81 lines
2.4 KiB
Python
81 lines
2.4 KiB
Python
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import pandas as pd
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy.optimize import curve_fit
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# --- Dati ---
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df = pd.read_csv("data.csv")
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df["time_s"] = df["time since start [ms]"] / 1000.0
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T_INF = 22.99 # temperatura ambiente media ponderata [°C]
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T_START = 115.0 # inizio finestra di fit [s]
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T0 = T_START # t0 coincide con il primo punto
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W_ZERO_START = 115.9
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W_ZERO_END = 117.2
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mask = df["time_s"] >= T_START
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t_fit = df.loc[mask, "time_s"].values
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T_fit = df.loc[mask, "temp_obj IR [C]"].values
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# Pesi espliciti: w=0 nell'intervallo escluso, w=1 altrove
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# curve_fit usa sigma come deviazione standard -> sigma grande = peso nullo
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sigma = np.where(
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(t_fit >= W_ZERO_START) & (t_fit <= W_ZERO_END),
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1e10, # peso ~ 0
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1.0 # peso pieno
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)
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# --- Modello con A e tau liberi (ottimizza R²) ---
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def modello(t, A, tau):
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return T_INF + A * np.exp(-(t - T0) / tau)
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A0 = T_fit[0] - T_INF
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tau0 = 20.0
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popt, pcov = curve_fit(
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modello, t_fit, T_fit,
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p0=[A0, tau0],
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sigma=sigma,
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absolute_sigma=True,
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method="trf",
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bounds=([0, 0.1], [np.inf, np.inf])
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)
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A_fit, tau_fit = popt
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perr = np.sqrt(np.diag(pcov))
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# --- R² (solo sui punti con peso pieno) ---
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mask_w = (t_fit < W_ZERO_START) | (t_fit > W_ZERO_END)
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T_pred_w = modello(t_fit[mask_w], *popt)
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ss_res = np.sum((T_fit[mask_w] - T_pred_w) ** 2)
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ss_tot = np.sum((T_fit[mask_w] - T_fit[mask_w].mean()) ** 2)
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r2 = 1 - ss_res / ss_tot
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print(f"A = {A_fit:.4f} ± {perr[0]:.4f} °C")
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print(f"tau = {tau_fit:.4f} ± {perr[1]:.4f} s")
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print(f"R² = {r2:.6f} (calcolato sui punti con peso pieno)")
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# --- Curva continua ---
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t_curve = np.linspace(T_START, df["time_s"].max(), 500)
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T_curve = modello(t_curve, *popt)
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# --- Plot ---
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fig, ax = plt.subplots(figsize=(12, 5))
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ax.plot(t_fit, T_fit,
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color="steelblue", linewidth=0.8, label="Dati raw (temp_obj)")
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ax.axvspan(W_ZERO_START, W_ZERO_END,
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color="orange", alpha=0.25, label=f"Zona esclusa [{W_ZERO_START}–{W_ZERO_END} s]")
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ax.plot(t_curve, T_curve,
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color="tomato", linewidth=2, linestyle="--",
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label=f"Fit: $T_{{\\infty}}$ + {A_fit:.2f}·exp(-(t-{T0})/{tau_fit:.2f})")
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ax.set_xlabel("Tempo [s]")
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ax.set_ylabel("Temperatura [°C]")
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ax.set_title(f"Fit con pesi espliciti (w=0 in [{W_ZERO_START}–{W_ZERO_END} s]) | R² = {r2:.4f}")
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ax.legend()
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ax.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig("fit_raffreddamento_intero.png", dpi=150, bbox_inches="tight")
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plt.show()
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