable.
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0. 引言
框架式稳定平台系统近年来发展迅速，广泛应用于飞行器上的目标探测系统、精确制导武器的导引系统等。三自由度框架式红外稳定平台实现惯性空间稳定和对目标跟踪的同时，还可以直接测量制导系统所需的视线角速度信息[1]。三自由度稳定平台在结构上由3个单轴运动框架复合而成，机械装配中产生的装调误差造成框架轴系偏差[2-3]、红外探测器位姿偏差以及陀螺敏感轴的交叉耦合[4-5]，使得基座角运动的耦合更加复杂[6]，对测量视线角速度带来不利的影响。
文献[7]研究了仅陀螺敏感轴交叉耦合情况下视线角速度的计算。所得结果是在框架轴系正交的假设下得到的。而实际系统中框架的装配必然会存在一定装调误差。本文系统研究了框架、陀螺和红外探测器均存在装调误差时，三自由度框架式红外视线角速度的计算方法，建立基于三轴稳定平台的轴系偏差的数学模型，分析了装调误差对视线角速度计算的影响，并进行仿真验证。
1. 稳定平台系统
三自由度框架式红外稳定平台系统的示意图如图 1。图中，O-XbYbZb表示载体坐标系。载体坐标系的原点取为稳定平台回转中心且坐标系和载体固连。
框架式红外稳定平台系统一般将探测成像系统和速率陀螺安装在稳定平台上，稳定平台固定在内环框架上，成为内环框架的负载。内环框架和稳定平台组成内环本体组合，通过内环框架转轴固定在中环框架上，成为中环框架的负载。中环框架和内环本体组合通过中环框架转轴固定在外环框架上，成为外环框架的负载。外环框架转轴架固定在红外稳定平台的载体上。外环框架相对载体可以做滚转运动；外环框架处于零位时，中环框架相对载体可以做偏航运动；外环框架和中环框架处于零位时，内环框架相对载体可以做俯仰运动。通过内环、中环、外环3个框架的运动合成，可以实现稳定平台在惯性空间中绕回转中心转动。
2. 轴系偏差建模
针对三自由度红外稳定平台的结构特点，除了前面定义的载体坐标系O-XbYbZb，再建立外环坐标系O-XoYoZo、中环坐标系O-XmYmZm、平台坐标系O-XpYpZp和探测坐标系O-XdYdZd。这4个坐标系原点均为稳定平台回转中心，其中，外环坐标系X轴和外环框架转轴固连；中环坐标系Y轴与中环框架转轴固连；平台坐标系Z轴和内环框架转轴固连；探测坐标系和探测器光敏面固连，其X轴对应光敏面的中垂线（即探测成像系统光轴），Y轴和Z轴分别对应探测器光敏面的行和列。
在设计的理想状态下，探测成像系统光轴与内环框架转轴、内环框架转轴与中环框架转轴、中环框架转轴与外环框架转轴应分别正交，而外环框架转轴和载体纵轴完全重合。探测坐标系和平台坐标系重合且各框架处于零位时，4个坐标系和载体坐标系重合。记外环框架角为φw，中环框架角为φz，内环框架角为φn，角度正负按右手规则确定，那么各坐标系相互间的变换关系如图 2所示。
实际装配时，框架轴系不可能做到零误差。本文描述轴系装调误差的参数为α1、β1、α2、β2、α3、β3、α4、β4和γ4。其中，α1为外环框架转轴在载体坐标系XOZ面的投影与载体系X轴的夹角；β1为外环框架转轴与载体系XOZ面的夹角；α2为中环框架转轴在外环坐标系YOZ面的投影与外环系Y轴的夹角；β2为中环框架转轴与载体系YOZ面的夹角；α3为内环框架转轴在中环坐标系XOZ面的投影与中环系Z轴的夹角；β3为内环框架转轴与中环系β3面的夹角；α4为探测器光敏面中垂线在平台系XOZ面的投影与平台系X轴的夹角；β4为光敏面中垂线与平台系XOZ面的夹角；γ4和α4、β4一起构成一组平台系到探测系的欧拉角。角度正负号按右手规则确定。当这些装调误差存在时，各坐标系相互间的变换关系如图 3所示。
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图 3 框架轴系偏差时各坐标系之间的变换关系Figure 3. Transformation of coordinate systems with axis system deviation3. 视线角速度的计算
当稳定跟踪目标时，探测成像系统光轴和视线重合，那么视线角速度$\dot{q}$近似为光轴在惯性空间中转动的角速度在探测系YOZ面的投影。由于探测成像系统是固连在稳定平台上的，所以光轴在惯性空间中转动的角速度也是平台转动的角速度$\tilde{\omega }$。为了简化分析，本文假设载体不动，并定义如下矩阵函数：
$$ {\mathit{\boldsymbol{T}}_x}(\phi ) = \left[ {\begin{array}{*{20}{c}} 1&0&0\\ 0&{\cos \phi }&{ - \sin \phi }\\ 0&{\sin \phi }&{\cos \phi } \end{array}} \right], $$ $$ {\mathit{\boldsymbol{T}}_y}(\phi ) = \left[ {\begin{array}{*{20}{c}} {\cos \phi }&0&{\sin \phi }\\ 0&1&0\\ { - \sin \phi }&0&{\cos \phi } \end{array}} \right], $$ $$ {\mathit{\boldsymbol{T}}_z}(\phi ) = \left[ {\begin{array}{*{20}{c}} {\cos \phi }&{ - \sin \phi }&0\\ {\sin \phi }&{\cos \phi }&0\\ 0&0&1 \end{array}} \right]。 $$ 当存在轴系偏差时，各坐标系之间按图 3的方式进行变换。此时在惯性空间中，平台转动的角速度$\tilde \omega $在探测系中的投影为：
$$ \begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{{\tilde \omega }_{{\rm{d}}x}}}\\ {{{\tilde \omega }_{{\rm{d}}y}}}\\ {{{\tilde \omega }_{{\rm{d}}z}}} \end{array}} \right] = \\T_x^{ - 1}({\gamma _4})T_z^{ - 1}({\beta _4})T_y^{ - 1}({\alpha _4})\left( {\left[ {\begin{array}{*{20}{c}} 0\\ 0\\ {{\omega _{\rm{n}}}} \end{array}} \right] + T_z^{ - 1}({\phi _{\rm{n}}})T_x^{ - 1}({\beta _3})T_y^{ - 1}({\alpha _3})\left( {\left[ {\begin{array}{*{20}{c}} 0\\ {{\omega _z}}\\ 0 \end{array}} \right] + T_y^{ - 1}({\phi _z})T_z^{ - 1}({\beta _2})T_x^{ - 1}({\alpha _2})\left[ {\begin{array}{*{20}{c}} {{\omega _w}}\\ 0\\ 0 \end{array}} \right]} \right)} \right)}\\ { = {A_{\tilde \omega }}({\phi _z}, \, {\phi _{\rm{n}}}, \, {\alpha _2}, \, {\beta _2}, \, {\alpha _3}, \, {\beta _3}, \, {\alpha _4}, \, {\beta _4}, {\gamma _4})\left[ {\begin{array}{*{20}{c}} {{\omega _{\rm{w}}}}\\ {{\omega _{\rm{z}}}}\\ {{\omega _{\rm{n}}}} \end{array}} \right]} \end{array} $$ (1) 式中：φn为内环框架角；φz为中环框架角；ωn是位标器内环框架转动的角速度，其方向沿平台坐标系的Z轴；ωz是位标器中环框架转动的角速度，其方向沿中环坐标系的Y轴。ωw是位标器外环框架转动的角速度，其方向沿外环坐标系的X轴。于是按本文中对视线角速度$\dot q$的近似，其在探测系中为：
$$ \left[ {\begin{array}{*{20}{c}} {{{\dot q}_{{\rm{d}}x}}}\\ {{{\dot q}_{{\rm{d}}y}}}\\ {{{\dot q}_{{\rm{d}}z}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{{\tilde \omega }_{{\rm{d}}x}}}\\ {{{\tilde \omega }_{{\rm{d}}y}}}\\ {{{\tilde \omega }_{{\rm{d}}z}}} \end{array}} \right] = {\mathit{\boldsymbol{A}}_{\dot q}}({\phi _{\rm{z}}}, \, {\phi _{\rm{n}}}, \, {\alpha _2}, \, {\beta _2}, \, {\alpha _3}, \, {\beta _3}, \, {\alpha _4}, \, {\beta _4}, {\gamma _4})\left[ {\begin{array}{*{20}{c}} {{\omega _{\rm{w}}}}\\ {{\omega _{\rm{z}}}}\\ {{\omega _{\rm{n}}}} \end{array}} \right] $$ (2) 式中：${\mathit{\boldsymbol{A}}_{\dot q}} = \left[ {\begin{array}{*{20}{c}} 0&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]{\mathit{\boldsymbol{A}}_{\bar \omega }}$。
对于三自由度框架式红外稳定平台系统，稳定平台上正交安装了偏航/俯仰陀螺分别测量平台相对惯性空间的偏航/俯仰角速度；外环框架上安装有外环陀螺，可以测量外框架相对惯性空间的滚转角速度。理想情况下，稳定平台偏航/俯仰陀螺的敏感轴分别平行于平台坐标系的Y轴和Z轴，外环陀螺敏感轴与外环坐标系X轴平行。这里仍用第2章轴系偏差建模的方法描述陀螺的装配误差，记误差参数为α5、β5、α6、β6、α7、β7。其中，α5为外环陀螺敏感轴在外环系XOZ面的投影与外环系X轴的夹角；β5为外环陀螺敏感轴与外环系XOZ面的夹角；α6为中环陀螺敏感轴在平台系YOZ面的投影与平台系Y轴的夹角；β6为中环陀螺敏感轴与平台系YOZ面的夹角；α7为内环陀螺敏感轴在平台系XOZ面的投影与平台系Z轴的夹角；β7为内环陀螺敏感轴与平台系XOZ面的夹角。角度正负号按右手规则确定。那么在考虑轴系偏差情形下，陀螺的输出和外、中、内环框架的角速度满足下式：
$$ \begin{array}{*{20}{c}} {\left[ {\begin{array}{*{20}{c}} {{{\hat \omega }_{\rm{w}}}}\\ {{{\hat \omega }_{\rm{z}}}}\\ {{{\hat \omega }_{\rm{n}}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\cos {\alpha _5}\cos {\beta _5}}&{\sin {\beta _5}}&{ - \sin {\alpha _5}\cos {\beta _5}}\\ 0&0&0\\ 0&0&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{\omega _{\rm{w}}}}\\ 0\\ 0 \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&0&0\\ { - \sin {\beta _6}}&{\cos {\alpha _6}\cos {\beta _6}}&{\sin {\alpha _6}\cos {\beta _6}}\\ {\sin {\alpha _7}\cos {\beta _7}}&{ - \sin {\beta _7}}&{\cos {\alpha _7}\cos {\beta _7}} \end{array}} \right]}\\ {\quad \quad \quad \cdot \left( {\left[ {\begin{array}{*{20}{c}} 0\\ 0\\ {{\omega _{\rm{n}}}} \end{array}} \right] + T_z^{ - 1}({\phi _n})T_x^{ - 1}({\beta _3})T_y^{ - 1}({\alpha _3})\left( {\left[ {\begin{array}{*{20}{c}} 0\\ {{\omega _z}}\\ 0 \end{array}} \right] + T_y^{ - 1}({\phi _z})T_z^{ - 1}({\beta _2})T_x^{ - 1}({\alpha _2})\left[ {\begin{array}{*{20}{c}} {{\omega _{\rm{w}}}}\\ 0\\ 0 \end{array}} \right]} \right)} \right)}\\ { = {\mathit{\boldsymbol{A}}_g}({\phi _z}, \, {\phi _n}, \, \, {\alpha _2}, \, {\beta _2}, \, {\alpha _3}, \, {\beta _3}, \, {\alpha _5}, \, {\beta _5}, \, {\alpha _6}, \, {\beta _6}, \, {\alpha _7}, \, {\beta _7})\left[ {\begin{array}{*{20}{c}} {{\omega _{\rm{w}}}}\\ {{\omega _{\rm{z}}}}\\ {{\omega _{\rm{n}}}} \end{array}} \right]} \end{array} $$ (3) 式中：${\hat \omega _{\rm{w}}}$是外环陀螺的输出；${\hat \omega _{\rm{z}}}$是偏航陀螺的输出；${\hat \omega _{\rm{n}}}$是内环陀螺的输出。
将式(3)代入式(2)，得到视线角速度在探测坐标系中的测量计算公式为：
$$ \left[ {\begin{array}{*{20}{c}} {{{\dot q}_{{\rm{d}}x}}}\\ {{{\dot q}_{{\rm{d}}y}}}\\ {{{\dot q}_{{\rm{d}}z}}} \end{array}} \right] = \mathit{\boldsymbol{T}}({\phi _z}, \, {\phi _n}, \, {\alpha _2}, \, {\beta _2}, \, {\alpha _3}, \, {\beta _3}, \, {\alpha _4}, \, {\beta _4}, {\gamma _4}\, {\alpha _5}, \, {\beta _5}, \, {\alpha _6}, \, {\beta _6}, \, {\alpha _7}, \, {\beta _7})\left[ {\begin{array}{*{20}{c}} {{{\hat \omega }_{\rm{w}}}}\\ {{{\hat \omega }_{\rm{z}}}}\\ {{{\hat \omega }_{\rm{n}}}} \end{array}} \right] $$ (4) 式中：$\mathit{\boldsymbol{T}} = {A_{\dot q}}A_g^{ - 1}$。
最后将其按图 3的坐标变换关系可得视线角速度在载体系中的测量计算公式为：
$$ \left[ {\begin{array}{*{20}{c}} {{{\dot q}_{bx}}}\\ {{{\dot q}_{by}}}\\ {{{\dot q}_{bz}}} \end{array}} \right] = {\mathit{\boldsymbol{T}}_y}({\alpha _1}){\mathit{\boldsymbol{T}}_z}({\beta _1}){\mathit{\boldsymbol{T}}_x}({\phi _w}){\mathit{\boldsymbol{T}}_x}({\alpha _2}){\mathit{\boldsymbol{T}}_z}({\beta _2}){\mathit{\boldsymbol{T}}_y}({\phi _z}){\mathit{\boldsymbol{T}}_y}({\alpha _3}){\mathit{\boldsymbol{T}}_x}({\beta _3}){\mathit{\boldsymbol{T}}_z}({\phi _n}){\mathit{\boldsymbol{T}}_y}({\alpha _4}){\mathit{\boldsymbol{T}}_z}({\beta _4}){\mathit{\boldsymbol{T}}_x}({\gamma _4})\mathit{\boldsymbol{T}}\left[ {\begin{array}{*{20}{c}} {{{\hat \omega }_{\rm{w}}}}\\ {{{\hat \omega }_{\rm{z}}}}\\ {{{\hat \omega }_{\rm{n}}}} \end{array}} \right] $$ (5) 当各误差参数都取零时，式(4)即蜕化成：
$$ \left[ {\begin{array}{*{20}{c}} {{{\dot q}_{{\rm{d}}x}}}\\ {{{\dot q}_{{\rm{d}}y}}}\\ {{{\dot q}_{{\rm{d}}z}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{{\hat \omega }_{\rm{w}}}}\\ {{{\hat \omega }_{\rm{z}}}}\\ {{{\hat \omega }_{\rm{n}}}} \end{array}} \right] $$ (6) 将其坐标变换到载体系可得：
$$ \left[ {\begin{array}{*{20}{c}} {{{\dot q}_{bx}}}\\ {{{\dot q}_{by}}}\\ {{{\dot q}_{bz}}} \end{array}} \right] = {\mathit{\boldsymbol{T}}_x}({\phi _w}){\mathit{\boldsymbol{T}}_y}({\phi _z}){\mathit{\boldsymbol{T}}_z}({\phi _{\rm{n}}})\left[ {\begin{array}{*{20}{c}} 0\\ {{{\hat \omega }_{\rm{z}}}}\\ {{{\hat \omega }_{\rm{n}}}} \end{array}} \right] $$ (7) 也即理想情况下，三自由度框架式红外稳定平台系统稳定跟踪目标时，稳定平台上正交安装的偏航/俯仰陀螺可以直接测量出视线角速度。特别当框架轴系误差参数取零时，式(4)即蜕化成文献[7]中的结果。因此，式(4)也可以认为是对装调误差进行补偿，而且较文献[7]中的结果更具有一般性。
4. 仿真分析
对三自由度框架式红外稳定平台系统进行视线角速度测量试验。试验中载体静止，目标转台做30°/s匀速运动。记录稳定跟踪目标时的陀螺输出和框架角输出，如图 4和图 5所示。
用实测数据按第3章的计算公式进行离线仿真。仿真时，设置4种条件：忽略所有误差、忽略陀螺安装误差、忽略框架轴系误差和综合考虑各装调误差，具体误差参数如表 1所示。
表 1 装调误差参数设置Table 1. Parameters setting of installation errorsAxis system deviation /° Alignment error of gyros/° (α1, β1) (α2, β2) (α3, β3) (α4, β4, γ4) (α5, β5) (α6, β6) (α7, β7) 1 (0, 0) (0, 0) (0, 0) (0, 0, 0) (0, 0) (0, 0) (0, 0) 2 (0, －0.02) (0.02, 0.1) (－0.03, 0) (0.03, 0.08, 2.5) (0, 0) (0, 0) (0, 0) 3 (0, 0) (0, 0) (0, 0) (0, 0, 0) (－0.05, 0.04) (0.03, －0.4) (－0.02, 0.1) 4 (0, －0.02) (0.02, 0.1) (－0.03, 0) (0.03, 0.08, 2.5) (－0.05, 0.04) (0.03, －0.4) (－0.02, 0.1) 图 6给出了4种情况下的视线角速度曲线，其中实线表示忽略所有误差测量得到的结果，点划线是忽略陀螺安装误差的结果，长虚线是忽略框架轴系误差的结果，带“+”实线是综合考虑各装调误差得到的结果。图 7是图 6的局部放大。
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图 6 仿真结果比较图Figure 6. Comparison with simulation results (solid line shows the result of neglecting all errors; dash dot line shows the result of neglecting alignment error of gyros; dash line shows the result of neglecting axis system deviation; solid line with "+" shows the result of considering all errors)仿真试验结果表明，对装调误差进行补偿，可以提高视线角速度测量的精度。忽略装调误差时，测量计算的视线角速度较理论值最大偏差为4.08°/s；仅对框架轴系误差补偿时，视线角速度最大偏差减小到2.53°/s；仅对陀螺安装误差时，视线角速度最大偏差减小到1.49°/s；综合考虑各装调误差进行补偿，视线角速度最大偏差进一步减小到1.18°/s。总体来看，陀螺敏感轴交叉耦合对视线角速度精度的影响较框架轴系误差更显著。
5. 结论
本文系统研究了框架和陀螺均存在装调误差时，三自由度框架式红外视线角速度的计算方法，并进行仿真分析。结果表明，在计算视线角速度时如果对误差进行补偿，可以提高视线角速度的测量精度。在提高线角速度测量精度方面，补偿陀螺敏感轴交叉耦合的效果比补偿框架轴系偏差更显著。所以陀螺敏感轴交叉耦合对视线角速度的影响在各装调误差中最大。此结果对新型框架式稳定平台系统总体设计时的误差指标分配有重要的参考价值。
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图 1 电缆接头表层红外温度特征采集示意图
Figure 1. Schematic diagram of collecting infrared temperature characteristics on the surface of cable joint
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图 2 深度双隐层自编码极限学习机网络模型
Figure 2. Deep two-hidden layer autoencoder extreme learning machine network model
表 1 各算法寻优结果统计
Table 1 Statistics of optimization results for each algorithm
Function Statistical result IQWFA QWPA QGA QBA f1(x) Optimal value 0.0086 0.0183 1.4461 0.9954 Mean value 0.1857 0.7629 16.1084 3.5226 Standard deviation 0.1035 0.1579 3.9382 1.0634 f2(x) Optimal value 0.0310 0.2882 2.9779 0.3292 Mean value 3.1861 5.9860 36.0357 8.7531 Standard deviation 1.0023 2.0500 8.1559 3.2950 f3(x) Optimal value 0.1216 0.1136 5.1347 0.1347 Mean value 1.9393 2.3087 23.2533 3.5533 Standard deviation 0.3821 0.8211 13.0955 0.8554 
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表 2 不同模型测试结果
Table 2 Test results of different model
DS Test item RF SHD-RF DHD-RF Lonosphere (L, T) (0, 386) (3, 265) (3, 307) Test precision/% 89.23 92.02 96.45 Shuttle (L, T) (0, 521) (5, 373) (4, 419) Test precision /% 90.52 93.04 98.31 USPS (L, T) (0, 603) (5, 570) (6, 606) Test precision/% 90.81 95.61 98.35
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表 3 诊断精确度和召回率统计
Table 3 Diagnostic accuracy and recall rate statistics
Method Ref.[12] Ref.[13] Ours Index ${P_{{\text{RE}}}}$ ${R_{{\text{EC}}}}$ ${P_{{\text{RE}}}}$ ${R_{{\text{EC}}}}$ ${P_{{\text{RE}}}}$ ${R_{{\text{EC}}}}$ Normal 90.3% 92.0% 92.8% 94.5% 96.0% 96.0% Overhaul 88.5% 87.3% 90.2% 91.7% 92.5% 93.0% Replace 91.5% 90.4% 94.5% 93.2% 95.7% 94.2% Fault 93.0% 94.5% 95.0% 96.5% 97.4% 98.4% Mean 90.8% 91.1% 93.1% 94.0% 95.4% 95.4% SD 1.65% 2.61% 1.88% 1.76% 1.79% 2.03%
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