《传热学》横掠管外对流换热系数测定实验中，奴赛尔数Nu与雷诺数Re的关系式，通过实验测定，并确定公式中的系数C和指数n。这里使用机器学习进行线性回归。
功能：输入x坐标和y坐标，进行线性拟合，并绘制曲线。
代码语言：javascript复制<!doctype html>
<html lang="en">
<head>
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<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/echarts-stat/dist/ecStat.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/@tensorflow/tfjs@0.14.2/dist/tf.min.js"></script>
<title>Hello, world!</title>
</head>
<body>
<div class="container">
<h5>分别输入x坐标和y坐标，并用英文逗号隔开</h5>
<form class="row g-3">
<div class="input-group mb-3">
<span class="input-group-text">x坐标</span>
<input type="text" class="form-control" id="xs" placeholder="x坐标，如填写：1,2,3" value="1000,2000,3000" aria-label="xs" aria-describedby="basic-addon1">
</div>
<div class="input-group mb-3">
<span class="input-group-text">y坐标</span>
<input type="text" class="form-control" id="ys" placeholder="y坐标，如填写：2,4,8" value="1008,2123,2899" aria-label="ys" aria-describedby="basic-addon2">
</div>
<div class="col-12">
<input type="button" class="btn btn-primary" onclick="learnCoefficients()" value="计算"></input>
</div>
</form>
</div>
<div class="row w100" id="container" style="height: 500px;border-color: black;"></div>
<div class="modal fade" id="myModal" tabindex="-1" aria-labelledby="exampleModalLabel" aria-hidden="true">
<div class="modal-dialog">
<div class="modal-content">
<div class="modal-header">
<h5 class="modal-title" id="exampleModalLabel">计算结果</h5>
<button type="button" class="btn-close" data-bs-dismiss="modal" aria-label="Close"></button>
</div>
<div class="modal-body" id="resultDiv">
hi
</div>
<div class="modal-footer">
<button type="button" class="btn btn-secondary" data-bs-dismiss="modal">关闭</button>
<button type="button" class="btn btn-primary">重新计算</button>
</div>
</div>
</div>
</div>
<script type="text/javascript">
var m,n,max,min,realK,realB,sx,sy;
function generateData(numPoints, coeff, sigma = 0.04) {
var x=document.getElementById("xs").value.split(',');
var y=document.getElementById("ys").value.split(',');
x= Array.from(x).map((x,i) => {return parseFloat(x)});
y= Array.from(y).map((y,i) => {return parseFloat(y)});
sx=x;sy=y;
console.log("Original xy data=",x,y);
max = Math.max.apply(null, x);
min = Math.min.apply(null, x);
console.log("min & max:",min,max);
var scaledX=x.map(x=>{return 2*(x-min)/(max-min)-1;});
console.log("scaledX:",scaledX);
m=2/(max-min);
n=-2*min/(max-min)-1;
console.log("m,n:",m,n);
return tf.tidy(() => {
const xs = tf.tensor(scaledX);
const ys = tf.tensor(y);
return {xs:xs, ys: ys};
})
}
// Step 1. Set up variables, these are the things we want the model
const k = tf.variable(tf.scalar(Math.random()));
const b = tf.variable(tf.scalar(Math.random()));
// Step 2. Create an optimizer, we will use this later. You can play
const numIterations = 75;
const learningRate = 0.5;
const optimizer = tf.train.sgd(learningRate);
// Step 3. Write our training process functions.
function predict(x) {// y = k * x b
return tf.tidy(() => {return k.mul(x).add(b);});
}
function loss(prediction, labels) {
const error = prediction.sub(labels).square().mean();
return error;
}
async function train(xs, ys, numIterations) {
for (let iter = 0; iter < numIterations; iter ) {
optimizer.minimize(() => {
// Feed the examples into the model
const pred = predict(xs);
return loss(pred, ys);
});
await tf.nextFrame();
}
}
async function learnCoefficients() {
const trueCoefficients = {k: 0.6, b: 0.8};
const trainingData = generateData(100, trueCoefficients);
//console.log("trainingData:",trainingData);
// 模型训练
await train(trainingData.xs, trainingData.ys, numIterations);
var xvals = await trainingData.xs.data();
var yvals = await trainingData.ys.data();
var sDatas = Array.from(sx).map((v,i) => {return [sx[i],sy[i]]});
var [kk,bb]=[k.dataSync()[0],b.dataSync()[0]]
console.log("kk & bb:",kk,bb);
realK=kk*m;realB=kk*n bb;
console.log("realK & realB:",realK,realB);
showResult(sDatas);
document.getElementById("resultDiv").innerText="斜率:" realK.toFixed(3) "n" "截距:" realB.toFixed(3);
var myModal = new bootstrap.Modal(document.getElementById('myModal'), {keyboard: false});
myModal.show();
}
function showResult(scatterData){
var dom = document.getElementById("container");
var myChart = echarts.init(dom);
function realFun(x){return realK*x realB;}//https://wenku.baidu.com/view/ed39e43ff12d2af90242e6fc.html
var realData = [[min,realFun(min)],[max,realFun(max)]];
var option = {
title: {
text: '线性函数拟合',
left: 'center'
},
tooltip: {trigger: 'axis',axisPointer: {type: 'cross'}},
xAxis: {
type: 'value',
splitLine: {lineStyle: {type: 'dashed'}},
},
yAxis: {
type: 'value',
splitLine: {lineStyle: {type: 'dashed'}}
},
series: [{
name: 'scatter',
type: 'scatter',
label: {
emphasis: {
show: true,
position: 'left',
textStyle: {
color: 'blue',
fontSize: 16
}
}
},
data: scatterData
}, {
name: 'line',
type: 'line',
showSymbol: false,
smooth: true,
data: realData,
}]
};
if (option && typeof option === "object") {
myChart.setOption(option, true);
}
}
</script>
<script src="https://cdn.jsdelivr.net/npm/bootstrap@5.0.1/dist/js/bootstrap.bundle.min.js" integrity="sha384-gtEjrD/SeCtmISkJkNUaaKMoLD0//ElJ19smozuHV6z3Iehds 3Ulb9Bn9Plx0x4" crossorigin="anonymous"></script>
</body>
</html>运行结果：
