TLBO Optimization Algorithm Based-Type2 Fuzzy Adaptive Filter for ECG Signals Denoising

2.1 Type-2 fuzzy adaptive filter

As mentioned previously, the concepts of fuzzy logic [29-33] was extended to type-2 fuzzy logic. In our work, Type-2 fuzzy logic will be used to design adaptive filters. The proposed filter combines the set of input-output measurement pairs with a set of fuzzy If-Then rules. The benefits of using a type2-fuzzy adaptive filter are its non-linear nature and simple design. This simplicity allows human experts to incorporate linguistic information into the filter. When there is no linguistic information available, the type-2 fuzzy adaptive filters can be re-defined as non-linear adaptive filters. The parameters of the membership functions are tuned with an adaptive procedure to characterize the If-Then rules through the use of some criterion function.

A dual-layered feed-forward network structure can be used to represent the type-2 fuzzy adaptive filter [34-36]. Therefore, it will be possible to train the type-2 fuzzy adaptive filter to determine the required input-output relationship through the use of some learning algorithms, such as the TLBO in this investigation. Within this study, the type-2 fuzzy adaptive filter's input $([x(k), x(k-1), \ldots, x(k-n+1)])$ is equal to the previous output, therefore the new input $x_{n}$ becomes $y_{n-1} .$ Hence, at the sampling instant $k,$ the role of the type-2 fuzzy adaptive filter is to filter the measured signal $\mathrm{y}(k)$ to obtain a smooth estimate $\hat{y}(k)$.

2.1.1 Type-2 fuzzy logic system structure

Type-n fuzzy sets were first proposed by Zadeh in 1975. They are characterized by membership functions that range over fuzzy type-(n-1) sets. In 1999, Karnik and Mendel have introduced some definitions, mechanisms, and algorithms for the type-2 fuzzy sets [37]. The membership function of the type-2 fuzzy set is itself a type-1 fuzzy set.

Type-2 fuzzy systems are hyperefficient compared to the type-1 fuzzy systems, specifically in the presence of the ambiguity, uncertainty, and noisy data [38-43]. Fuzzy systems are able to approximate any unknown function or nonlinear system using a set of input-output data. Any type-2 fuzzy system is composed of five modules: a fuzzifier, a rule base, an inference engine, a type reducer, and a deffuzzifier (see Figure 1). Type-reducer block is used to carry out the type-reduction operation, which is an extension of the type-1 defuzzification. This block produces type-1 sets from type-2 output sets. The type-reduced set must be defuzzified to obtain crisp outputs.

The rule base of the type-2 fuzzy system is a set of If-Then rules. These rules describe the relationship between the input-output spaces, and can be expressed as [44]:

Rule $^{i}$ : If $x_{1}$ is $\tilde{F}_{1}^{i}$ and,..., and $x_{n}$ is $\tilde{F}_{n}^{i}$ Then $y^{-i}$ is $\tilde{G}^{i}$     (1)

where,

$x_{j}$: are premise variables;

$\tilde{F}_{j}^{i}$: are type-2 fuzzy membership functions of the premise sets with j= 1, 2, …, n, and n is the number of regressors;

$y_{i} \in Y$: is the i^th output;

$\tilde{G}^{i}$: are type-2 fuzzy sets of the consequences with i=1, 2, …, N, where N is the number of If-Thenrules in the rule base.

The type reduction block is introduced to map the type-2 fuzzy outputs of the inference engine to type1-fuzzy sets. Among the most important methods for type reduction operations are Karnik-Mendel algorithm and Wu-Mendel uncertainty bounds, which are based on the estimation of the centroid. There are other techniques proposed in the literature for the purpose of enhancing the robustness, performance, and time execution, such as the MEKM algorithm [45], the EKM algorithm, the EIASC, and many others reported by Tai et al. [46]. In our investigation the conventional Karnik-Mendal center of sets is used which is written as [47]:

$Y \cos \left(Y^{1}, \ldots, Y^{N R}, W^{1}, \ldots, W^{N R}\right)$$=\int_{y^{1}}^{0} \ldots \int_{Y^{N R}}^{0} \int_{w^{1}}^{0} \int_{w^{N R}}^{0} \frac{\frac{1}{\sum_{i=1}^{N R} w^{i} y^{i}}}{\sum_{i=1}^{N R} w^{i}}=\left[y_{1}, y_{r}\right]$     (2)

where, Ycos is the interval set bounded by two points y₁and y_r, $y^{i} \in Y^{i}=\left[y_{l}^{i}, y_{r}^{i}\right]$, Yⁱ is the centroid of the type-2 interval consequent set Gⁱ and $w^{i} \in W^{i}=\left[\underline{w}^{i}, \bar{w}^{i}\right]$  is the firing interval.

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Figure 1. Type-2 fuzzy logic system structure

2.1.2 Parameter update rules

The determination of the unknown parameters of the antecedent and the consequent parts of the type2-fuzzy If-Then rules is crucial to design the type2–fuzzy adaptative filter. The input space in the antecedent parts is decomposed into a set of type-2 fuzzy regions, while the consequence parts are decomposed into regions which are automatically determined. The ambiguity in the Gaussian type-2 membership functions can be attributed to the center (mean) and the standard deviation. In this investigation, the Gaussian type-2 fuzzy membership functions were chosen due to their ability to uniformly estimate continuous functions, and to their ability to universal approximation [48]. Figure 2 represents the Gaussian type-2 fuzzy membership function where the uncertainty is associated with the center (mean) and with the standard deviation (width). The Gaussian membership function can be expressed mathematically as:

$\tilde{\mu}(x)=\exp \left(\frac{1}{2} \frac{(x-c)^{2}}{\sigma^{2}}\right)$     (3)

where,

c: the center (mean) of the membership function;

$\sigma$:  the width (standard deviation) of the membership function;

x: is the data.

In this paper, uncertainty is considered both on the center (mean) $c=\left[c_{1}, c_{2}\right]$ and on the standard deviation $\sigma=\left[\sigma_{1}, \sigma_{2}\right]$, where $c_{1}, \sigma_{1}$ and $c_{2}, \sigma_{2}$ are the lower and upper bounds of the uncertainty interval, respectively.

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Figure 2. Gaussian type-2 fuzzy membership function with: (a) uncertain standard deviation; (b) uncertain center (mean)

2.2 Teacher-learning-based optimization algorithm

Rao [49] have proposed a new evolutionary algorithm labeled TLBO (Teaching Learning Based Optimization), which is inspired by the education process at school. This optimization algorithm is based on the impact of the teacher on the learners in the classroom. This optimization algorithm uses a population of solutions which contains a possible solution (feasible solution) of the optimization problem under consideration. Basically, this population is a group of learners. Several subjects given to the learners can be considered to be the design variables which are the parameters associated with the objective function of the optimization problem. Learner’s result is analogs to the fitness value of the feasible solution of the optimization problem.

TLBO algorithm is divided into two phases: “Teacher phase” and “learner phase” which are described below:

2.2.1 Teacher phase

Learning of the learners form the teacher is considered to be the first phase of the TLBO algorithm, where the teacher is considered as the highly learned and skilled person in society. For simulations, we assume that there are ‘m’ number of subjects (design variables, $j=1,2, \ldots, m$), ‘n’ number of learners (population size, $k=1,2, \ldots, n$) and $M_{j}^{i}$ be the mean results of the students in a particular subject ‘j’ at any teaching-learning cycle ($i=0,1,2 \ldots, I_{n}$). A Teacher is the most experienced, knowledgeable, and highly learned person in society. To simulate this concept, the best learner (feasible solution) in the entire population is considered as a teacher. Let $X_{j}^{i}$ be the best feasible solution of the population at the $i^{t h}$ teaching-learning cycle and $X_{T, j}^{i}$ denotes the $j^{t h}$ design variable in the best feasible solution of the population at the $i^{t h}$ teaching-learning cycle or the result of the teacher in subject $j$ ". The difference between the result of the teacher and the mean result of the learners in subject $j$ ' can be expressed as:

$D_{j}^{i}=r\left(X_{T, i}^{i}-T_{F} M_{j}^{i}\right)$    (4)

where,

$X_{T, j}^{i}$ is the result of the best student in subject $^{\prime} j^{\prime} \cdot r$ is a random number in the range [0,1]. $T_{F}$ is the teaching factor which decides the value of the mean to be changed, the value of $T_{F}$ can be either 0 or 1. $T_{F}$ is not a parameter of the TLBO algorithm, and is not given as an input to the algorithm and its value is randomly decided by the algorithm using the following equation:

$T F=$ round $[1+$ rand (0,1)$\{2-1\}]$     (5)

Based on the difference between the result of the teacher and the mean result of the learners in subject ‘j’ ($D_{j}^{i}$), the existing solution is updated in the teacher phase according to the following expression:

$X_{n e w, k, j}^{i}=X_{o l d, k, j}^{i}+D_{j}^{i}$     (6)

$X_{n e w, k}^{k}$ is accepted if it gives better function value than $X_{\text {old}, k}^{k}$. All the accepted feasible solutions are maintained and these become the input to the student phase. The student phase depends upon the teacher phase.

2.2.2 Learner phase

It is the second part of the TLBO algorithm where learners increase their knowledge by interaction among themselves. A learner interacts randomly with other students for enhancing his or her knowledge. A learner (u) learns new things if the other learner (v) has more knowledge than him or her. The learning philosophy of this phase is simulated as below:

Randomly select two students u and v, where their feasible solutions are $X_{u}^{i}$ and $X_{v}^{i}$, respectively and then:

if $F\left(X_{u}^{i}\right)>F\left(X_{v}^{k}\right)$

$X_{n e w_{S P}, u, j}^{i}=X_{u, j}^{i}+r\left(X_{u, j}^{i}-X_{v, j}^{i}\right)$

else $X_{n e w, u}^{i}=X_{n e w, u}^{i}$

end if

where,

F(x): is a fitness function that is used to find the fitness value of a feasible solution;

$X_{n e w_{S P}, u, j}^{i}$: is the j^th design variable of the modified feasible solution in student phase at i^th teaching-learning cycle and it is accepted if it gives a better function value as follows:

If $F\left(X_{\text {new } S P, u}^{i}\right)>F\left(X_{\text {new }, u}^{i}\right)$

$X_{\text {new}, u}^{i}=X_{\text {new } S P, u}^{k}$

else $X_{n e w, u}^{i}=X_{n e w, u}^{i}$

end if

proposed method to filter ECG signals. For this purpose, 200 signal segments of real ECG signals from different subjects are selected from the MIT-BIH database [50, 51]. The suggested method was simulated with $N=40$ rules. Therefore, the filter was structured using a set of 40 rules with $40 \times 3=120$ adjustable parameters. consequently, there was two regressors to every rule and one consequence interval $(2 \times 40$ antecedent parameters and $1 \times 40$ consequence parameters). The type-2 fuzzy adaptive filter's initial input vector $x$ is set as $x=\left[x_{1}, x_{2}\right]^{T}=[0,0]^{T} .$ The effectiveness of the proposed approach will be fully investigated by assessing its performance in some noisy environments. These include the typical noises associated with ambulatory ECG recordings, which involve MA and EM. These are individually selected from the MIT-BIH stress data [28]. In addition, the proposed method will be also tested with artificially generated white Gaussian noise, which will be added to the original ECG segments with a number of input $S N R$ levels. In general, evaluation of signal denoising methods usually involves a measure of similarity between the denoised signal and the original signal. In order to assess the obtained type-2 fuzzy filter output fit, four of the frequently used criteria from other experimental studies have been applied.

Signal-to noise output ration ($S N R_{\text {out}}$):

$S N R_{\text {output}}=10 \times \log \left(\frac{\sum_{k=1}^{N}\left(x_{k}\right)^{2}}{\sum_{k=1}^{N}\left(\hat{y}_{k}-x_{k}\right)^{2}}\right)$     (11)

Mean Square Error ($M S E$):

$M S E=\frac{1}{N} \sum_{k=1}^{N}\left(\hat{y}_{k}-x_{k}\right)^{2}$     (12)

The SNR improvement ($S N R_{i m p}$):

$S N R_{i m p}=S N R_{\text {output}}-S N R_{\text {input}}$     (13)

The Root Mean Square Error (RMSE):

$R M S E=\sqrt{\frac{1}{N} \sum_{k=1}^{N}\left(\hat{y}_{k}-x_{k}\right)^{2}}$     (14)

where, $x_{k}$ is the clean signal, $\hat{y}_{k}$ is its estimate and N is the length of the data.

4.1 Denoising

To evaluate the outcomes of the proposed technique, three types of noise are utilized (real and artificial noises) and added to the real ECG referenced 18177.dat, taken from the MIT-BIH database [51]. The denoising results for different noise types are shown in Figures 4-7.

The results show that with the addition of white Gaussian noise at 3dB SNR level, the denoised ECG signal is very close to the clean ECG morphology (see Figure 4). Meanwhile, Figure 5 shows that the denoised signal does not show any EMG artefacts with real MA noises at 3dB SNR level. Nevertheless, whilst the most troublesome noise is the EM, due to its ability to mimic ectopic beats, a very successful outcome is obtained with this experiment. Normally, undesired notches and EM noise are seen on the ST segment, and it is very difficult to remove them using simple bandpass filters; however, the proposed method is able to remove these motion artefacts (EM), as shown in Figure 6, whilst also preserving the signal’s diagnostic morphology information. In order to assess the proposed method’s efficiency to remove more complicated noises, all three noises (EM, MA and white Gaussian noise) are added to the same signal (18177.dat). Comparing the noised ECG with the denoised one, it can be seen that the proposed method produces a very smooth signal (see Figure 7).

In what follows, the recording 18177.dat is used to evaluate the effectiveness of the proposed technique under different $S N R$ input levels of real EM and MA, and artificial WGN noises where severe distortion occurs. Fuzzy filter output is assessed for each noise power case by using the criteria formulas (11)-(14). The SNR_output, SNR_imp, MSE and RMSE generated by the proposed framework for WGN, MA and EM versus different SNR_input(0dB to 10dB) are shown in Figure 8. These results show that the method achieves positive results in all different noise environments for a number of SNR_inputlevels. This can be seen in Figure 8 where the slope of the different criteria, particularly the SNR_output, are not flat and there is an obvious increase of the SNR_output with a corresponding decrease in SNR_input. So, this confirms that the framework is capable of optimally filter the ECG signal even in the presence of artefacts such as WGN, MA, and EM and with severe distortions.

Next, the proposed type-2 fuzzy adaptive filter is applied to a series of real ECG signals to further test the validity of the approach. The considered records are 100.dat, 103.dat, 200.dat and 208.dat taken from the MIT-BIH arrhythmia database. The noisy ECG signal is constructed by adding 5dB Gaussian white noise (taking into account the real existing noise in the records). Visual inspections of Figures 9, 10, 11 and 12 show the filtering efficiency.

4.2 Comparison

The performances of the introduced filter will be compared to the results obtained by recently published methods in ECG signal denoising. Tables 1-4 give detailed results obtained by comparing the proposed method with the adaptive dual threshold filter and discrete wavelet transform (ADTF-DWT) method [7]. The results given by Jenkal et al. [7] were validated by the works of several authors who compared the ADTF-DWT with the parallel-type fractional zero-phase filtering (FZP) [10], the Reimann- Liouville (RL) integrator [11], and the zero-phase average window filter (AZP) [10]. The EMG artefact comparison results are shown in Table 1. The noises are simulated in the same manner as the experiment described in the study [7]. Denoising comparison of 5dB white Gaussian noise from the selected entries of the MIT-BIH arrhythmia database [41] is shown in Table 2. The original paper [7] compares its results with a number of different methods, including the adaptive dependent wavelet thresholding technique (ADWT) and the multi-adaptive bionic-wavelet transform (MABWT) [12]. Tables 3 and 4 show the results of the comparison between the proposed method and some benchmark methods at the same levels of WGN.

This survey comparison shows that the results obtained from the proposed filter are much better than those obtained from the other benchmark methods, namely the ADTF-DWT, RL, AZP, FZP, ADWT, MABWT methods as detailed by Jenkal et al. [7]. Indeed, the results show that the proposed method shows an increased SNR improvement and a reduced mean square error (MSE). In order to generate further validity in our results, we also compared the proposed approach performance against another recently published method [9] that is based on the adaptive Fourier decomposition (AFD). In [9], the authors made comparisons of the AFD based method with a number of other EMD and EEMD based methods described by Chang et al. [13]. The results of the comparison between the AFD method and the proposed method are presented in Table 5. They show that again, the introduced method performs better in terms of MSE criterion (These results that are presented in Table 5 are calculated with signal magnitude that has been increased by 200 times from its original value).

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Figure 4. (a) Typical filtering of the proposed method for the record 18177.dat; with an added WGN at 3dB SNR level (b) Zoomed segment of denoised ECG signal

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Figure 5. (a) Typical filtering of the proposed for the Record 18177.dat; with muscle artifact (MA) at 3dB SNR level (b) Zoomed segment of denoised ECG signal

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Figure 6. (a) Typical filtering of the proposed method for the Record 18177.dat; with electrode motion artifact (EM) at 3dB SNR level (b) Zoomed segment of denoised ECG signal

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Figure 7. Typical filtering of the proposed method for the record 18177.dat with the three noises (WGN+MA+EM)

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Figure 8. Measures performances of the proposed method versus different input SNRs for WGN, EM and AM noise: (a) SNR_output(b) SNR _improvement (c) MSE (d) RMSE

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Figure 9. (a) Typical filtering of the proposed method for the Record 100.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal

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Figure 10. (a) Typical filtering of the proposed method for the Record 103.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal

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Figure 11. (a) Typical filtering of the proposed method for the Record 200.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal

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Figure 12. (a) Typical filtering of the proposed method for the Record 208.dat with WGN at 5dB SNR level (b) Zoomed segment of denoised ECG signal

Table 1. Comparison of the denoising results of the EMG artefact in the record 115.dat

Table 2. Comparison of the denoising results of the WGN noise at 5dB in some record taken from the MIT-BIH arrhythmia database

Table 3. Comparison of the denoising results of the WGN (5dB) in the record 101.dat

Table 4. SNR_imp comparison of denoising results of the WGN (5dB) in some record taken from MIT-BIH database

Table 5. Comparison between filtered results using the AFD, EEMD, EMD and the proposed method with noisy signals at 10dB SNR level in terms of MSE criterion

Table 6. Comparison between the filtered results of MP-EKF, EKS, EKF and the proposed method in the presence of artificial and real noises in terms of MSEPWRD index

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Figure 13. Comparative results in the terms of SNR_output

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Figure 14. Comparative results in the terms of RMSE

In order to further assess the efficiency of the proposed technique, Figures 13 and 14 show the comparisons based on SNR_output and RMSE, for the proposed method and the new approaches labeled (FSSTH-NLM and NLM) [6] applied on a synthetic ECG signal simulated using Open-source electrophysiological Toolbox (OSET) [52], distorted by many noises of various SNR_input levels. By a visual inspection of Figures 13 and 14 we can see that the proposed approach outperforms the other three techniques by achieving higher SNR_outputand lower RMSE.

Following this analysis, the proposed method will be further tested against a model-based method described by Hesar and Mohebbi [15], which presents an ECG signal denoising method labelled MPEKF. This method uses an automatic particle weighting strategy and an extended Kalman filter. The proposed method is compared to our method in terms of an ECG diagnostic distortion measure called the Multi-Scale Entropy based Weighted Distortion Measure [15, 53]. We use a similar method as that utilized by Hesar and Mohebbi [15] to calculate this measure. A weighted percentage root square difference (WPRD) is used as a metric, which is generated by comparing the original sub-band wavelet coefficient with the filtered signals. It uses weights that are the same as the corresponding sub-band’s multi-scale entropies. Using this measure allows to achieve an accurate representation of the distortion of the filtered signal at all sub-bands [15, 53]. It was necessary to decompose both signals using wavelet filters up to L levels in order to calculate this metric. Both the sampling frequency and the nature of the signal dictate the number of levels. An accurate ECG trace will include a sharp QRS complex segment and the slow P and T waves, therefore, effective decomposition of an ECG should display an effective representation of the detail coefficients of the QRS complexes and the approximation coefficients of the P and T waves. As such, Daubechies 9/7 bi-orthogonal wavelet filter [54] was used for decomposition purposes. This led us to choose L=4 for sampling frequency of 128Hz [55].

The multiscale entropy-based weighted PRD measure is defined as:

$M S E W P R D=w_{A_{L}} \times$$\left(\sqrt{\frac{\sum_{k=1}^{N_{A_L}}\left[A_{L}(k)-\tilde{A}_{L}\right]^{2}}{\sum_{k=1}^{N_{A_L}}\left[A_{L}(k)\right]^{2}}} \times 100\right)$$+\sum_{j=1}^{L} w_{D_{j}} \times\left(\sqrt{\frac{\sum_{k=1}^{N_{D} j}\left[D_{j}(k)-\tilde{D}_{j}(k)\right]^{2}}{\sum_{k=1}^{N_{D} j}\left[D_{j}(k)\right]^{2}}} \times 100\right)$     (15)

where: $w_{A_{L}}$ denotes the weight of the L^th approximation band; $W_{D j}$ denotes the weight of the j^th level details sub band; A_L and $\tilde{A}_{L}$ denote the L^th approximation band coefficients of the original and the denoised signals, respectively; and $D_{j}$ and $\widetilde{D}_{i}$ denote the j^th details band coefficients of the original and the denoised signals, respectively. The weights are: $w_{A_{L}}$ and $w_{D j}$.

The results of the comparison between our method and that of MP-EKF, EKF and EKS, as detailed in Hesar and Mohebbi study [15], using a MSEWPRD with various input SNR levels, are shown in Table 6. These results were generated by determining the MSEWPRDs of 200 filtered ECG segments that were selected from the MIT-BIH database. However, the chosen segments used in our algorithm can be not the same as those segments used by Hesar and Mohebbi [15].

4.3 Discussion

Using a set of type2-fuzzy If-Then rules, we constructed a type-2 fuzzy adaptive filter that was able to adaptively change in order to reduce the criterion functions to their minimum values. The obtained results show that the proposed filter is highly effective in denoising the ECG signal; however, the efficiency of the method’s performance is determined by the number of fuzzy adaptive filter rules and the parameters of the optimization algorithm. The effectiveness of the investigated technique was compared to simulation results from both model and non-model-based methods using SNR, MSE and RMSE criteria, with the SNR being the power ratio between signal and noise. As such, a larger SNR indicates reduced background noise and, therefore, an increase signal denoising performance. Conversely, the MSE is a tracking accuracy measurement of the filtered signal compared to the original signal, therefore, the performance of the signal information retention is better when the MSE is smaller and the RMSE is used to calculate the variance between the real signal and its estimate. A smaller RMSE leads to a smaller difference. Figures 4-14 show that the proposed method is very effective when we are dealing with real noises, white Gaussian noise and their combination with different SNR_input levels. As such, it can be deduced that this method is both accurate and robust. Furthermore, by filtering the EMG artefact and comparing the outcomes with those of other benchmark methods, it can be seen that the proposed filter is statistically more effective than FSSTH-NL, ADTF-DWT and other methods described by Bing et al. [6-11]. Comparison results between the proposed method’s denoising performance using white Gaussian noise of 5dB SNR level with the ADTF-DWT and other methods [7-12] are shown in Tables 2-4. These results show that the proposed method has improved results in terms of MSE, RMSE and SNR_imp when compared to ADTF-DWT, ADWT and MABWT methods. Furthermore, the proposed approach provides an important solution for the problem of high-density noise as shown with the results of the 5dB white Gaussian noise. Table 5 displays a deeper comparison of the filtered results under MSE performance using the proposed approach and the AFD, EEMD and EMD methods detail [9-13]. These results also show that the proposed approach is again, more effective. Moreover, the results displayed in Table 6 shows the comparison between the proposed method and MP-EKF and EKF/EKS [15] using the MSEWPRD on two types of noise with four different input SNRs (0dB, -1dB, -3dB and -5dB). Notice that the MP-EKF and EKF/EKS have higher MSEWPRDs for each noise type at all SNR_inputlevels compared to the proposed method indicating that our method is more effective than the MP-EKF and EKF/EKS in preserving the diagnostic information and morphology of the ECG signals.