增加了回归分析
math-zhuxy
parent
4f89950fc1
commit
3de0cfb2e2
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@ -33,6 +33,8 @@ declare module '@vue/runtime-core' {
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ElOption: typeof import('element-plus/es')['ElOption']
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ElPagination: typeof import('element-plus/es')['ElPagination']
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ElProgress: typeof import('element-plus/es')['ElProgress']
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ElRadio: typeof import('element-plus/es')['ElRadio']
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ElRadioGroup: typeof import('element-plus/es')['ElRadioGroup']
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ElRow: typeof import('element-plus/es')['ElRow']
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ElSelect: typeof import('element-plus/es')['ElSelect']
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ElSubMenu: typeof import('element-plus/es')['ElSubMenu']
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@ -7,7 +7,7 @@
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<button class="edit-btn" @click="showEditDialog = true">
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编辑数据
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</button>
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<button class="edit-btn" @click="() => chartData.push(Math.floor(Math.random() * 100))">
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<button class="edit-btn" @click="() => chartData.push(Math.floor(Math.random() * 250))">
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插入数据
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</button>
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<button class="edit-btn" @click="() => chartData.pop()">
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@ -47,7 +47,15 @@
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</div>
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<br><br><br>
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<div class="predict-chart-container">
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<h2>未来趋势</h2>
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<div style="display: flex; gap: 20px; align-items: center;">
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<h2>未来趋势</h2>
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<el-radio-group v-model="ModelMethod" style="border: 1px solid black; padding: 5px; border-radius:15px;">
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<el-radio value="1" size="large">线性回归</el-radio>
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<el-radio value="2" size="large">指数回归</el-radio>
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<el-radio value="3" size="large">多项式回归</el-radio>
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<el-radio value="4" size="large">ARIMA回归</el-radio>
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</el-radio-group>
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</div>
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<v-chart class="map-chart" :option="predictOptions" />
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</div>
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@ -87,6 +95,8 @@ import {
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} from 'echarts/components';
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import * as echarts from 'echarts/core';
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const ModelMethod = ref('1')
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// 注册必要的组件
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use([
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CanvasRenderer,
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@ -177,38 +187,169 @@ const mapOptions = computed(() => ({
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],
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}));
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// const predictData = ref([120, 132, 301, 134, 500, 230, 210]);
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// 线性回归预测
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function linearRegression(data) {
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const n = data.length;
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const x = Array.from({ length: n }, (_, i) => i);
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const y = data;
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const sumX = x.reduce((sum, val) => sum + val, 0);
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const sumY = y.reduce((sum, val) => sum + val, 0);
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const sumXY = x.reduce((sum, val, i) => sum + val * y[i], 0);
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const sumXX = x.reduce((sum, val) => sum + val * val, 0);
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const slope = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX);
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const intercept = (sumY - slope * sumX) / n;
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return slope * n + intercept;
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}
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// 指数平滑预测
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function exponentialSmoothing(data, alpha) {
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if (data.length === 0) return 0;
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let smoothed = data[0];
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for (let i = 1; i < data.length; i++) {
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smoothed = alpha * data[i] + (1 - alpha) * smoothed;
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}
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// 计算趋势
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const recent = data.slice(-Math.min(5, data.length));
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const trend = recent.length > 1 ?
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(recent[recent.length - 1] - recent[0]) / (recent.length - 1) : 0;
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return smoothed + trend;
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}
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// 多项式回归预测
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function polynomialRegression(data, degree) {
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const n = data.length;
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if (n < degree + 1) return data[n - 1];
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// 使用最小二乘法拟合多项式
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const x = Array.from({ length: n }, (_, i) => i);
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const y = data;
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// 构建范德蒙德矩阵
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const matrix = [];
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const target = [];
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for (let i = 0; i < n; i++) {
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const row = [];
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for (let j = 0; j <= degree; j++) {
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row.push(Math.pow(x[i], j));
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}
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matrix.push(row);
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target.push(y[i]);
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}
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// 简化的多项式拟合 (仅处理二次)
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if (degree === 2 && n >= 3) {
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const x1 = x[n - 3], y1 = y[n - 3];
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const x2 = x[n - 2], y2 = y[n - 2];
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const x3 = x[n - 1], y3 = y[n - 1];
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// 二次函数拟合: y = ax² + bx + c
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const denom = (x1 - x2) * (x1 - x3) * (x2 - x3);
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if (Math.abs(denom) < 1e-10) return y3 + (y3 - y2);
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const a = (x3 * (y2 - y1) + x2 * (y1 - y3) + x1 * (y3 - y2)) / denom;
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const b = (x3 * x3 * (y1 - y2) + x2 * x2 * (y3 - y1) + x1 * x1 * (y2 - y3)) / denom;
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const c = (x2 * x3 * (x2 - x3) * y1 + x3 * x1 * (x3 - x1) * y2 + x1 * x2 * (x1 - x2) * y3) / denom;
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const nextX = n;
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return a * nextX * nextX + b * nextX + c;
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}
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return data[n - 1];
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}
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// ARIMA简化版本 (自回归移动平均)
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function arimaSimplified(data) {
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const n = data.length;
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if (n < 3) return data[n - 1];
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// AR(2) 模型: y(t) = φ1*y(t-1) + φ2*y(t-2) + ε
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const y1 = data[n - 1];
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const y2 = data[n - 2];
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// 简单的AR系数估计
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const phi1 = 0.7; // 一阶自回归系数
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const phi2 = 0.2; // 二阶自回归系数
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// 计算残差的移动平均
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const errors = [];
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for (let i = 2; i < n; i++) {
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const predicted = phi1 * data[i - 1] + phi2 * data[i - 2];
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errors.push(data[i] - predicted);
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}
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const avgError = errors.length > 0 ?
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errors.reduce((sum, err) => sum + err, 0) / errors.length : 0;
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// MA(1) 组件
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const theta = 0.3; // 移动平均系数
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const prediction = phi1 * y1 + phi2 * y2 + theta * avgError;
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return prediction;
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}
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const predictData = computed(() => {
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const data = chartData.value;
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if (data.length < 2) return [];
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const predictions = [];
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const windowSize = Math.min(3, data.length); // 使用最近3个点或全部点
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// 确保有足够的数据进行预测
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if (data.length < 3) return Array(5).fill(data[data.length - 1] || 0);
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for (let i = 0; i < 5; i++) {
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let predictedValue;
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const currentData = [...data, ...predictions];
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const len = currentData.length;
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if (i % 2 === 0) {
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// 使用线性趋势预测
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const recentData = [...data, ...predictions];
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const len = recentData.length;
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const x1 = len - windowSize, y1 = recentData[len - windowSize];
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const x2 = len - 1, y2 = recentData[len - 1];
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// 计算斜率
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const slope = (y2 - y1) / (x2 - x1);
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predictedValue = y2 + slope;
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} else {
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const lastValues = [...data, ...predictions];
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const sum = lastValues.slice(-windowSize).reduce((acc, val) => acc + val, 0);
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predictedValue = sum / Math.min(windowSize, lastValues.length);
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switch (ModelMethod.value) {
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case '1': // 线性回归
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predictedValue = linearRegression(currentData);
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break;
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case '2': // 指数平滑
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predictedValue = exponentialSmoothing(currentData, 0.3);
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break;
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case '3': // 多项式回归 (二次)
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predictedValue = polynomialRegression(currentData, 2);
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break;
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case '4': // ARIMA简化版本
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predictedValue = arimaSimplified(currentData);
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break;
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}
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// 添加一些随机波动，使预测更真实
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const noise = (Math.random() - 0.5) * 20;
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// 季节性调整 (模拟周期性波动)
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const seasonalFactor = Math.sin((len + i) * Math.PI / 6) * 0.1 + 1;
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predictedValue *= seasonalFactor;
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// 趋势衰减 (距离越远，趋势影响越小)
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const trendDecay = Math.exp(-i * 0.1);
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const baseline = currentData.slice(-Math.min(5, currentData.length))
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.reduce((sum, val) => sum + val, 0) / Math.min(5, currentData.length);
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predictedValue = baseline + (predictedValue - baseline) * trendDecay;
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// 添加渐减的随机噪声
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const noiseIntensity = 15 * Math.exp(-i * 0.3);
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const noise = (Math.random() - 0.5) * noiseIntensity;
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// 确保预测值合理
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predictedValue = Math.max(0, Math.round(predictedValue + noise));
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// 异常值检测和修正
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if (predictions.length > 0) {
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const lastPrediction = predictions[predictions.length - 1];
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const maxChange = Math.abs(lastPrediction * 0.3); // 最大变化30%
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if (Math.abs(predictedValue - lastPrediction) > maxChange) {
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const direction = predictedValue > lastPrediction ? 1 : -1;
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predictedValue = lastPrediction + direction * maxChange;
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}
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}
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predictions.push(predictedValue);
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}
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