MATLAB 2022a中基于牛顿-拉夫逊优化器的CEEMDAN参数优化新算法-自动调整白噪声幅值权重与噪声添加次数，灵活适应度函数替换与应用,MATLAB 2022a中的牛顿-拉夫逊优化器及其在C
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MATLAB 2022a中基于牛顿-拉夫逊优化器的CEEMDAN参数优化新算法——自动调整白噪声幅值权重与噪声添加次数，灵活适应度函数替换与应用,MATLAB 2022a中的牛顿-拉夫逊优化器及其在CEEMDAN噪声参数优化中的应用——基于包络熵与样本熵的自动适应度函数优化算法,MATLAB2022a2024新算法牛顿-拉夫逊优化器（Newton-Raphson-based optimizer，NRBO）, 优化CEEMDAN的白噪声幅值权重(Nstd)和噪声添加次数（NE），以包络熵、样本熵为适应度函数，如果有自己适应度函数替就行。保证程序正确运行，,MATLAB2022a; 牛顿-拉夫逊优化器（NRBO）; CEEMDAN白噪声幅值权重; 噪声添加次数; 适应度函数; 程序正确运行,MATLAB 2022a中基于牛顿-拉夫逊优化器的CEEMDAN参数优化 <link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/90371908/2/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/90371908/bg1.jpg"/><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">MATLAB 2022a<span class="_ _0"> </span><span class="ff2">下的牛顿</span>-<span class="ff2">拉夫逊优化器<span class="ff3">（</span></span>NRBO<span class="ff3">）<span class="ff2">在<span class="_ _1"> </span></span></span>CEEMDAN<span class="_ _0"> </span><span class="ff2">参数优化中的应用</span></div><div class="t m0 x1 h2 y2 ff2 fs0 fc0 sc0 ls0 ws0">一<span class="ff4">、</span>引言</div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 ls0 ws0">在信号处理领域<span class="ff3">，<span class="ff1">CEEMDAN</span>（<span class="ff1">Complete Ensemble Empirical Mode Decomposition with </span></span></div><div class="t m0 x1 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0">Adaptive Noise<span class="ff3">）<span class="ff2">是一种非常有效的自适应噪声分解方法<span class="ff4">。</span>其核心在于对白噪声幅值权重</span>（</span>Nstd</div><div class="t m0 x1 h2 y5 ff3 fs0 fc0 sc0 ls0 ws0">）<span class="ff2">和噪声添加次数</span>（<span class="ff1">NE</span>）<span class="ff2">的优化</span>，<span class="ff2">这两个参数的选择对算法的准确性和效率至关重要<span class="ff4">。</span>本文将介绍如</span></div><div class="t m0 x1 h2 y6 ff2 fs0 fc0 sc0 ls0 ws0">何使用<span class="_ _1"> </span><span class="ff1">MATLAB 2022a<span class="_ _0"> </span></span>中的牛顿<span class="ff1">-</span>拉夫逊优化器<span class="ff3">（<span class="ff1">NRBO</span>）</span>来优化这两个参数<span class="ff3">，</span>并利用包络熵和样本</div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls0 ws0">熵作为适应度函数来保证程序的正确运行<span class="ff4">。</span></div><div class="t m0 x1 h2 y8 ff2 fs0 fc0 sc0 ls0 ws0">二<span class="ff4">、</span>算法基础</div><div class="t m0 x1 h2 y9 ff1 fs0 fc0 sc0 ls0 ws0">1.<span class="_ _2"> </span>CEEMDAN<span class="ff3">：<span class="ff2">这是一种在经验模态分解</span>（</span>Empirical Mode Decomposition, EMD<span class="ff3">）<span class="ff2">的基础上</span></span></div><div class="t m0 x2 h2 ya ff2 fs0 fc0 sc0 ls0 ws0">发展的新型自适应噪声分解方法<span class="ff4">。</span>其通过在原始信号中添加白噪声<span class="ff3">，</span>然后进行多次<span class="_ _1"> </span><span class="ff1">EMD<span class="_ _0"> </span></span>分解<span class="ff3">，</span></div><div class="t m0 x2 h2 yb ff2 fs0 fc0 sc0 ls0 ws0">最后对所有结果进行集成<span class="ff3">，</span>得到最终的分解结果<span class="ff4">。</span></div><div class="t m0 x1 h2 yc ff1 fs0 fc0 sc0 ls0 ws0">2.<span class="_ _2"> </span><span class="ff2">牛顿</span>-<span class="ff2">拉夫逊优化器<span class="ff3">（</span></span>NRBO<span class="ff3">）：<span class="ff2">这是一种基于牛顿法的迭代优化算法</span>，<span class="ff2">具有较高的收敛速度和精</span></span></div><div class="t m0 x2 h2 yd ff2 fs0 fc0 sc0 ls0 ws0">度<span class="ff4">。</span>它通过利用梯度信息来快速找到最优解<span class="ff4">。</span></div><div class="t m0 x1 h2 ye ff2 fs0 fc0 sc0 ls0 ws0">三<span class="ff4">、</span>参数优化</div><div class="t m0 x1 h2 yf ff2 fs0 fc0 sc0 ls0 ws0">我们将使用<span class="_ _1"> </span><span class="ff1">NRBO<span class="_ _0"> </span></span>来优化<span class="_ _1"> </span><span class="ff1">CEEMDAN<span class="_ _0"> </span></span>中的<span class="_ _1"> </span><span class="ff1">Nstd<span class="_ _0"> </span></span>和<span class="_ _1"> </span><span class="ff1">NE<span class="_ _0"> </span></span>两个参数<span class="ff4">。</span>首先<span class="ff3">，</span>我们需要定义一个目标函数<span class="ff3">，</span></div><div class="t m0 x1 h2 y10 ff2 fs0 fc0 sc0 ls0 ws0">该函数以这两个参数为输入<span class="ff3">，</span>并以包络熵或样本熵作为输出值<span class="ff3">（</span>当然也可以使用其他的适应度函数<span class="ff3">）</span></div><div class="t m0 x1 h2 y11 ff4 fs0 fc0 sc0 ls0 ws0">。<span class="ff2">我们的目标是找到使得该输出值最小的参数组合</span>。</div><div class="t m0 x1 h2 y12 ff1 fs0 fc0 sc0 ls0 ws0">1.<span class="_ _2"> </span><span class="ff2">定义适应度函数<span class="ff3">：</span>我们将选择包络熵或样本熵作为适应度函数<span class="ff4">。</span>这些函数能够有效地衡量信号的</span></div><div class="t m0 x2 h2 y13 ff2 fs0 fc0 sc0 ls0 ws0">复杂性和结构信息<span class="ff3">，</span>是衡量<span class="_ _1"> </span><span class="ff1">CEEMDAN<span class="_ _0"> </span></span>分解效果的重要指标<span class="ff4">。</span></div><div class="t m0 x1 h2 y14 ff1 fs0 fc0 sc0 ls0 ws0">2.<span class="_ _2"> </span><span class="ff2">设置初始参数<span class="ff3">：</span>设定<span class="_ _1"> </span></span>Nstd<span class="_ _0"> </span><span class="ff2">和<span class="_ _1"> </span></span>NE<span class="_ _0"> </span><span class="ff2">的初始值以及它们的搜索范围<span class="ff4">。</span></span></div><div class="t m0 x1 h2 y15 ff1 fs0 fc0 sc0 ls0 ws0">3.<span class="_ _2"> </span><span class="ff2">运行<span class="_ _1"> </span></span>NRBO<span class="ff3">：<span class="ff2">使用<span class="_ _1"> </span></span></span>NRBO<span class="_ _0"> </span><span class="ff2">在给定的参数范围内进行迭代优化<span class="ff3">，</span>寻找使适应度函数最小的<span class="_ _1"> </span></span>Nstd<span class="_ _0"> </span><span class="ff2">和</span></div><div class="t m0 x2 h2 y16 ff1 fs0 fc0 sc0 ls0 ws0">NE<span class="_ _0"> </span><span class="ff2">值<span class="ff4">。</span></span></div><div class="t m0 x1 h2 y17 ff2 fs0 fc0 sc0 ls0 ws0">四<span class="ff4">、</span>程序实现</div><div class="t m0 x1 h2 y18 ff2 fs0 fc0 sc0 ls0 ws0">在<span class="_ _1"> </span><span class="ff1">MATLAB 2022a<span class="_ _0"> </span></span>中<span class="ff3">，</span>我们可以使用内置的优化工具箱来实现上述过程<span class="ff4">。</span>首先<span class="ff3">，</span>我们需要编写一个</div><div class="t m0 x1 h2 y19 ff2 fs0 fc0 sc0 ls0 ws0">函数来计算适应度函数的值<span class="ff3">（</span>即包络熵或样本熵<span class="ff3">），</span>然后调用<span class="_ _1"> </span><span class="ff1">NRBO<span class="_ _0"> </span></span>函数进行优化<span class="ff4">。</span>下面是一个简单</div><div class="t m0 x1 h2 y1a ff2 fs0 fc0 sc0 ls0 ws0">的程序框架<span class="ff3">：</span></div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div>