【论文精选】基于参数学习的燃气调压器故障诊断网络优化
<h1 style="color: black; text-align: left; margin-bottom: 10px;"><a style="color: black;"><strong style="color: blue;"><strong style="color: blue;"><span style="color: black;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbGtZ07J2ia33XNxV8nlXMz7peHdUiasEAWo0C6DAciatvInR3gk6ibTClyFfuzXrjRk7A6Ht5BorKxcCw/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></span></strong></strong></a></h1>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">官网注册后</span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">http://www.gasheat.cn</span></strong></span></a></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">免费下载论文</span></strong></span></p><strong style="color: blue;"><span style="color: black;"><a style="color: black;">http://www.gasheat.cn/Periodical/index.html</a></span></strong>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">作</span><span style="color: black;">者：</span><span style="color: black;">田露，郝学军，李琪</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">第1</span>作者单位：北京建筑大学 环境与能源工程学院</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">摘自《煤气与热力》2022年7月刊</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;">参考文献示例</strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">田露，郝学军，李琪</span>.</span><span style="color: black;"><span style="color: black;"><span style="color: black;"><span style="color: black;">基于参数学习的燃气调压器故障诊断网络优化</span></span></span>［J］.</span><span style="color: black;">煤气与热力，<span style="color: black;">2022，42（7）</span>：B31-B36.</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;"><span style="color: black;">关联</span>推广</strong></p>1<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">调压器、调压站</span></strong></span></a></p>2<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><strong style="color: blue;"><a style="color: black;"><strong style="color: blue;"><span style="color: black;">检测和抢险设备</span></strong></a></strong></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">1 <span style="color: black;">概述</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">随着我国城镇燃气行业<span style="color: black;">连续</span>快速发展，政府、社会对燃气输配系统的安全运营、用户体验、节能环保提出了更高的<span style="color: black;">需求</span></span><span style="color: black;"><span style="color: black;">［</span>1<span style="color: black;">］</span></span><span style="color: black;">。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">燃气</span><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">调压器</span></strong></span></a><span style="color: black;">运行故障直接影响到下游供气压力的稳定，轻则<span style="color: black;">导致</span>供气压力<span style="color: black;">反常</span><span style="color: black;">引起</span>工业用户<span style="color: black;">制品</span>报废、民用燃气设备运行故障，重则<span style="color: black;">导致</span>停止供气或超压放散，停气检修后的恢复供气过程<span style="color: black;">亦</span>可能产生燃气</span><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">泄漏</span></strong></span></a><span style="color: black;">、火灾或爆炸事故</span><span style="color: black;"><span style="color: black;">［</span>2<span style="color: black;">］</span></span><span style="color: black;">。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">高中压</span><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">调压器</span></strong></span></a><span style="color: black;">的故障诊断、<span style="color: black;">检测</span>、保养、<span style="color: black;">守护</span>管理等<span style="color: black;">针对</span>排除潜在的安全隐患<span style="color: black;">拥有</span>重大<span style="color: black;">道理</span>。<span style="color: black;">因为</span>高中压燃气调压器结构<span style="color: black;">繁杂</span>、与管网相互影响、缺少已有故障案例</span><span style="color: black;"><span style="color: black;">［</span>3<span style="color: black;">］</span></span><span style="color: black;"><span style="color: black;">，本文利用专家先验知识，<span style="color: black;">创立</span>高中压燃气调压器贝叶斯网络模型。在该模型<span style="color: black;">基本</span>上，应用最大期望</span>EM<span style="color: black;">参数学习的<span style="color: black;">办法</span>优化，<span style="color: black;">最后</span>得到更<span style="color: black;">恰当</span>的检修<span style="color: black;">次序</span>，并与<span style="color: black;">实质</span>案例进行比较验证。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">2 <span style="color: black;"><span style="color: black;">创立</span>贝叶斯网络故障诊断拓扑模型</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">贝叶斯网络结构学习即利用样本数据和先验信息，找到与样本数据匹配程度最高的贝叶斯网络拓扑结构。再依靠<span style="color: black;">行业</span>专家对<span style="color: black;">科研</span>对象的整体把握，得出各<span style="color: black;">原因</span>之间的相互<span style="color: black;">功效</span>关系，统计先验信息，得到调压器<span style="color: black;">显现</span><span style="color: black;">区别</span>故障表征时，对应<span style="color: black;">出现</span>故障<span style="color: black;">原由</span>的统计概率，以下简<span style="color: black;">叫作</span>统计概率。搭建贝叶斯网络，结合该网路，得出</span><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">调压器</span></strong></span></a><span style="color: black;"><span style="color: black;">显现</span><span style="color: black;">区别</span>故障表征时，对应<span style="color: black;">出现</span>故障<span style="color: black;">原由</span>的计算概率，以下简<span style="color: black;">叫作</span>计算概率。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">2.1 <span style="color: black;">获取统计概率及<span style="color: black;">要求</span>概率</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">在诊断网络中，子节点<span style="color: black;">暗示</span>顶层故障，即故障表征；父节点<span style="color: black;">暗示</span>底层故障，即故障<span style="color: black;">原由</span>。高中压调压器贝叶斯网络模型故障节点类型及名<span style="color: black;">叫作</span>见表</span>1<span style="color: black;">。本文中的</span>F</span><span style="color: black;">1</span><span style="color: black;"><span style="color: black;">，</span>F</span><span style="color: black;">2</span><span style="color: black;"><span style="color: black;">，</span>F</span><span style="color: black;">3</span><span style="color: black;"><span style="color: black;">，</span></span><span style="color: black;">F</span><span style="color: black;">4</span><span style="color: black;"><span style="color: black;">，</span>X<span style="color: black;">1</span></span><span style="color: black;"><span style="color: black;">，…，</span></span><span style="color: black;">X</span><span style="color: black;">9</span><span style="color: black;">为复用变量，<span style="color: black;">暗示</span>事件<span style="color: black;">亦</span><span style="color: black;">暗示</span>随机变量。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">表</span>1 <span style="color: black;">高中压调压器贝叶斯网络模型故障节点类型及名<span style="color: black;">叫作</span></span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icds112WQoibCAV9Uv4C8nNRrkRfShes7nfpEXrPj5hicH9ibQVn1fVgBL3GQ/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">为<span style="color: black;">保证</span>安全，会对燃气</span><a style="color: black;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">调压器</span></strong></span></a><span style="color: black;"><span style="color: black;">进行<span style="color: black;">即时</span>检修及更换，现有故障案例样本较少。<span style="color: black;">因此呢</span>请<span style="color: black;">拥有</span>资质的燃气专家对调压器故障表征问题进行问卷填写，<span style="color: black;">按照</span>问卷结果，统计在<span style="color: black;">区别</span>故障表征<span style="color: black;">出现</span>的<span style="color: black;">要求</span>下故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的统计概率（以下简<span style="color: black;">叫作</span>统计概率），见图</span>1<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icds6xJnMb7Gasrb2DvHFd1OE2Rco9oa9VPFf0tWYniasRaxKUkJczgKIKA/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">图</span>1 <span style="color: black;"><span style="color: black;">区别</span>故障表征<span style="color: black;">出现</span>的<span style="color: black;">要求</span>下故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的统计概率</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">结合专家经验，对调压器故障<span style="color: black;">原由</span><span style="color: black;">出现</span>或不<span style="color: black;">出现</span>的<span style="color: black;">要求</span>下，故障表征<span style="color: black;">出现</span>的可能性进行赋值，填写在问卷中，<span style="color: black;">按照</span>问卷结果，得出在各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>或不<span style="color: black;">出现</span>的<span style="color: black;">要求</span>下故障表征<span style="color: black;">出现</span>的<span style="color: black;">要求</span>概率（以下简<span style="color: black;">叫作</span><span style="color: black;">要求</span>概率），见表</span>2~5<span style="color: black;">。表中</span>b</span><span style="color: black;">1</span><span style="color: black;">~
b</span><span style="color: black;">9</span><span style="color: black;"><span style="color: black;">为中间参数，</span>1<span style="color: black;"><span style="color: black;">暗示</span><span style="color: black;">出现</span>，</span>0<span style="color: black;"><span style="color: black;">暗示</span>不<span style="color: black;">出现</span>。<span style="color: black;">要求</span>概率用以<span style="color: black;">暗示</span>贝叶斯网络中各节点的<span style="color: black;">关联</span>程度，以下表格<span style="color: black;">包括</span>了<span style="color: black;">每一个</span>节点与其他节点之间存在依赖关系的所有<span style="color: black;">要求</span>概率</span></span><span style="color: black;"><span style="color: black;">［</span>3<span style="color: black;">］</span></span><span style="color: black;">。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">表</span>2 <span style="color: black;">调压器出口压力过高对应<span style="color: black;">要求</span>概率</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdspmPT4qasCB74Iia1plxecYkELD1NNpwWm0VuqVypKzj9KqSeibNiaBFBg/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">表</span>3 <span style="color: black;">调压器出口压力过低对应<span style="color: black;">要求</span>概率</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdsvWKjCSPgjnNwEIAKO1KwgPrTaWqDSM24nLxdYANKMUQLLIWwID3vPQ/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">表</span>4 <span style="color: black;">调压器喘振对应<span style="color: black;">要求</span>概率</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdspyniaxtY4ibxLko5TJ4IRFSwnBgOnc4QomL6r5jBKCbOUZhYbQGHA7vw/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">表</span>5 <span style="color: black;">调压器关闭不严对应<span style="color: black;">要求</span>概率</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdsIe1zn49ktRsqmkelOLgFnR0lJYbU7YtFJVnkv3txsRwficdujaUVIwQ/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">2.2 <span style="color: black;">搭建贝叶斯网络</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">按照</span>以上所有先验信息，得到映射关系，<span style="color: black;">创立</span>贝叶斯网络拓扑结构，高中压燃气调压器故障贝叶斯网络拓扑结构见图</span>2<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdspicvjbygt6HVx39hFY4bNGJAvgAPjly5wS0QSraAJ01pkLyvBcSeWLg/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">图</span>2 <span style="color: black;">高中压燃气调压器故障贝叶斯网络拓扑结构</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">按照</span>以上统计概率、<span style="color: black;">要求</span>概率及映射关系，运用</span>MATLAB<span style="color: black;">平台搭建高中压燃气调压器贝叶斯网络故障诊断结构，此为原贝叶斯网络故障诊断拓扑模型，将用于优化，以及后续生成若干组贝叶斯网络训练数据。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">3 <span style="color: black;">应用最大期望</span>EM<span style="color: black;">算法进行参数学习</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">故障诊断的关键是<span style="color: black;">精细</span>的贝叶斯网络建模，原贝叶斯网络的节点<span style="color: black;">要求</span>概率基于专家经验的赋值得到，存在<span style="color: black;">必定</span>主观性。<span style="color: black;">因此</span>需要利用故障案例训练数据集进行参数学习，对原贝叶斯网络模型进行修正，弥补依赖专家知识建模的不足</span><span style="color: black;"><span style="color: black;">［</span>4<span style="color: black;">］</span></span><span style="color: black;">。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">详细</span>方式为：输入原贝叶斯网络模型，基于参数学习<span style="color: black;">办法</span>，利用训练数据集，<span style="color: black;">经过</span></span>EM<span style="color: black;">算法更新优化<span style="color: black;">每一个</span>网络节点的<span style="color: black;">要求</span>概率，得到优化后贝叶斯网络，并输出更为准确的计算概率。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">3.1 <span style="color: black;">训练数据集的<span style="color: black;">形成</span></span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">经过</span>某燃气<span style="color: black;">机构</span>次高压调压站及高压调压站的检修台账统计数据得到若干组训练数据，<span style="color: black;">经过</span>原贝叶斯网络训练<span style="color: black;">亦</span>可得到若干组训练数据，对这些数据进行筛选和预处理，得到</span>1 000<span style="color: black;">组训练数据，<span style="color: black;">形成</span>训练数据集。每组数据<span style="color: black;">包括</span></span>13<span style="color: black;">个随机变量，即</span>4<span style="color: black;">个故障表征随机变量和</span>9<span style="color: black;">个故障<span style="color: black;">原由</span>随机变量，</span>1<span style="color: black;"><span style="color: black;">暗示</span><span style="color: black;">出现</span>，</span>0<span style="color: black;"><span style="color: black;">暗示</span>不<span style="color: black;">出现</span>。将训练数据集输入</span>EM<span style="color: black;">算法进行参数学习。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">3.2 <span style="color: black;">最大期望</span>EM<span style="color: black;">算法</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">贝叶斯网络的参数学习<span style="color: black;">指的是</span>确定网络结构后，<span style="color: black;">经过</span>合适的参数学习<span style="color: black;">办法</span>，利用训练数据集对节点间的概率依存关系进行训练，<span style="color: black;">调节</span>更新贝叶斯网络内在关系的节点<span style="color: black;">要求</span>概率</span><span style="color: black;"><span style="color: black;">［</span>5<span style="color: black;">］</span></span><span style="color: black;">。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">因为</span>燃气调压器故障诊断<span style="color: black;">拥有</span>重大安全<span style="color: black;">道理</span>，并且现实<span style="color: black;">要求</span>中，贝叶斯网络参数学习所需要的数据集很大可能会存在<span style="color: black;">区别</span>程度的数据缺失，为了学习结果的精确性，本文采用<span style="color: black;">拥有</span>迭代优化思想的最大期望</span>EM<span style="color: black;">算法。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">EM<span style="color: black;">算法整体是求解收敛到局部最优参数的过程，<span style="color: black;">重点</span>思想是先以某种方式初始化局部最优参数，再<span style="color: black;">经过</span>期望计算和最大化期望值两步迭代来<span style="color: black;">持续</span>地修正直到收敛</span></span><span style="color: black;"><span style="color: black;">［</span>6<span style="color: black;">］</span></span><span style="color: black;"><span style="color: black;">。<span style="color: black;">详细</span>应用为：</span>EM<span style="color: black;">算法输入为贝叶斯网络、训练数据集、收敛阈值；<span style="color: black;">首要</span><span style="color: black;">经过</span></span>E<span style="color: black;">步期望计算，<span style="color: black;">而后</span><span style="color: black;">经过</span></span>M<span style="color: black;">步最大化期望计划，再进行<span style="color: black;">持续</span>迭代优化的<span style="color: black;">过程</span>；<span style="color: black;">最后</span>输出为更新贝叶斯网络节点<span style="color: black;">要求</span>概率。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">从当前节点<span style="color: black;">要求</span>概率到下一代节点<span style="color: black;">要求</span>概率的计算<span style="color: black;">过程</span>如下。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">①</span>E<span style="color: black;">步期望计算</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">经过</span>概率分布函数，求出对数似然函数的期望值，数学表达式见文献［</span>6<span style="color: black;">］。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">②</span>M<span style="color: black;">步最大化期望计划</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">修改概率分布函数取值，使对数似然函数达到最大值的期望存在。<span style="color: black;">这儿</span><span style="color: black;">运用</span>最大似然估计，数学表达式见文献［</span>6<span style="color: black;">］。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;"><span style="color: black;">经过</span><span style="color: black;">持续</span>迭代<span style="color: black;">以上</span></span>2<span style="color: black;">个<span style="color: black;">过程</span>，进行参数的更新优化，<span style="color: black;">最后</span>得到更为准确的贝叶斯网络模型。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">在</span>MATLAB<span style="color: black;">平台中可<span style="color: black;">经过</span>调用最大期望和最大似然估计函数，完成<span style="color: black;">全部</span>参数学习的<span style="color: black;">创立</span>、求解和优化。寻优过程中，将<span style="color: black;">全部</span>贝叶斯网络所构建的条件概率（表</span>2~5<span style="color: black;">）代入</span>EM<span style="color: black;">算法中，进行<span style="color: black;">持续</span>迭代，寻找最优解</span></span><span style="color: black;"><span style="color: black;">［</span>7-8<span style="color: black;">］</span></span><span style="color: black;">。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">3.3 <span style="color: black;">全局联合树推理</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">为了<span style="color: black;">加强</span>运算速度，使</span>EM<span style="color: black;">算法能够有效应用，需要利用推理引擎机制，用来完成<span style="color: black;">全部</span>贝叶斯参数学习模型转换、细化和求解。在</span>EM<span style="color: black;">算法参数学习<span style="color: black;">基本</span>上，贝叶斯网络调用全局联合树推理引擎（</span>global_joint_inf_engine<span style="color: black;">）</span></span><span style="color: black;"><span style="color: black;">［</span>4<span style="color: black;">］</span></span><span style="color: black;">。其中转换和细化是将贝叶斯网络转换成一个次结构联合树，<span style="color: black;">经过</span>定义在联合树上的<span style="color: black;">信息</span>传递过程，进行概率计算。<span style="color: black;">信息</span>传递法使得<span style="color: black;">信息</span><span style="color: black;">能够</span>依次传遍联合树的所有子节点和父节点，并使联合树满足全局一致性。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">4 <span style="color: black;">结果分析</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">经过</span>统计概率结合优化后的<span style="color: black;">要求</span>概率，计算得出在故障表征<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率（以下简<span style="color: black;">叫作</span>计算概率），计算概率由大到小排序，<span style="color: black;">做为</span>故障节点定位<span style="color: black;">次序</span>。<span style="color: black;">经过</span>概率变化（统计概率与计算概率差值的绝对值）分析计算概率的准确性。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">①出口压力过高故障</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">在出口压力过高<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化见图</span>3<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdsGFCLz3m0sr6tUSddgPp3k43UGGwxQdtChQiapPkz53FlEQQcmLcA5hw/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">图</span>3 <span style="color: black;">在出口压力过高<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">由计算概率可得，最有可能<span style="color: black;">诱发</span>出口压力过高故障的<span style="color: black;">原由</span>是气质杂质冲击阀芯<span style="color: black;">导致</span>阀口处泄漏。并确定故障节点定位<span style="color: black;">次序</span>为</span>X</span><span style="color: black;">2</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">1</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">3</span><span style="color: black;">，即当调压器<span style="color: black;">出现</span>出口压力过高故障时，检修人员应<span style="color: black;">根据</span>气质杂质冲击阀芯<span style="color: black;">导致</span>阀口处泄漏→密封件破损老化→指挥器故障<span style="color: black;">次序</span>进行检修。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">②出口压力过低故障</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">在出口压力过低<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化见图</span>4<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdsXq3fnysKz6g4rBNzqKPUia1jLsYicOkXicXxu50RzC2yOp8iahaf6Jzr3g/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">图</span>4 <span style="color: black;">在出口压力过低<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">由计算概率可得，最有可能<span style="color: black;">诱发</span>出口压力过低故障的<span style="color: black;">原由</span><span style="color: black;">指的是</span>挥器故障。确定故障节点定位<span style="color: black;">次序</span>为</span>X</span><span style="color: black;">3</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">5</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">4</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">6</span><span style="color: black;">，即当调压器<span style="color: black;">出现</span>出口压力过低故障时，检修人员应<span style="color: black;">根据</span>指挥器故障→阀筒壁气蚀<span style="color: black;">损害</span>→皮膜破损→调压站进口段的过滤器<span style="color: black;">出现</span>堵塞<span style="color: black;">次序</span>进行检修。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">③喘振故障</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">在喘振<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化见图</span>5<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="https://mmbiz.qpic.cn/mmbiz_png/zToaqOibicYbEJdsaQpt8hgsn1z0icV5icdsCVFSbiaKJJrt1zSpvrexibcpp1ibtGwPO0SicHlTibO7QH479kscZJV1wHA/640?wx_fmt=png&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">图</span>5 <span style="color: black;">在喘振<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">由计算概率可得，最有可能<span style="color: black;">诱发</span>喘振故障的<span style="color: black;">原由</span><span style="color: black;">指的是</span>挥器故障。并确定故障节点定位<span style="color: black;">次序</span>为</span>X</span><span style="color: black;">3</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">8</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">7</span><span style="color: black;">，即当调压器发生喘振故障时，检修人员应<span style="color: black;">根据</span>指挥器故障→法兰盘螺栓螺母松动→信号管安装故障<span style="color: black;">次序</span>进行检修。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">④关闭不严故障</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">在关闭不严<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化见图</span>6<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">图</span>6 <span style="color: black;">在关闭不严<span style="color: black;">出现</span><span style="color: black;">要求</span>下各故障<span style="color: black;">原由</span><span style="color: black;">出现</span>的计算概率、统计概率、概率变化</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">由计算概率可得，最有可能<span style="color: black;">诱发</span>关闭不严故障的<span style="color: black;">原由</span>是阀口<span style="color: black;">或</span>阀筒磨损。并确定故障节点定位<span style="color: black;">次序</span>为</span>X</span><span style="color: black;">9</span><span style="color: black;"><span style="color: black;">→</span>X</span><span style="color: black;">3</span><span style="color: black;">，即当调压器<span style="color: black;">出现</span>关闭不严故障时，检修人员应<span style="color: black;">根据</span>阀口<span style="color: black;">或</span>阀筒磨损→指挥器故障<span style="color: black;">次序</span>进行检修。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">⑤小结</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">概率变化总体在</span>30%<span style="color: black;">以内，说明概率变化在可控范围内，<span style="color: black;">同期</span><span style="color: black;">亦</span>说明计算概率的准确度高。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">5 <span style="color: black;">结果验证</span></span></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">为验证参数学习优化的概率分布准确性，<span style="color: black;">选择</span>某燃气<span style="color: black;">机构</span>多个次高压站及高压站的检修统计台账与检测报告单。<span style="color: black;">重点</span>检修内容<span style="color: black;">包含</span>：法兰水线、信号管接头、弹簧<span style="color: black;">检测</span>、阀筒<span style="color: black;">检测</span>、进出口端耐磨环及密封圈、筒壁气蚀刮痕等；<span style="color: black;">重点</span><span style="color: black;">掌控</span>数据<span style="color: black;">包含</span>：入口压力、出口压力、调节阀开度、流量记录等。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">总结多个次高压调压站及高压调压站调压器检修<span style="color: black;">守护</span>台账记录及历史故障拆解检测记录，结合构建的贝叶斯网络拓扑结构，进行调压器故障表征归类及故障<span style="color: black;">原由</span>统计，见表</span>6<span style="color: black;">。</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">表</span>6 <span style="color: black;">调压器故障表征归类及故障<span style="color: black;">原由</span>统计</span></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></p><span style="color: black;"><span style="color: black;">由表</span>6<span style="color: black;"><span style="color: black;">能够</span>看出，<span style="color: black;">实质</span>案例故障统计与计算概率总体一致，反映了参数学习优化贝叶斯网络的正确性。</span></span><span style="color: black;"><strong style="color: blue;"><span style="color: black;">6 <span style="color: black;">结论及展望</span></span></strong></span><span style="color: black;">①当调压器<span style="color: black;">出现</span>出口压力过高故障时，检修人员应<span style="color: black;">根据</span>气质杂质冲击阀芯<span style="color: black;">导致</span>阀口处泄漏→密封件破损老化→指挥器故障<span style="color: black;">次序</span>进行检修。</span><span style="color: black;">②当调压器<span style="color: black;">出现</span>出口压力过低故障时，检修人员应<span style="color: black;">根据</span>指挥器故障→阀筒壁气蚀<span style="color: black;">损害</span>→皮膜破损→调压站进口段的过滤器<span style="color: black;">出现</span>堵塞<span style="color: black;">次序</span>进行检修。</span><span style="color: black;">③当调压器<span style="color: black;">出现</span>喘振故障时，检修人员应<span style="color: black;">根据</span>指挥器故障→法兰盘螺栓螺母松动→信号管安装故障<span style="color: black;">次序</span>进行检修。</span><span style="color: black;">④当调压器<span style="color: black;">出现</span>关闭不严故障时，检修人员应<span style="color: black;">根据</span>阀口<span style="color: black;">或</span>阀筒磨损→指挥器故障<span style="color: black;">次序</span>进行检修。</span><span style="color: black;"><span style="color: black;">⑤<span style="color: black;">因为</span>贝叶斯网络模型的强大学习能力，且不依赖于数据完备性，<span style="color: black;">因此</span>输入训练数据集，并采用</span>EM<span style="color: black;">算法进行参数学习后，<span style="color: black;">能够</span>对原模型进行较为准确的<span style="color: black;">调节</span>和优化。参数学习既规避了无<span style="color: black;">要求</span>相信专家知识的片面性，<span style="color: black;">亦</span>很好地给<span style="color: black;">将来</span>不需要固定网络结构和<span style="color: black;">要求</span>概率的模型自学习打下<span style="color: black;">基本</span>，<span style="color: black;">针对</span>缺少故障案例的高中压燃气调压器故障诊断<span style="color: black;">拥有</span>实用<span style="color: black;">道理</span>。</span></span><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"><span style="color: black;"><strong style="color: blue;"><span style="color: black;">参考文献：</span></strong></span><span style="color: black;">［</span><span style="color: black;">1</span><span style="color: black;">］潘继平，杨丽丽，王陆新，等</span><span style="color: black;">. </span><span style="color: black;">新形势下中国天然气资源发展战略思考［</span><span style="color: black;">J</span><span style="color: black;">］</span><span style="color: black;">. </span><span style="color: black;">国际石油经济，</span><span style="color: black;">2017</span><span style="color: black;">（</span><span style="color: black;">6</span><span style="color: black;">）：</span><span style="color: black;"> 12-18.</span><span style="color: black;"><span style="color: black;">［</span>2<span style="color: black;">］傅娟</span>. <span style="color: black;">燃气管道在线焊接<span style="color: black;">要求</span>及热工特性模拟（硕士学位论文）［</span>D<span style="color: black;">］</span>. <span style="color: black;">哈尔滨：哈尔滨工业大学，</span>2011<span style="color: black;">：</span>5-10.</span><a style="color: black;"><span style="color: black;"><span style="color: black;">［</span>3<span style="color: black;">］李琪，郝学军</span>. ARIMA</span></a><span style="color: black;">模型在燃气调压器故障诊断的应用［</span>J<span style="color: black;">］</span>. <span style="color: black;">煤气与热力，</span> 2019<span style="color: black;">（</span>10<span style="color: black;">）：</span>B07-B12.<span style="color: black;"><span style="color: black;">［</span>4<span style="color: black;">］张慧莹，宁媛，邵晓非</span>. <span style="color: black;"><span style="color: black;">设备</span>学习中的贝叶斯网络及其推理分析［</span>J<span style="color: black;">］</span>. <span style="color: black;">现代机械，</span>2012<span style="color: black;">（</span>2<span style="color: black;">）：</span>91-94.</span><span style="color: black;"><span style="color: black;">［</span>5<span style="color: black;">］</span>PEARL J. Fusion<span style="color: black;">，</span>propagation<span style="color: black;">，</span>and structuring in belief networks<span style="color: black;">［</span>J<span style="color: black;">］</span>. Artificial Intelligence<span style="color: black;">，</span>1986<span style="color: black;">（</span>3<span style="color: black;">）：</span>241-288.</span><span style="color: black;"><span style="color: black;">［</span>6<span style="color: black;">］雷江南</span>. <span style="color: black;">贝叶斯网络参数学习算法<span style="color: black;">科研</span>与实现（硕士学位论文）［</span>D<span style="color: black;">］</span>. <span style="color: black;">西安：西安电子科技大学，</span>2018<span style="color: black;">：</span>23-29.</span><span style="color: black;"><span style="color: black;">［</span>7<span style="color: black;">］张连文，郭海鹏</span>. <span style="color: black;">贝叶斯网引论［</span>M<span style="color: black;">］</span>. <span style="color: black;">北京：科学出版社，</span>2006<span style="color: black;">：</span>17-39.</span><span style="color: black;"><span style="color: black;">［</span>8<span style="color: black;">］裴迪</span>. <span style="color: black;">基于贝叶斯网络的货车空气制动系统故障诊断<span style="color: black;">科研</span>（硕士学位论文）［</span>D<span style="color: black;">］</span>. <span style="color: black;">北京：北京交通大学，</span>2018<span style="color: black;">：</span>42-59.</span><span style="color: black;">（本文<span style="color: black;">责任编辑：网友投稿</span>刘灵芝）</span><strong style="color: blue;">同类论文</strong>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">1、</span><span style="color: black;"><a style="color: black;">基于贝叶斯网络的燃气调压器故障诊断<span style="color: black;">科研</span></a></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">2、</span><span style="color: black;"><a style="color: black;">小波包和Apriori算法燃气调压器故障诊断与预警</a></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">3、</span><span style="color: black;"><a style="color: black;">小波包和RBF神经网络的燃气调压器</a>故障诊断</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">4、</span><span style="color: black;"><a style="color: black;">ARIMA模型在燃气调压器故障诊断的应用</a></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;">维普免费下载《煤气与热力》论文（现刊和过刊均可）</strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">日前，《煤气与热力》杂志社有限<span style="color: black;">机构</span>在维普网站</span><a style="color: black;"><span style="color: black;">http://cqvip.com/</span></a><span style="color: black;">开通论文免费下载服务，论文刊出后两个月后，可在维普网站<span style="color: black;">查找</span>，并直接免费下载。在维普网站<strong style="color: blue;"><span style="color: black;">免费下载《煤气与热力》论文</span></strong><span style="color: black;">过程</span>如下：</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">1. 在维普网站注册会员。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">2. 搜索出《煤气与热力》论文，点击进入。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">3. 论文免费下载界面截图见上图。点击“免费下载”，可直接下载该论文。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;">声明：本文著作权（版权）归《煤气与热力》杂志社所有，严禁任何<span style="color: black;">微X</span>号及<span style="color: black;">媒介</span>未经授权许可随意转载。</span><span style="color: black;">PS: 当然欢迎<span style="color: black;">大众</span>转发到<span style="color: black;">伴侣</span>圈！</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><span style="color: black;">更加多</span>论文请登录煤气与热力杂志官方网站，免费注册会员阅读电子期刊。阅读<span style="color: black;">过程</span>：登录http://www.gasheat.cn/→页面右上角注册会员→注册成功后点击《煤气与热力》→期刊索引→点击某期期刊封面<span style="color: black;">就可</span>阅读当期<span style="color: black;">文案</span>。</span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><span style="color: black;"><strong style="color: blue;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></strong></span></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></p>
<p style="font-size: 16px; color: black; line-height: 40px; text-align: left; margin-bottom: 15px;"><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;"></p><img src="data:image/svg+xml,%3C%3Fxml version=1.0 encoding=UTF-8%3F%3E%3Csvg width=1px height=1px viewBox=0 0 1 1 version=1.1 xmlns=http://www.w3.org/2000/svg xmlns:xlink=http://www.w3.org/1999/xlink%3E%3Ctitle%3E%3C/title%3E%3Cg stroke=none stroke-width=1 fill=none fill-rule=evenodd fill-opacity=0%3E%3Cg transform=translate(-249.000000, -126.000000) fill=%23FFFFFF%3E%3Crect x=249 y=126 width=1 height=1%3E%3C/rect%3E%3C/g%3E%3C/g%3E%3C/svg%3E" style="width: 50%; margin-bottom: 20px;">
谷歌网站排名优化 http://www.fok120.com/ 我完全同意你的观点，说得太对了。 楼主果然英明！不得不赞美你一下！ 期待楼主的下一次分享！” 回顾历史，我们不难发现：无数先辈用鲜血和生命铺就了中华民族复兴的康庄大道。 系统提示我验证码错误1500次 ＼~゛， 回顾历史，我们感慨万千；放眼未来，我们信心百倍。 楼主果然英明！不得不赞美你一下！
页:
[1]