基于Holt-Winters方法对资源进行预测

Posted 2023-03-15 _雪辉_

文章目录

  Holt-Winters方法是一种时间序列分析和预报方法。该方法对含有线性趋势和周期波动的非平稳序列适用，利用指数平滑法（EMA）让模型参数不断适应非平稳序列的变化，并对未来趋势进行短期预报。现实场景中如国家GDP历年数据，机器cpu利用率，内存数据等都是时间序列。对未来时间的观测值进行预测是有意义的工作，提前预知未来的数据的走势，可以提前做出行动，如预测cpu使用率，如果cpu飙高，可以及早进行调整，避免机器负载过高而宕机，这个在AIOPS是很常见的一个应用场景。

代码示例

# import needed packages
#-----------------------

import math
import numpy  as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn        import linear_model
from scipy.optimize import fmin_l_bfgs_b

sdata = open('data.csv')
tsA = sdata.read().split('\\n')
tsA.remove("")
tsA = list(map(int, tsA))
source_len = len(tsA)

def holtWinters(ts, p, sp, ahead, mtype, alpha = None, beta = None, gamma = None):

    a, b, s = _initValues(mtype, ts, p, sp)

    if alpha == None or beta == None or gamma == None:
        ituning   = [0.1, 0.1, 0.1]
        ibounds   = [(0,1), (0,1), (0,1)]
        optimized = fmin_l_bfgs_b(_MSD, ituning, args = (mtype, ts, p, a, b, s[:]), bounds = ibounds, approx_grad = True)
        alpha, beta, gamma = optimized[0]

    MSD, params, smoothed = _expSmooth(mtype, ts, p, a, b, s[:], alpha, beta, gamma)
    predicted = _predictValues(mtype, p, ahead, params)

    return 'alpha': alpha, 'beta': beta, 'gamma': gamma, 'MSD': MSD, 'params': params, 'smoothed': smoothed, 'predicted': predicted

def _initValues(mtype, ts, p, sp):

    initSeries = pd.Series(ts[:p*sp])
    if mtype == 'additive':
        rawSeason = initSeries - initSeries.rolling(window=p, min_periods=p, center=True).mean()
        initSeason = [np.nanmean(rawSeason[i::p]) for i in range(p)]
        initSeason = pd.Series(initSeason) - np.mean(initSeason)
        deSeasoned = [initSeries[v] - initSeason[v % p] for v in range(len(initSeries))]
    else:
        rawSeason  = initSeries / initSeries.rolling(window = p, min_periods = p, center = True).mean()
        initSeason = [np.nanmean(rawSeason[i::p]) for i in range(p)]
        initSeason = pd.Series(initSeason) / math.pow(np.prod(np.array(initSeason)), 1/p)
        deSeasoned = [initSeries[v] / initSeason[v % p] for v in range(len(initSeries))]

    lm = linear_model.LinearRegression()
    lm.fit(pd.DataFrame('time': [t+1 for t in range(len(initSeries))]), pd.Series(deSeasoned))
    return float(lm.intercept_), float(lm.coef_), list(initSeason)

def _MSD(tuning, *args):

    predicted = []
    mtype     = args[0]
    ts, p     = args[1:3]
    Lt1, Tt1  = args[3:5]
    St1       = args[5][:]
    alpha, beta, gamma = tuning[:]

    for t in range(len(ts)):

        if mtype == 'additive':
            Lt = alpha * (ts[t] - St1[t % p]) + (1 - alpha) * (Lt1 + Tt1)
            Tt = beta  * (Lt - Lt1)           + (1 - beta)  * (Tt1)
            St = gamma * (ts[t] - Lt)         + (1 - gamma) * (St1[t % p])
            predicted.append(Lt1 + Tt1 + St1[t % p])
        else:
            Lt = alpha * (ts[t] / St1[t % p]) + (1 - alpha) * (Lt1 + Tt1)
            Tt = beta  * (Lt - Lt1)           + (1 - beta)  * (Tt1)
            St = gamma * (ts[t] / Lt)         + (1 - gamma) * (St1[t % p])
            predicted.append((Lt1 + Tt1) * St1[t % p])

        Lt1, Tt1, St1[t % p] = Lt, Tt, St

    return sum([(ts[t] - predicted[t])**2 for t in range(len(predicted))])/len(predicted)

def _expSmooth(mtype, ts, p, a, b, s, alpha, beta, gamma):

    smoothed = []
    Lt1, Tt1, St1 = a, b, s[:]

    for t in range(len(ts)):

        if mtype == 'additive':
            Lt = alpha * (ts[t] - St1[t % p]) + (1 - alpha) * (Lt1 + Tt1)
            Tt = beta  * (Lt - Lt1)           + (1 - beta)  * (Tt1)
            St = gamma * (ts[t] - Lt)         + (1 - gamma) * (St1[t % p])
            smoothed.append(Lt1 + Tt1 + St1[t % p])
        else:
            Lt = alpha * (ts[t] / St1[t % p]) + (1 - alpha) * (Lt1 + Tt1)
            Tt = beta  * (Lt - Lt1)           + (1 - beta)  * (Tt1)
            St = gamma * (ts[t] / Lt)         + (1 - gamma) * (St1[t % p])
            smoothed.append((Lt1 + Tt1) * St1[t % p])

        Lt1, Tt1, St1[t % p] = Lt, Tt, St

    MSD = sum([(ts[t] - smoothed[t])**2 for t in range(len(smoothed))])/len(smoothed)
    return MSD, (Lt1, Tt1, St1), smoothed

def _predictValues(mtype, p, ahead, params):
    '''subroutine to generate predicted values @ahead periods into the future'''

    Lt, Tt, St = params
    if mtype == 'additive':
        return [Lt + (t+1)*Tt + St[t % p] for t in range(ahead)]
    else:
        return [(Lt + (t+1)*Tt) * St[t % p] for t in range(ahead)]


results = holtWinters(tsA, 12, 4, 24, mtype = 'additive')
results = holtWinters(tsA, 12, 4, 24, mtype = 'multiplicative')

print("TUNING: ", results['alpha'], results['beta'], results['gamma'], results['MSD'])
print("FINAL PARAMETERS: ", results['params'])
print("PREDICTED VALUES: ", results['predicted'])
last_len =len(results['predicted'])
x1 = range(0, source_len)
x2 = range(source_len, source_len + last_len)
y1 = tsA
y2 = results['predicted']
fig = plt.figure()
plt.plot(x1, y1, marker=r'', color=u'blue', linestyle='-', label='Initial value')
plt.plot(x2, y2, marker=r'', color=u'red', linestyle='-', label='Estimate value')
plt.xlabel('time')
plt.ylabel('value')
plt.legend(loc='best')
plt.savefig('line_plot.png', dpi=400, bbox_inches='tight')
plt.show()