基于FAHP的核电用不锈钢焊丝工艺性综合量化评价

邹小平; 姜英龙; 朱旭; 魏超; 徐锴; 郭枭; 于可心

doi:10.7512/j.issn.1001-2303.2022.07.18

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基于FAHP的核电用不锈钢焊丝工艺性综合量化评价
Comprehensive Quantitative Evaluation of Stainless Steel Welding Wire Processability for Nuclear Power Based on FAHP
纸质出版日期： 2022-07-25 ，
DOI： 10.7512/j.issn.1001-2303.2022.07.18

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引用
邹小平，姜英龙，朱旭，等.基于FAHP的核电用不锈钢焊丝工艺性综合量化评价［J］.电焊机，2022，52（7）：121-127.

ZOU Xiaoping, JIANG Yinglong, ZHU Xu, et al.Comprehensive Quantitative Evaluation of Stainless Steel Welding Wire Processability for Nuclear Power Based on FAHP[J].Electric Welding Machine, 2022, 52(7): 121-127.
邹小平，姜英龙，朱旭，等.基于FAHP的核电用不锈钢焊丝工艺性综合量化评价［J］.电焊机，2022，52（7）：121-127. DOI： 10.7512/j.issn.1001-2303.2022.07.18.

ZOU Xiaoping, JIANG Yinglong, ZHU Xu, et al.Comprehensive Quantitative Evaluation of Stainless Steel Welding Wire Processability for Nuclear Power Based on FAHP[J].Electric Welding Machine, 2022, 52(7): 121-127. DOI： 10.7512/j.issn.1001-2303.2022.07.18.

基于FAHP的核电用不锈钢焊丝工艺性综合量化评价 Comprehensive Quantitative Evaluation of Stainless Steel Welding Wire Processability for Nuclear Power Based on FAHP 1 first-author 邹小平（1975—），男，硕士研究生，主要从事焊接材料研发和焊接工艺的研究工作。邹小平（1975—），男，硕士研究生，主要从事焊接材料研发和焊接工艺的研究工作。 2 1 2 2 2 corresp 郭　枭，高级工程师。E-mail：guoxiaogarden@163.com。郭　枭，高级工程师。E-mail：guoxiaogarden@163.com。 guoxiaogarden@163.com 2 中广核工程有限公司,广东深圳 518124 中广核工程有限公司,广东深圳 518124 China Nuclear Power Engineering Co., Ltd., Shenzhen 518124, China China Nuclear Power Engineering Co., Ltd., Shenzhen 518124, China 哈尔滨焊接研究院有限公司,黑龙江哈尔滨 150028 哈尔滨焊接研究院有限公司,黑龙江哈尔滨 150028 Harbin Welding Institute Co., Ltd., Harbin 150028, China Harbin Welding Institute Co., Ltd., Harbin 150028, China 近年来焊接材料的焊接工艺稳定性受到了广泛的关注，对焊材的工艺性一般依据经验进行感性评价，缺乏客观依据，为此对焊丝焊道成形质量进行综合量化评价，对于设计方、焊材研制单位、制造厂意义重大。本文基于模糊层次分析法（Fuzzy Analytical Hierarchy Process ，FAHP），建立不锈钢焊丝焊道成形质量综合评价体系，包括了焊道尺寸、焊道颜色、焊道直线度三个一级指标，并建立相对应的二、三级评价指标，权重确定重点突出成形稳定性，建立了优先关系矩阵，对优先关系矩阵进行加性一致性改造成模糊一致矩阵，计算出各指标的权重向量，再次依托TS模糊模型，根据底层采样的范围确定隶属度函数对采样数据进行层层计算，最终实现了综合量化评价，并设计试验对模型进行了验证，对评价结果进行了最大隶属度原则有效性检验，最终结果表明：四个厂家的焊道成形质量隶属“优+良”的程度由高到低排序为2#、3#、1#、4#。 In recent years, the welding process stability of welding materials has received extensive attention. The processability of welding material is generally evaluated by experience without objective basis. Therefore, comprehensive quantitative evaluation of welding wire weld bead quality is of great significance to the designers, welding materials development units and manufacturers. Based on the Fuzzy Analytical Hierarchy Process (FAHP) method, a comprehensive evaluation system is established for the weld bead quality of stainless steel welding wire, including three first-grade index of weld bead size, bead color and bead straightness, and corresponding second-grade and third-grade evaluation index are also established. The weight determination focuses on forming stability, and the priority relationship matrix is established. The priority relationship matrix is transformed into a fuzzy consistent matrix with additive consistency, and the weight vectors of each index are calculated. Relying on the TS fuzzy and according to the scope of the bottom layer sampling model, the membership function is determined, and the sampled data is calculated layer by layer, and finally a comprehensive quantitative evaluation is realized. The model is tested and verified by design tests, and the evaluation results are tested for the validity of the maximum membership principle. The result shows that the bead forming quality of the four manufacturers is ranked 2#, 3#, 1#, 4# in descending order of "excellent + good". 模糊层次分析法不锈钢焊丝量化评价成形质量 fuzzy analytic hierarchy process stainless steel welding wire quantitative evaluation forming quality 前言 1 焊接工艺性作为焊缝质量十分关键的影响因素，会直接影响接头的完整性，并对焊接构件的服役性能造成重要影响，是反映焊接质量的一个重要考察指标。焊材焊接工艺性受焊接材料、焊接电源、焊接工艺窗口、试验方法、焊工技能等多因素交互影响，焊道最终的成形性能会直接反应焊接材料的工艺稳定性［ 1 1 - 2 2 1-2 ］。目前，针对焊道成形的焊接工艺性研究大多数停留在经验阶段，尚无满足工程需求的综合定量化评价标准，缺乏有效、可靠的定量化评价方法。GB/T 25776《焊接材料焊接工艺性能评价方法》中包含的评价指标大多数为单项，未提供多指标综合性量化评价方法。国内外对于焊材工艺性的评价已开展了一定研究，在焊接材料工艺质量评价方面，中北大学与德国汉诺威大学材料连接焊接工艺研究中心合作开发了汉诺威弧焊质量分析系统，实现了焊接材料工艺质量的定量化评价［ 3 3 ］。在焊条工艺性评价方面，太原理工大学李亮玉等人应用模糊数学原理建立了焊条工艺性能综合评判数学模型，选取了稳弧性、脱渣性、焊缝成形、熔化系数、飞溅、粉尘五个指标对焊条工艺性进行综合评价［ 4 4 ］。在焊接电弧稳定性方面，日本大阪大学Masaya Shigeta等人研究了基于图像处理的焊条电弧焊（Shileded Metal Arc Welding，SMAW）对电弧稳定性和焊接飞溅产生的定量评价，采用二值化图像中白色像素的计数方法对焊接飞溅的数量和大小进行评价［ 5 5 ］。在采用层次分析法进行工艺性评价方面，安纳马莱大学的V. Balasubramanian等人采用层次结构模型通过稀释率对碳钢采用焊条电弧焊（Shileded Metal Arc Welding，SMAW）、熔化极气体保护电弧焊（Gas Metal Arc Welding，GMAW）、钨极气体保护电弧焊（Gas Tungsten Arc Welding，GTAW）、埋弧焊（Submerged Arc Welding，SAW）、等离子弧焊（Plasma Arc Welding，PAW）方法的堆焊工艺性能进行定量和定性的研究［ 6 6 ］。装甲兵工程学院孟凡军等人采用层次分析法理论，与实际焊接经验相结合，建立了一种评价焊道表面成形质量的评价体系［ 7 7 ］。虽然国内外相关学者对焊材焊接工艺性的评价做了相关研究，但大多采用部分主要指标进行评价，考虑因素不够全面，没有进行全面、综合的量化评价。核电行业作为高科技产业，其设计与制造的技术含量高，质量要求严，焊接工艺性尤为重要，影响核级焊材焊接工艺性的因素繁多。为实现核岛主设备核级焊材焊接工艺性全面性、综合性的量化评价，文中以核电用不锈钢GTAW焊丝为研究对象，建立了焊接工艺性评价体系，避免了人为主观因素，解决了影响因素复杂的问题，通过建立FAHP模型，着重考虑焊接过程稳定性，提出了焊道颜色、焊道直线度的量化评价指标，实现了核电用不锈钢GTAW焊丝焊接工艺性量化综合评价，并设计试验对模型的有效性、科学性进行了验证。 FAHP 模型建立 1 核电用不锈钢焊丝工艺性评价体系建立 2 焊接工艺性的影响因素众多且复杂，按照阶段过程可将焊丝工艺性分解为焊丝本征指标、焊接过程稳定性、最终焊道成形三个方面。其中焊丝本征指标包括翘距、松弛直径、直径公差等，焊接过程稳定性包括电弧稳定性、熔滴过渡形式等，二者均会直接或间接地影响焊道最终成形。因此，文中以最终的焊道成形为研究重点。按照焊道成形影响因素的重要性程度及其考察指标，通过FAHP算法对不锈钢焊丝焊道成形进行量化评价，建立了不锈钢焊丝焊道成形评价体系，如图1 图1 所示。体系中一级指标包括焊道尺寸、焊道颜色和直线度三个，其中焊道尺寸由熔宽、熔深、余高、接触角四个二级指标评价，焊道颜色由颜色类型、面积占比评价，直线度由拐点、极差评价，熔宽、熔深、余高、接触角二级指标由对应的均值、方差三级指标评价。各级指标建立优先关系矩阵，采用加性一致性将优先关系矩阵转化为模糊一致矩阵，计算各级指标的权重向量，创建底层指标的隶属度函数，通过向量计算得出最终评价焊道成形的向量，为焊接工艺性提供量化数值，为决策提供依据［ 8 8 - 9 9 8-9 ］。权重分配与计算 2 对于核电用不锈钢焊丝，焊缝成形的主要关注点为焊接接头的几何尺寸、焊道边缘的整齐一致程度、焊道外观颜色三个方面，采用模糊一致的方法，建立了0.1~0.9的优先关系矩阵（也称模糊互补矩阵）。对于不锈钢焊丝焊道成形构建的一级指标优先关系矩阵 a （见表1 表1 ），焊道尺寸的二级指标优先关系矩阵 b 1 、焊道颜色的二级指标优先关系矩阵 b 2 、直线度的二级指标优先关系矩阵 b 3 ，熔宽的三级指标优先关系矩阵 c 1 、熔深的三级指标优先关系矩阵 c 2 、余高的三级指标优先关系矩阵 c 3 、接触角的三级指标优先关系矩阵 c 4 ，根据各指标对于焊接质量影响的大小建立优先关系矩阵，表1 表1 中数值为行指标相对于列指标的模糊关系，且相对数值之和为1。一级指标焊道尺寸焊道颜色直线度焊道尺寸 0.5 0.1 0.3 焊道颜色 0.9 0.5 0.6 直线度 0.7 0.4 0.5 a <math id="M1"><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.5</mn></mtd><mtd><mn mathvariant="normal">0.1</mn></mtd><mtd><mn mathvariant="normal">0.3</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.9</mn></mtd><mtd><mn mathvariant="normal">0.5</mn></mtd><mtd><mn 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<math display="block" id="M10"><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi><mi>j</mi><mtext> </mtext></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn><mi>n</mi></mrow></mfrac><mo>+</mo><mn mathvariant="normal">0.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182081&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182076&type= 24.21466637 7.61999989 α <math id="M11"><mtext> </mtext><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.5</mn></mtd><mtd><mn mathvariant="normal">0.317</mn></mtd><mtd><mn mathvariant="normal">0.383</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.683</mn></mtd><mtd><mn mathvariant="normal">0.5</mn></mtd><mtd><mn mathvariant="normal">0.567</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.617</mn></mtd><mtd><mn mathvariant="normal">0.433</mn></mtd><mtd><mn mathvariant="normal">0.5</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182090&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182086&type= 39.79333496 13.03866673 再根据式（2）式（2）对各级指标进行权重向量的计算。 <math display="block" id="M12"><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn><mi>a</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi><mi>a</mi></mrow></mfrac><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182097&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182094&type= 39.45466614 7.28133297 计算可得一级指标的权重向量为［0.533 0.167 0.300］，其中第一列为焊道尺寸占比，第二列为焊道颜色占比，第三列为直线度占比，各级指标权重向量计算结果如表2 表2 所示。指标等级权重向量一级指标［0.533 0.167 0.300］焊道尺寸的二级指标［0.317 0.217 0.200 0.267］直线度的二级指标［0.55 0.45］焊道颜色的二级指标［0.6 0.4］熔宽的三级指标［0.35 0.65］熔深的三级指标［0.4 0.6］余高的三级指标［0.45 0.55］接触角的三级指标［0.55 0.45］隶属度函数的确定与评价 2 隶属度函数采用相同规范下采样指标均覆盖在本隶属度函数内，各级指标建立优、良、中、劣、差五个评价。本次试验采用TS模糊模型，采用常用的三角形分布的隶属度函数［ 11 11 - 13 13 11-13 ］，该方法可应用于焊接质量评价领域，但由于其主要针对带极堆焊，考察因素与气体保护焊有所不同，如图2 图2 所示。其中横坐标为最底层采样数据的集合范围，纵坐标为隶属程度，同一个数值隶属程度之和为1。量化评价指标计算 1 试验采用TIG自动焊方法，在Q345B钢板上依次进行单道堆焊，在相同工艺参数下采用四个厂家规格为Ф1.2 mm的ER309L焊丝进行单道焊接，分别标记为1#、2#、3#、4#。焊接后对焊道颜色进行拍照，如图3 图3 所示，图中从上到下依次为1#~4#焊丝的焊道成形。对照片采用求积仪进行颜色面积的测量，导入绘图软件绘制焊道边缘的理想直线，测量焊道边缘与理想直线之间的拐点数量和最大偏差值，焊道颜色和直线度的指标采样结果分别如表3 表3 、表4 表4 所示。观察图3 图3 中四个焊道的外观形貌，根据经验可以确定2#焊道形貌最佳，但是1#、3#、4#焊道根据个人经验不同可能得出不同的结果，无法对其进行客观准确的评价。焊道编号颜色占比/% 1# 五彩 93.03 2# 五彩 100 3# 五彩 91.08 4# 五彩 96.12 焊道编号拐点数量/个最大偏差值/mm 1# 12 2.25 2# 3 1.47 3# 5 2.08 4# 14 0.92 焊道尺寸对于焊接质量有很大影响，从外观上无法准确获得熔深信息，因此对每个焊道进行解剖，每个焊道均取5个横截面金相试件，采用体式显微镜分别测量每个焊道横截面的熔宽、熔深、余高、接触角，其中接触角为焊道边缘与母材之间的夹角。测量的四个焊道尺寸5组金相图中的1组如图4 图4 所示，对采样后的数据进行均值和方差的计算，其结果分别如表5 表5 、表6 表6 所示。焊道编号指标均值/（°）方差/% 1# 4 接触角 131.44 186.40 2# 154.26 18.63 3# 130.87 51.24 4# 134.89 69.30 焊道编号指标均值/mm 方差/% 1# 4 熔宽 8.10 0.11 2# 11.20 0.08 3# 8.39 0.05 4# 8.33 0.61 1# 4 熔深 1.32 0.01 2# 0.78 0.01 3# 1.04 0.01 4# 1.56 0.07 1# 4 余高 1.93 0.04 2# 1.49 0.00 3# 1.96 0.01 4# 1.82 0.03 根据熔宽、熔深、余高、接触角的隶属度函数和对应的三级指标的权重向量［0.35 0.65］、［0.4 0.6］、［0.45 0.55］、［0.55 0.45］，计算得出的三级指标的评价向量为C 1 、C 2 、C 3 、C 4 ，其中每列分别对应优、良、中、劣、差，每行分别对应熔宽、熔深、余高、接触角。 <math display="block" id="M13"><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.364</mn></mtd><mtd><mn mathvariant="normal">0.286</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.040</mn></mtd><mtd><mn mathvariant="normal">0.310</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.360</mn></mtd><mtd><mn mathvariant="normal">0.314</mn></mtd><mtd><mn mathvariant="normal">0.326</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.346</mn></mtd><mtd><mn mathvariant="normal">0.654</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.148</mn></mtd><mtd><mn mathvariant="normal">0.402</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.45</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182172&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182170&type= 67.14067078 17.86466599 <math display="block" id="M14"><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.671</mn></mtd><mtd><mn mathvariant="normal">0.329</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.360</mn></mtd><mtd><mn mathvariant="normal">0.240</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.299</mn></mtd><mtd><mn mathvariant="normal">0.101</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">1.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.192</mn></mtd><mtd><mn mathvariant="normal">0.258</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.363</mn></mtd><mtd><mn mathvariant="normal">0.187</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182175&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182174&type= 67.14067078 17.86466599 <math display="block" id="M15"><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.520</mn></mtd><mtd><mn mathvariant="normal">0.130</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.156</mn></mtd><mtd><mn mathvariant="normal">0.194</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.360</mn></mtd><mtd><mn mathvariant="normal">0.240</mn></mtd><mtd><mn mathvariant="normal">0.176</mn></mtd><mtd><mn mathvariant="normal">0.224</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.330</mn></mtd><mtd><mn mathvariant="normal">0.292</mn></mtd><mtd><mn mathvariant="normal">0.378</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.183</mn></mtd><mtd><mn mathvariant="normal">0.391</mn></mtd><mtd><mn mathvariant="normal">0.426</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182179&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182176&type= 67.14067078 17.86466599 <math display="block" id="M16"><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0364</mn></mtd><mtd><mn mathvariant="normal">0.418</mn></mtd><mtd><mn mathvariant="normal">0.218</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.329</mn></mtd><mtd><mn mathvariant="normal">0.191</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.764</mn></mtd><mtd><mn mathvariant="normal">0.236</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.481</mn></mtd><mtd><mn mathvariant="normal">0.201</mn></mtd><mtd><mn mathvariant="normal">0.318</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182183&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182181&type= 67.14067078 17.86466599 根据焊道尺寸、焊道颜色和直线度的二级指标权重向量［0.317 0.217 0.200 0.267］、［0.55 0.45］、［0.6 0.4］和三级指标计算得出的评价向量相乘得到二级指标的评价向量为B 1 、B 2 、B 3 、B 4 ，其中每列分别对应优、良、中、劣、差，每行分别对应焊道尺寸、焊道颜色、直线度。 <math display="block" id="M17"><msub><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.233</mn></mtd><mtd><mn mathvariant="normal">0.335</mn></mtd><mtd><mn mathvariant="normal">0.201</mn></mtd><mtd><mn mathvariant="normal">0.013</mn></mtd><mtd><mn mathvariant="normal">0.218</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.028</mn></mtd><mtd><mn mathvariant="normal">0.972</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.044</mn></mtd><mtd><mn mathvariant="normal">0.506</mn></mtd><mtd><mn mathvariant="normal">0.450</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182187&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182185&type= 67.14067078 13.03866673 <math display="block" id="M18"><msub><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.542</mn></mtd><mtd><mn mathvariant="normal">0.225</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.162</mn></mtd><mtd><mn mathvariant="normal">0.072</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.400</mn></mtd><mtd><mn mathvariant="normal">0.600</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.286</mn></mtd><mtd><mn mathvariant="normal">0.282</mn></mtd><mtd><mn mathvariant="normal">0.432</mn></mtd><mtd><mn mathvariant="normal">0.450</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182191&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182190&type= 67.14067078 13.03866673 <math display="block" id="M19"><msub><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.357</mn></mtd><mtd><mn mathvariant="normal">0.256</mn></mtd><mtd><mn mathvariant="normal">0.227</mn></mtd><mtd><mn mathvariant="normal">0.098</mn></mtd><mtd><mn mathvariant="normal">0.061</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.924</mn></mtd><mtd><mn mathvariant="normal">0.076</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.110</mn></mtd><mtd><mn mathvariant="normal">0.440</mn></mtd><mtd><mn mathvariant="normal">0.102</mn></mtd><mtd><mn mathvariant="normal">0.348</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182195&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182193&type= 67.14067078 13.03866673 <math display="block" id="M20"><msub><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.352</mn></mtd><mtd><mn mathvariant="normal">0.257</mn></mtd><mtd><mn mathvariant="normal">0.217</mn></mtd><mtd><mn mathvariant="normal">0.069</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.193</mn></mtd><mtd><mn mathvariant="normal">0.807</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.000</mn></mtd><mtd><mn mathvariant="normal">0.348</mn></mtd><mtd><mn mathvariant="normal">0.521</mn></mtd><mtd><mn mathvariant="normal">0.131</mn></mtd><mtd><mn mathvariant="normal">0.000</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182198&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182197&type= 67.14067078 13.03866673 根据一级指标的权重向量和二级指标计算得出的评价向量相乘得到一级指标的最终评价向量为A 1 、A 2 、A 3 、A 4 ，向量中数值依次对应优、良、中、劣、差的隶属程度。 <math display="block" id="M21"><msub><mrow><mi mathvariant="normal">A</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.129</mn></mtd><mtd><mn mathvariant="normal">0.354</mn></mtd><mtd><mn mathvariant="normal">0.259</mn></mtd><mtd><mn mathvariant="normal">0.142</mn></mtd><mtd><mn mathvariant="normal">0.116</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182202&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182200&type= 67.39466858 3.72533321 <math display="block" id="M22"><msub><mrow><mi mathvariant="normal">A</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.442</mn></mtd><mtd><mn mathvariant="normal">0.305</mn></mtd><mtd><mn mathvariant="normal">0.130</mn></mtd><mtd><mn mathvariant="normal">0.086</mn></mtd><mtd><mn mathvariant="normal">0.038</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182206&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182205&type= 67.39466858 3.72533321 <math display="block" id="M23"><msub><mrow><mi mathvariant="normal">A</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.223</mn></mtd><mtd><mn mathvariant="normal">0.423</mn></mtd><mtd><mn mathvariant="normal">0.164</mn></mtd><mtd><mn mathvariant="normal">0.157</mn></mtd><mtd><mn mathvariant="normal">0.033</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182213&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182209&type= 67.39466858 3.72533321 <math display="block" id="M24"><msub><mrow><mi mathvariant="normal">A</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mn mathvariant="normal">0.032</mn></mtd><mtd><mn mathvariant="normal">0.427</mn></mtd><mtd><mn mathvariant="normal">0.293</mn></mtd><mtd><mn mathvariant="normal">0.155</mn></mtd><mtd><mn mathvariant="normal">0.037</mn></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182217&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182216&type= 67.39466858 3.72533321 结果分析 1 针对四个厂家的ER309L焊丝最终输出的评价等级与评价结果如图5 图5 所示，根据常用的最大隶属度原则，可判定2#焊道隶属“优”的程度最高，1#、3#、4#焊道均隶属“良”的程度最高，隶属度由高到低排序为4#、3#、1#，这与实际情况不符，无法按照最大隶属度原则实现1#、3#、4#的比较，这与基于经验对焊道成形的判断结果一致，进一步证实了在四个焊道中2#是最优。虽然根据最大隶属度原则可以简单方便的得出结论，但丢失的信息较多，有必要对根据最大隶属度原则得出的结论进行有效性验证，因此采用最大隶属度有效性验证方法对1#、3#、4#评价结果进行验证［ 14 14 ］： <math display="block" id="M25"><mi>β</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow><mrow><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mrow></mfrac><mo>;</mo><mi>γ</mi><mo>=</mo><mfrac><mrow><mi>s</mi><mi>e</mi><mi>c</mi><mfenced open="{" close="}" separators="|"><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow><mrow><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mrow></mfrac><mo>;</mo><mo stretchy="false">(</mo><mi>j</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi mathvariant="normal">n</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182220&type= 59.18199921 11.51466751 式中　 β 和 γ 分别表示最大向量和次大向量占各分量总和的比例， <math id="M26"><mi>β</mi><mo>∈</mo><mo stretchy="false">[</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>,</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182226&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182224&type= 13.46199989 7.28133297 ， <math id="M27"><mi>γ</mi><mo>∈</mo><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>,</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182231&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182228&type= 13.46199989 7.19666624 ，令 <math display="block" id="M28"><mi>β</mi><mi>'</mi><mo>=</mo><mfrac><mrow><mi>β</mi><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mi>β</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><mo>;</mo><mi>γ</mi><mi>'</mi><mo>=</mo><mfrac><mrow><mi>γ</mi><mo>-</mo><mn mathvariant="normal">0</mn></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>-</mo><mn mathvariant="normal">0</mn></mrow></mfrac><mo>=</mo><mn mathvariant="normal">2</mn><mi>γ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182236&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182234&type= 56.55733109 15.74800014 定义 <math id="M29"><mi>α</mi><mo>=</mo><mi>β</mi><mi>'</mi><mo>/</mo><mi>γ</mi><mi>'</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182238&type= 11.17599964 3.38666677 ， <math id="M30"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182244&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182241&type= 1.94733346 2.62466669 越大，最大隶属度原则越有效，一般情况下，认为 <math id="M31"><mi>α</mi><mo><</mo><mn mathvariant="normal">0.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182247&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182245&type= 9.90600014 2.62466669 ，不宜采用最大隶属度原则。对于1#， <math id="M32"><mi>α</mi><mo>=</mo><mn mathvariant="normal">0.37</mn><mo><</mo><mn mathvariant="normal">0.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182249&type= 19.64266586 2.62466669 ，不宜采用最大隶属度原则，对于3#， <math id="M33"><mi>α</mi><mo>=</mo><mn mathvariant="normal">0.63</mn><mo>></mo><mn mathvariant="normal">0.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182256&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182254&type= 19.64266586 2.62466669 ，采用最大隶属度原则得出的结论比较有效，对于4#， <math id="M34"><mi>α</mi><mo>=</mo><mn mathvariant="normal">0.48</mn><mo><</mo><mn mathvariant="normal">0.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182260&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33182258&type= 19.64266586 2.62466669 不宜采用最大隶属度原则。在1#、3#、4#焊丝焊接外形质量相差不大的情况下，仅凭经验无法给出准确评价。从次大隶属度分布来看，1#、2#、3#、4#分别对应中、良、优、中。为实现四个厂家焊丝的综合比较排序，采用优的隶属度和优、良的隶属度合并加和后评价对比结果，如图6 图6 所示，其结果一致，从好到差的结果依次为2#、3#、1#、4#。通过FAHP的方法，可以在相同条件下给出其量化的评价指标，并且可以按照输出向量优的结果对焊道优选提供支撑，后续可进一步优化各参数集合的设定，使得评价更加合理。焊道评价主要以优、良、中、劣、差五个等级进行评价，优先采用优的评价，在相同数值情况下采用优和良之和进行评价。结论 1 （1）建立了核电用不锈钢焊丝工艺性量化评价FAHP模型，模型考虑了焊道尺寸、焊道颜色、直线度三个一级指标，并对各级指标细化分解为二、三级指标。（2）试验模型结果表明，模型对不同厂家焊丝的工艺性评价有较好的效果，能够实现最终焊道成形的综合量化评价。（3）根据最大隶属度原则判定，除2#隶属于“优”，1#、3#、4#均隶属于“良”，按照量化指标优、良综合隶属度排序，依次为2#、3#、1#、4#。参考文献 GAO Xiangdong ， WANG Lin ， CHEN Ziqin ， et al . 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