Automatic Robust Crackle Detection and Localization Approach Using AR-Based Spectral Estimation and Support Vector Machine

Abstract

Auscultation primarily relies upon the acoustic expertise of individual doctors in identifying, through the use of a stethoscope, the presence of abnormal sounds such as crackles because the recognition of these sound patterns has critical importance in the context of early detection and diagnosis of respiratory pathologies. In this paper, we propose a novel method combining autoregressive (AR)-based spectral features and a support vector machine (SVM) classifier to detect the presence of crackle events and their temporal location within the input signal. A preprocessing stage is performed to discard information out of the band of interest and define the segments for short-time signal analysis. The AR parameters are estimated for each segment to be classified by means of support vector machine (SVM) classifier into crackles and normal lung sounds using a set of synthetic crackle waveforms that have been modeled to train the classifier. A dataset composed of simulated and real coarse and fine crackles sound signals was created with several signal-to-noise (SNR) ratios to evaluate the robustness of the proposed method. Each simulated and real signal was mixed with noise that shows the same spectral energy distribution as typically found in breath noise from a healthy subject. This study makes a significant contribution by achieving competitive results. The proposed method yields values ranging from 80% in the lowest signal-to-noise ratio scenario to a perfect 100% in the highest signal-to-noise ratio scenario. Notably, these results surpass those of other methods presented by a margin of at least 15%. The combination of an autoregressive (AR) model with a support vector machine (SVM) classifier offers an effective solution for detecting the presented events. This approach exhibits enhanced robustness against variations in the signal-to-noise ratio that the input signals may encounter.

1. Introduction

An increasing amount of economic and technological resources are being invested in accelerating the early detection of respiratory diseases (for example, pneumonia) as it is essential to providing effective medical treatment that minimizes risks to the health of the patient and optimizes healthcare costs at the same time. According to the World Health Organization (WHO), pneumonia is the leading cause of death in children, with one million deaths in children under 5 years of age in 2017, which is equivalent to 15% of all deaths in this population worldwide [1]. Although there are more sophisticated clinical tests (for example, blood tests and chest X-rays) to diagnose most lung diseases than the auscultation process [2], auscultation is the most widely used tool in health centers in low-income countries and even in most rural areas of high-income countries when a first respiratory system examination is performed mainly due to its low cost and non-invasiveness. However, auscultation depends largely on the acoustic training of each pulmonologist to recognize, through the stethoscope, the presence of abnormal sounds that are often associated with various respiratory pathologies, as occurs between crackles and specific lung diseases such as congestive heart failure and pneumonia [3,4,5]. In addition, it is important to note that crackles may not be heard by the doctor due to their short duration, low rate of occurrence, and often low amplitude, which makes them difficult to be detected by the human auditory system [6].

Respiratory sounds can be categorized into normal and abnormal sounds according to the COmputerized Respiratory Sound Analysis (CORSA) guidelines [7]. Normal respiratory sounds (RSs) heard in healthy lungs are represented by a broadband spectrum locating most of the energy between 60–1000 Hz [8]. One of these abnormal or adventitious respiratory sounds are called crackles sounds (CSs), which are superimposed onto the RS, generated by unhealthy lungs as a consequence of pulmonary disorders. Crackles can be defined as discontinuous, short, explosive, and non-musical sounds with a spectral energy located between 100 Hz and 2000 Hz [9] as shown in Figure 1. Specifically, crackles can be classified as either coarse or fine. Coarse crackle sounds (CCs) are characterized by a temporal duration ≤20 ms and can be heard in the early inspiratory and the expiratory phases, showing a low pitch located around 350 Hz. One of the causes of these is the presence of air bubbles in large bronchi [10]. Fine crackle sounds (FCSs) are characterized by a temporal duration of ≤5 ms, active in the late inspiratory phase with a high pitch located around 650 Hz. The cause of FCSs is the abrupt opening of small airways [10]. In the literature [11,12,13], it is common characterize both CCSs and FCSs using temporal waveforms by means of two parameters: (i) $t_{IDW}$ (initial deflection width), which indicates the temporal duration between the beginning of the crackle and the first deflection; and (ii) $t_{2CD}$ (two-cycle deflection), which represents the time duration from the beginning of the crackle to the time point where two cycles are completed. Specifically, (i) FCSs show on average $t_{IDW}=0.5$ ms and $t_{2CD}=3.3$ ms whereas CCSs are represented on average by $t_{IDW}=1.0$ ms and $t_{2CD}=5.1$ ms according to Hoevers et al. [11]; (ii) FCSs show on average $t_{IDW}=0.9$ ms and $t_{2CD}=6.0$ ms whereas CCSs are represented on average by $t_{IDW}=1.25$ ms and $t_{2CD}=9.50$ ms according to Cohen et al. [12]; (iii) FCSs show on average $t_{IDW}=0.7$ ms and $t_{2CD}=5$ ms whereas CCSs are represented on average by $t_{IDW}=1.5$ ms and $t_{2CD}=10$ ms according to the American Thoracic Society (ATS) [13].

For many years, signal processing and machine learning approaches have been combined for event detection and classification tasks using spectro-temporal features [14,15,16]. Specifically for the task of crackle sound detection, several approaches have been proposed based on spectrogram analysis [17,18], autoregressive (AR) models [19,20], wavelet transform [21,22,23,24], fractal dimension filtering [25,26,27,28], entropy [29,30], empirical mode decomposition (EMD) [31], fuzzy systems [32], Gaussian mixture models (GMM) [33], logistic regression [34], support vector machines (SVM) [35,36,37], independent component analysis (ICA) [38], multi-perceptron networks (MPNs) [39], non-negative matrix factorization (NMF) [40], convolutional neural networks (CNNs) [41,42], recurrent neural networks (RNNs) [43,44] and hybrid neural networks [45,46]. Serbes et al. [23] detected crackle sounds testing different windows and wavelets for time-scale analysis. The extracted features were fed into SVM and k-nearest neighbor (kNN) models, but frequency bands containing no crackle information were removed using a dual-tree complex wavelet to reduce redundancy. Li and Hong [35] developed a crackle detection method using preprocessing, feature extraction (ratio between frequency of limbic signal, standard deviation of the limbic signal time, and the smoothing time of the limbic signal) and classification based on SVM. In [43], an event detection approach for crackle detection, based on RNNs using spectral features, was proposed. The approach exploited spectral information and temporal dependencies of the lung sounds, showing robustness regarding the contamination of the lung sound recordings with noise, bowel, and heart sounds. Garcia et al. [38] proposed to evaluate the efficiency of three popular ICA algorithms (FastICA, information maximization, and temporal decorrelation source separation) to determine the best method to extract crackle sounds. Information maximization achieved the best results, determining the presence of crackles in the independent components by means of their kurtosis and skewness, whereas the type of crackle was indicated by their characterization via the spectrogram of those components. In [42], CNNs were used to recognize lung sounds (including coarse and fine crackles) by means of spectrograms, Mel frequency cepstrum coefficient (MFCC) features and local binary pattern (LBP) features. Results demonstrated that the performance depends on learning parameters, batch size, and of iterations, band moreover, CNNs can replace conventional classifiers using fully connected layers to train the previous features. In [24], a classification system was proposed based on wavelets, genetic algorithms, and SVMs in order to discriminate between the presence or absence of crackles caused by pneumonia. Recently, Pal and Barney [28] proposed a crackle separation and detection technique combining an iterative envelope mean (IEM) method with the established fractal dimension (FD) technique [47]. The IEM method estimated the non-stationary and stationary parts of the lung sound signal and then the FD technique was applied to the estimated non-stationary output of the IEM method for further removing elements related to normal breath sounds. Authors indicated that IEM-FD filtering showed a high rate of crackle detectability when several signal-to-noise ratios (SNRs) were evaluated.

Crackle detection is a complex task due to factors such as: (a) nonstationarity of lung and crackle sounds, (b) low-magnitude relation between crackles and lung sounds (SNR), (c) crackle overlapping, (d) crackle waveform distortion by lung sounds, and (e) difficulty to establish the time domain parameters such as $t_{IDW}$, $t_{2CD}$, and $t_{LDW}$. The autoregressive (AR) model has proved useful for processing stationary random process, for example, for spectral analysis even with short time segments of information. In fact, respiratory sounds can be represented as a response of a system formed by lung parenchyma and chest wall to a white noise input which models the respiratory sounds source; hence, the system may be modeled as an all-pole filter.

Several AR-based models have been presented in the literature. In [48], AR-based features were used to feed two classifiers, a k-nearest neighbour (k-NN) classifier and a quadratic classifier, in order to discriminate between pathological and healthy patients. In [49], the authors combined sixth-order AR coefficients, wavelet coefficients, and crackle parameters as input for a k-NN and single layer perceptron. In a multichannel scenario (i.e., using several microphones), multivariate AR version called vector AR (VAR) has been used in [50] as input for SVM and Gaussian mixture model (GMM) classifiers. Moreover, in [51], the authors proposed a crackle detection system using a threshold over the coefficients of a time-varying AR (TVAR) model showing superior results than using waveform analysis.

There are studies that have evaluated the detection of abnormal lung sounds from a physical perspective. In [52], it was asserted that determining the origin of abnormal sounds can provide valuable insights, potentially narrowing down the range of possible pathological causes and pinpointing the specific affected lung region. This information can prove invaluable in the context of diagnosis and treatment planning. To address this matter, [53] introduced an algorithm capable of effectively imaging sound sources, a capability demonstrated through computer simulations and experiments involving life-sized gelatin models of the human thorax. Their findings suggest that meaningful spatial information can be extracted from recordings employing as few as 16 microphones. Recently, in [54], a discussion of these types of studies covering auscultatory methods was presented. Alternatively, in this paper we aim to detect and localize the temporal occurrence of adventitious sounds on an input single-channel respiratory signal. In fact, the information about the temporal location will serve to focus a doctor’s attention on the regions of the signal where crackles are present.

In this paper, we investigate the effect of the autoregressive (AR)-based frequency features that characterizes the spectral envelope of a breathing signal. In particular, we propose the utilization of complex valued poles derived from the AR model as inputs for a support vector machine (SVM) classifier using the radial basis function (RBF) kernel. The proposed approach has been compared with other state-of-the-art approaches including the iterative envelope mean-fractal dimension (IEM-FD) and the time-varying autoregressive (TVAR) methods. Finally, the proposed AR-based features are combined with a state-of-the-art convolutional neural network (CNN) architecture for crackle detection [55]. The outcomes of this comparison revealed notable enhancements in the performance metrics associated with the proposed methodology for characterizing and detecting crackles events. In fact, when dealing with limited data quantities, SVM presents a preferable choice whereas deep learning models typically entail a substantial number of tunable weights (free variables) that necessitate calibration with data. Actually, when the quantity of these weights exceeds or approximates the number of available training examples, deep models tend to essentially “memorize” the data, which can lead to overfitting. On the contrary, when a suitable kernel function is applied, SVM provides a robust, efficient, easily interpretable solution and is less prone to overfitting in classification problems.

The paper is organized as follows. Section 2 reviews the dataset used in this work and details the proposed method. Section 3 describes the metrics, setup, and the state-of-the-art methods in order to discuss the experimental results. Finally, conclusions and future work are presented in Section 4.

2. Materials and Methods

2.1. Dataset

In order to assess the crackle detection performance of the proposed method in a biomedical sound scenario, the dataset $\psi$ was created using the same available software provided by the authors [28,56]. Specifically, the dataset $\psi$ is composed of 2520 signals: (i) simulated signals related to FCSs and CCSs by modifying both parameters $t_{IDW}$ and $t_{2CD}$ according to [11,12,57]; (ii) real signals related to FCSs and CCSs with different $t_{IDW}$ and $t_{2CD}$ extracted from lung sound recordings. Specifically, real FCSs were extracted from a patient with idiopathic pulmonary fibrosis (IPF), and real CCSs were selected from a patient with bronchiectasis (BE) [56]. Each simulated and real signal has been mixed with noise $N_R$ that shows the same spectral energy distribution as typically found in breath noise from a healthy subject measured over the lung bases on the right-hand side of the back as occurs in [56]. Moreover, several signal-to-noise ratios (SNRs) ranged from −10 to 10 dB in steps of 1 dB have been created to evaluate the robustness of the proposed method detecting crackles. For each SNR, 15 simulated signals of every scenario have been evaluated, considering the effect of random variations of the local SNR around any given crackle. In this manner, a set of 315 signals have been generated considering all the SNRs for each type of simulated or real crackle signal. Although the dataset $\psi$ is detailed in

Table 1. Dataset $\psi$. FCS: (i) ATS: $t_{IDW}$ = 0.7 ms & $t_{2CD}$ = 5 ms, (ii) Hoevers: $t_{IDW}$ = 0.5 ms & $t_{2CD}$ = 3.3 ms [45], (iii) Cohen: $t_{IDW}$ = 0.9 ms & $t_{2CD}$ = 6 ms. CCS: (i) ATS: $t_{IDW}$ = 1.5 ms & $t_{2CD}$ = 10 ms, (ii) Hoevers: $t_{IDW}$ = 1 ms & $t_{2CD}$ = 5.1 ms, (iii) Cohen: $t_{IDW}$ = 1.25 ms & $t_{2CD}$ = 9.5 ms. $K_C$: number of crackles per signal. $NOTS$: number of signals per SNR. $N_S$: number of signals generated taking into account all SNRs evaluated.

Scenario	Type	Model	${\mathit{K}}_{\mathit{C}}$	$\mathit{N}\mathit{O}\mathit{T}\mathit{S}$	Noise	Diagnosis	SNR	${\mathit{N}}_{\mathit{S}}$
Simulated	FCS [57]	ATS	10	15	$N_R$	-	[−10 dB, 10 dB]	315
	FCS [11]	Hoevers	10	15	$N_R$	-	[−10 dB, 10 dB]	315
	FCS [12]	Cohen	10	15	$N_R$	-	[−10 dB, 10 dB]	315
	CCS [57]	ATS	10	15	$N_R$	-	[−10 dB, 10 dB]	315
	CCS [11]	Hoevers	10	15	$N_R$	-	[−10 dB, 10 dB]	315
	CCS [12]	Cohen	10	15	$N_R$	-	[−10 dB, 10 dB]	315
Real	FCS [28,56]	-	10	15	$N_R$	IPF	[−10 dB, 10 dB]	315
	CCS [28,56]	-	10	15	$N_R$	BE	[−10 dB, 10 dB]	315

, more details can be found in [28,56].

2.2. Modeling of Simulated Crackle Sounds

In order to train the classifier, a set of synthetic crackle sounds have been generated. Similar to [58], a crackle waveform $y\left(t\right)$ is created (Equations (1)–(4)) assuming: (i) the crackle has two cycles represented by the parameter $t_{2CD}$, (ii) the location where the first cycle of the waveform $y\left(t\right)$ equals zero is explicitly indicated by the parameter $t_{IDW}$, and (iii) most of the power in $y\left(t\right)$ is concentrated near the beginning of the waveform. To time shift most of the power to the beginning of the waveform, a modulating function $m\left(t\right)$ is generated. An example of simulated crackles in the time domain is shown in Figure 2.

$$t_0=\frac{t_{IDW}}{t_{2CD}}$$

(1)

$$y{}_0\left(t\right)=sin\left(4\pi t^{\alpha }\right), \alpha =\frac{lo{g}_{10}\left(0.25\right)}{lo{g}_{10}\left(t_0\right)}$$

(2)

$$m\left(t\right)=\frac{1}{2}\left(1+cos\left(2\pi \left(t^{\frac{1}{2}}-\frac{1}{2}\right)\right)\right)$$

(3)

$$y\left(t\right)=y{}_0\left(t\right)m\left(t\right)$$

(4)

In this work, a set of K = 187 crackle waveforms was created based on a conservative strategy using all combinations between both parameters $t_{IDW}$ and $t_{2CD}$ [11,12,57]. Specifically, $t_{IDW}\in [0.5,1.5]$ ms with a step size of 0.1 ms and $t_{2CD}\in [3.3,20]$ ms with a step size of 1 ms. Finally, each signal $y\left(t\right)$ is normalized in energy, that is, ${\sum }_t{y}^2\left(t\right)=1.0$. The magnitude Fourier transform (spectral pattern) of the previous set of K crackle waveforms is shown in Figure 3.

2.3. Proposed Method

In Figure 4, a block diagram of the structure of our proposed method is shown. First, a preprocessing stage is performed to discard information out of the band of interest and define the segments for the short-time signal analysis. Then, we window the initial signal into frames (parameters used are explained in the Setup section). We calculate the 14 complex envelope coefficients for each frame by using our AR model. Finally, we use these data to feed the support vector machine system.

2.3.1. Preprocessing

For the task of crackle detection, the signals are low-pass filtered and resampled to 4 kHz. The window length for the short-time analysis was chosen to be 256 samples (64 ms) with a hop size of 16 ms. This interval was a good compromise between parameter accuracy and stationary requirements. Finally, the sliding segments were weighted by a Hamming window to reduce the spectral leakage.

2.3.2. Autoregressive (AR) Parameter Estimation

In this paper, AR parameters are estimated for each segment of the respiratory sound as

$$x_s\left(n\right)=-\sum _{k=1}^K{a}_s\left(k\right)x_s(n-k)+e_s\left(n\right),$$

(5)

where $s=1,\dots ,S$ denotes the segment index, $a_s\left(k\right)$ is the k-th AR coefficient with K denoting the model order. $e_s\left(n\right)$ is IID Gaussian noise with zero mean and variance ${\sigma }^2$. Levinson–Durbin recursion was used in order to estimate the AR parameters. This recursion also gives the total mean square prediction error of a k-th order predictor. In this work, sixth-order AR model coefficients are extracted from respiratory sounds to form the feature set for the classifier as was shown in [48,49,59].

The above equation can be solved by using the z-transform. This allows the equation to be written as

$$X_s\left(z\right)\left(1+\sum _{k=1}^K{a}_s\left(k\right)z^{-k}\right)=E_s\left(z\right)$$

(6)

and the transfer function $H_s\left(z\right)$ can be expressed using a rational format

$$H_s\left(z\right)=z^K\frac{1}{{\prod }_{k=1}^K\left(z-p_s\left(k\right)\right)}$$

(7)

where $p_s\left(k\right)$ are the poles describing the estimated spectral envelope of the input segment. This approach has been widely used to characterize and synthesize the speech formants [60].

As shown in Figure 5, the frequency response of the all-pole AR model is depicted for two healthy and unhealthy excerpts. These features gave us the aim to proceed into the creation of a classification system between these two classes (healthy and unhealthy patients).

2.3.3. SVM Classifier

SVM is a supervised learning method which is often applied to classification or regression. It is a method for obtaining the optimal boundary of two sets in a vector space independently from the probabilistic distributions of training vectors in the sets. A support vector machine is used here to classify crackles and normal lung sounds. The RBF kernel function is used in this work to achieve an optimal result. In addition, the parameters of the SVM are optimized to obtain a better performance, which will be introduced in the third section.

Support vector machines (SVMs) are the famous and widely utilized supervised classifiers developed by [61]. A support vector machine (SVM) is a powerful and versatile machine learning algorithm used primarily for classification and regression tasks. SVMs are particularly effective in scenarios where the data are not linearly separable, meaning that the classes cannot be separated by a single straight line or hyperplane. SVMs achieve this by transforming the input data into a higher-dimensional space where separation becomes possible through the use of a hyperplane.

In a classification context, an SVM attempts to find the hyperplane that best separates different classes of data points while maximizing the margin between the two classes. The margin is the distance between the hyperplane and the nearest data points from each class. The SVM seeks to find the hyperplane that not only separates the classes but also maximizes this margin, which theoretically reduces the risk of overfitting and enhances the model’s generalization capabilities.

The data points that are closest to the hyperplane and have the most influence on determining its position are referred to as “support vectors”. These are the data points located at the edges of the margin or those that might be misclassified if the margin were to shift. The SVM focuses on these support vectors, making it a robust algorithm even in the presence of outliers or noisy data.

SVMs offer flexibility in dealing with different types of data through the use of various kernel functions, which can implicitly map the data into higher-dimensional spaces. This allows SVMs to handle non-linear relationships between variables.

3. Evaluation

3.1. Metrics

Three metrics are proposed to detect the presence or absence of crackle events: accuracy ($Acc$), sensitivity ($S_e$) and precision ($P_r$). All of them are calculated analyzing each signal within the dataset $\psi$ by matching the original data and the estimated data provided by the proposed method. The metric $Acc$ represents the ability to correctly detect the presence or absence of the crackles events when they are active or inactive in the signal, $S_e$ represents the ability to detect the number of missed crackle events within the dataset, and $P_r$ represents the ability to detect frames within a signal with crackles when no crackles events are active. These three mentioned metrics are calculated as shown in Equations (8)–(10). The parameter $t_p$ indicates true positives, that is, number of active crackle events within the dataset $\psi$ correctly detected as crackle. The parameter $f_p$ represents false positives or false alarm events, that is, the number of crackles events inactive within the dataset $\psi$ incorrectly detected as crackles. The parameter $f_n$ indicates false negatives or missed events, that is, the number of crackles events active within the dataset $\psi$ incorrectly detected as no crackle.

$$Acc=\frac{t_p}{t_p+f_p+f_n}$$

(8)

$$S_e=\frac{t_p}{t_p+f_n}$$

(9)

$$P_r=\frac{t_p}{t_p+f_p}$$

(10)

3.2. Setup

We conducted preliminary experiments that showed that the following parameters, used in this paper, provide the best trade-off between crackle detection performance and the computational cost: sampling rate $f_s$ = 4410 Hz, window size N = 18 samples (approximately 4.1 ms), hop size of four samples (approximately 0.9 ms), and a number of FFT points equal to twice the window size in samples.

3.3. State-of-the-Art Methods for Comparison

Two recent and relevant state-of-the-art crackle detection methods IEM-FD [28] and TVAR [51] have been implemented in order to evaluate the performance of crackle detection of the proposed method.

3.4. Results and Discussion

In this section, we detail a systematic comparison of the results section obtained from the implemented methods: the IEM-FD, TVAR, and the proposed method. All of the separation techniques were implemented using the MATLAB (R2020b) programming language. The metrics employed to evaluate the implemented methods are described in Section 3.1. For evaluation, we compared the ground-truth and estimated temporal location and length of each crackle using a tolerance window of $0.6$ ms.

The overall results for the implemented methods are shown in Figure 6. The boxplot displays the distribution of data based on a five-number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”). It details information about the atypical values and the location of them within the entire range of possible values. At the same time, it indicates whether the data are symmetrical, how tightly the data are grouped, and how the data are skewed.

Figure 6 shows these results in terms of accuracy $Acc$, sensitivity $S_e$ and precision $P_r$ of the IEM-FD method on the left side, TVAR method on the center and the proposed method on the right side. Additionally, Figure 7 displays the accuracy results of the compared methods as a function of the SNR value (between $-10$ and 10 dB).

In general terms, the values obtained from the proposed method are significantly higher in terms of accuracy $Acc$ and precision $P_r$ among the compared methods. Moreover, our method also outperforms the IEM-FD and the TVAR in terms of sensitivity ($S_e$).

Regarding the boxplot accuracy values of the IEM-FD method, the median is $45.45$%, the first quartile (Q1) is $32.25$%, the second quartile (Q2) is 50%, the maximum is $61.54$%, and the minimum is $5.66$%. In fact, the performance of this method is limited by the number of false positives (i.e., normal events detected as crackles) as be seen in the precision values in Figure 6.

In the case of the TVAR method, the following measurements are found: the median is 70%, the first quartile (Q1) is 90%, the second quartile (Q2) is 40%, the maximum is 100%, and the minimum is 0%. This variability in the results suggests that the method is too dependent on the conditions of the input signals, as can be seen in Figure 7. In fact, the TVAR method provides the worst results among the compared methods when dealing with low SNR values.

The proposed method shows the minimum standard deviation among the compared methods. In particular, the median is 100%, the first quartile (Q1) is $90.90$%, the second quartile (Q2) is 100%, the maximum is 100%, and the minimum is 80%. Additionally, as can be seen in Figure 7, the results are robust independently of the input signal SNR conditions.

Now, focusing on a specific type of crackles, Figure 8 presents the $Acc$, $S_e$, and $P_e$ results as a function of type of crackle (coarse (right side of the figure) or fine (left side of the figure)) and SNR value. As can be seen, the performance of the proposed method is clearly superior to the other compared methods in both cases (coarse and fine crackle detection). Comparing both sides of the figure, the results reveal that the proposed method underperforms when dealing with coarse crackles under low SNR scenarios. Similar behavior is observed in the case of the TVAR method although, as previously commented, the results are limited by the number of false positives, which provokes a clear underperformance in terms of $S_e$. Interestingly, the results seem more stable in the case of IEM-FD when comparing the performance of fine vs. coarse crackle detection. In any case, it is worth mentioning that the results are worse than the compared approaches and specially limited by the number of false negatives (i.e., crackles events detected as normal), which provokes a clear underperformance in terms of $P_r$. Note that the $Acc$ can be seen as general metric accounting for both $S_e$ and $P_r$ values.

Table 2. Detailed results in terms of accuracy, sensitivity, and precision (mean values per crackle type) $K_C$: number of crackles per signal. $NOTS$: number of signals per SNR. $N_S$: number of signals generated taking into account all SNRs evaluated.

Scenario	Type	${\mathit{K}}_{\mathit{C}}$	$\mathit{N}\mathit{O}\mathit{T}\mathit{S}$	Noise	Diagnosis	SNR	Accuracy [Acc]			Sensitivity [${\mathit{S}}_{\mathit{e}}$]			Precision [${\mathit{P}}_{\mathit{r}}$]
							IEM-FD	TVAR	Proposed	IEM-FD	TVAR	Proposed	IEM-FD	TVAR	Proposed
Simulated 1	FCS [57]	10	15	NR	-	[−10 dB, 10 dB]	46.94%	69.23%	98.36%	97.46%	73.02%	99.94%	46.94%	93.33%	98.42%
Simulated 2	FCS [11]	10	15	NR	-	[−10 dB, 10 dB]	33.21%	81.36%	95.85%	100%	92.60%	97.81%	33.21%	87.27%	97.93%
Simulated 3	FCS [12]	10	15	NR	-	[−10 dB, 10 dB]	47.72%	76.21%	98.03%	97.14%	81.56%	99.94%	47.72%	91.98%	98.08%
Simulated 4	CCS [57]	10	15	NR	-	[−10 dB, 10 dB]	41.86%	46.00%	96.57%	93.17%	48.54%	98.25%	42.15%	82.64%	98.27%
Simulated 5	CCS [11]	10	15	NR	-	[−10 dB, 10 dB]	47.63%	71.86%	98.63%	97.46%	76.73%	99.90%	47.63%	91.68%	98.71%
Simulated 6	CCS [12]	10	15	NR	-	[−10 dB, 10 dB]	41.12%	38.68%	95.47%	91.49%	40.76%	96.86%	41.46%	76.70%	98.54%
Real 1	FCS [28,56]	10	15	NR	IPF	[−10 dB, 10 dB]	30.70%	92.04%	94.59%	79.96%	97.30%	96.10%	33.26%	94.39%	98.32%
Real 2	CCS [28,56]	10	15	NR	BE	[−10 dB, 10 dB]	30.64%	22.70%	74.78%	46.54%	23.87%	76.03%	53.86%	66.33%	97.72%

shows the mean values in terms of accuracy $Acc$, sensitivity $S_e$ and precision $P_r$ for the IEM-FD method, TVAR method, and the proposed method for test samples $\psi$ at SNR from $-10$ dB and until $+10$ dB for real and simulated crackles. In contrast to the previous results shown in this document, here we make a distinction by type of crackle within the test sample: ATS, Hoevers, Cohen, IPF, or BE, labeled here as simulated scenarios 1 to 6 and real scenarios 1 and 2. From these results, we can highlight the fact that our proposed method has widely higher percentage values in comparison with the IEM-FD and TVAR methods. It is important to note that all the methods have a clear underperformance in real scenario 2. That is, when dealing with real sounds with coarse crackles (i.e., bronchitis) superposed to simulated breathing. This suggests that the difference between simulated and real fine crackles allows a suitable modeling valid for both cases whereas in the case of coarse crackles, the parameters may vary between simulated and real cases.

Once we have evaluated the robustness of the proposed method against different type of signals and SNR conditions and compared the results with classical approaches, we aim to also compare the results with more recent techniques based on deep learning. In fact, deep learning approaches have recently been widely investigated for the task of adventitious sound detection [41,62,63,64,65,66,67,68].

The investigation carried out by [55] highlighted the usage of convolutional neural networks (CNNs) as state-of-the-art solutions across various research domains. Leveraging the CNN architecture as detailed in [55], we subjected the same scenarios as previously outlined to testing, subsequently conducting a comparative analysis between the outcomes generated by the support vector machine (SVM) classifier and the CNN classifier. The comparative results, presented in

Table 3. Comparison of the results of the proposed method as input of an SVM and CNN in terms of accuracy, sensitivity, and precision (mean values per crackle type) $K_C$: number of crackles per signal. $NOTS$: number of signals per SNR. $N_S$: number of signals generated considering all SNRs evaluated.

Scenario	Type	${\mathit{K}}_{\mathit{C}}$	$\mathit{N}\mathit{O}\mathit{T}\mathit{S}$	Noise	Diagnosis	SNR	Accuracy (%) [$\mathbf{Acc}$]		Sensitivity (%) [${\mathit{S}}_{\mathit{e}}$]		Precision (%) [${\mathit{P}}_{\mathit{r}}$]
							SVM	CNN	SVM	CNN	SVM	CNN
Simulated 1	FCS [57]	10	15	NR	-	[−10 dB, 10 dB]	98.36	97.61	99.94	97.94	98.42	99.49
Simulated 2	FCS [11]	10	15	NR	-	[−10 dB, 10 dB]	95.85	97.93	97.81	98.28	97.93	99.53
Simulated 3	FCS [12]	10	15	NR	-	[−10 dB, 10 dB]	98.03	97.44	99.94	97.72	98.08	99.50
Simulated 4	CCS [57]	10	15	NR	-	[−10 dB, 10 dB]	96.57	92.98	98.25	92.73	98.27	99.60
Simulated 5	CCS [11]	10	15	NR	-	[−10 dB, 10 dB]	98.63	98.25	99.90	98.54	98.71	99.55
Simulated 6	CCS [12]	10	15	NR	-	[−10 dB, 10 dB]	95.47	94.34	96.86	94.21	98.54	99.58
Real 1	FCS [28,56]	10	15	NR	IPF	[−10 dB, 10 dB]	94.58	91.42	96.10	93.11	98.32	99.34
Real 2	CCS [28,56]	10	15	NR	BE	[−10 dB, 10 dB]	74.78	72.34	76.03	74.00	97.72	98.12

, delineate the performance contrast in terms of accuracy ($Acc$), sensitivity ($S_e$), and precision ($P_r$) across the eight scenarios encompassing our proposed method. As can be observed in Table 3, both classifiers (SVM and CNN) achieve excellent results (>90%) in all metrics except in the real coarse crackle scenario. In any case, a slight improvement can be observed using the SVM-based classifier in terms of accuracy ($Acc$) and sensitivity ($S_e$). Conversely, CNN performs slightly better in terms of precision ($P_r$). This suggests that the proposed system is somewhat more robust in determining the occurrence of crackle events, which is very interesting from a clinical perspective. However, it is worth noting that SVM is simpler to train, has fewer parameters, and therefore is more robust to overfitting. Additionally, its parameters are much more interpretable than those of CNN.

It is pertinent to underscore the notable performance decline observed in the real-world scenarios examined in this study. As evident in Table 3, these scenarios exhibit discernible decreases across all three metrics. These findings shed light on the potential limitations inherent in the proposed methodology. In the context of real patient scenarios, it is imperative to recognize that the properties of the input signals may undergo fluctuations, resulting in consequential reductions in performance outcomes. As articulated in the preceding Section 4, forthcoming research endeavors will be geared towards data characteristic extraction and the modeling of time–frequency behaviors. These efforts are envisioned to foster improved generalization regarding the authentic behaviors exhibited by such sound signals in real-world contexts.

4. Conclusions and Future Work

In this paper, a new crackle event detection method based on the combination of an autoregressive model, and a support vector machine classification model is proposed. We conclude that the proposed method is a suitable model for detection of the existence or non-existence of crackle events within a dataset with a significant high success rate.

The proposed method has achieved highly competitive results in the detection of crackle events in spite of the environmental factors, such as type of crackle (fine or coarse) or very low signal-to-noise ratio.

Future work will focus on combining recurrent and convolutional neural networks approaches using different time–frequency representations in order to develop novel criteria to determine the most reliable and discriminant feature map in terms of the abnormal respiratory sound to be detected.