
Citation: Jin Yi, Chao Lu, Guomin Li. A literature review on latest developments of Harmony Search and its applications to intelligent manufacturing[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2086-2117. doi: 10.3934/mbe.2019102
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HRV analysis is widely used for cardiovascular health monitoring and disease prediction [1,2]. It is also considered an important indicator to evaluate the control of cardiac autonomic nervous balance [3,4], which is related to physical activity [2], mental stress [1] and sleep health [5,6]. The crux of HRV analysis involves studying the fluctuations in time intervals between successive heartbeats, known as inter-beat intervals. Typically, the inter-beat interval is gauged as the time between two consecutive R-peak (R-R interval or RRi) ECG signals. Given that the precision of HRV analysis is contingent on accurately pinpointing R-peaks within the ECG signal, the development of a high-precision R-peak localization algorithm is of paramount significance.
For over four decades, the field of automated R-peak detection has undergone extensive exploration. Numerous algorithms targeting R-peak or QRS detection have been made available to the public [7,8], leveraging diverse principles like template matching [9,10,11], derivative analysis [12,13], digital filtering [14,15,16], wavelet transform [17,18], Hilbert transform [19,20], morphology classification [21], phase space reconstruction [22] and dynamic thresholding [23,24,25,26,27]. Despite these advancements, formulating a robust and universally accepted algorithm remains a challenge, given the diverse morphological differenes present in ECG signals [28]. The incorporation of machine learning, particularly deep neural networks [29,30,31], has significantly enhanced the sensitivity of R-peak or QRS detection, surpassing the 99.9% mark. However, the crux of the matter is that, instead of accurately pinpointing the chronological localization of R-peaks, current algorithms primarily emphasize sensitivity and overall accuracy in detecting R-peaks, accommodating a certain temporal discrepancy between actual and detected R-peaks [32].
This study centers on developing an algorithm to accurately identify the exact positions of R-peaks within ECG signals. This is achieved by enhancing an existing R-peak detection method. Among the available algorithms, we initiated our work by adapting the PT algorithm [33], which remains widely employed due to its robustness, efficiency and accuracy in R-peak detection [34]. The PT algorithm utilizes a moving-window-integration of 150 ms, a step that can occasionally lead to a random shift in the detected R-peak location. To address the lack of precision in R-peak localization, in particular from noisy or low-quality ECG data, we propose to first roughly localize the QRS complex through the computation and identification of the QRS envelope, and then refine the localization with a template matching method.
The assessment of the proposed technique was carried out using the MIT-BIH Arrhythmia database [35], available through PhysioNet [36]. The database contained 48 thirty-minute records with a sample rate of 360 Hz, which were captured from a group of patients with 22 females and 25 males aged between 23 and 89 years. Notably, some of these records exhibited noticeable morphological distortions, particularly evident in the P and T waves of the ECG signal. Expert cardiologists annotated the database as a point of reference. Each record contained 2 leads, and lead I was used to evaluate the proposed algorithm.
According to the Special Requirements for the Safety and Basic Performance of Dynamic ECG Systems from international standard IEC60601-2-47:2001, it is considered that the R-peak position is correctly detected by an algorithm if the R-peak position obtained by the algorithm is within 150 ms of the annotated position. The proposed algorithm is evaluated in terms of both the sensitivity of R-peak detection and the accuracy of the detected R-peak location. Sensitivity (Se), positive prediction value (PPV) and detection error rate (DER) are calculated by Eq (1) for the evaluation of R-peak detection [32]:
Se=TPTP+FN×100%;PPV=TPTP+FP×100%;DER=FN+FPTP+FN×100% | (1) |
where TP (true positive) refers to the number of correctly detected R-peaks, FN (false negative) refers to the number of undetected R-peaks which exist in annotation and FP (false positive) refers to the number of falsely detected R-peaks which do not exist in annotation (i.e., > 150 ms away from any annotated R-peaks).
The accuracy of the detected R-peak location is evaluated by the annotated-detected error (ADE) with unit ms calculated by Eq (2) [32]:
ADE=√1TPTP∑n=1(Kn−Dn)2∗Ts | (2) |
where Kn refers to the annotated R-peak location, Dn refers to the detected R-peak location and Ts refers to ECG signal sampling period with unit ms.
The R-peak position detected by the algorithm may have a group time delay with the annotated R-peak position. The final R-peak position group time delay needs to be compensated once for best alignment between the detected R-peaks and the annotated R-peaks with a fixed shift of several samples in each record. The group time delay is related to the filtering operation and also to the spectral characteristics of the QRS complex. Group time delay compensation is only used for fair comparison between different algorithms and has no effect on RRi calculation. Group time delay TD with unit ms can be simply calculated by Eq (3):
TD=[1TPTP∑n=1(Kn−Dn)]∗Ts | (3) |
The PT algorithm consists of 5 processes: band-pass filter (BPF), derivative, squaring, moving window integration (MWI) and R-peak detection [33], as shown in Figure 1.
The 5–15 Hz BPF was achieved by cascading a 15 Hz low-pass filter (LPF) cascaded with a 5 Hz high-pass filter (HPF). LPF was used to remove the high-frequency noise such as electromyogram (EMG) and power line interference [34]. HPF was used to remove the low-frequency interference, such as the baseline wander. Taking the derivative would enhance the slope information of the QRS complex and suppress the low-frequency P-wave and T-waves [34]. The squaring process was applied so that the positive and negative values were not canceled out in the following MWI process, and the QRS complex were further enhanced. The MWI process was performed with a 150 ms integration window to acquire the envelope of the R-wave. The 150-ms window width is used since it is slightly larger than that of a normal QRS complex for better adaptivity. We chose a third-party PT algorithm from NeuroKit [37] as a reference for performance evaluation. The source code is publicly available in Python on www.github.com.
In the PT algorithm, the MWI process may result in an R-peak location shift because the maximum slope position of the rising edge of the integration waveform was not the precise R-peak temporal location [33]. The precise R-peak is on the point of minimum slope position of the rising edge of integration waveform in theory, which will be illustrated in discussion section. In addition, the 5–15 Hz BPF may result in distortion of QRS complex which will also be illustrated in the discussion section. These processes could result in temporal shifts of R-peaks from their real positions and need to be further improved for more precise localization of R-peaks.
The proposed algorithm includes three stages (Figure 2). The first is the preprocessing stage, where the raw ECG signal is filtered by a 5–35 Hz BPF, which is achieved by a 35 Hz LPF cascaded with a 5 Hz HPF. The second stage calculates a window that marks the QRS complex, including 3 processes: squaring, 5 Hz LPF and windowing. The third stage is the template matching stage, in which a program auto-selected QRS template is taken to localize the R-peak by finding the maximum moving-window cross-correlation (CC) with the windowed pre-processed ECG signal.
The windowing stage is inspired from the PT algorithm. A 5–35 Hz pass band is used here instead of the 5–15 Hz pass band for better performance and adaptability. The derivative process can highlight the slope characteristic of the QRS complex, but can also induce a phase shift, so it is not used in our algorithm. The MWI process is replaced by a forward-backward digital 5 Hz LPF for better noise filtering and zero-time delay. After the windowing transformation of L(i), windows with 200-ms width are generated in accordance with the center of the QRS envelopes.
The template matching stage is an improvement for precise R-peak position detection. The QRS template is generated by automatic selection among the first five QRS windows from each ECG recording Y(i). Among the first five QRS complexes inside the window, the one with the median R-peak amplitude (absolute value) is selected. A 120 ms segment from the selected ECG waveform symmetrical about the R-peak position is taken as the template. One hundred twenty ms is determined because the width of 120 ms is the maximum width of normal QRS complexes [38]. The QRS template has a window width of N = 43 samples with a 360 Hz sampling rate, where N must be an odd number to ensure that the R-peak position is centered.
The proposed method was implemented on Python 3.9 software and evaluated over the MIT-BIH Arrhythmia database to compare with the state-of-the-art PT algorithm.
The filters used in the algorithm are all second-order forward-backward Butterworth infinite impulse response (IIR) filters with zero-phase delay. The forward-backward filtering processes are implemented as Eq (4) to Eq (6):
Z(i)=b0⋅X(i)+b1⋅X(i−1)+b2⋅X(i−2)−c1⋅Z(i−1)−c2⋅Z(i−2) | (4) |
Z(i)=Z(−i) | (5) |
Y(i)=b0⋅Z(i)+b1⋅Z(i−1)+b2⋅Z(i−2)−c1⋅Y(i−1)−c2⋅Y(i−2) | (6) |
where X(i) is the original ECG data, Y(i) is the filtered signal and b0, b1, b2, c1, c2 are filter parameters. Equations (4) and (6) are difference equations of the IIR filter. Equation (5) is included to reverse Z(i) and pass it through the IIR filter again for zero-phase delay.
Here, the 5–35 Hz BPF process is achieved by a 35 Hz LPF cascaded with a 5 Hz HPF. All filters are implemented with SciPy.signal.sosfiltfilt function available in Python. The first 4 s segment from record 209 was used to display the results of this stage, as shown in Figure 3.
This stage calculates a window to mark the QRS complex in each ECG beat. First, the Y(i) signal is squared to obtain S(i) according to Eq (7), which enhances the QRS complex:
S(i)=Y(i)2 | (7) |
Second, S(i) passes through a 5 Hz low-pass filter to obtain L(i) as the envelope of the QRS complex. Third, L(i) is converted into the window signal W(i) through dynamic thresholding. W(i) is composed of "0" and "1", where "1" indicates the interval of QRS window. The conversion logic is shown as Eqs (8) and (9):
D(n)=M(n)+D(n−1)∗(n−1)n | (8) |
W(i)={1,L(i)>max(0.3∗M(n)+0.1∗D(n),0.05∗A(n))0,L(i)≤max(0.3∗M(n)+0.1∗D(n),0.05∗A(n)) | (9) |
where M(n) is the maximum value of the n-th 400 ms window, D(n) is the average of all past maximum value of windows and A(n) is the maximum value of the 2 s segment of the signal (five consecutive 400 ms windows). W(i) is set to "1" or "0" according to Eq (9). The window threshold D(n) is dynamically updated every 400 ms according to Eq (8) and A(n) is updated every 400 ms with the forward-moving 2 s segment. We also verified the performance of different window widths, such as 200,300,400 and 500 ms, in which the 400 ms window had the best result.
The 400 ms window segmentation would cause some QRS complexes to be split, resulting in duplicate windows. Hence, W(i) was further processed to remove small windows resulting from window segmentation. Small-width windows, whose width were less than 1/4 of the average window width, were removed. And, the window with the smaller width was removed when there was another window within 0.4 s. Finally, the windows were symmetrically widened to 200 ms (72 samples for 360 Hz sample rate) about the center position. The windows whose width were greater than 200 ms remained unchanged. Figure 4 shows the first 4 s segment from record 209 as an example.
The QRS template is an N-sample time series T(n) extracted from Y(i). The CC is calculated by Eq (10):
C(i)=∑jn=−j(T(n)−¯T)(Y(i+n)−¯Y)√∑jn=−j(T(n)−¯T)2∑jn=−j(Y(i+n)−¯Y)2 | (10) |
where the parameter j=(N−1)/2 is half the QRS window width. C(i) is the CC result of moving window correlation between QRS template T(n) and Y(i).
The R-peak location (R(k) where k is the index of R-peaks number) is determined by finding the largest CC (Cp(k)). Figure 5 shows the first 4 s segment from record 209 as an example. R(k) and Cp(k) were further processed to reduce false detection of R-peaks. When the RRi is less than 0.4 times the average RRi, remove the corresponding R-peak with the smaller Cp value. The Cp(k) is used to select the R-peak because it shows the similarity of QRS complexes with the QRS template and may be used as an indicator for the reliability of R-peak detection. The final complete Cp(k) of record 209 was showed in Figure 6.
ECG signals are highly susceptible to external interference and noise, which often leads to distortions in the ECG waveform. This introduces significant challenges in detecting R-peaks accurately. Most QRS detection algorithms are structured around three essential steps: denoising, R-peak enhancement and R-peak detection [39]. The algorithm proposed in this paper aligns with this strategy as well. The initial preprocessing stage serves the purpose of noise reduction, followed by the application of windowing to enhance R-peaks. Ultimately, the template matching stage is used for R-peak detection. The 5–35 Hz band-pass filter effectively captures the spectrum energy of the QRS complex while preserving the essential morphology of QRS and simultaneously attenuating interference and noise. Employing the template matching technique stands out as a potent method for precisely identifying the exact positions of R-peaks.
The performances of the proposed algorithm on the Arrhythmia database are shown in Appendix Table A1. TB represents the total number of R-peaks annotated in the record. DB represents the total number of detected R-peaks. TD is the group time delay between TB and DB with an integer number of samples. DB is 109491, only 3 less than TB of 109494. Average TD is only 0.17 ms (0.0625 sample). The maximum FP value was 139 and the maximum FN value is 43. In general, the number of false detections (FP = 242) was slightly less than the number of missed detections (FN = 245).
The performances of the PT algorithm on the Arrhythmia database were shown in Appendix Table A2. The maximum FP value was 591 and the maximum FN value was 482, appearing in the same record, 108. In general, the number of false detections (FP = 934) was less than the number of missed detections (FN = 1233). The average TD of the PT algorithm was 30.49 ms (10.975 samples), much larger than that of the proposed algorithm, which was 0.17 ms on average.
Performance comparison between the two algorithms was also evaluated with different tolerance for R-peak detection, as shown in Table 1, in which: 150 ms was the time of 54 sample periods, 25 ms was the time of 9 sample periods, 2.78 ms was the time of 1 sample period. The proposed algorithm outperformed the PT algorithm on all metrics.
Pan-Tompkins Algorithm | Proposed Algorithm | |||||||
Tolerance | Se(%) | PPV(%) | DER(%) | ADE(ms) | Se(%) | PPV(%) | DER(%) | ADE(ms) |
150 ms | 98.87 | 99.14 | 1.98 | 21.65 | 99.78 | 99.78 | 0.44 | 8.35 |
25 ms | 79.41 | 79.63 | 40.90 | 13.37 | 96.82 | 96.82 | 6.36 | 3.17 |
2.78 ms | 11.85 | 11.88 | 176.03 | 2.42 | 86.18 | 86.18 | 27.64 | 1.86 |
Note: TB: total beats annotated; Se: sensitivity; PPV: positive prediction value; DER: detection error rate; ADE: annotated-detected error. |
The main purpose of this algorithm is to improve the detection accuracy of R-peak location, paying less attention to Se/PPV/DER metrics. Yet, the algorithm derives satisfying performance in the Se/PPV/DER metrics on the Arrhythmia database. Additionally, the proposed algorithm completely surpassed the comparison algorithm in the accuracy of R-peak location [32]. Refer to Table 2 for details.
Method | TB | Se(%) | PPV(%) | DER(%) | ADE(ms) |
Proposed | 109,494 | 99.78 | 99.78 | 0.44 | 8.35 |
Kai Zhao et al. [32] | 109,966 | 99.81 | 99.88 | 0.31 | 12.2 |
* Pan and Tompkins [33] | 109,966 | 99.13 | 99.63 | 1.24 | 13.4 |
* Indicates that the data is quoted from literature [32]. |
The introduced algorithm showcased superior performance over the PT algorithm across all metrics including SE, PPV, DER and ADE when tested on the Arrhythmia database. Notably, the achieved ADE of 8.35 ms surpassed the 12.2 ms reported in a comparative study [32]. To optimize the integrity of QRS morphology, a 5–35 Hz BPF was employed in the proposed algorithm. Furthermore, the template matching method was proved an effective strategy to identify the precise location of R-peaks.
The Arrhythmia database is widely used to evaluate the QRS detection algorithm, because it includes various arrhythmic QRS complexes, different types of noise and various QRS morphology with detailed annotation. However, the Arrhythmia database still has the problem of inaccurate R-peak annotation [40]. A large number of literatures with nearly perfect performance also have a problem with non-standardized R-peak numbers. There are various different values for the total number of R-peaks suggested for this database, such as 109,494 [10], 109,966 [27], 106,581 [41], 109,475 [42]. The Arrhythmia database have many categories of annotation: "*", "N", "L", "R", "a", "V", "F", "J", "A", "S", " "E", "j", "/", "Q", "e", "n", "f". This paper used 109,494 as the total R-peak number, and the categories excluded in the statistics were: "*", "n". The poor performance in ADE may result from not only the error of R-peak position detected, but also the error of R-peak position annotated. As shown in Figure 7, there are annotation errors in record 104, obviously, which results in detection error in both algorithms, although more in the PT algorithm.
We extracted record 122 and record 115 from the best ADE of the Arrhythmia database, and compared them with record 104 and record 208 from the worst ADE as shown in Table 3. Record 122 and record 115 only have normal beats. While the proportion of the number of "V" categories in TB (total number of R-peaks) is obviously larger in record 208 and record 104, which may be a reason for the poor ADE performance. "V" refers to the category of premature ventricular contract, "/" refers to the paced beat, 'f ' refers to fusion of paced and normal beat. Those kinds of QRS morphology differ from normal QRS morphology (and therefore the QRS template), which could result in degraded performance in template matching. These categories have different QRS templates which are not covered in the proposed method. But, the method still has the ability to detect R-peaks in a wrong position with a lower cross-correlation peak value, which induce detected R-peak shift from the real location and reduce the ADE performance.
File | ADE(ms) | TB | N | V | / | Q | F | f | S |
122 | 1.12 | 2476 | 2476 | ||||||
115 | 1.19 | 1953 | 1953 | ||||||
104 | 16.75 | 2229 | 163 | 2 | 1380 | 18 | 1 | 666 | |
208 | 24.96 | 2955 | 1586 | 992 | 2 | 373 | 2 | ||
Note: normal beats; V: beats of premature ventricular contract; /: paced beats; f: fusion of paced and normal beats; Q: Unclassifiable beats; F: fusion of ventricular and normal beats; S: supraventricular premature beats. |
There is another reason for false R-peak detection in the PT algorithm. The narrow-band BPF would distort the QRS morphology, causing the wrong R-peak position to be detected. Examples are shown in Figure 8. Comparing Figure 8(a), (c), 5–15 Hz BPF could shift the R-peak location forward about 22 samples while R-peak location nearly has no shift with 5–35 Hz BPF. And, the MWI process is another possible reason for R-peak location shift. In Figure 8(b), the blue line is the real R-peak location in raw ECG data, while the red line is the final detected R-peak by the PT algorithm with a shift of 26 samples. In Figure 8(d), the blue line is the real R-peak location in raw ECG data, while the red line is the final detected R-peak by the PT algorithm with a shift of 11 samples. The MWI process will result in a time delay of Trs (R-wave peak to S-wave offset) for R-peak position [33], where Trs is related with the QRS morphology and varies with noise.
This paper presents an enhanced version of the PT algorithm, wherein the inclusion of the QRS template matching substantially enhances the accuracy of R-peak position detection. This advancement is particularly effective in refining the precision of R-peak localization. Moving forward, the potential exists to expand the algorithm's versatility by incorporating various templates for atypical QRS patterns, thereby bolstering its adaptability. The contribution of this study lies in the introduction of a highly precise R-peak position detection algorithm capable of accurately pinpointing R-peak locations. This advancement holds the promise of significantly amplifying the clinical applications of HRV analysis.
The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.
The authors wish to acknowledge the funding support from Science and Technology Program of Guangzhou (No. 2019050001), Program for Chang Jiang Scholars and Innovative Research Teams in Universities (No. IRT_17R40), Guangdong Provincial Key Laboratory of Optical Information Materials and Technology (No. 2017B030301007), Guangzhou Key Laboratory of Electronic Paper Displays Materials and Devices (201705030007), MOE International Laboratory for Optical Information Technologies, the 111 Project.
The authors declare there is no conflict of interest.
File | TD(ms) | TB | DB | TP | FP | FN | Se(%) | PPV(%) | DER(%) | ADE(ms) |
100 | 0.00 | 2273 | 2273 | 2273 | 0 | 0 | 100 | 100 | 0 | 2.21 |
101 | 0.00 | 1865 | 1865 | 1862 | 3 | 3 | 99.84 | 99.84 | 0.00 | 2.53 |
102 | 0.00 | 2187 | 2187 | 2187 | 0 | 0 | 100 | 100 | 0 | 10.80 |
103 | 0.00 | 2084 | 2083 | 2083 | 0 | 1 | 99.95 | 100 | 0.00 | 2.32 |
104 | 0.00 | 2229 | 2237 | 2228 | 9 | 1 | 99.96 | 99.60 | 0.00 | 16.75 |
105 | 0.00 | 2572 | 2590 | 2557 | 33 | 15 | 99.42 | 98.73 | 0.02 | 9.54 |
106 | 0.00 | 2027 | 2021 | 2020 | 1 | 7 | 99.65 | 99.95 | 0.00 | 5.30 |
107 | –2.78 | 2137 | 2136 | 2135 | 1 | 2 | 99.91 | 99.95 | 0.00 | 7.47 |
108 | 2.78 | 1763 | 1758 | 1754 | 4 | 9 | 99.49 | 99.77 | 0.01 | 14.95 |
109 | –2.78 | 2532 | 2530 | 2530 | 0 | 2 | 99.92 | 100 | 0.00 | 5.08 |
111 | 0.00 | 2124 | 2123 | 2123 | 0 | 1 | 99.95 | 100 | 0.00 | 5.78 |
112 | 0.00 | 2539 | 2539 | 2539 | 0 | 0 | 100 | 100 | 0 | 2.14 |
113 | 0.00 | 1795 | 1795 | 1795 | 0 | 0 | 100 | 100 | 0 | 1.93 |
114 | 30.56 | 1879 | 1880 | 1876 | 4 | 3 | 99.84 | 99.79 | 0.00 | 8.02 |
115 | 2.78 | 1953 | 1953 | 1953 | 0 | 0 | 100 | 100 | 0 | 1.12 |
116 | 0.00 | 2412 | 2390 | 2387 | 3 | 25 | 98.96 | 99.87 | 0.01 | 2.91 |
117 | –19.44 | 1535 | 1535 | 1535 | 0 | 0 | 100 | 100 | 0 | 6.97 |
118 | 0.00 | 2278 | 2278 | 2278 | 0 | 0 | 100 | 100 | 0 | 3.15 |
119 | 0.00 | 1987 | 1988 | 1987 | 1 | 0 | 100 | 99.95 | 0.00 | 6.00 |
121 | –2.78 | 1863 | 1861 | 1861 | 0 | 2 | 99.89 | 100 | 0.00 | 2.26 |
122 | 0.00 | 2476 | 2476 | 2476 | 0 | 0 | 100 | 100 | 0 | 1.19 |
123 | 0.00 | 1518 | 1518 | 1518 | 0 | 0 | 100 | 100 | 0 | 1.82 |
124 | 0.00 | 1619 | 1619 | 1619 | 0 | 0 | 100 | 100 | 0 | 6.99 |
200 | –5.56 | 2601 | 2601 | 2599 | 2 | 2 | 99.92 | 99.92 | 0.00 | 17.64 |
201 | 0.00 | 1963 | 1942 | 1942 | 0 | 21 | 98.93 | 100 | 0.01 | 4.15 |
202 | 0.00 | 2136 | 2122 | 2122 | 0 | 14 | 99.34 | 100 | 0.01 | 2.47 |
203 | –5.56 | 2980 | 2954 | 2937 | 17 | 43 | 98.56 | 99.42 | 0.02 | 15.28 |
205 | 0.00 | 2656 | 2648 | 2648 | 0 | 8 | 99.70 | 100 | 0.00 | 5.27 |
207 | 0.00 | 1860 | 1991 | 1852 | 139 | 8 | 99.57 | 93.02 | 0.08 | 12.98 |
208 | 8.33 | 2955 | 2939 | 2936 | 3 | 19 | 99.36 | 99.90 | 0.01 | 24.96 |
209 | 0.00 | 3005 | 3005 | 3005 | 0 | 0 | 100 | 100 | 0 | 1.54 |
210 | 0.00 | 2650 | 2623 | 2621 | 2 | 29 | 98.91 | 99.92 | 0.01 | 7.34 |
212 | 0.00 | 2748 | 2748 | 2748 | 0 | 0 | 100 | 100 | 0 | 2.24 |
213 | 0.00 | 3251 | 3248 | 3248 | 0 | 3 | 99.91 | 100 | 0.00 | 5.78 |
214 | 0.00 | 2262 | 2258 | 2258 | 0 | 4 | 99.82 | 100 | 0.00 | 4.60 |
215 | 0.00 | 3363 | 3359 | 3359 | 0 | 4 | 99.88 | 100 | 0.00 | 3.18 |
217 | –13.89 | 2208 | 2205 | 2204 | 1 | 4 | 99.82 | 99.95 | 0.00 | 8.09 |
219 | 0.00 | 2154 | 2154 | 2154 | 0 | 0 | 100 | 100 | 0 | 1.46 |
220 | 2.78 | 2048 | 2048 | 2048 | 0 | 0 | 100 | 100 | 0 | 1.82 |
221 | 0.00 | 2427 | 2425 | 2425 | 0 | 2 | 99.92 | 100 | 0.00 | 2.65 |
222 | 0.00 | 2483 | 2485 | 2483 | 2 | 0 | 100 | 99.92 | 0.00 | 1.81 |
223 | 0.00 | 2605 | 2603 | 2603 | 0 | 2 | 99.92 | 100 | 0.00 | 7.61 |
228 | 0.00 | 2053 | 2062 | 2047 | 15 | 6 | 99.71 | 99.27 | 0.01 | 5.69 |
230 | 2.78 | 2256 | 2256 | 2256 | 0 | 0 | 100 | 100 | 0 | 1.64 |
231 | 0.00 | 1571 | 1570 | 1570 | 0 | 1 | 99.94 | 100 | 0.00 | 1.55 |
232 | 0.00 | 1780 | 1782 | 1780 | 2 | 0 | 100 | 99.89 | 0.00 | 1.68 |
233 | –5.56 | 3079 | 3076 | 3076 | 0 | 3 | 99.90 | 100 | 0.00 | 16.33 |
234 | 0.00 | 2753 | 2752 | 2752 | 0 | 1 | 99.96 | 100 | 0.00 | 0.86 |
Total | 109,494 | 109,491 | 109,249 | 242 | 245 | 99.78 | 99.78 | 0.44 | 8.35 | |
TB: total beats annotated; DB: detected beats by algorithm; TD: Group time delay between TB and DB; TP: true positive, the number of correctly detected R-peaks; FP: false positive, the number of false detected R-peaks; FN: false negative, the number of undetected R-peaks; Se: sensitivity; PPV: positive prediction value; DER: detection error rate; ADE: annotated-detected error. |
File | TD(ms) | TB | DB | TP | FP | FN | Se(%) | PPV(%) | DER(%) | ADE(ms) |
100 | 44.44 | 2273 | 2271 | 2271 | 0 | 2 | 99.91 | 100 | 0.00 | 25.01 |
101 | 30.56 | 1865 | 1868 | 1863 | 5 | 2 | 99.89 | 99.73 | 0.00 | 13.98 |
102 | 22.22 | 2187 | 2187 | 2187 | 0 | 0 | 100 | 100 | 0 | 18.24 |
103 | 36.11 | 2084 | 2080 | 2079 | 1 | 5 | 99.76 | 99.95 | 0.00 | 16.79 |
104 | 16.67 | 2229 | 2273 | 2221 | 52 | 8 | 99.64 | 97.71 | 0.03 | 21.90 |
105 | 0.00 | 2572 | 2599 | 2561 | 38 | 11 | 99.57 | 98.54 | 0.02 | 18.40 |
106 | 25.00 | 2027 | 1996 | 1995 | 1 | 32 | 98.42 | 99.95 | 0.02 | 23.96 |
107 | 50.00 | 2137 | 2135 | 2135 | 0 | 2 | 99.91 | 100 | 0.00 | 26.49 |
108 | 19.44 | 1763 | 1872 | 1281 | 591 | 482 | 72.66 | 68.43 | 0.61 | 43.72 |
109 | 25.00 | 2532 | 2528 | 2527 | 1 | 5 | 99.80 | 99.96 | 0.00 | 24.43 |
111 | 25.00 | 2124 | 2125 | 2123 | 2 | 1 | 99.95 | 99.91 | 0.00 | 21.21 |
112 | 36.11 | 2539 | 2539 | 2539 | 0 | 0 | 100 | 100 | 0 | 32.70 |
113 | 44.44 | 1795 | 1794 | 1793 | 1 | 2 | 99.89 | 99.94 | 0.00 | 24.20 |
114 | 47.22 | 1879 | 1882 | 1876 | 6 | 3 | 99.84 | 99.68 | 0.00 | 15.68 |
115 | 38.89 | 1953 | 1953 | 1952 | 1 | 1 | 99.95 | 99.95 | 0.00 | 10.89 |
116 | 30.56 | 2412 | 2391 | 2387 | 4 | 25 | 98.96 | 99.83 | 0.01 | 16.35 |
117 | 25.00 | 1535 | 1535 | 1533 | 2 | 2 | 99.87 | 99.87 | 0.00 | 22.72 |
118 | 41.67 | 2278 | 2278 | 2274 | 4 | 4 | 99.82 | 99.82 | 0.00 | 25.16 |
119 | 30.56 | 1987 | 1988 | 1986 | 2 | 1 | 99.95 | 99.90 | 0.00 | 25.33 |
121 | 16.67 | 1863 | 1864 | 1858 | 6 | 5 | 99.73 | 99.68 | 0.01 | 23.31 |
122 | 2.78 | 2476 | 2476 | 2475 | 1 | 1 | 99.96 | 99.96 | 0.00 | 15.93 |
123 | 52.78 | 1518 | 1515 | 1513 | 2 | 5 | 99.67 | 99.87 | 0.00 | 18.09 |
124 | 8.33 | 1619 | 1620 | 1619 | 1 | 0 | 100 | 99.94 | 0.00 | 21.26 |
200 | 33.33 | 2601 | 2603 | 2596 | 7 | 5 | 99.81 | 99.73 | 0.00 | 22.39 |
201 | 33.33 | 1963 | 1912 | 1912 | 0 | 51 | 97.40 | 100 | 0.03 | 18.87 |
202 | 22.22 | 2136 | 2128 | 2127 | 1 | 9 | 99.58 | 99.95 | 0.00 | 15.54 |
203 | 19.44 | 2980 | 2957 | 2924 | 33 | 57 | 98.09 | 98.88 | 0.03 | 22.66 |
205 | 25.00 | 2656 | 2649 | 2648 | 1 | 8 | 99.70 | 99.96 | 0.00 | 14.22 |
207 | 36.11 | 1860 | 1919 | 1826 | 93 | 34 | 98.17 | 95.15 | 0.07 | 24.20 |
208 | 38.89 | 2955 | 2658 | 2654 | 4 | 301 | 89.81 | 99.85 | 0.10 | 28.16 |
209 | 41.67 | 3005 | 3005 | 3003 | 2 | 2 | 99.93 | 99.93 | 0.00 | 20.36 |
210 | 27.78 | 2650 | 2607 | 2603 | 4 | 47 | 98.23 | 99.85 | 0.02 | 15.29 |
212 | 13.89 | 2748 | 2749 | 2748 | 1 | 0 | 100 | 99.96 | 0.00 | 18.92 |
213 | 16.67 | 3251 | 3249 | 3249 | 0 | 2 | 99.94 | 100 | 0.00 | 26.62 |
214 | 22.22 | 2262 | 2255 | 2253 | 2 | 9 | 99.60 | 99.91 | 0.00 | 14.22 |
215 | 47.22 | 3363 | 3363 | 3362 | 1 | 1 | 99.97 | 99.97 | 0.00 | 19.16 |
217 | 41.67 | 2208 | 2205 | 2202 | 3 | 6 | 99.73 | 99.86 | 0.00 | 25.10 |
219 | 33.33 | 2154 | 2152 | 2150 | 2 | 4 | 99.81 | 99.91 | 0.00 | 17.94 |
220 | 38.89 | 2048 | 2048 | 2046 | 2 | 2 | 99.90 | 99.90 | 0.00 | 17.17 |
221 | 38.89 | 2427 | 2361 | 2360 | 1 | 67 | 97.24 | 99.96 | 0.03 | 21.64 |
222 | 19.44 | 2483 | 2488 | 2483 | 5 | 0 | 100 | 99.80 | 0.00 | 15.72 |
223 | 33.33 | 2605 | 2603 | 2602 | 1 | 3 | 99.88 | 99.96 | 0.00 | 29.88 |
228 | 19.44 | 2053 | 2080 | 2045 | 35 | 8 | 99.61 | 98.32 | 0.02 | 20.37 |
230 | 50.00 | 2256 | 2255 | 2255 | 0 | 1 | 99.96 | 100 | 0.00 | 15.21 |
231 | 41.67 | 1571 | 1569 | 1568 | 1 | 3 | 99.81 | 99.94 | 0.00 | 29.59 |
232 | 44.44 | 1780 | 1790 | 1776 | 14 | 4 | 99.78 | 99.22 | 0.01 | 25.12 |
233 | 22.22 | 3079 | 3072 | 3072 | 0 | 7 | 99.77 | 100 | 0.00 | 19.89 |
234 | 19.44 | 2753 | 2750 | 2750 | 0 | 3 | 99.89 | 100 | 0.00 | 11.04 |
Total | 109,494 | 109,196 | 108,262 | 934 | 1233 | 98.87 | 99.14 | 1.98 | 21.65 |
[1] | Z.W. Geem, Music-inspired harmony search algorithm: theory and applications, Springer, 2009. |
[2] | J. Kennedy, Particle swarm optimization, in Encyclopedia of machine learning, Springer, 2011, 760–766. |
[3] | M. Dorigo, V. Maniezzo and A. Colorni, Ant system: optimization by a colony of cooperating agents, IEEE T. Syst. Man. Cy. B., 26 (1996), 29–41. |
[4] | D. Karaboga and B. Basturk, A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm, J. Global. Optim., 39 (2007), 459–471. |
[5] | X. S. Yang and S. Deb, Cuckoo search via lévy flights, in Nature & Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on, IEEE, 2009, 210–214. |
[6] | J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, MIT press, 1992. |
[7] | R. Storn and K. Price, Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces, J. Global. Optim., 11 (1997), 341–359. |
[8] | S. Kirkpatrick, Optimization by simulated annealing: Quantitative studies, J. Stat. Phy., 34 (1984), 975–986. |
[9] | A. Y. Lam and V. O. Li, Chemical-reaction-inspired metaheuristic for optimization, IEEE Trans. Evol. Comput., 14 (2010), 381–399. |
[10] | Z. W. Geem, J. H. Kim and G. V. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation, 76 (2001), 60–68. |
[11] | J. Yi, X. Li, L. Gao, et al., Optimal design of photovoltaic-wind hybrid renewable energy system using a discrete geometric selective harmony search, in Computer Supported Cooperative Work in Design (CSCWD), 2015 IEEE 19th International Conference on, IEEE, (2015), 499–504. |
[12] | A. Chauhan and R. Saini, Discrete harmony search based size optimization of integrated renewable energy system for remote rural areas of uttarakhand state in india, Renew. Energy, 94 (2016), 587–604. |
[13] | Z. W. Geem and Y. Yoon, Harmony search optimization of renewable energy charging with energy storage system, Int. J. Electr. Power Energy Syst., 86 (2017), 120–126. |
[14] | C. Camacho-Gómez, S. Jiménez-Fernández, R. Mallol-Poyato, et al., Optimal design of microgrid's network topology and location of the distributed renewable energy resources using the harmony search algorithm, Soft Comput., 1 (2018), 1–16. |
[15] | H. B. Ouyang, L. Q. Gao, S. Li, et al., Improved novel global harmony search with a new relaxation method for reliability optimization problems, Inform. Sci., 305 (2015), 14–55. |
[16] | W. Zeng, J. Yi, X. Rao, et al., A two-stage path planning approach for multiple car-like robots based on ph curves and a modified harmony search algorithm, Eng. Optimiz., 49 (2017), 1995– 2012. |
[17] | S. Kundu and D. R. Parhi, Navigation of underwater robot based on dynamically adaptive harmony search algorithm, Memet. Comput., 8 (2016), 125–146. |
[18] | J. P. Papa, W. Scheirer and D. D. Cox, Fine-tuning deep belief networks using harmony search, Appl. Soft. Comput., 46 (2016), 875–885. |
[19] | W. Y. Lee, S. M. Park and K. B. Sim, Optimal hyperparameter tuning of convolutional neural networks based on the parameter-setting-free harmony search algorithm, Optik, 172 (2018), 359– 367. |
[20] | S. Kulluk, L. Ozbakir and A. Baykasoglu, Training neural networks with harmony search algorithms for classification problems, Eng. Appl. Artif. Intell., 25 (2012), 11–19. |
[21] | S. Mun and Y. H. Cho, Modified harmony search optimization for constrained design problems, Expert. Syst. Appl., 39 (2012), 419–423. |
[22] | V. R. Pandi and B. K. Panigrahi, Dynamic economic load dispatch using hybrid swarm intelligence based harmony search algorithm, Expert. Syst. Appl., 38 (2011), 8509–8514. |
[23] | A. Kusiak, Intelligent manufacturing systems., Prentice Hall Press, 200 Old Tappan Toad, Old Tappan, NJ 07675, USA, (1990), 448. |
[24] | T. Ghosh, S. Sengupta, M. Chattopadhyay, et al., Meta-heuristics in cellular manufacturing: A state-of-the-art review, Int. J. Ind. Eng. Comput., 2 (2011), 87–122. |
[25] | M. Alavidoost, M. F. Zarandi, M. Tarimoradi, et al., Modified genetic algorithm for simple straight and u-shaped assembly line balancing with fuzzy processing times, J. Intell. Manuf., 28 (2017), 313–336. |
[26] | C. L. Kuo, C. H. Chu, Y. Li, et al., Electromagnetism-like algorithms for optimized tool path planning in 5-axis flank machining, Comput. Ind. Eng., 84 (2015), 70–78. |
[27] | X. Li, C. Lu, L. Gao, et al., An effective multi-objective algorithm for energy efficient scheduling in a real-life welding shop, IEEE T. Ind. Inform., 14 (2018), 5400–5409. |
[28] | C. Lu, L. Gao, X. Li, et al., A multi-objective approach to welding shop scheduling for makespan, noise pollution and energy consumption, J. Cleaner. Prod., 196 (2018), 773–787. |
[29] | C. Lu, L. Gao, Q. Pan, et al., A multi-objective cellular grey wolf optimizer for hybrid flowshop scheduling problem considering noise pollution, Appl. Soft. Comput., 75 (2019), 728–749. |
[30] | X. S. Yang, Harmony search as a metaheuristic algorithm, in Music-inspired harmony search algorithm, Springer, (2009), 1–14. |
[31] | G. Ingram and T. Zhang, Overview of applications and developments in the harmony search algorithm, in Music-inspired harmony search algorithm, Springer, (2009), 15–37. |
[32] | O. Moh'd Alia and R. Mandava, The variants of the harmony search algorithm: an overview, Artif. Intell. Rev., 36 (2011), 49–68. |
[33] | X. Wang, X. Z. Gao and K. Zenger, The variations of harmony search and its current research trends, in An Introduction to Harmony Search Optimization Method, Springer, (2015), 21–30. |
[34] | A. Askarzadeh, Solving electrical power system problems by harmony search: a review, Artif. Intell. Rev., 47 (2017), 217–251. |
[35] | A. Askarzadeh and E. Rashedi, Harmony search algorithm: Basic concepts and engineering applications, in Intelligent Systems: Concepts, Methodologies, Tools, and Applications, 1–30. |
[36] | J. Yi, X. Li, C. H. Chu, et al., Parallel chaotic local search enhanced harmony search algorithm for engineering design optimization, J. Intell. Manuf., 30 (2019), 405–428. |
[37] | M. Mahdavi, M. Fesanghary and E. Damangir, An improved harmony search algorithm for solving optimization problems, Appl. Math. Comput., 188 (2007), 1567–1579. |
[38] | M. G. Omran and M. Mahdavi, Global-best harmony search, Appl. Math. Comput., 198 (2008), 643–656. |
[39] | Q. K. Pan, P. N. Suganthan, M. F. Tasgetiren, et al., A self-adaptive global best harmony search algorithm for continuous optimization problems, Appl. Math. Comput., 216 (2010), 830–848. |
[40] | D. Zou, L. Gao, J.Wu, et al., Novel global harmony search algorithm for unconstrained problems, Neurocomputing, 73 (2010), 3308–3318. |
[41] | J. Chen, Q. K. Pan and J. Q. Li, Harmony search algorithm with dynamic control parameters, Appl. Math. Comput., 219 (2012), 592–604. |
[42] | R. Enayatifar, M. Yousefi, A. H. Abdullah, et al., Lahs: a novel harmony search algorithm based on learning automata, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 3481–3497. |
[43] | A. Kattan and R. Abdullah, A dynamic self-adaptive harmony search algorithm for continuous optimization problems, Appl. Math. Comput., 219 (2013), 8542–8567. |
[44] | K. Luo, A novel self-adaptive harmony search algorithm, J. Appl. Math., 2013 (2013), 1–16. |
[45] | X.Wang and X. Yan, Global best harmony search algorithm with control parameters co-evolution based on pso and its application to constrained optimal problems, Appl. Math. Comput., 219 (2013), 10059–10072. |
[46] | J. Contreras, I. Amaya and R. Correa, An improved variant of the conventional harmony search algorithm, Appl. Math. Comput., 227 (2014), 821–830. |
[47] | M. Khalili, R. Kharrat, K. Salahshoor, et al., Global dynamic harmony search algorithm: Gdhs, Appl. Math. Comput., 228 (2014), 195–219. |
[48] | V. Kumar, J. K. Chhabra and D. Kumar, Parameter adaptive harmony search algorithm for unimodal and multimodal optimization problems, J. Comput. Sci., 5 (2014), 144–155. |
[49] | G. Li and Q. Wang, A cooperative harmony search algorithm for function optimization, Math. Probl. Eng., 2014 (2014), 1–14. |
[50] | I. Amaya, J. Cruz and R. Correa, Harmony search algorithm: a variant with self-regulated fretwidth, Appl. Math. Comput., 266 (2015), 1127–1152. |
[51] | J. Kalivarapu, S. Jain and S. Bag, An improved harmony search algorithm with dynamically varying bandwidth, Eng. Optimiz., 48 (2016), 1091–1108. |
[52] | Y. Wang, Z. Guo and Y. Wang, Enhanced harmony search with dual strategies and adaptive parameters, Soft Comput., 21 (2017), 4431–4445. |
[53] | Z. Guo, H. Yang, S. Wang, et al., Adaptive harmony search with best-based search strategy, Soft Comput., 22 (2018), 1335–1349. |
[54] | M. A. Al-Betar, I. A. Doush, A. T. Khader, et al., Novel selection schemes for harmony search, Appl. Math. Comput., 218 (2012), 6095–6117. |
[55] | M. A. Al-Betar, A. T. Khader, Z. W. Geem, et al., An analysis of selection methods in memory consideration for harmony search, Appl. Math. Comput., 219 (2013), 10753–10767. |
[56] | M. Castelli, S. Silva, L. Manzoni, et al., Geometric selective harmony search, Inform. Sci., 279 (2014), 468–482. |
[57] | X. Gao, X. Wang, S. Ovaska, et al., A hybrid optimization method of harmony search and opposition-based learning, Eng. Optimiz., 44 (2012), 895–914. |
[58] | A. Kaveh and M. Ahangaran, Social harmony search algorithm for continuous optimization, Iran. J. Sci. Technol. Trans. B-Eng., 36 (2012), 121–137. |
[59] | P. Yadav, R. Kumar, S. K. Panda, et al., An intelligent tuned harmony search algorithm for optimisation, Inform. Sci., 196 (2012), 47–72. |
[60] | M. A. Al-Betar, A. T. Khader, M. A. Awadallah, et al., Cellular harmony search for optimization problems, J. Appl. Math., 2013 (2013), 1–20. |
[61] | S. Ashrafi and A. Dariane, Performance evaluation of an improved harmony search algorithm for numerical optimization: Melody search (ms), Eng. Appl. Artif. Intell., 26 (2013), 1301–1321. |
[62] | M. El-Abd, An improved global-best harmony search algorithm, Appl. Math. Comput., 222 (2013), 94–106. |
[63] | B. H. F. Hasan, I. A. Doush, E. Al Maghayreh, et al., Hybridizing harmony search algorithm with different mutation operators for continuous problems, Appl. Math. Comput., 232 (2014), 1166–1182. |
[64] | E. Valian, S. Tavakoli and S. Mohanna, An intelligent global harmony search approach to continuous optimization problems, Appl. Math. Comput., 232 (2014), 670–684. |
[65] | A. M. Turky and S. Abdullah, A multi-population harmony search algorithm with external archive for dynamic optimization problems, Inform. Sci., 272 (2014), 84–95. |
[66] | M. A. Al-Betar, M. A. Awadallah, A. T. Khader, et al., Island-based harmony search for optimization problems, Expert. Syst. Appl., 42 (2015), 2026–2035. |
[67] | J. Yi, L. Gao, X. Li, et al., An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems, Appl. Intell., 44 (2016), 725–753. |
[68] | B. Keshtegar and M. O. Sadeq, Gaussian global-best harmony search algorithm for optimization problems, Soft Comput., 21 (2017), 7337–7349. |
[69] | H. B. Ouyang, L. Q. Gao, S. Li, et al., Improved harmony search algorithm: Lhs, Appl. Soft. Comput., 53 (2017), 133–167. |
[70] | E. A. Portilla-Flores, Á . Sańchez-Maŕquez, L. Flores-Pulido, et al., Enhancing the harmony search algorithm performance on constrained numerical optimization, IEEE Access, 5 (2017), 25759–25780. |
[71] | S. Tuo, L. Yong and T. Zhou, An improved harmony search based on teaching-learning strategy for unconstrained optimization problems, Math. Probl. Eng., 2013 (2013), 1–21. |
[72] | G. Wang, L. Guo, H. Duan, et al., Hybridizing harmony search with biogeography based optimization for global numerical optimization, J. Comput. Theor. Nanosci., 10 (2013), 2312–2322. |
[73] | G. G.Wang, A. H. Gandomi, X. Zhao, et al., Hybridizing harmony search algorithm with cuckoo search for global numerical optimization, Soft Comput., 20 (2016), 273–285. |
[74] | X. Yuan, J. Zhao, Y. Yang, et al., Hybrid parallel chaos optimization algorithm with harmony search algorithm, Appl. Soft. Comput., 17 (2014), 12–22. |
[75] | F. Zhao, Y. Liu, C. Zhang, et al., A self-adaptive harmony pso search algorithm and its performance analysis, Expert. Syst. Appl., 42 (2015), 7436–7455. |
[76] | A. Fouad, D. Boukhetala, F. Boudjema, et al., A novel global harmony search method based on ant colony optimisation algorithm, J. Exp. Theor. Artif. Intell., 28 (2016), 215–238. |
[77] | G. Zhang and Y. Li, A memetic algorithm for global optimization of multimodal nonseparable problems, IEEE T. Cy., 46 (2016), 1375–1387. |
[78] | A. Assad and K. Deep, A hybrid harmony search and simulated annealing algorithm for continuous optimization, Inform. Sci., 450 (2018), 246–266. |
[79] | A. Sadollah, H. Sayyaadi, D. G. Yoo, et al., Mine blast harmony search: A new hybrid optimization method for improving exploration and exploitation capabilities, Appl. Soft. Comput., 68 (2018), 548–564. |
[80] | L. Wang, H. Hu, R. Liu, et al., An improved differential harmony search algorithm for function optimization problems, Soft Comput., (2018), 1–26. |
[81] | B. L. Miller and D. E. Goldberg, Genetic algorithms, selection schemes, and the varying effects of noise, Evol. Comput., 4 (1996), 113–131. |
[82] | Y. Shi, H. Liu, L. Gao, et al., Cellular particle swarm optimization, Inform. Sci., 181 (2011), 4460–4493. |
[83] | C. Lu, L. Gao and J. Yi, Grey wolf optimizer with cellular topological structure, Expert. Syst. Appl., 107 (2018), 89–114. |
[84] | A. Turky, S. Abdullah and A. Dawod, A dual-population multi operators harmony search algorithm for dynamic optimization problems, Comput. Ind. Eng., 117 (2018), 19–28. |
[85] | G. Wang and L. Guo, A novel hybrid bat algorithm with harmony search for global numerical optimization, J. Appl. Math., 2013 (2013), 1–21. |
[86] | K. Z. Gao, P. N. Suganthan, Q. K. Pan, et al., Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling, Inform. Sci., 289 (2014), 76–90. |
[87] | K. Z. Gao, P. N. Suganthan, Q. K. Pan, et al., An effective discrete harmony search algorithm for flexible job shop scheduling problem with fuzzy processing time, Int. J. Prod. Res., 53 (2015), 5896–5911. |
[88] | K. Z. Gao, P. N. Suganthan, Q. K. Pan, et al., Discrete harmony search algorithm for flexible job shop scheduling problem with multiple objectives, J. Intell. Manuf., 27 (2016), 363–374. |
[89] | K. Gao, L.Wang, J. Luo, et al., Discrete harmony search algorithm for scheduling and rescheduling the reprocessing problems in remanufacturing: a case study, Eng. Optimiz., 50 (2018), 965– 981. |
[90] | L. Liu and H. Zhou, Hybridization of harmony search with variable neighborhood search for restrictive single-machine earliness/tardiness problem, Inform. Sci., 226 (2013), 68–92. |
[91] | Y. Yuan, H. Xu and J. Yang, A hybrid harmony search algorithm for the flexible job shop scheduling problem, Appl. Soft. Comput., 13 (2013), 3259–3272. |
[92] | F. Zammori, M. Braglia and D. Castellano, Harmony search algorithm for single-machine scheduling problem with planned maintenance, Comput. Ind. Eng., 76 (2014), 333–346. |
[93] | Y. Li, X. Li and J. N. Gupta, Solving the multi-objective flowline manufacturing cell scheduling problem by hybrid harmony search, Expert. Syst. Appl., 42 (2015), 1409–1417. |
[94] | C. Garcia-Santiago, J. Del Ser, C. Upton, et al., A random-key encoded harmony search approach for energy-efficient production scheduling with shared resources, Eng. Optimiz., 47 (2015), 1481–1496. |
[95] | A. Maroosi, R. C. Muniyandi, E. Sundararajan, et al., A parallel membrane inspired harmony search for optimization problems: A case study based on a flexible job shop scheduling problem, Appl. Soft. Comput., 49 (2016), 120–136. |
[96] | Z. Guo, L. Shi, L. Chen, et al., A harmony search-based memetic optimization model for integrated production and transportation scheduling in mto manufacturing, Omega, 66 (2017), 327– 343. |
[97] | F. Zhao, Y. Liu, Y. Zhang, et al., A hybrid harmony search algorithm with efficient job sequence scheme and variable neighborhood search for the permutation flow shop scheduling problems, Eng. Appl. Artif. Intell., 65 (2017), 178–199. |
[98] | M. Gaham, B. Bouzouia and N. Achour, An effective operations permutation-based discrete harmony search approach for the flexible job shop scheduling problem with makespan criterion, Appl. Intell., 48 (2018), 1423–1441. |
[99] | F. Zhao, S. Qin, G. Yang, et al., A differential-based harmony search algorithm with variable neighborhood search for job shop scheduling problem and its runtime analysis, IEEE Access, 6 (2018), 76313–76330. |
[100] | S. M. Lee and S. Y. Han, Topology optimization scheme for dynamic stiffness problems using harmony search method, Int. J. Precis. Eng. Manuf., 17 (2016), 1187–1194. |
[101] | S. M. Lee and S. Y. Han, Topology optimization based on the harmony search method, J. Mech. Sci. Technol., 31 (2017), 2875–2882. |
[102] | J. Yi, X. Li, M. Xiao, et al., Construction of nested maximin designs based on successive local enumeration and modified novel global harmony search algorithm, Eng. Optimiz., 49 (2017), 161–180. |
[103] | B. Keshtegar, P. Hao, Y. Wang, et al., Optimum design of aircraft panels based on adaptive dynamic harmony search, Thin-Walled Struct., 118 (2017), 37–45. |
[104] | B. Keshtegar, P. Hao, Y. Wang, et al., An adaptive response surface method and gaussian globalbest harmony search algorithm for optimization of aircraft stiffened panels, Appl. Soft. Comput., 66 (2018), 196–207. |
[105] | H. Ouyang, W. Wu, C. Zhang, et al., Improved harmony search with general iteration models for engineering design optimization problems, Soft Comput., 0 (2018), 1–36. |
[106] | X. Li, K. Qin, B. Zeng, et al., Assembly sequence planning based on an improved harmony search algorithm, Int. J. Adv. Manuf. Tech., 84 (2016), 2367–2380. |
[107] | X. Li, K. Qin, B. Zeng, et al., A dynamic parameter controlled harmony search algorithm for assembly sequence planning, Int. J. Adv. Manuf. Tech., 92 (2017), 3399–3411. |
[108] | G. Li, B. Zeng, W. Liao, et al., A new agv scheduling algorithm based on harmony search for material transfer in a real-world manufacturing system, Adv. Mech. Eng., 10 (2018), 1–13. |
[109] | G. Li, X. Li, L. Gao, et al., Tasks assigning and sequencing of multiple agvs based on an improved harmony search algorithm, J. Ambient Intell. Humaniz., 0 (2018), 1–14. |
[110] | M. B. B. Mahaleh and S. A. Mirroshandel, Harmony search path detection for vision based automated guided vehicle, Robot. Auton. Syst., 107 (2018), 156–166. |
[111] | M. Ayyıldız and K. C¸ etinkaya, Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-dof serial robot manipulator, Neural Comput. Appl., 27 (2016), 825–836. |
[112] | O. Zarei, M. Fesanghary, B. Farshi, et al., Optimization of multi-pass face-milling via harmony search algorithm, J. Mater. Process. Technol., 209 (2009), 2386–2392. |
[113] | K. Abhishek, S. Datta and S. S. Mahapatra, Multi-objective optimization in drilling of cfrp (polyester) Measurement, 77 (2016), 222–239. |
[114] | S. Kumari, A. Kumar, R. K. Yadav, et al., Optimisation of machining parameters using grey relation analysis integrated with harmony search for turning of aisi d2 steel, Materials Today: Proceedings, 5 (2018), 12750–12756. |
[115] | J. Yi, C. H. Chu, C. L. Kuo, et al., Optimized tool path planning for five-axis flank milling of ruled surfaces using geometric decomposition strategy and multi-population harmony search algorithm, Appl. Soft. Comput., 73 (2018), 547–561. |
[116] | S. Atta, P. R. S. Mahapatra and A. Mukhopadhyay, Solving tool indexing problem using harmony search algorithm with harmony refinement, Soft Comput., (2018), 1–17. |
[117] | C. C. Lin, D. J. Deng, Z. Y. Chen, et al., Key design of driving industry 4.0: Joint energy-efficient deployment and scheduling in group-based industrial wireless sensor networks, IEEE Commun. Mag., 54 (2016), 46–52. |
[118] | B. Zeng and Y. Dong, An improved harmony search based energy-efficient routing algorithm for wireless sensor networks, Appl. Soft. Comput., 41 (2016), 135–147. |
[119] | L. Wang, L. An, H. Q. Ni, et al., Pareto-based multi-objective node placement of industrial wireless sensor networks using binary differential evolution harmony search, Adv. Manuf., 4 (2016), 66–78. |
[120] | O. Moh'd Alia and A. Al-Ajouri, Maximizing wireless sensor network coverage with minimum cost using harmony search algorithm, IEEE Sens. J., 17 (2017), 882–896. |
[121] | C. C. Lin, D. J. Deng, J. R. Kang, et al., Forecasting rare faults of critical components in led epitaxy plants using a hybrid grey forecasting and harmony search approach, IEEE Trans. Ind. Inform., 12 (2016), 2228–2235. |
[122] | S. Kang and J. Chae, Harmony search for the layout design of an unequal area facility, Expert. Syst. Appl., 79 (2017), 269–281. |
[123] | J. Lin, M. Liu, J. Hao, et al., Many-objective harmony search for integrated order planning in steelmaking-continuous casting-hot rolling production of multi-plants, Int. J. Prod. Res., 55 (2017), 4003–4020. |
[124] | Y. H. Kim, Y. Yoon and Z. W. Geem, A comparison study of harmony search and genetic algorithm for the max-cut problem, Swarm Evol. Comput., 44 (2018), 130–135. |
[125] | B. Naderi, R. Tavakkoli-Moghaddam, et al., Electromagnetism-like mechanism and simulated annealing algorithms for flowshop scheduling problems minimizing the total weighted tardiness and makespan, Knowledge-Based Syst., 23 (2010), 77–85. |
[126] | M. R. Garey, D. S. Johnson and R. Sethi, The complexity of flowshop and jobshop scheduling, Math. Oper. Res., 1 (1976), 117–129. |
[127] | P. J. Van Laarhoven, E. H. Aarts and J. K. Lenstra, Job shop scheduling by simulated annealing, Oper. Res., 40 (1992), 113–125. |
[128] | M. Dell'Amico and M. Trubian, Applying tabu search to the job-shop scheduling problem, Ann. Oper. Res., 41 (1993), 231–252. |
[129] | I. Kacem, S. Hammadi and P. Borne, Approach by localization and multiobjective evolutionary optimization for flexible job-shop scheduling problems, IEEE T. Syst. Man. Cy. C., 32 (2002), 1–13. |
[130] | W. Xia and Z. Wu, An effective hybrid optimization approach for multi-objective flexible jobshop scheduling problems, Comput. Ind. Eng., 48 (2005), 409–425. |
[131] | G. Zhang, X. Shao, P. Li, et al., An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem, Comput. Ind. Eng., 56 (2009), 1309–1318. |
[132] | G. Zhang, L. Gao and Y. Shi, An effective genetic algorithm for the flexible job-shop scheduling problem, Expert. Syst. Appl., 38 (2011), 3563–3573. |
[133] | Q. Lin, L. Gao, X. Li, et al., A hybrid backtracking search algorithm for permutation flow-shop scheduling problem, Comput. Ind. Eng., 85 (2015), 437–446. |
[134] | C. Lu, L. Gao, X. Li, et al., Energy-efficient permutation flow shop scheduling problem using a hybrid multi-objective backtracking search algorithm, J. Cleaner. Prod., 144 (2017), 228–238. |
[135] | C. Viergutz and S. Knust, Integrated production and distribution scheduling with lifespan constraints, Ann. Oper. Res., 213 (2014), 293–318. |
[136] | R. T. Lund, Remanufacturing, Technol. Rev., 87 (1984), 18. |
[137] | Y. Liu, H. Dong, N. Lohse, et al., An investigation into minimising total energy consumption and total weighted tardiness in job shops, J. Cleaner. Prod., 65 (2014), 87–96. |
[138] | M. Mashayekhi, E. Salajegheh and M. Dehghani, Topology optimization of double and triple layer grid structures using a modified gravitational harmony search algorithm with efficient member grouping strategy, Comput. Struct., 172 (2016), 40–58. |
[139] | M. F. F. Rashid, W. Hutabarat and A. Tiwari, A review on assembly sequence planning and assembly line balancing optimisation using soft computing approaches, Int. J. Adv. Manuf. Tech., 59 (2012), 335–349. |
[140] | D. Ghosh, A new genetic algorithm for the tool indexing problem, Technical report, Indian Institute of Management Ahmedabad, 2016. |
[141] | D. Ghosh, Exploring Lin Kernighan neighborhoods for the indexing problem, Technical report, Indian Institute of Management Ahmedabad, 2016. |
[142] | M. Hermann, T. Pentek and B. Otto, Design principles for industrie 4.0 scenarios, in System Sciences (HICSS), 2016 49th Hawaii International Conference on, IEEE, (2016), 3928–3937. |
[143] | S. Das, A. Mukhopadhyay, A. Roy, et al., Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization, IEEE T. Syst. Man. Cy. B., 41 (2011), 89–106. |
[144] | L. Q. Gao, S. Li, X. Kong, et al., On the iterative convergence of harmony search algorithm and a proposed modification, Appl. Math. Comput., 247 (2014), 1064–1095. |
[145] | T. G. Dietterich, Ensemble methods in machine learning, in International workshop on multiple classifier systems, Springer, 2000, 1–15. |
[146] | S. Mahdavi, M. E. Shiri and S. Rahnamayan, Metaheuristics in large-scale global continues optimization: A survey, Inform. Sci., 295 (2015), 407–428. |
[147] | G. Karafotias, M. Hoogendoorn and Á . E. Eiben, Parameter control in evolutionary algorithms: Trends and challenges, IEEE Trans. Evol. Comput., 19 (2015), 167–187. |
1. | Hend Karoui, Sihem Hamza, Yassine Ben Ayed, 2024, Chapter 14, 978-3-031-70815-2, 170, 10.1007/978-3-031-70816-9_14 |
Pan-Tompkins Algorithm | Proposed Algorithm | |||||||
Tolerance | Se(%) | PPV(%) | DER(%) | ADE(ms) | Se(%) | PPV(%) | DER(%) | ADE(ms) |
150 ms | 98.87 | 99.14 | 1.98 | 21.65 | 99.78 | 99.78 | 0.44 | 8.35 |
25 ms | 79.41 | 79.63 | 40.90 | 13.37 | 96.82 | 96.82 | 6.36 | 3.17 |
2.78 ms | 11.85 | 11.88 | 176.03 | 2.42 | 86.18 | 86.18 | 27.64 | 1.86 |
Note: TB: total beats annotated; Se: sensitivity; PPV: positive prediction value; DER: detection error rate; ADE: annotated-detected error. |
File | ADE(ms) | TB | N | V | / | Q | F | f | S |
122 | 1.12 | 2476 | 2476 | ||||||
115 | 1.19 | 1953 | 1953 | ||||||
104 | 16.75 | 2229 | 163 | 2 | 1380 | 18 | 1 | 666 | |
208 | 24.96 | 2955 | 1586 | 992 | 2 | 373 | 2 | ||
Note: normal beats; V: beats of premature ventricular contract; /: paced beats; f: fusion of paced and normal beats; Q: Unclassifiable beats; F: fusion of ventricular and normal beats; S: supraventricular premature beats. |
File | TD(ms) | TB | DB | TP | FP | FN | Se(%) | PPV(%) | DER(%) | ADE(ms) |
100 | 0.00 | 2273 | 2273 | 2273 | 0 | 0 | 100 | 100 | 0 | 2.21 |
101 | 0.00 | 1865 | 1865 | 1862 | 3 | 3 | 99.84 | 99.84 | 0.00 | 2.53 |
102 | 0.00 | 2187 | 2187 | 2187 | 0 | 0 | 100 | 100 | 0 | 10.80 |
103 | 0.00 | 2084 | 2083 | 2083 | 0 | 1 | 99.95 | 100 | 0.00 | 2.32 |
104 | 0.00 | 2229 | 2237 | 2228 | 9 | 1 | 99.96 | 99.60 | 0.00 | 16.75 |
105 | 0.00 | 2572 | 2590 | 2557 | 33 | 15 | 99.42 | 98.73 | 0.02 | 9.54 |
106 | 0.00 | 2027 | 2021 | 2020 | 1 | 7 | 99.65 | 99.95 | 0.00 | 5.30 |
107 | –2.78 | 2137 | 2136 | 2135 | 1 | 2 | 99.91 | 99.95 | 0.00 | 7.47 |
108 | 2.78 | 1763 | 1758 | 1754 | 4 | 9 | 99.49 | 99.77 | 0.01 | 14.95 |
109 | –2.78 | 2532 | 2530 | 2530 | 0 | 2 | 99.92 | 100 | 0.00 | 5.08 |
111 | 0.00 | 2124 | 2123 | 2123 | 0 | 1 | 99.95 | 100 | 0.00 | 5.78 |
112 | 0.00 | 2539 | 2539 | 2539 | 0 | 0 | 100 | 100 | 0 | 2.14 |
113 | 0.00 | 1795 | 1795 | 1795 | 0 | 0 | 100 | 100 | 0 | 1.93 |
114 | 30.56 | 1879 | 1880 | 1876 | 4 | 3 | 99.84 | 99.79 | 0.00 | 8.02 |
115 | 2.78 | 1953 | 1953 | 1953 | 0 | 0 | 100 | 100 | 0 | 1.12 |
116 | 0.00 | 2412 | 2390 | 2387 | 3 | 25 | 98.96 | 99.87 | 0.01 | 2.91 |
117 | –19.44 | 1535 | 1535 | 1535 | 0 | 0 | 100 | 100 | 0 | 6.97 |
118 | 0.00 | 2278 | 2278 | 2278 | 0 | 0 | 100 | 100 | 0 | 3.15 |
119 | 0.00 | 1987 | 1988 | 1987 | 1 | 0 | 100 | 99.95 | 0.00 | 6.00 |
121 | –2.78 | 1863 | 1861 | 1861 | 0 | 2 | 99.89 | 100 | 0.00 | 2.26 |
122 | 0.00 | 2476 | 2476 | 2476 | 0 | 0 | 100 | 100 | 0 | 1.19 |
123 | 0.00 | 1518 | 1518 | 1518 | 0 | 0 | 100 | 100 | 0 | 1.82 |
124 | 0.00 | 1619 | 1619 | 1619 | 0 | 0 | 100 | 100 | 0 | 6.99 |
200 | –5.56 | 2601 | 2601 | 2599 | 2 | 2 | 99.92 | 99.92 | 0.00 | 17.64 |
201 | 0.00 | 1963 | 1942 | 1942 | 0 | 21 | 98.93 | 100 | 0.01 | 4.15 |
202 | 0.00 | 2136 | 2122 | 2122 | 0 | 14 | 99.34 | 100 | 0.01 | 2.47 |
203 | –5.56 | 2980 | 2954 | 2937 | 17 | 43 | 98.56 | 99.42 | 0.02 | 15.28 |
205 | 0.00 | 2656 | 2648 | 2648 | 0 | 8 | 99.70 | 100 | 0.00 | 5.27 |
207 | 0.00 | 1860 | 1991 | 1852 | 139 | 8 | 99.57 | 93.02 | 0.08 | 12.98 |
208 | 8.33 | 2955 | 2939 | 2936 | 3 | 19 | 99.36 | 99.90 | 0.01 | 24.96 |
209 | 0.00 | 3005 | 3005 | 3005 | 0 | 0 | 100 | 100 | 0 | 1.54 |
210 | 0.00 | 2650 | 2623 | 2621 | 2 | 29 | 98.91 | 99.92 | 0.01 | 7.34 |
212 | 0.00 | 2748 | 2748 | 2748 | 0 | 0 | 100 | 100 | 0 | 2.24 |
213 | 0.00 | 3251 | 3248 | 3248 | 0 | 3 | 99.91 | 100 | 0.00 | 5.78 |
214 | 0.00 | 2262 | 2258 | 2258 | 0 | 4 | 99.82 | 100 | 0.00 | 4.60 |
215 | 0.00 | 3363 | 3359 | 3359 | 0 | 4 | 99.88 | 100 | 0.00 | 3.18 |
217 | –13.89 | 2208 | 2205 | 2204 | 1 | 4 | 99.82 | 99.95 | 0.00 | 8.09 |
219 | 0.00 | 2154 | 2154 | 2154 | 0 | 0 | 100 | 100 | 0 | 1.46 |
220 | 2.78 | 2048 | 2048 | 2048 | 0 | 0 | 100 | 100 | 0 | 1.82 |
221 | 0.00 | 2427 | 2425 | 2425 | 0 | 2 | 99.92 | 100 | 0.00 | 2.65 |
222 | 0.00 | 2483 | 2485 | 2483 | 2 | 0 | 100 | 99.92 | 0.00 | 1.81 |
223 | 0.00 | 2605 | 2603 | 2603 | 0 | 2 | 99.92 | 100 | 0.00 | 7.61 |
228 | 0.00 | 2053 | 2062 | 2047 | 15 | 6 | 99.71 | 99.27 | 0.01 | 5.69 |
230 | 2.78 | 2256 | 2256 | 2256 | 0 | 0 | 100 | 100 | 0 | 1.64 |
231 | 0.00 | 1571 | 1570 | 1570 | 0 | 1 | 99.94 | 100 | 0.00 | 1.55 |
232 | 0.00 | 1780 | 1782 | 1780 | 2 | 0 | 100 | 99.89 | 0.00 | 1.68 |
233 | –5.56 | 3079 | 3076 | 3076 | 0 | 3 | 99.90 | 100 | 0.00 | 16.33 |
234 | 0.00 | 2753 | 2752 | 2752 | 0 | 1 | 99.96 | 100 | 0.00 | 0.86 |
Total | 109,494 | 109,491 | 109,249 | 242 | 245 | 99.78 | 99.78 | 0.44 | 8.35 | |
TB: total beats annotated; DB: detected beats by algorithm; TD: Group time delay between TB and DB; TP: true positive, the number of correctly detected R-peaks; FP: false positive, the number of false detected R-peaks; FN: false negative, the number of undetected R-peaks; Se: sensitivity; PPV: positive prediction value; DER: detection error rate; ADE: annotated-detected error. |
File | TD(ms) | TB | DB | TP | FP | FN | Se(%) | PPV(%) | DER(%) | ADE(ms) |
100 | 44.44 | 2273 | 2271 | 2271 | 0 | 2 | 99.91 | 100 | 0.00 | 25.01 |
101 | 30.56 | 1865 | 1868 | 1863 | 5 | 2 | 99.89 | 99.73 | 0.00 | 13.98 |
102 | 22.22 | 2187 | 2187 | 2187 | 0 | 0 | 100 | 100 | 0 | 18.24 |
103 | 36.11 | 2084 | 2080 | 2079 | 1 | 5 | 99.76 | 99.95 | 0.00 | 16.79 |
104 | 16.67 | 2229 | 2273 | 2221 | 52 | 8 | 99.64 | 97.71 | 0.03 | 21.90 |
105 | 0.00 | 2572 | 2599 | 2561 | 38 | 11 | 99.57 | 98.54 | 0.02 | 18.40 |
106 | 25.00 | 2027 | 1996 | 1995 | 1 | 32 | 98.42 | 99.95 | 0.02 | 23.96 |
107 | 50.00 | 2137 | 2135 | 2135 | 0 | 2 | 99.91 | 100 | 0.00 | 26.49 |
108 | 19.44 | 1763 | 1872 | 1281 | 591 | 482 | 72.66 | 68.43 | 0.61 | 43.72 |
109 | 25.00 | 2532 | 2528 | 2527 | 1 | 5 | 99.80 | 99.96 | 0.00 | 24.43 |
111 | 25.00 | 2124 | 2125 | 2123 | 2 | 1 | 99.95 | 99.91 | 0.00 | 21.21 |
112 | 36.11 | 2539 | 2539 | 2539 | 0 | 0 | 100 | 100 | 0 | 32.70 |
113 | 44.44 | 1795 | 1794 | 1793 | 1 | 2 | 99.89 | 99.94 | 0.00 | 24.20 |
114 | 47.22 | 1879 | 1882 | 1876 | 6 | 3 | 99.84 | 99.68 | 0.00 | 15.68 |
115 | 38.89 | 1953 | 1953 | 1952 | 1 | 1 | 99.95 | 99.95 | 0.00 | 10.89 |
116 | 30.56 | 2412 | 2391 | 2387 | 4 | 25 | 98.96 | 99.83 | 0.01 | 16.35 |
117 | 25.00 | 1535 | 1535 | 1533 | 2 | 2 | 99.87 | 99.87 | 0.00 | 22.72 |
118 | 41.67 | 2278 | 2278 | 2274 | 4 | 4 | 99.82 | 99.82 | 0.00 | 25.16 |
119 | 30.56 | 1987 | 1988 | 1986 | 2 | 1 | 99.95 | 99.90 | 0.00 | 25.33 |
121 | 16.67 | 1863 | 1864 | 1858 | 6 | 5 | 99.73 | 99.68 | 0.01 | 23.31 |
122 | 2.78 | 2476 | 2476 | 2475 | 1 | 1 | 99.96 | 99.96 | 0.00 | 15.93 |
123 | 52.78 | 1518 | 1515 | 1513 | 2 | 5 | 99.67 | 99.87 | 0.00 | 18.09 |
124 | 8.33 | 1619 | 1620 | 1619 | 1 | 0 | 100 | 99.94 | 0.00 | 21.26 |
200 | 33.33 | 2601 | 2603 | 2596 | 7 | 5 | 99.81 | 99.73 | 0.00 | 22.39 |
201 | 33.33 | 1963 | 1912 | 1912 | 0 | 51 | 97.40 | 100 | 0.03 | 18.87 |
202 | 22.22 | 2136 | 2128 | 2127 | 1 | 9 | 99.58 | 99.95 | 0.00 | 15.54 |
203 | 19.44 | 2980 | 2957 | 2924 | 33 | 57 | 98.09 | 98.88 | 0.03 | 22.66 |
205 | 25.00 | 2656 | 2649 | 2648 | 1 | 8 | 99.70 | 99.96 | 0.00 | 14.22 |
207 | 36.11 | 1860 | 1919 | 1826 | 93 | 34 | 98.17 | 95.15 | 0.07 | 24.20 |
208 | 38.89 | 2955 | 2658 | 2654 | 4 | 301 | 89.81 | 99.85 | 0.10 | 28.16 |
209 | 41.67 | 3005 | 3005 | 3003 | 2 | 2 | 99.93 | 99.93 | 0.00 | 20.36 |
210 | 27.78 | 2650 | 2607 | 2603 | 4 | 47 | 98.23 | 99.85 | 0.02 | 15.29 |
212 | 13.89 | 2748 | 2749 | 2748 | 1 | 0 | 100 | 99.96 | 0.00 | 18.92 |
213 | 16.67 | 3251 | 3249 | 3249 | 0 | 2 | 99.94 | 100 | 0.00 | 26.62 |
214 | 22.22 | 2262 | 2255 | 2253 | 2 | 9 | 99.60 | 99.91 | 0.00 | 14.22 |
215 | 47.22 | 3363 | 3363 | 3362 | 1 | 1 | 99.97 | 99.97 | 0.00 | 19.16 |
217 | 41.67 | 2208 | 2205 | 2202 | 3 | 6 | 99.73 | 99.86 | 0.00 | 25.10 |
219 | 33.33 | 2154 | 2152 | 2150 | 2 | 4 | 99.81 | 99.91 | 0.00 | 17.94 |
220 | 38.89 | 2048 | 2048 | 2046 | 2 | 2 | 99.90 | 99.90 | 0.00 | 17.17 |
221 | 38.89 | 2427 | 2361 | 2360 | 1 | 67 | 97.24 | 99.96 | 0.03 | 21.64 |
222 | 19.44 | 2483 | 2488 | 2483 | 5 | 0 | 100 | 99.80 | 0.00 | 15.72 |
223 | 33.33 | 2605 | 2603 | 2602 | 1 | 3 | 99.88 | 99.96 | 0.00 | 29.88 |
228 | 19.44 | 2053 | 2080 | 2045 | 35 | 8 | 99.61 | 98.32 | 0.02 | 20.37 |
230 | 50.00 | 2256 | 2255 | 2255 | 0 | 1 | 99.96 | 100 | 0.00 | 15.21 |
231 | 41.67 | 1571 | 1569 | 1568 | 1 | 3 | 99.81 | 99.94 | 0.00 | 29.59 |
232 | 44.44 | 1780 | 1790 | 1776 | 14 | 4 | 99.78 | 99.22 | 0.01 | 25.12 |
233 | 22.22 | 3079 | 3072 | 3072 | 0 | 7 | 99.77 | 100 | 0.00 | 19.89 |
234 | 19.44 | 2753 | 2750 | 2750 | 0 | 3 | 99.89 | 100 | 0.00 | 11.04 |
Total | 109,494 | 109,196 | 108,262 | 934 | 1233 | 98.87 | 99.14 | 1.98 | 21.65 |
Pan-Tompkins Algorithm | Proposed Algorithm | |||||||
Tolerance | Se(%) | PPV(%) | DER(%) | ADE(ms) | Se(%) | PPV(%) | DER(%) | ADE(ms) |
150 ms | 98.87 | 99.14 | 1.98 | 21.65 | 99.78 | 99.78 | 0.44 | 8.35 |
25 ms | 79.41 | 79.63 | 40.90 | 13.37 | 96.82 | 96.82 | 6.36 | 3.17 |
2.78 ms | 11.85 | 11.88 | 176.03 | 2.42 | 86.18 | 86.18 | 27.64 | 1.86 |
Note: TB: total beats annotated; Se: sensitivity; PPV: positive prediction value; DER: detection error rate; ADE: annotated-detected error. |
Method | TB | Se(%) | PPV(%) | DER(%) | ADE(ms) |
Proposed | 109,494 | 99.78 | 99.78 | 0.44 | 8.35 |
Kai Zhao et al. [32] | 109,966 | 99.81 | 99.88 | 0.31 | 12.2 |
* Pan and Tompkins [33] | 109,966 | 99.13 | 99.63 | 1.24 | 13.4 |
* Indicates that the data is quoted from literature [32]. |
File | ADE(ms) | TB | N | V | / | Q | F | f | S |
122 | 1.12 | 2476 | 2476 | ||||||
115 | 1.19 | 1953 | 1953 | ||||||
104 | 16.75 | 2229 | 163 | 2 | 1380 | 18 | 1 | 666 | |
208 | 24.96 | 2955 | 1586 | 992 | 2 | 373 | 2 | ||
Note: normal beats; V: beats of premature ventricular contract; /: paced beats; f: fusion of paced and normal beats; Q: Unclassifiable beats; F: fusion of ventricular and normal beats; S: supraventricular premature beats. |
File | TD(ms) | TB | DB | TP | FP | FN | Se(%) | PPV(%) | DER(%) | ADE(ms) |
100 | 0.00 | 2273 | 2273 | 2273 | 0 | 0 | 100 | 100 | 0 | 2.21 |
101 | 0.00 | 1865 | 1865 | 1862 | 3 | 3 | 99.84 | 99.84 | 0.00 | 2.53 |
102 | 0.00 | 2187 | 2187 | 2187 | 0 | 0 | 100 | 100 | 0 | 10.80 |
103 | 0.00 | 2084 | 2083 | 2083 | 0 | 1 | 99.95 | 100 | 0.00 | 2.32 |
104 | 0.00 | 2229 | 2237 | 2228 | 9 | 1 | 99.96 | 99.60 | 0.00 | 16.75 |
105 | 0.00 | 2572 | 2590 | 2557 | 33 | 15 | 99.42 | 98.73 | 0.02 | 9.54 |
106 | 0.00 | 2027 | 2021 | 2020 | 1 | 7 | 99.65 | 99.95 | 0.00 | 5.30 |
107 | –2.78 | 2137 | 2136 | 2135 | 1 | 2 | 99.91 | 99.95 | 0.00 | 7.47 |
108 | 2.78 | 1763 | 1758 | 1754 | 4 | 9 | 99.49 | 99.77 | 0.01 | 14.95 |
109 | –2.78 | 2532 | 2530 | 2530 | 0 | 2 | 99.92 | 100 | 0.00 | 5.08 |
111 | 0.00 | 2124 | 2123 | 2123 | 0 | 1 | 99.95 | 100 | 0.00 | 5.78 |
112 | 0.00 | 2539 | 2539 | 2539 | 0 | 0 | 100 | 100 | 0 | 2.14 |
113 | 0.00 | 1795 | 1795 | 1795 | 0 | 0 | 100 | 100 | 0 | 1.93 |
114 | 30.56 | 1879 | 1880 | 1876 | 4 | 3 | 99.84 | 99.79 | 0.00 | 8.02 |
115 | 2.78 | 1953 | 1953 | 1953 | 0 | 0 | 100 | 100 | 0 | 1.12 |
116 | 0.00 | 2412 | 2390 | 2387 | 3 | 25 | 98.96 | 99.87 | 0.01 | 2.91 |
117 | –19.44 | 1535 | 1535 | 1535 | 0 | 0 | 100 | 100 | 0 | 6.97 |
118 | 0.00 | 2278 | 2278 | 2278 | 0 | 0 | 100 | 100 | 0 | 3.15 |
119 | 0.00 | 1987 | 1988 | 1987 | 1 | 0 | 100 | 99.95 | 0.00 | 6.00 |
121 | –2.78 | 1863 | 1861 | 1861 | 0 | 2 | 99.89 | 100 | 0.00 | 2.26 |
122 | 0.00 | 2476 | 2476 | 2476 | 0 | 0 | 100 | 100 | 0 | 1.19 |
123 | 0.00 | 1518 | 1518 | 1518 | 0 | 0 | 100 | 100 | 0 | 1.82 |
124 | 0.00 | 1619 | 1619 | 1619 | 0 | 0 | 100 | 100 | 0 | 6.99 |
200 | –5.56 | 2601 | 2601 | 2599 | 2 | 2 | 99.92 | 99.92 | 0.00 | 17.64 |
201 | 0.00 | 1963 | 1942 | 1942 | 0 | 21 | 98.93 | 100 | 0.01 | 4.15 |
202 | 0.00 | 2136 | 2122 | 2122 | 0 | 14 | 99.34 | 100 | 0.01 | 2.47 |
203 | –5.56 | 2980 | 2954 | 2937 | 17 | 43 | 98.56 | 99.42 | 0.02 | 15.28 |
205 | 0.00 | 2656 | 2648 | 2648 | 0 | 8 | 99.70 | 100 | 0.00 | 5.27 |
207 | 0.00 | 1860 | 1991 | 1852 | 139 | 8 | 99.57 | 93.02 | 0.08 | 12.98 |
208 | 8.33 | 2955 | 2939 | 2936 | 3 | 19 | 99.36 | 99.90 | 0.01 | 24.96 |
209 | 0.00 | 3005 | 3005 | 3005 | 0 | 0 | 100 | 100 | 0 | 1.54 |
210 | 0.00 | 2650 | 2623 | 2621 | 2 | 29 | 98.91 | 99.92 | 0.01 | 7.34 |
212 | 0.00 | 2748 | 2748 | 2748 | 0 | 0 | 100 | 100 | 0 | 2.24 |
213 | 0.00 | 3251 | 3248 | 3248 | 0 | 3 | 99.91 | 100 | 0.00 | 5.78 |
214 | 0.00 | 2262 | 2258 | 2258 | 0 | 4 | 99.82 | 100 | 0.00 | 4.60 |
215 | 0.00 | 3363 | 3359 | 3359 | 0 | 4 | 99.88 | 100 | 0.00 | 3.18 |
217 | –13.89 | 2208 | 2205 | 2204 | 1 | 4 | 99.82 | 99.95 | 0.00 | 8.09 |
219 | 0.00 | 2154 | 2154 | 2154 | 0 | 0 | 100 | 100 | 0 | 1.46 |
220 | 2.78 | 2048 | 2048 | 2048 | 0 | 0 | 100 | 100 | 0 | 1.82 |
221 | 0.00 | 2427 | 2425 | 2425 | 0 | 2 | 99.92 | 100 | 0.00 | 2.65 |
222 | 0.00 | 2483 | 2485 | 2483 | 2 | 0 | 100 | 99.92 | 0.00 | 1.81 |
223 | 0.00 | 2605 | 2603 | 2603 | 0 | 2 | 99.92 | 100 | 0.00 | 7.61 |
228 | 0.00 | 2053 | 2062 | 2047 | 15 | 6 | 99.71 | 99.27 | 0.01 | 5.69 |
230 | 2.78 | 2256 | 2256 | 2256 | 0 | 0 | 100 | 100 | 0 | 1.64 |
231 | 0.00 | 1571 | 1570 | 1570 | 0 | 1 | 99.94 | 100 | 0.00 | 1.55 |
232 | 0.00 | 1780 | 1782 | 1780 | 2 | 0 | 100 | 99.89 | 0.00 | 1.68 |
233 | –5.56 | 3079 | 3076 | 3076 | 0 | 3 | 99.90 | 100 | 0.00 | 16.33 |
234 | 0.00 | 2753 | 2752 | 2752 | 0 | 1 | 99.96 | 100 | 0.00 | 0.86 |
Total | 109,494 | 109,491 | 109,249 | 242 | 245 | 99.78 | 99.78 | 0.44 | 8.35 | |
TB: total beats annotated; DB: detected beats by algorithm; TD: Group time delay between TB and DB; TP: true positive, the number of correctly detected R-peaks; FP: false positive, the number of false detected R-peaks; FN: false negative, the number of undetected R-peaks; Se: sensitivity; PPV: positive prediction value; DER: detection error rate; ADE: annotated-detected error. |
File | TD(ms) | TB | DB | TP | FP | FN | Se(%) | PPV(%) | DER(%) | ADE(ms) |
100 | 44.44 | 2273 | 2271 | 2271 | 0 | 2 | 99.91 | 100 | 0.00 | 25.01 |
101 | 30.56 | 1865 | 1868 | 1863 | 5 | 2 | 99.89 | 99.73 | 0.00 | 13.98 |
102 | 22.22 | 2187 | 2187 | 2187 | 0 | 0 | 100 | 100 | 0 | 18.24 |
103 | 36.11 | 2084 | 2080 | 2079 | 1 | 5 | 99.76 | 99.95 | 0.00 | 16.79 |
104 | 16.67 | 2229 | 2273 | 2221 | 52 | 8 | 99.64 | 97.71 | 0.03 | 21.90 |
105 | 0.00 | 2572 | 2599 | 2561 | 38 | 11 | 99.57 | 98.54 | 0.02 | 18.40 |
106 | 25.00 | 2027 | 1996 | 1995 | 1 | 32 | 98.42 | 99.95 | 0.02 | 23.96 |
107 | 50.00 | 2137 | 2135 | 2135 | 0 | 2 | 99.91 | 100 | 0.00 | 26.49 |
108 | 19.44 | 1763 | 1872 | 1281 | 591 | 482 | 72.66 | 68.43 | 0.61 | 43.72 |
109 | 25.00 | 2532 | 2528 | 2527 | 1 | 5 | 99.80 | 99.96 | 0.00 | 24.43 |
111 | 25.00 | 2124 | 2125 | 2123 | 2 | 1 | 99.95 | 99.91 | 0.00 | 21.21 |
112 | 36.11 | 2539 | 2539 | 2539 | 0 | 0 | 100 | 100 | 0 | 32.70 |
113 | 44.44 | 1795 | 1794 | 1793 | 1 | 2 | 99.89 | 99.94 | 0.00 | 24.20 |
114 | 47.22 | 1879 | 1882 | 1876 | 6 | 3 | 99.84 | 99.68 | 0.00 | 15.68 |
115 | 38.89 | 1953 | 1953 | 1952 | 1 | 1 | 99.95 | 99.95 | 0.00 | 10.89 |
116 | 30.56 | 2412 | 2391 | 2387 | 4 | 25 | 98.96 | 99.83 | 0.01 | 16.35 |
117 | 25.00 | 1535 | 1535 | 1533 | 2 | 2 | 99.87 | 99.87 | 0.00 | 22.72 |
118 | 41.67 | 2278 | 2278 | 2274 | 4 | 4 | 99.82 | 99.82 | 0.00 | 25.16 |
119 | 30.56 | 1987 | 1988 | 1986 | 2 | 1 | 99.95 | 99.90 | 0.00 | 25.33 |
121 | 16.67 | 1863 | 1864 | 1858 | 6 | 5 | 99.73 | 99.68 | 0.01 | 23.31 |
122 | 2.78 | 2476 | 2476 | 2475 | 1 | 1 | 99.96 | 99.96 | 0.00 | 15.93 |
123 | 52.78 | 1518 | 1515 | 1513 | 2 | 5 | 99.67 | 99.87 | 0.00 | 18.09 |
124 | 8.33 | 1619 | 1620 | 1619 | 1 | 0 | 100 | 99.94 | 0.00 | 21.26 |
200 | 33.33 | 2601 | 2603 | 2596 | 7 | 5 | 99.81 | 99.73 | 0.00 | 22.39 |
201 | 33.33 | 1963 | 1912 | 1912 | 0 | 51 | 97.40 | 100 | 0.03 | 18.87 |
202 | 22.22 | 2136 | 2128 | 2127 | 1 | 9 | 99.58 | 99.95 | 0.00 | 15.54 |
203 | 19.44 | 2980 | 2957 | 2924 | 33 | 57 | 98.09 | 98.88 | 0.03 | 22.66 |
205 | 25.00 | 2656 | 2649 | 2648 | 1 | 8 | 99.70 | 99.96 | 0.00 | 14.22 |
207 | 36.11 | 1860 | 1919 | 1826 | 93 | 34 | 98.17 | 95.15 | 0.07 | 24.20 |
208 | 38.89 | 2955 | 2658 | 2654 | 4 | 301 | 89.81 | 99.85 | 0.10 | 28.16 |
209 | 41.67 | 3005 | 3005 | 3003 | 2 | 2 | 99.93 | 99.93 | 0.00 | 20.36 |
210 | 27.78 | 2650 | 2607 | 2603 | 4 | 47 | 98.23 | 99.85 | 0.02 | 15.29 |
212 | 13.89 | 2748 | 2749 | 2748 | 1 | 0 | 100 | 99.96 | 0.00 | 18.92 |
213 | 16.67 | 3251 | 3249 | 3249 | 0 | 2 | 99.94 | 100 | 0.00 | 26.62 |
214 | 22.22 | 2262 | 2255 | 2253 | 2 | 9 | 99.60 | 99.91 | 0.00 | 14.22 |
215 | 47.22 | 3363 | 3363 | 3362 | 1 | 1 | 99.97 | 99.97 | 0.00 | 19.16 |
217 | 41.67 | 2208 | 2205 | 2202 | 3 | 6 | 99.73 | 99.86 | 0.00 | 25.10 |
219 | 33.33 | 2154 | 2152 | 2150 | 2 | 4 | 99.81 | 99.91 | 0.00 | 17.94 |
220 | 38.89 | 2048 | 2048 | 2046 | 2 | 2 | 99.90 | 99.90 | 0.00 | 17.17 |
221 | 38.89 | 2427 | 2361 | 2360 | 1 | 67 | 97.24 | 99.96 | 0.03 | 21.64 |
222 | 19.44 | 2483 | 2488 | 2483 | 5 | 0 | 100 | 99.80 | 0.00 | 15.72 |
223 | 33.33 | 2605 | 2603 | 2602 | 1 | 3 | 99.88 | 99.96 | 0.00 | 29.88 |
228 | 19.44 | 2053 | 2080 | 2045 | 35 | 8 | 99.61 | 98.32 | 0.02 | 20.37 |
230 | 50.00 | 2256 | 2255 | 2255 | 0 | 1 | 99.96 | 100 | 0.00 | 15.21 |
231 | 41.67 | 1571 | 1569 | 1568 | 1 | 3 | 99.81 | 99.94 | 0.00 | 29.59 |
232 | 44.44 | 1780 | 1790 | 1776 | 14 | 4 | 99.78 | 99.22 | 0.01 | 25.12 |
233 | 22.22 | 3079 | 3072 | 3072 | 0 | 7 | 99.77 | 100 | 0.00 | 19.89 |
234 | 19.44 | 2753 | 2750 | 2750 | 0 | 3 | 99.89 | 100 | 0.00 | 11.04 |
Total | 109,494 | 109,196 | 108,262 | 934 | 1233 | 98.87 | 99.14 | 1.98 | 21.65 |