A versatile dynamic noise control framework based on computer simulation and modeling

1 Introduction

With the advancement of industry and transportation, noise pollution has become one of the four significant environmental contaminations (noise contamination, water contamination, air contamination, and solid waste contamination) recognized worldwide, seriously threatening people’s physical and mental health and living environment, at the same time, as the standard of living continues to improve, made the problem of noise pollution has increased. The sound pressure and sound pressure level are generally used to evaluate the noise intensity, the higher the pressure level of sound, the stronger the noise, and vice versa [1]. The human ear’s perception of noise is not only related to the pressure level of noise, but the duration, frequency, and other factors of noise, will also affect the perception of the human ear. The human ear is more delicate to high-frequency noise and sluggish to low-frequency noise. Therefore, for sounds of different frequencies and the same sound pressure level, how we sound and feel may be different. To better reflect different factors such as noise pressure, frequency, and the degree of impact on the human body, it is required to propose a more comprehensive and effective noise evaluation standard. The following are some commonly used evaluation criteria [2]. The human ear’s judgment of sound strength is called loudness, and the unit is sone. We define 1 song as the loudness of a 1,000 Hz pure tone with a sound pressure level of 40 dB. Hearing is not only related to the pressure level of sound, but the frequency of the sound also has an impact on the hearing. Two different frequencies, but the sound with the same sound pressure level, the human ears may hear different feelings, i.e., the loudness of the sound is different. Like the sound pressure level, according to the loudness, the frequency-related loudness level can also be defined, and the unit of loudness level is phon. In terms of loudness and loudness level, to show that people’s subjective perception of noise is very cumbersome, it is inconvenient to use. At the same time, they cannot accurately represent the effect of sound on the human ear; therefore, people widely use A sound level and equivalent continuous A sound level to make a subjective evaluation of noise. A sound level is through the A-weighting network to evaluate the perception of noise to the human ear’s, the principle of A weighting network is to imitate the inverted 40 phon equal loudness curve.

A sound level measurement result is approximately the same as the human ear’s subjective perception of noise, i.e., high-frequency sensitivity, not sensitivity to low frequencies. If it is to evaluate steady-state continuous noise, A sound level can better represent the actual feeling of the human ear. But A sound level is not suitable for evaluating unsteady noise, so equivalent to continuous A sound level is applied to evaluate the non-steady-state noise. Noise control is an important issue that many industries and fields must face [3]. Traditional methods are mainly based on acoustic control technology, including sound absorption, sound insulation, use of mufflers, isolation and vibration reduction, etc. The mechanism is that the noise sound waves and acoustic materials, or the structure interacts and consumes sound energy, thereby reducing noise; this method is a passive or passive control method. In general, passive control methods are more effective in reducing mid- and high-frequency noise, but the control effect of low-frequency noise is not obvious. Therefore, the inventor Leung proposed the idea of active noise cancellation in 1933, but not until the late 1970s and early 1980s it attracted attention [4]. After many years, it has developed into a new noise control technology complementary to the traditional controlling mechanism – active noise control (ANC), namely active control of noise. The flowchart of ANC is depicted in Figure 1. The proposal and development of this concept is a milestone in terms of noise control. It promotes the development of basic theories of acoustics, signal processing, and control technology, and expanded the application fields of sound field and vibration control. ANC is through the amplitude and phase adjustable sound source (secondary sound source) sound waves, it destructively interferes with the sound wave to be canceled (primary noise) to reduce the noise. Compared with the traditional passive noise reduction measures, in addition to the inherent characteristics of good low-frequency noise reduction, there are also advantages such as the lightweight and strong environmental adaptability of the system. ANC technology has formed a relatively mature basic theory, system structure, and implementation method, it has become an indispensable means of noise control, and products with certain market prospects and social influence have been developed [4].

Figure 1

Flow chart of ANC.

The techniques for determining a closed-structured noise lessening condition in relation to the optional way for delay and noise bandwidth are presented in this section. By including the autoregressive (AR) model into the linear prediction model, the bandwidth of noise is specified. This technique of bandwidth parameterization for noise makes it possible to derive the combined effects analytically. To foster a closed-structured noise reduction condition, two critical actual boundaries of feedback active noise control (FBANC), optional way of delay, and noise bandwidth are chosen in this study and their combined impacts are analytically examined.

The electro-acoustic connection among speaker scheme and the sensing microphone scheme gives the secondary track its name. The outcome of the ANC system’s noise reduction is greatly reduced by the interruption in the secondary track. As a result, there is a trade-off between noise reduction effectiveness and noise cancelling’s spatial coverage range. The delay further increments the coherence time of noise correlation and the performance deprivation gets noticeably worse. The noise bandwidth has an inverse relationship with the coherence time. The examination of combined influence of subordinate path delay and noise bandwidth on the outcome deprivation of the FBANC earmuffs scheme is therefore highly important. The rest of article is organized as the most recent work in the field of ANC based on computer simulation and other applications is presented in Section 2. The adopted methodology is presented in Section 3 which is followed by the results and discussion in Section 4. At last, the conclusion is discussed in Section 5.

2 Literature review

Chilipi et al. [5] stated that with the development of science and technology, people’s lives are getting richer, and the pace is getting faster and faster, the information received every day is also increasing, and sound is one of the most information we receive every day, the sound is inseparable from watching TV, calling, chatting, etc. Hemanth et al. [6] believe that sound is the carrier of people’s thoughts and emotions; it is the oldest and most convenient way of communication for mankind. Therefore, the sound is like food, clothing, shelter, and transportation, and it is indispensable in people’s life, study, and work. However, not all sound information is what people need. For example, the roar of the machine, the sound of an airplane taking off, the sound of compressor intake/exhaust, etc., these sounds that are of no use to us are called noise. Zheng et al. [7] stated that with the development of modern industry and transportation since the middle of the last century, the problem of noise pollution has attracted more and more attention, and has become one of the four major environmental pollutions (noise pollution, water pollution, air pollution, and solid waste pollution) recognized worldwide, a serious threat to human physical and mental health and living environment. Zhao et al. [8] believe that due to the peculiar nature of noise, noise pollution is different from other pollution. First, because the noise source is relatively close to the victim, the geographical scope of noise pollution is limited. Second, noise pollution does not produce actual pollutants, its effect is real-time, and when noise is present, it will cause pollution problems, when the noise disappears, the problem will be solved. Finally, since no pollutants are generated from noise pollution, we cannot recycle the pollutants; therefore, it is difficult to improve the reuse rate and utilization value of noise pollution. According to the statistics of Fujimoto [9], more than 70% of the inhabitants of the earth (most of them are urban residents) live in different degrees of the noise environment.

Bashashin et al. [10] stated that if in a high-noise environment for a long time, people may experience symptoms such as mild hearing fatigue, insomnia, irritability, neurasthenia, and mental decline, affecting people’s normal life. In severe cases, noise may induce some diseases, such as high blood pressure, and heart disease will cause certain harm to our health. Bohaienko and Bulavatskiy [11] believe that noise will also affect some high-precision production machines, testing instruments, and special industrial structures in modern industries; it will cause them to experience acoustic fatigue, and even greatly shorten their service life, or cause production accidents. Therefore, to improve people’s living environment and people’s living standards, we must pay attention to the problem of noise pollution. Ahmed and Kakkar [12] pointed out that the essence of achieving active control in a specific space is to achieve inverse matching of spatial distribution and time history. The two sound sources generated are referred to as the primary sound source (artificially generated sound field) and the secondary sound source (sound field to be eliminated). Cadena-Ramirez et al. [13] proposed the first step in designing an ANC system to analyze the characteristics of the primary sound field, complete the layout design of the secondary sound source according to the control target, i.e., determine the type, quantity, and placement position of the secondary sound source. The primary sound field in active control is divided into two types: free sound field and bounded sound field, the latter can be divided into two forms: one-dimensional pipe sound field and three-dimensional enclosed space sound field. Li et al. [14] believe that according to the size of the acoustic mode density, the three-dimensional enclosed space sound field can be further subdivided into a standing wave sound field and a diffuse sound field. To achieve active noise cancellation in local and full spaces, in theory, the principle of optimal placement of secondary sound sources should follow the Haygens principle, i.e., it requires a secondary sound source with the characteristics of a three-pole (a monopole and a dipole at the same position), continuously placed to surround the primary sound source, or on the closed surface of the local space that needs to be silenced.

The ANC earmuffs are designed to block out outside noises with predominant low-frequency components, such as those produced by house heaters, aviation engines, and other spinning machinery [15,16]. Passive earmuffs are often quite expensive and cumbersome, and they are poor at suppressing noise components at frequencies below a few hundred Hertz. The feedforward ANC method is the foundation for a large number of commercial ANC headset applications. However, nonstationary orientation efforts, noise quantity, and acoustic feedback seriously impair the stability and performance of feedforward ANC systems for headsets [17,18]. Since the microphone is placed inside the ear-cup of the headset, adaptive FBANC, as opposed to feedforward ANC, offers a more accurate noise cancellation.

3 Methods

MATLAB is a widely used mathematical calculation software, with powerful functions, easy to learn, and other advantages. MATLAB can be used in numerical calculations, mathematical drawing, physical/electrical system simulation analysis, and control system research. MATLAB provides a wealth of built-in functions, users only need to learn to call MATLAB functions to achieve many functions, which eliminates many troubles for users [19]. At the same time, users can also write the functions they need in MATLAB. The functional language can use programming languages such as C language and M language, this greatly broadens the scope of software usage, and increased user convenience. To verify the step factor μ , filter order L , and other parameters, the impact on algorithm performance, the algorithm is simulated and calculated in MATLAB software [20]. The parameters are set to f s : sampling frequency; N : number of sampling points; L : filter order; μ : step factor; w : filter weight coefficient; noise: noise signal; x : reference signal; d : expected signal; v : observation noise, Gaussian white noise that is not related to the reference signal y : output signal error; and MSE : signal mean square error. To better reflect the effect of the algorithm, all simulation experiments are repeated 200 times, and the mean square error of each algorithm takes the average of these 200 experimental data. Parameter initialization: d = sin ⁡ ( 2 π 100 t , x = awgn ( d , 20 ) , f s = 5,000 Hz , N = 1,000 , L = 16 , μ = 0.01 , v = 0.01 * randn ( 1 , N ) MSE are all initialized to zero, then the simulation result of the standard least mean square (LMS) algorithm are as shown in Figures 2 and 3 [21].

Figure 2

Error curve of LMS algorithm.

Figure 3

LMS algorithm learning curve.

As can be seen from the above two figures, in the presence of interference, the LMS algorithm can remove the noise in the signal very well. Under the above initial conditions, after about 100 iterations, the algorithm approaches complete convergence, and the mean square error is about 10 − 8 . The step size factor μ of the normalized LMS algorithm is not fixed, and is related to the power of the input signal. When the filter order is greater, the power of the input signal will be greater, then the corresponding step factor μ will be smaller [22]. Therefore, the filter order of the normalized LMS algorithm should be appropriately smaller. Parameter initialization: x = randn ( 1 , N ) , d = x , v = 0.01 * randn ( 1 , N ) , f s = 5,000 Hz , N = 1,000 , L = 4 , r = 0.0001 , μ 0 = 0.03 . The step factor of the LMS algorithm is 0.005 , other parameter settings are the same as the standardized LMS process. The performance of the standardized LMS process and the LMS process are compared, and the simulation outcomes are presented in Figure 4 [23].

Figure 4

The learning curve when the LMS algorithm does not synchronize the length factor.

As can be seen from Figure 4, when the step factor is 0.005, it takes about 700 iterations to converge; when the step factor is 0.01, the algorithm converges after 400 iterations; and when the step size factor is 0.02, the algorithm completely converges after 200 iterations. Therefore, within the range of convergence, the larger the value of the step factor, the faster the convergence; however, the steady-state fault of the algorithm will also increase [24]. This is the contradictory connection among the convergence speediness of the LMS process and the steady-state error, which is difficult to reconcile. In practical applications, we need to follow the actual needs of the two, and choose an appropriate step factor. When a faster convergence speed is required, a larger step factor can be selected. Conversely, if the steady-state error after convergence is higher, a smaller step factor needs to be selected. Parameter initialization: x = randn ( 1 , N ) , d = x , v = 0.01 * randn ( 1 , N ) , f s = 5,000 Hz , N = 100 , μ = 0.01 , the filter order Z is respectively 8, 16, 32; when the step factor is fixed, the convergence speed does not change with the change of the filter order [25]. But the larger the filter order, the larger the steady-state error of the algorithm, i.e., the offset of the LMS algorithm is proportional to the order of the filter. Filter order mainly affects the computational complexity of the algorithm and the distribution of the eigenvalues of the autocorrelation matrix. The lower the filter order, the computational complexity and the steady-state fault will be inferior. At the identical time, the maximum value of the eigenvalue of the autocorrelation matrix will be smaller making the value range of the step factor increase, and the algorithm converges faster. From the above characteristics, the filter order should be as small as possible [26]. But in actual applications, the filter order is too small, and cannot realistically simulate the expected impulse response of the FIR filter and frequency response characteristics. In the path identification application, if the filter order is selected, when it is smaller than the filter order of the actual unknown system, there will be an under-filter order problem, and it will be difficult for the filter weight vector to converge to the optimal solution, which may cause the algorithm to diverge. In path identification, set the unknown system path to be identified, the order of the modeling filter is 4 and 8, and the modeling filter is initialized to zero, the input signal is x = randn ( 1 , N ) , the observed noise is v = 0.01 * randn ( 1 , N ) , and the simulation result is shown in Figure 5 [27].

Figure 5

Learning curve for different filter orders in path identification.

From Figure 5, it can be seen that when modeling the order of the filter, its order must be smaller than the order of the system to be identified, and the algorithm is not convergent. Therefore, we should choose the filter order reasonably according to the actual situation [28].

4 Results and analysis

In the system identification environment, regarding the standardized LMS process, the existing enhanced process, compare and analyze the simulation with the improved algorithm proposed by the author. Parameter initialization: the step size feature of the standardized LMS process is 0.3. Based on existing algorithms, the author proposes an improved algorithm. The normalization factors of the three algorithms are all initialized to zero. The system has a sudden change at the 500th sampling point, and the simulation result is shown in Figure 6 [29].

Figure 6

Comparison of the learning curve between the improved algorithm and other algorithms.

It can be seen from Figure 6 that when the steady-state error is the same, the convergence speed of the improved algorithm is faster than the normalized LMS algorithm. Compared with the improved algorithm proposed by the author, the convergence speed is the same, but the steady-state error is smaller. It can be seen that the improved algorithm proposed by the author is better than the improved algorithm in steady-state error, but there is a certain increase in computational complexity. The algorithm simulation result interface mainly realizes algorithm type selection and algorithm simulation parameter initialization [30]. In the algorithm selection panel, the algorithm type drop-down list includes: LMS algorithm, variable step size LMS algorithm, normalized LMS algorithm, leaked LMS algorithm, symbolic LMS algorithm, momentum LMS algorithm, filtered least mean square algorithm, delayed LMS algorithm, RLMS algorithm, and RLS algorithm. The simulation parameters of the LMS algorithm are the filter order and step factor; other algorithms also include some unique parameters, such as the leakage factor of the leaked LMS algorithm. When the algorithm is selected, the simulation parameters of that algorithm will be enabled, and the others will be grayed out for the user to distinguish. In the navigation key panel, click the save data button, and can save the data calculated by the algorithm as a mat file. The mat file can be used in the simulation comparison and analysis interface. The display range of the X and Y axis can be adjusted in the coordinate axis adjustment panel, and is convenient for users to observe the graph [31]. The user can choose to draw the graph as a simulation curve graph, or the mean square error graph, the mean square error graph is shown in Figure 7.

Figure 7

Algorithm simulation results (mean square error).

In the simulation comparison and analysis interface, users can compare and analyze the mean square error of the algorithm in different situations. The analysis type drop-down list includes four modules: algorithm analysis, step factor analysis, filter order analysis, and input signal analysis. In the curve setting panel, the number in the curve sequence indicates the number of analysis items. For example, in the case of step factor analysis, the curve sequence is 3, which represents the analysis of the algorithm characteristics under the three-step size factors as shown in Figure 8 [32].

Figure 8

Simulation comparison analysis (step factor).

A 30-band analog equalizer is also fitted to fine-tune the frequency response of the headphone speaker in order to get the investigational atmosphere as close to the streamlined model atmosphere used in the examination, where the subordinate track is observed as pure time delay. Comparisons between the 30-band equalizer-equipped headphones’ magnitude responses are presented in Figure 9. This figure presents the headphones magnitude responses comparison with and without equalizer of 30-band. The assessment of noise reduction for second-order AR noises in terms of analytic results, simulation results, and experimental results are depicted in Figure 10. The experimental results, which used noises with a bandwidth of 1–100 Hz for the second-order AR model, demonstrate good agreement with the analytical results with differences of less than 1.5 dB.

Figure 9

Headphones’ magnitude responses comparison with and without equalizer of 30-band.

Figure 10

Noise reduction comparison for second-order AR noises.

5 Conclusion

ANC is a new research direction in the field of noise control, and is mainly used in the control of low-frequency noise. The author first introduced the development prospects of ANC and some basic knowledge of noise. The related algorithm of adaptive ANC is derived in detail, and a variable step size normalization algorithm based on relative error is proposed. MATLAB is used to simulate the algorithm, build a versatile dynamic noise control framework with DSP chip as the core, and conduct field experiments. Deduced in detail the LMS algorithm and filtering-XLMS algorithm, at the same time, the factors affecting their convergence speed and steady-state performance are analyzed, and proposed a variable step size normalization algorithm based on a relative error. In the MATLAB environment, various algorithms of adaptive ANC were simulated, and several algorithm parameters such as step factor, filter order, etc., are analyzed. The degree of influence on the performance of the algorithm is also analyzed and based on the analysis an ANC hardware system is constructed. In common command set software simulation of algorithms and software design of ANC systems, on the generalized comfort degree experiment platform, a single-channel adaptive ANC experiment was carried out. High levels of noise lessening which is 15 dB for airplane noise and 21 dB for household heater noise is attained from experiments with recorded noises further demonstrate the viability of using the FBANC earmuffs in real-world applications.