From 1b34c706f75228a9eaacce0016a22179b3e847ac Mon Sep 17 00:00:00 2001 From: yile0611 Date: Tue, 23 Dec 2025 18:57:01 +0900 Subject: [PATCH 1/3] =?UTF-8?q?Fix:=20FFT=20=EB=B6=84=EC=84=9D=EC=97=90=20?= =?UTF-8?q?Band=20CV=EC=B6=94=EA=B0=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- FFT/FFT_analysis_threshold_ver.py | 426 ++++++++++++++++++++++-------- 1 file changed, 317 insertions(+), 109 deletions(-) diff --git a/FFT/FFT_analysis_threshold_ver.py b/FFT/FFT_analysis_threshold_ver.py index 27c3c93..e2bfbeb 100644 --- a/FFT/FFT_analysis_threshold_ver.py +++ b/FFT/FFT_analysis_threshold_ver.py @@ -3,37 +3,102 @@ import numpy as np import matplotlib.pyplot as plt from scipy.fft import fft, fftfreq -from scipy.signal import butter, filtfilt from pathlib import Path +# 칼만 필터 클래스 +class KalmanFilter: + def __init__(self, process_variance=1e-5, measurement_variance=1e-2, estimated_measurement_variance=1e-2): + """ + 1D 칼만 필터 초기화 + Parameters: + ----------- + process_variance : float + 프로세스 노이즈 분산 (Q) - 시스템 모델의 불확실성 + measurement_variance : float + 측정 노이즈 분산 (R) - 센서 측정의 불확실성 + estimated_measurement_variance : float + 초기 추정 오차 공분산 (P) + """ + self.process_variance = process_variance # Q + self.measurement_variance = measurement_variance # R + self.estimated_measurement_variance = estimated_measurement_variance # P + self.posteri_estimate = 0.0 # 사후 추정값 + self.posteri_error_estimate = 1.0 # 사후 오차 추정 + + def update(self, measurement): + """ + 칼만 필터 업데이트 + Parameters: + ----------- + measurement : float + 새로운 측정값 + Returns: + -------- + float : 필터링된 값 + """ + # 예측 단계 (Prediction) + priori_estimate = self.posteri_estimate + priori_error_estimate = self.posteri_error_estimate + self.process_variance + + # 업데이트 단계 (Update) + kalman_gain = priori_error_estimate / (priori_error_estimate + self.measurement_variance) + self.posteri_estimate = priori_estimate + kalman_gain * (measurement - priori_estimate) + self.posteri_error_estimate = (1 - kalman_gain) * priori_error_estimate + + return self.posteri_estimate + + +def apply_kalman_filter(data, process_variance=1e-5, measurement_variance=1e-2): + """ + 데이터에 칼만 필터 적용 + Parameters: + ----------- + data : numpy.array + 필터링할 데이터 + process_variance : float + 프로세스 노이즈 분산 + measurement_variance : float + 측정 노이즈 분산 + Returns: + -------- + numpy.array : 필터링된 데이터 + """ + kf = KalmanFilter( + process_variance=process_variance, + measurement_variance=measurement_variance + ) + filtered_data = np.zeros(len(data)) + for i, measurement in enumerate(data): + filtered_data[i] = kf.update(measurement) + return filtered_data -# =============================== -# Sampling rate 계산 -# =============================== -def calculate_sample_rate(df, time_column="Time_us"): + +# 샘플링 레이트 계산 함수 +def calculate_sample_rate(df, time_column='Time_us'): + """ + CSV 파일의 시간 열(마이크로초)에서 샘플링 레이트를 계산합니다. + """ if time_column not in df.columns: time_column = df.columns[0] time_data = df[time_column].dropna().values - time_diffs = np.diff(time_data) - avg_dt_sec = np.mean(time_diffs) / 1_000_000 - return 1.0 / avg_dt_sec - + if len(time_data) < 2: + raise ValueError("시간 데이터가 충분하지 않습니다.") -# =============================== -# Butterworth LPF -# =============================== -def apply_butterworth_filter(data, sample_rate, cutoff=100.0, order=4): - nyq = 0.5 * sample_rate - normal_cutoff = cutoff / nyq - b, a = butter(order, normal_cutoff, btype="low") - return filtfilt(b, a, data) + time_diffs = np.diff(time_data) + avg_time_diff_us = np.mean(time_diffs) + avg_time_diff_sec = avg_time_diff_us / 1_000_000 + sample_rate = 1 / avg_time_diff_sec + return sample_rate # =============================== -# Band-limited CV +# Band-limited CV (1번 코드에서 추가) # =============================== def calculate_band_cv(freqs, amps, f_min=1.0, f_max=100.0): + """ + 특정 주파수 대역의 Coefficient of Variation 계산 + """ band = (freqs >= f_min) & (freqs <= f_max) band_amps = amps[band] @@ -44,160 +109,303 @@ def calculate_band_cv(freqs, amps, f_min=1.0, f_max=100.0): return np.std(band_amps) / mean_val * 100.0 -# =============================== -# FFT 분석 -# =============================== -def fft_analysis(data, sample_rate, window_size=4096, fft_size=16384): - data = data[:window_size] +# Threshold 계산 함수 +def calculate_threshold(amps, method="std", n_std=2.75, recon_error_value=0.3): + if method == "std": + mean = np.mean(amps) + std = np.std(amps) + threshold = mean + n_std * std + elif method == "percentile": + threshold = np.percentile(amps, 97.5) + elif method == "recon_error": + threshold = recon_error_value + else: + raise ValueError("지원하지 않는 threshold 방법입니다.") + return threshold + + +# FFT 분석 함수 +def fft_analysis( + data, + sample_rate=296, + fft_size=None, + threshold_method="std", + n_std=2.75, + recon_error_value=0.3 +): data = data - np.mean(data) - - if fft_size > window_size: - data = np.pad(data, (0, fft_size - window_size)) + n = fft_size if fft_size else len(data) + data = data[:n] y = fft(data) - x = fftfreq(fft_size, 1 / sample_rate) + x = fftfreq(n, 1 / sample_rate) - freqs = x[:fft_size // 2] - amps = np.abs(y[:fft_size // 2]) * 2 / window_size + positive_freqs = x[:n // 2] + positive_amps = np.abs(y[:n // 2]) * 2 / n - resonance_freq = freqs[np.argmax(amps)] - return freqs, amps, resonance_freq + resonance_freq = positive_freqs[np.argmax(positive_amps)] + threshold = calculate_threshold(positive_amps, threshold_method, n_std, recon_error_value) + # Threshold 이상 구간 탐색 + threshold_ranges = [] + above_threshold = positive_amps >= threshold + in_range = False + for i in range(len(positive_freqs)): + if above_threshold[i] and not in_range: + range_start = positive_freqs[i] + in_range = True + elif not above_threshold[i] and in_range: + range_end = positive_freqs[i - 1] + threshold_ranges.append((range_start, range_end)) + in_range = False + if in_range: + threshold_ranges.append((range_start, positive_freqs[-1])) -# =============================== -# Class 추출 함수 (★ 추가된 부분) -# =============================== -def extract_class_from_filename(filename): - parts = filename.split("_") - for p in parts: - if p.lower().startswith("class"): - return p - return "Unknown" + return positive_freqs, positive_amps, resonance_freq, threshold_ranges, threshold -# =============================== -# 단일 파일 분석 -# =============================== +# 단일 파일 분석 함수 def analyze_single_file( file_path, axes, - window_size=4096, fft_size=16384, - cutoff_freq=100.0, - time_column="Time_us" + filter_type='kalman', # 'none', 'kalman' + kalman_process_var=1e-5, + kalman_measurement_var=1e-2, + threshold_method="std", + n_std=2.75, + recon_error_value=0.3, + time_column='Time_us', + band_cv_f_min=0.3, # Band CV 주파수 범위 + band_cv_f_max=60.0 ): df = pd.read_csv(file_path) file_title = os.path.splitext(os.path.basename(file_path))[0] - class_name = extract_class_from_filename(file_title) + # 샘플링 레이트 자동 계산 sample_rate = calculate_sample_rate(df, time_column) - print(f" Sample rate: {sample_rate:.2f} Hz") + print(f" 계산된 샘플링 레이트: {sample_rate:.2f} Hz") results = [] + num_rows = 2 + num_cols = 3 plt.figure(figsize=(18, 8)) for idx, axis in enumerate(axes): if axis not in df.columns: + print(f"[경고] {axis} 열이 CSV 파일에 없습니다: {file_path}") continue data = df[axis].dropna().values + filter_applied_str = filter_type + + # 칼만 필터 적용 + if filter_type == 'kalman': + data = apply_kalman_filter(data, kalman_process_var, kalman_measurement_var) - data = apply_butterworth_filter( + freqs, amps, resonance_freq, threshold_ranges, threshold = fft_analysis( data, sample_rate=sample_rate, - cutoff=cutoff_freq, - order=4 + fft_size=fft_size, + threshold_method=threshold_method, + n_std=n_std, + recon_error_value=recon_error_value ) - freqs, amps, resonance_freq = fft_analysis( - data, - sample_rate, - window_size, - fft_size - ) + # =============================== + # Band CV 계산 (1번 코드에서 추가) + # =============================== + band_cv = calculate_band_cv(freqs, amps, f_min=band_cv_f_min, f_max=band_cv_f_max) - band_cv = calculate_band_cv(freqs, amps, f_min=0.3, f_max=60.0) + # Threshold 범위를 문자열로 변환 + threshold_ranges_str = "" + if threshold_ranges: + ranges_list = [f"{r[0]:.2f}-{r[1]:.2f}Hz" for r in threshold_ranges] + threshold_ranges_str = "; ".join(ranges_list) + else: + threshold_ranges_str = "없음" results.append({ - "Class": class_name, # ★ 추가 - "File": file_title, - "Axis": axis, - "Resonance_Frequency_Hz": round(resonance_freq, 2), - "Band_CV_1_100Hz": round(band_cv, 2), - "Sample_Rate": round(sample_rate, 2), - "Window_Size": window_size, - "FFT_Size": fft_size, - "Filter": "Butterworth", - "Cutoff_Hz": cutoff_freq + 'File': file_title, + 'Axis': axis, + 'Resonance_Frequency_Hz': round(resonance_freq, 2), + 'Band_CV': round(band_cv, 2) if not np.isnan(band_cv) else 'N/A', # Band CV 추가 + 'Threshold_Value': round(threshold, 4), + 'Threshold_Method': threshold_method, + 'Threshold_Ranges': threshold_ranges_str, + 'Sample_Rate': round(sample_rate, 2), + 'FFT_Size': fft_size, + 'Filter_Type': filter_applied_str, + 'Kalman_Process_Var': kalman_process_var if filter_type == 'kalman' else 'N/A', + 'Kalman_Measurement_Var': kalman_measurement_var if filter_type == 'kalman' else 'N/A', + 'Band_CV_Freq_Range': f"{band_cv_f_min}-{band_cv_f_max}Hz" # Band CV 주파수 범위 추가 }) - plt.subplot(2, 3, idx + 1) - plt.plot(freqs, amps) - plt.axvline(resonance_freq, color="r", linestyle="--") - plt.title(f"{axis} | {resonance_freq:.2f} Hz") + # subplot 그리기 + plt.subplot(num_rows, num_cols, idx + 1) + plt.plot(freqs, amps, label="Amplitude") + plt.axvline(resonance_freq, color='r', linestyle='--', label=f'Resonance: {resonance_freq:.2f} Hz') + plt.axhline(y=threshold, color='g', linestyle=':', label=f'Threshold: {threshold:.3f}') + plt.title(f"{axis}\nResonance: {resonance_freq:.2f} Hz | CV: {band_cv:.2f}%") plt.xlabel("Frequency (Hz)") plt.ylabel("Amplitude") plt.grid(True) + plt.legend() - plt.suptitle(f"FFT Spectrum - {file_title}", fontsize=16) + plt.suptitle(f"FFT Frequency Spectrum - {file_title} (Filter: {filter_type})", fontsize=16) plt.tight_layout(rect=[0, 0, 1, 0.93]) - plt.savefig( - os.path.join(os.path.dirname(file_path), f"{file_title}_fft.png"), - dpi=150 - ) + plt.savefig(os.path.join(os.path.dirname(file_path), f"{file_title}_fft_plot_{filter_type}.png"), dpi=150) plt.close() return results -# =============================== -# 전체 파일 분석 -# =============================== +# 배치 분석 함수 (모든 파일 처리) def analyze_all_files( data_dir, - axes, - window_size=4096, + axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], fft_size=16384, - cutoff_freq=100.0, - time_column="Time_us" + filter_type='kalman', # 'none', 'kalman' + kalman_process_var=1e-5, + kalman_measurement_var=1e-2, + threshold_method="std", + n_std=2.75, + recon_error_value=0.3, + time_column='Time_us', + band_cv_f_min=0.3, + band_cv_f_max=60.0 ): + """ + 지정된 디렉토리의 모든 CSV 파일에 대해 FFT 분석을 수행합니다. + """ data_path = Path(data_dir) - csv_files = sorted(data_path.glob("mpu_raw_optimized_*.csv")) + # CSV 파일 목록 가져오기 + csv_files = sorted(list(data_path.glob("mpu_raw_optimized_*.csv"))) + + if not csv_files: + print(f"[오류] {data_dir}에서 CSV 파일을 찾을 수 없습니다.") + return None + + print(f"총 {len(csv_files)}개의 파일을 찾았습니다.\n") + print(f"사용 필터: {filter_type}") + + # 클래스별로 파일 분류 + class_files = { + 'driving': [], + 'lidar': [], + 'motor': [], + 'lidar_driving': [], + 'motor_driving': [] + } + + for file in csv_files: + filename = file.name + if 'motor_driving' in filename: + class_files['motor_driving'].append(file) + elif 'lidar_driving' in filename: + class_files['lidar_driving'].append(file) + elif 'driving' in filename: + class_files['driving'].append(file) + elif 'lidar' in filename: + class_files['lidar'].append(file) + elif 'motor' in filename: + class_files['motor'].append(file) + + # 전체 결과를 저장할 리스트 all_results = [] - for idx, file_path in enumerate(csv_files, 1): - print(f"\n[{idx}/{len(csv_files)}] {file_path.name}") - - file_results = analyze_single_file( - file_path, - axes, - window_size, - fft_size, - cutoff_freq, - time_column - ) - all_results.extend(file_results) - - results_df = pd.DataFrame(all_results) - output_path = data_path / "fft_results_butterworth_bandCV.csv" - results_df.to_csv(output_path, index=False, encoding="utf-8-sig") + # 각 클래스별로 처리 + for class_name, files in class_files.items(): + if not files: + continue - print(f"\n결과 저장 완료: {output_path}") - return results_df + print(f"\n{'=' * 60}") + print(f"클래스: {class_name.upper()} ({len(files)}개 파일)") + print(f"{'=' * 60}") + + for idx, file_path in enumerate(files, 1): + print(f"\n[{idx}/{len(files)}] 분석 중: {file_path.name}") + try: + file_results = analyze_single_file( + file_path=str(file_path), + axes=axes, + fft_size=fft_size, + filter_type=filter_type, + kalman_process_var=kalman_process_var, + kalman_measurement_var=kalman_measurement_var, + threshold_method=threshold_method, + n_std=n_std, + recon_error_value=recon_error_value, + time_column=time_column, + band_cv_f_min=band_cv_f_min, + band_cv_f_max=band_cv_f_max + ) + + # 클래스 정보 추가 + for result in file_results: + result['Class'] = class_name + + all_results.extend(file_results) + print(f" ✓ 완료") + except Exception as e: + print(f" ✗ 오류 발생: {e}") + continue + + # 전체 결과를 하나의 CSV로 저장 + if all_results: + results_df = pd.DataFrame(all_results) + + # 컬럼 순서 재정렬 + column_order = ['Class', 'File', 'Axis', 'Resonance_Frequency_Hz', 'Band_CV', + 'Band_CV_Freq_Range', 'Threshold_Value', 'Threshold_Method', + 'Threshold_Ranges', 'Sample_Rate', 'FFT_Size', 'Filter_Type', + 'Kalman_Process_Var', 'Kalman_Measurement_Var'] + results_df = results_df[column_order] + + output_path = data_path / f"all_files_fft_analysis_results_{filter_type}_with_bandCV.csv" + results_df.to_csv(output_path, index=False, encoding='utf-8-sig') + + print(f"\n{'=' * 60}") + print(f"[완료] 전체 분석 결과 저장됨: {output_path}") + print(f"총 {len(all_results)}개의 분석 결과 (파일 {len(csv_files)}개 × 축 {len(axes)}개)") + print(f"{'=' * 60}") + + # 클래스별 요약 통계 + print("\n[클래스별 요약]") + for class_name in class_files.keys(): + class_data = results_df[results_df['Class'] == class_name] + if len(class_data) > 0: + print(f" {class_name}: {len(class_data) // len(axes)}개 파일") + + return results_df + else: + print("[오류] 분석된 결과가 없습니다.") + return None -# =============================== # 실행 -# =============================== if __name__ == "__main__": + # 데이터 디렉토리 경로 설정 DATA_DIR = "/Users/seohyeon/PycharmProjects/AT_data/data_v1" - analyze_all_files( + # 배치 분석 실행 + # filter_type 옵션: 'none', 'kalman' + results = analyze_all_files( data_dir=DATA_DIR, axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], - window_size=4096, fft_size=16384, - cutoff_freq=100.0, - time_column="Time_us" + filter_type='kalman', # 칼만 필터 사용 + kalman_process_var=1e-5, # 칼만 필터 프로세스 노이즈 + kalman_measurement_var=1e-2, # 칼만 필터 측정 노이즈 + threshold_method="std", + n_std=2.75, + recon_error_value=0.3, + time_column='Time_us', + band_cv_f_min=0.3, # Band CV 계산 주파수 범위 (1번 코드와 동일) + band_cv_f_max=60.0 ) + + if results is not None: + print("\n[결과 미리보기]") + print(results.head(10)) \ No newline at end of file From 1168e4dbd4fe071f648da9f272d2d4b6033139f1 Mon Sep 17 00:00:00 2001 From: yile0611 Date: Tue, 23 Dec 2025 19:02:57 +0900 Subject: [PATCH 2/3] =?UTF-8?q?Fix:=20FFT=20=EB=B6=84=EC=84=9D=EC=97=90=20?= =?UTF-8?q?Band=20CV=EC=B6=94=EA=B0=80=20+=20=EC=B9=BC=EB=A7=8C=ED=95=84?= =?UTF-8?q?=ED=84=B0=20=EC=A0=9C=EA=B1=B0=20+=20=EC=9C=88=EB=8F=84?= =?UTF-8?q?=EC=9A=B0=20=EC=82=AC=EC=9D=B4=EC=A6=88=EB=9E=91=20FFT=20?= =?UTF-8?q?=EC=82=AC=EC=9D=B4=EC=A6=88=20=EB=B3=80=EA=B2=BD=20(4096,16384)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- FFT/FFT_analysis_threshold_ver.py | 164 +++++++++++------------------- 1 file changed, 59 insertions(+), 105 deletions(-) diff --git a/FFT/FFT_analysis_threshold_ver.py b/FFT/FFT_analysis_threshold_ver.py index e2bfbeb..9440c77 100644 --- a/FFT/FFT_analysis_threshold_ver.py +++ b/FFT/FFT_analysis_threshold_ver.py @@ -3,74 +3,21 @@ import numpy as np import matplotlib.pyplot as plt from scipy.fft import fft, fftfreq +from scipy.signal import butter, filtfilt from pathlib import Path -# 칼만 필터 클래스 -class KalmanFilter: - def __init__(self, process_variance=1e-5, measurement_variance=1e-2, estimated_measurement_variance=1e-2): - """ - 1D 칼만 필터 초기화 - Parameters: - ----------- - process_variance : float - 프로세스 노이즈 분산 (Q) - 시스템 모델의 불확실성 - measurement_variance : float - 측정 노이즈 분산 (R) - 센서 측정의 불확실성 - estimated_measurement_variance : float - 초기 추정 오차 공분산 (P) - """ - self.process_variance = process_variance # Q - self.measurement_variance = measurement_variance # R - self.estimated_measurement_variance = estimated_measurement_variance # P - self.posteri_estimate = 0.0 # 사후 추정값 - self.posteri_error_estimate = 1.0 # 사후 오차 추정 - - def update(self, measurement): - """ - 칼만 필터 업데이트 - Parameters: - ----------- - measurement : float - 새로운 측정값 - Returns: - -------- - float : 필터링된 값 - """ - # 예측 단계 (Prediction) - priori_estimate = self.posteri_estimate - priori_error_estimate = self.posteri_error_estimate + self.process_variance - - # 업데이트 단계 (Update) - kalman_gain = priori_error_estimate / (priori_error_estimate + self.measurement_variance) - self.posteri_estimate = priori_estimate + kalman_gain * (measurement - priori_estimate) - self.posteri_error_estimate = (1 - kalman_gain) * priori_error_estimate - - return self.posteri_estimate - - -def apply_kalman_filter(data, process_variance=1e-5, measurement_variance=1e-2): + +# =============================== +# Butterworth LPF +# =============================== +def apply_butterworth_filter(data, sample_rate, cutoff=100.0, order=4): """ - 데이터에 칼만 필터 적용 - Parameters: - ----------- - data : numpy.array - 필터링할 데이터 - process_variance : float - 프로세스 노이즈 분산 - measurement_variance : float - 측정 노이즈 분산 - Returns: - -------- - numpy.array : 필터링된 데이터 + Butterworth 저역통과 필터 적용 """ - kf = KalmanFilter( - process_variance=process_variance, - measurement_variance=measurement_variance - ) - filtered_data = np.zeros(len(data)) - for i, measurement in enumerate(data): - filtered_data[i] = kf.update(measurement) - return filtered_data + nyq = 0.5 * sample_rate + normal_cutoff = cutoff / nyq + b, a = butter(order, normal_cutoff, btype="low") + return filtfilt(b, a, data) # 샘플링 레이트 계산 함수 @@ -93,7 +40,7 @@ def calculate_sample_rate(df, time_column='Time_us'): # =============================== -# Band-limited CV (1번 코드에서 추가) +# Band-limited CV # =============================== def calculate_band_cv(freqs, amps, f_min=1.0, f_max=100.0): """ @@ -127,21 +74,30 @@ def calculate_threshold(amps, method="std", n_std=2.75, recon_error_value=0.3): # FFT 분석 함수 def fft_analysis( data, - sample_rate=296, - fft_size=None, + sample_rate, + window_size=4096, + fft_size=16384, threshold_method="std", n_std=2.75, recon_error_value=0.3 ): + """ + FFT 분석 수행 + window_size 만큼의 데이터를 사용하고, fft_size로 zero-padding + """ + # window_size 만큼만 사용 + data = data[:window_size] data = data - np.mean(data) - n = fft_size if fft_size else len(data) - data = data[:n] + + # zero-padding + if fft_size > window_size: + data = np.pad(data, (0, fft_size - window_size)) y = fft(data) - x = fftfreq(n, 1 / sample_rate) + x = fftfreq(fft_size, 1 / sample_rate) - positive_freqs = x[:n // 2] - positive_amps = np.abs(y[:n // 2]) * 2 / n + positive_freqs = x[:fft_size // 2] + positive_amps = np.abs(y[:fft_size // 2]) * 2 / window_size resonance_freq = positive_freqs[np.argmax(positive_amps)] threshold = calculate_threshold(positive_amps, threshold_method, n_std, recon_error_value) @@ -168,15 +124,14 @@ def fft_analysis( def analyze_single_file( file_path, axes, + window_size=4096, fft_size=16384, - filter_type='kalman', # 'none', 'kalman' - kalman_process_var=1e-5, - kalman_measurement_var=1e-2, + cutoff_freq=100.0, threshold_method="std", n_std=2.75, recon_error_value=0.3, time_column='Time_us', - band_cv_f_min=0.3, # Band CV 주파수 범위 + band_cv_f_min=0.3, band_cv_f_max=60.0 ): df = pd.read_csv(file_path) @@ -197,24 +152,26 @@ def analyze_single_file( continue data = df[axis].dropna().values - filter_applied_str = filter_type - # 칼만 필터 적용 - if filter_type == 'kalman': - data = apply_kalman_filter(data, kalman_process_var, kalman_measurement_var) + # Butterworth 필터 적용 + data = apply_butterworth_filter( + data, + sample_rate=sample_rate, + cutoff=cutoff_freq, + order=4 + ) freqs, amps, resonance_freq, threshold_ranges, threshold = fft_analysis( data, sample_rate=sample_rate, + window_size=window_size, fft_size=fft_size, threshold_method=threshold_method, n_std=n_std, recon_error_value=recon_error_value ) - # =============================== - # Band CV 계산 (1번 코드에서 추가) - # =============================== + # Band CV 계산 band_cv = calculate_band_cv(freqs, amps, f_min=band_cv_f_min, f_max=band_cv_f_max) # Threshold 범위를 문자열로 변환 @@ -229,16 +186,16 @@ def analyze_single_file( 'File': file_title, 'Axis': axis, 'Resonance_Frequency_Hz': round(resonance_freq, 2), - 'Band_CV': round(band_cv, 2) if not np.isnan(band_cv) else 'N/A', # Band CV 추가 + 'Band_CV': round(band_cv, 2) if not np.isnan(band_cv) else 'N/A', + 'Band_CV_Freq_Range': f"{band_cv_f_min}-{band_cv_f_max}Hz", 'Threshold_Value': round(threshold, 4), 'Threshold_Method': threshold_method, 'Threshold_Ranges': threshold_ranges_str, 'Sample_Rate': round(sample_rate, 2), + 'Window_Size': window_size, 'FFT_Size': fft_size, - 'Filter_Type': filter_applied_str, - 'Kalman_Process_Var': kalman_process_var if filter_type == 'kalman' else 'N/A', - 'Kalman_Measurement_Var': kalman_measurement_var if filter_type == 'kalman' else 'N/A', - 'Band_CV_Freq_Range': f"{band_cv_f_min}-{band_cv_f_max}Hz" # Band CV 주파수 범위 추가 + 'Filter_Type': 'Butterworth', + 'Cutoff_Hz': cutoff_freq }) # subplot 그리기 @@ -252,9 +209,9 @@ def analyze_single_file( plt.grid(True) plt.legend() - plt.suptitle(f"FFT Frequency Spectrum - {file_title} (Filter: {filter_type})", fontsize=16) + plt.suptitle(f"FFT Frequency Spectrum - {file_title} (Filter: Butterworth)", fontsize=16) plt.tight_layout(rect=[0, 0, 1, 0.93]) - plt.savefig(os.path.join(os.path.dirname(file_path), f"{file_title}_fft_plot_{filter_type}.png"), dpi=150) + plt.savefig(os.path.join(os.path.dirname(file_path), f"{file_title}_fft_plot_butterworth.png"), dpi=150) plt.close() return results @@ -264,10 +221,9 @@ def analyze_single_file( def analyze_all_files( data_dir, axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], + window_size=4096, fft_size=16384, - filter_type='kalman', # 'none', 'kalman' - kalman_process_var=1e-5, - kalman_measurement_var=1e-2, + cutoff_freq=100.0, threshold_method="std", n_std=2.75, recon_error_value=0.3, @@ -288,7 +244,8 @@ def analyze_all_files( return None print(f"총 {len(csv_files)}개의 파일을 찾았습니다.\n") - print(f"사용 필터: {filter_type}") + print(f"사용 필터: Butterworth (Cutoff: {cutoff_freq} Hz)") + print(f"Window Size: {window_size}, FFT Size: {fft_size}") # 클래스별로 파일 분류 class_files = { @@ -330,10 +287,9 @@ def analyze_all_files( file_results = analyze_single_file( file_path=str(file_path), axes=axes, + window_size=window_size, fft_size=fft_size, - filter_type=filter_type, - kalman_process_var=kalman_process_var, - kalman_measurement_var=kalman_measurement_var, + cutoff_freq=cutoff_freq, threshold_method=threshold_method, n_std=n_std, recon_error_value=recon_error_value, @@ -359,11 +315,11 @@ def analyze_all_files( # 컬럼 순서 재정렬 column_order = ['Class', 'File', 'Axis', 'Resonance_Frequency_Hz', 'Band_CV', 'Band_CV_Freq_Range', 'Threshold_Value', 'Threshold_Method', - 'Threshold_Ranges', 'Sample_Rate', 'FFT_Size', 'Filter_Type', - 'Kalman_Process_Var', 'Kalman_Measurement_Var'] + 'Threshold_Ranges', 'Sample_Rate', 'Window_Size', 'FFT_Size', + 'Filter_Type', 'Cutoff_Hz'] results_df = results_df[column_order] - output_path = data_path / f"all_files_fft_analysis_results_{filter_type}_with_bandCV.csv" + output_path = data_path / f"all_files_fft_analysis_butterworth_bandCV.csv" results_df.to_csv(output_path, index=False, encoding='utf-8-sig') print(f"\n{'=' * 60}") @@ -390,19 +346,17 @@ def analyze_all_files( DATA_DIR = "/Users/seohyeon/PycharmProjects/AT_data/data_v1" # 배치 분석 실행 - # filter_type 옵션: 'none', 'kalman' results = analyze_all_files( data_dir=DATA_DIR, axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], + window_size=4096, fft_size=16384, - filter_type='kalman', # 칼만 필터 사용 - kalman_process_var=1e-5, # 칼만 필터 프로세스 노이즈 - kalman_measurement_var=1e-2, # 칼만 필터 측정 노이즈 + cutoff_freq=100.0, threshold_method="std", n_std=2.75, recon_error_value=0.3, time_column='Time_us', - band_cv_f_min=0.3, # Band CV 계산 주파수 범위 (1번 코드와 동일) + band_cv_f_min=0.3, band_cv_f_max=60.0 ) From 950b3ece59b3ec1dea2d1f9855b67e28f1fe5fe8 Mon Sep 17 00:00:00 2001 From: kseohyuz Date: Tue, 23 Dec 2025 20:47:13 +0900 Subject: [PATCH 3/3] =?UTF-8?q?Feat:=20baseline(=EC=A0=95=EC=A0=81=20?= =?UTF-8?q?=EC=83=81=ED=83=9C)=20=EC=B6=94=EA=B0=80,=20FFT=20=EB=B6=84?= =?UTF-8?q?=EC=84=9D,=20=EC=98=A4=EC=B0=A8=EC=9C=A8=20=EB=B6=84=EC=84=9D?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- FFT/FFT_analysis_threshold_ver.py | 288 ++++------ .../frequency_comparison_boxplot_base.png | Bin 0 -> 42498 bytes .../frequency_distribution_base.png | Bin 0 -> 90014 bytes ...u_raw_base_10_20251223_200921_fft_plot.png | Bin 0 -> 240280 bytes ...pu_raw_base_2_20251223_194400_fft_plot.png | Bin 0 -> 221603 bytes ...pu_raw_base_3_20251223_194807_fft_plot.png | Bin 0 -> 235945 bytes ...pu_raw_base_4_20251223_195053_fft_plot.png | Bin 0 -> 225895 bytes ...pu_raw_base_5_20251223_195345_fft_plot.png | Bin 0 -> 229188 bytes ...pu_raw_base_6_20251223_195633_fft_plot.png | Bin 0 -> 233830 bytes ...pu_raw_base_7_20251223_195920_fft_plot.png | Bin 0 -> 233617 bytes ...pu_raw_base_8_20251223_200314_fft_plot.png | Bin 0 -> 228961 bytes ...pu_raw_base_9_20251223_200604_fft_plot.png | Bin 0 -> 240991 bytes .../stats_bar_comparison_base.png | Bin 0 -> 31951 bytes .../stats_bar_mean_comparison_base.png | Bin 0 -> 40779 bytes .../stats_heatmaps_base.png | Bin 0 -> 103295 bytes FFT/frequency_error_analysis.py | 505 +++--------------- 16 files changed, 191 insertions(+), 602 deletions(-) create mode 100644 FFT/fft_analysis_results_baseline/frequency_comparison_boxplot_base.png create mode 100644 FFT/fft_analysis_results_baseline/frequency_distribution_base.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_10_20251223_200921_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_2_20251223_194400_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_3_20251223_194807_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_4_20251223_195053_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_5_20251223_195345_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_6_20251223_195633_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_7_20251223_195920_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_8_20251223_200314_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/mpu_raw_base_9_20251223_200604_fft_plot.png create mode 100644 FFT/fft_analysis_results_baseline/stats_bar_comparison_base.png create mode 100644 FFT/fft_analysis_results_baseline/stats_bar_mean_comparison_base.png create mode 100644 FFT/fft_analysis_results_baseline/stats_heatmaps_base.png diff --git a/FFT/FFT_analysis_threshold_ver.py b/FFT/FFT_analysis_threshold_ver.py index 9440c77..4412e54 100644 --- a/FFT/FFT_analysis_threshold_ver.py +++ b/FFT/FFT_analysis_threshold_ver.py @@ -7,16 +7,16 @@ from pathlib import Path -# =============================== -# Butterworth LPF -# =============================== -def apply_butterworth_filter(data, sample_rate, cutoff=100.0, order=4): - """ - Butterworth 저역통과 필터 적용 - """ - nyq = 0.5 * sample_rate +# 저역통과 필터 함수 +def butter_lowpass(cutoff, fs, order=5): + nyq = 0.5 * fs normal_cutoff = cutoff / nyq - b, a = butter(order, normal_cutoff, btype="low") + b, a = butter(order, normal_cutoff, btype='low', analog=False) + return b, a + + +def butter_lowpass_filter(data, cutoff, fs, order=5): + b, a = butter_lowpass(cutoff, fs, order=order) return filtfilt(b, a, data) @@ -26,34 +26,27 @@ def calculate_sample_rate(df, time_column='Time_us'): CSV 파일의 시간 열(마이크로초)에서 샘플링 레이트를 계산합니다. """ if time_column not in df.columns: + # 시간 열이 없으면 첫 번째 열을 시간으로 간주 time_column = df.columns[0] time_data = df[time_column].dropna().values + if len(time_data) < 2: raise ValueError("시간 데이터가 충분하지 않습니다.") + # 시간 간격 계산 (마이크로초 단위) time_diffs = np.diff(time_data) - avg_time_diff_us = np.mean(time_diffs) - avg_time_diff_sec = avg_time_diff_us / 1_000_000 - sample_rate = 1 / avg_time_diff_sec - return sample_rate + # 평균 시간 간격 (마이크로초) + avg_time_diff_us = np.mean(time_diffs) -# =============================== -# Band-limited CV -# =============================== -def calculate_band_cv(freqs, amps, f_min=1.0, f_max=100.0): - """ - 특정 주파수 대역의 Coefficient of Variation 계산 - """ - band = (freqs >= f_min) & (freqs <= f_max) - band_amps = amps[band] + # 평균 시간 간격을 초 단위로 변환 + avg_time_diff_sec = avg_time_diff_us / 1_000_000 - mean_val = np.mean(band_amps) - if mean_val < 1e-12: - return np.nan + # 샘플링 레이트 = 1 / 평균 시간 간격 + sample_rate = 1 / avg_time_diff_sec - return np.std(band_amps) / mean_val * 100.0 + return sample_rate # Threshold 계산 함수 @@ -73,33 +66,23 @@ def calculate_threshold(amps, method="std", n_std=2.75, recon_error_value=0.3): # FFT 분석 함수 def fft_analysis( - data, - sample_rate, - window_size=4096, - fft_size=16384, - threshold_method="std", - n_std=2.75, - recon_error_value=0.3 + data, + sample_rate=296, + fft_size=None, + threshold_method="std", + n_std=2.75, + recon_error_value=0.3 ): - """ - FFT 분석 수행 - window_size 만큼의 데이터를 사용하고, fft_size로 zero-padding - """ - # window_size 만큼만 사용 - data = data[:window_size] data = data - np.mean(data) - - # zero-padding - if fft_size > window_size: - data = np.pad(data, (0, fft_size - window_size)) + n = fft_size if fft_size else len(data) + data = data[:n] y = fft(data) - x = fftfreq(fft_size, 1 / sample_rate) - - positive_freqs = x[:fft_size // 2] - positive_amps = np.abs(y[:fft_size // 2]) * 2 / window_size - + x = fftfreq(n, 1 / sample_rate) + positive_freqs = x[:n // 2] + positive_amps = np.abs(y[:n // 2]) * 2 / n resonance_freq = positive_freqs[np.argmax(positive_amps)] + threshold = calculate_threshold(positive_amps, threshold_method, n_std, recon_error_value) # Threshold 이상 구간 탐색 @@ -122,17 +105,15 @@ def fft_analysis( # 단일 파일 분석 함수 def analyze_single_file( - file_path, - axes, - window_size=4096, - fft_size=16384, - cutoff_freq=100.0, - threshold_method="std", - n_std=2.75, - recon_error_value=0.3, - time_column='Time_us', - band_cv_f_min=0.3, - band_cv_f_max=60.0 + file_path, + axes, + fft_size=8192, + apply_filter=True, + filter_order=5, + threshold_method="std", + n_std=2.75, + recon_error_value=0.3, + time_column='Time_us' ): df = pd.read_csv(file_path) file_title = os.path.splitext(os.path.basename(file_path))[0] @@ -142,8 +123,10 @@ def analyze_single_file( print(f" 계산된 샘플링 레이트: {sample_rate:.2f} Hz") results = [] + num_rows = 2 num_cols = 3 + plt.figure(figsize=(18, 8)) for idx, axis in enumerate(axes): @@ -153,27 +136,19 @@ def analyze_single_file( data = df[axis].dropna().values - # Butterworth 필터 적용 - data = apply_butterworth_filter( - data, - sample_rate=sample_rate, - cutoff=cutoff_freq, - order=4 - ) + if apply_filter: + cutoff = sample_rate / 4 + data = butter_lowpass_filter(data, cutoff=cutoff, fs=sample_rate, order=filter_order) freqs, amps, resonance_freq, threshold_ranges, threshold = fft_analysis( data, sample_rate=sample_rate, - window_size=window_size, fft_size=fft_size, threshold_method=threshold_method, n_std=n_std, recon_error_value=recon_error_value ) - # Band CV 계산 - band_cv = calculate_band_cv(freqs, amps, f_min=band_cv_f_min, f_max=band_cv_f_max) - # Threshold 범위를 문자열로 변환 threshold_ranges_str = "" if threshold_ranges: @@ -186,16 +161,13 @@ def analyze_single_file( 'File': file_title, 'Axis': axis, 'Resonance_Frequency_Hz': round(resonance_freq, 2), - 'Band_CV': round(band_cv, 2) if not np.isnan(band_cv) else 'N/A', - 'Band_CV_Freq_Range': f"{band_cv_f_min}-{band_cv_f_max}Hz", 'Threshold_Value': round(threshold, 4), 'Threshold_Method': threshold_method, 'Threshold_Ranges': threshold_ranges_str, 'Sample_Rate': round(sample_rate, 2), - 'Window_Size': window_size, 'FFT_Size': fft_size, - 'Filter_Type': 'Butterworth', - 'Cutoff_Hz': cutoff_freq + 'Filter_Applied': apply_filter, + 'Filter_Order': filter_order if apply_filter else 'N/A' }) # subplot 그리기 @@ -203,15 +175,15 @@ def analyze_single_file( plt.plot(freqs, amps, label="Amplitude") plt.axvline(resonance_freq, color='r', linestyle='--', label=f'Resonance: {resonance_freq:.2f} Hz') plt.axhline(y=threshold, color='g', linestyle=':', label=f'Threshold: {threshold:.3f}') - plt.title(f"{axis}\nResonance: {resonance_freq:.2f} Hz | CV: {band_cv:.2f}%") + plt.title(f"{axis}\nResonance: {resonance_freq:.2f} Hz") plt.xlabel("Frequency (Hz)") plt.ylabel("Amplitude") plt.grid(True) plt.legend() - plt.suptitle(f"FFT Frequency Spectrum - {file_title} (Filter: Butterworth)", fontsize=16) + plt.suptitle(f"FFT Frequency Spectrum - {file_title}", fontsize=16) plt.tight_layout(rect=[0, 0, 1, 0.93]) - plt.savefig(os.path.join(os.path.dirname(file_path), f"{file_title}_fft_plot_butterworth.png"), dpi=150) + plt.savefig(os.path.join(os.path.dirname(file_path), f"{file_title}_fft_plot.png"), dpi=150) plt.close() return results @@ -219,107 +191,82 @@ def analyze_single_file( # 배치 분석 함수 (모든 파일 처리) def analyze_all_files( - data_dir, - axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], - window_size=4096, - fft_size=16384, - cutoff_freq=100.0, - threshold_method="std", - n_std=2.75, - recon_error_value=0.3, - time_column='Time_us', - band_cv_f_min=0.3, - band_cv_f_max=60.0 + data_dir, + axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], + fft_size=8192, + apply_filter=True, + filter_order=5, + threshold_method="std", + n_std=2.75, + recon_error_value=0.3, + time_column='Time_us' ): """ 지정된 디렉토리의 모든 CSV 파일에 대해 FFT 분석을 수행합니다. """ data_path = Path(data_dir) - # CSV 파일 목록 가져오기 - csv_files = sorted(list(data_path.glob("mpu_raw_optimized_*.csv"))) + # CSV 파일 목록 가져오기 - mpu_raw_base_ 패턴으로 변경 + csv_files = sorted(list(data_path.glob("mpu_raw_base_*.csv"))) if not csv_files: - print(f"[오류] {data_dir}에서 CSV 파일을 찾을 수 없습니다.") + print(f"[오류] {data_dir}에서 mpu_raw_base_*.csv 파일을 찾을 수 없습니다.") return None print(f"총 {len(csv_files)}개의 파일을 찾았습니다.\n") - print(f"사용 필터: Butterworth (Cutoff: {cutoff_freq} Hz)") - print(f"Window Size: {window_size}, FFT Size: {fft_size}") - - # 클래스별로 파일 분류 - class_files = { - 'driving': [], - 'lidar': [], - 'motor': [], - 'lidar_driving': [], - 'motor_driving': [] - } - - for file in csv_files: - filename = file.name - if 'motor_driving' in filename: - class_files['motor_driving'].append(file) - elif 'lidar_driving' in filename: - class_files['lidar_driving'].append(file) - elif 'driving' in filename: - class_files['driving'].append(file) - elif 'lidar' in filename: - class_files['lidar'].append(file) - elif 'motor' in filename: - class_files['motor'].append(file) + print(f"[파일 목록]") + for f in csv_files: + print(f" - {f.name}") # 전체 결과를 저장할 리스트 all_results = [] - # 각 클래스별로 처리 - for class_name, files in class_files.items(): - if not files: + print(f"\n{'=' * 60}") + print(f"BASE 파일 분석 시작 ({len(csv_files)}개 파일)") + print(f"{'=' * 60}") + + # 모든 파일 처리 + for idx, file_path in enumerate(csv_files, 1): + print(f"\n[{idx}/{len(csv_files)}] 분석 중: {file_path.name}") + + try: + file_results = analyze_single_file( + file_path=str(file_path), + axes=axes, + fft_size=fft_size, + apply_filter=apply_filter, + filter_order=filter_order, + threshold_method=threshold_method, + n_std=n_std, + recon_error_value=recon_error_value, + time_column=time_column + ) + + # 클래스 정보를 'base'로 추가 + for result in file_results: + result['Class'] = 'base' + + all_results.extend(file_results) + print(f" ✓ 완료 ({len(file_results)}개 축 분석)") + + except Exception as e: + import traceback + print(f" ✗ 오류 발생: {e}") + print(f" ✗ 상세 오류:") + traceback.print_exc() continue - print(f"\n{'=' * 60}") - print(f"클래스: {class_name.upper()} ({len(files)}개 파일)") - print(f"{'=' * 60}") - - for idx, file_path in enumerate(files, 1): - print(f"\n[{idx}/{len(files)}] 분석 중: {file_path.name}") - try: - file_results = analyze_single_file( - file_path=str(file_path), - axes=axes, - window_size=window_size, - fft_size=fft_size, - cutoff_freq=cutoff_freq, - threshold_method=threshold_method, - n_std=n_std, - recon_error_value=recon_error_value, - time_column=time_column, - band_cv_f_min=band_cv_f_min, - band_cv_f_max=band_cv_f_max - ) - - # 클래스 정보 추가 - for result in file_results: - result['Class'] = class_name - - all_results.extend(file_results) - print(f" ✓ 완료") - except Exception as e: - print(f" ✗ 오류 발생: {e}") - continue - # 전체 결과를 하나의 CSV로 저장 if all_results: results_df = pd.DataFrame(all_results) # 컬럼 순서 재정렬 - column_order = ['Class', 'File', 'Axis', 'Resonance_Frequency_Hz', 'Band_CV', - 'Band_CV_Freq_Range', 'Threshold_Value', 'Threshold_Method', - 'Threshold_Ranges', 'Sample_Rate', 'Window_Size', 'FFT_Size', - 'Filter_Type', 'Cutoff_Hz'] + column_order = ['Class', 'File', 'Axis', 'Resonance_Frequency_Hz', + 'Threshold_Value', 'Threshold_Method', 'Threshold_Ranges', + 'Sample_Rate', 'FFT_Size', 'Filter_Applied', 'Filter_Order'] results_df = results_df[column_order] - output_path = data_path / f"all_files_fft_analysis_butterworth_bandCV.csv" + output_path = data_path / "fft_analysis_base_results.csv" results_df.to_csv(output_path, index=False, encoding='utf-8-sig') print(f"\n{'=' * 60}") @@ -327,37 +274,38 @@ def analyze_all_files( print(f"총 {len(all_results)}개의 분석 결과 (파일 {len(csv_files)}개 × 축 {len(axes)}개)") print(f"{'=' * 60}") - # 클래스별 요약 통계 - print("\n[클래스별 요약]") - for class_name in class_files.keys(): - class_data = results_df[results_df['Class'] == class_name] - if len(class_data) > 0: - print(f" {class_name}: {len(class_data) // len(axes)}개 파일") + # 요약 통계 + print("\n[분석 요약]") + print(f" 분석된 파일 수: {len(csv_files)}개") + print(f" 분석된 축: {', '.join(axes)}") + print(f" 총 결과 개수: {len(all_results)}개") return results_df else: - print("[오류] 분석된 결과가 없습니다.") + print("\n[오류] 분석된 결과가 없습니다.") + print("[가능한 원인]") + print(" 1. 모든 파일에서 예외가 발생했습니다") + print(" 2. CSV 파일의 열 이름이 예상과 다릅니다") + print(" 3. 데이터가 충분하지 않습니다") return None # 실행 if __name__ == "__main__": # 데이터 디렉토리 경로 설정 - DATA_DIR = "/Users/seohyeon/PycharmProjects/AT_data/data_v1" + DATA_DIR = "/Users/seohyeon/PycharmProjects/AT_data/data_v2" # 배치 분석 실행 results = analyze_all_files( data_dir=DATA_DIR, axes=["Accel_X", "Accel_Y", "Accel_Z", "Gyro_X", "Gyro_Y", "Gyro_Z"], - window_size=4096, - fft_size=16384, - cutoff_freq=100.0, - threshold_method="std", + fft_size=8192, # FFT 크기 8192로 설정 + apply_filter=True, + filter_order=5, + threshold_method="std", # "std", "percentile", "recon_error" n_std=2.75, recon_error_value=0.3, - time_column='Time_us', - band_cv_f_min=0.3, - band_cv_f_max=60.0 + time_column='Time_us' # 시간 열 이름 (마이크로초 단위) ) if results is not None: diff --git a/FFT/fft_analysis_results_baseline/frequency_comparison_boxplot_base.png b/FFT/fft_analysis_results_baseline/frequency_comparison_boxplot_base.png new file mode 100644 index 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