在R语言中测试正弦曲线模板与测试数据的拟合效果

已将数据集划分为训练集和测试集，用训练集拟合正弦曲线的R代码及结果如下：

freq = seq(from=21, to=80, by=0.5)
amp = c(-45.22247,-44.87434,-44.30659, -44.104, -44.08027 ,-44.32827, -44.52562, -44.81116, -45.11858, -45.61112, -45.88737, -45.9517, -46.00517,-45.78666, -45.64515, -45.32656, -45.12009, -44.92572, -44.58918,-44.18919, -43.75679, -43.4801, -43.13948, -42.86826 ,-42.59199,-42.23767, -42.06125, -41.99265 ,-41.91103, -41.96361, -42.10183,-42.47087, -42.86456, -43.17823 ,-43.41674, -43.6427 ,-43.79429,-43.71881, -43.58482 ,-43.53886, -43.29379, -43.00895 ,-42.69728,-42.331 ,-42.11675, -41.84402, -41.63068 ,-41.28213, -40.88509,-40.64461 ,-40.47236 ,-40.49424, -40.73463, -41.02037, -41.49101, -41.95741 ,-42.36682, -42.83582 ,-43.08535, -43.16926, -43.20281,-43.08085, -43.08461, -42.96666, -42.70192, -42.57608 ,-42.30105,-42.01737, -41.58435 ,-41.24757, -40.96 ,-40.68981 ,-40.39803,-40.2478, -40.23024, -40.48872, -40.68104, -41.04532, -41.53119,-41.88053, -42.17658, -42.32618, -42.41549 ,-42.36513, -42.38881,-42.25508, -42.13853, -41.89402, -41.66664, -41.3869, -41.02896, -40.83986, -40.44932 ,-40.14661, -39.84292, -39.66413, -39.60376, -39.63048, -39.75595 ,-39.88888, -40.18054 ,-40.491, -40.62274, -40.8282, -40.92761, -41.1448, -41.0102 ,-41.06486, -40.96643,-40.93895 ,-40.72338, -40.58406, -40.44275 ,-40.28842, -40.23578, -40.04179, -39.93855, -39.94855, -39.90564)
ssp <- data.frame(freq, amp)

A<- (max(ssp$amp)-min(ssp$amp)/2)
C<-((max(ssp$amp)+min(ssp$amp))/2)

res1<- nlsLM(amp ~ A*sin(omega*freq+phi)+C, data=ssp, start=list(A=A,omega=pi/6,phi=1,C=C))
sumres=summary(res1)
co <- coef(res1)
#resid(res1)
#sum(resid(res1)^2)
fit <- function(x, a, b, c, d) {a*sin(b*x+c)+d}
# Plot result
plot(ssp)
curve(fit(x, a=co["A"], b=co["omega"], c=co["phi"], d=co["C"]), add=TRUE ,lwd=2, col="steelblue")

拟合结果：

sumres

Formula: amp ~ A * sin(omega * freq + phi) + C

Parameters:
       Estimate Std. Error  t value Pr(>|t|)    
A      -1.00030    0.20105   -4.975  2.3e-06 ***
omega   0.53007    0.01196   44.332  < 2e-16 ***
phi    -0.31121    0.64156   -0.485    0.629    
C     -42.19834    0.14390 -293.248  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.552 on 115 degrees of freedom

Number of iterations to convergence: 7 
Achieved convergence tolerance: 1.49e-08

尝试用训练得到的系数拟合测试数据时，执行以下代码报错：

newssp = similar to data above
res2<- nls(amp ~ co["A"]*sin(co["omega"]*freq+co["phi"])+co["C"], data=newssp)

错误信息：

Error in getInitial.default(func, data, mCall = as.list(match.call(func,  : 
  no 'getInitial' method found for "function" objects

需要了解该正弦曲线模板与测试数据的拟合效果，求合适方法。

1. 直接计算预测值并评估拟合指标 #

不需要用nls重新拟合，因为所有参数已固定为训练得到的值，直接用这些参数对测试集的freq计算预测amp，再通过残差平方和、R²等指标评估拟合效果：

# 计算测试集的预测值
newssp$pred_amp <- fit(newssp$freq, a=co["A"], b=co["omega"], c=co["phi"], d=co["C"])

# 计算残差平方和（RSS）
rss <- sum((newssp$amp - newssp$pred_amp)^2)
# 计算总平方和（TSS）
tss <- sum((newssp$amp - mean(newssp$amp))^2)
# 计算R²
r_squared <- 1 - (rss/tss)

# 输出评估指标
cat("残差平方和：", rss, "\n")
cat("R²：", r_squared, "\n")

2. 可视化拟合效果 #

将测试集原始数据和预测曲线绘制在一起，直观观察拟合情况：

# 绘制测试集原始数据
plot(amp ~ freq, data=newssp, main="测试集拟合效果", xlab="频率", ylab="振幅")
# 添加预测曲线
curve(fit(x, a=co["A"], b=co["omega"], c=co["phi"], d=co["C"]), add=TRUE, lwd=2, col="steelblue")
# 可选：叠加原始点和预测点的连线
lines(newssp$freq, newssp$pred_amp, col="red", type="p", pch=20)

3. 微调部分参数（可选） #

如果想在训练集参数基础上微调部分参数适配测试集（比如固定omega和phi，只调整振幅A和偏移C），可以用nls指定固定参数：

# 固定omega和phi，仅拟合A和C
res2 <- nls(amp ~ A*sin(co["omega"]*freq + co["phi"]) + C, 
            data=newssp, 
            start=list(A=co["A"], C=co["C"]))
# 查看微调后的结果
summary(res2)
# 计算微调后的预测值并评估
newssp$pred_amp_tuned <- predict(res2)

内容的提问来源于stack exchange，提问作者etgriffiths