Narrowband FxLMS active noise reduction method with low calculation complexity

Abstract

The invention discloses a narrow-band FxLMS active noise reduction method with low calculation complexity, and relates to the technical field of active noise control. The method comprises the following steps: generating a synchronous reference signal group based on a noise fundamental frequency and a harmonic frequency thereof; calculating and storing the phase offset of the reference signal group filtered by the secondary path estimation model in advance; collecting an error signal, and iteratively updating an accumulated value related to the reference signal group; and calculating and outputting a control signal based on the phase offset and the accumulated value. According to the method, convolution operation which is carried out in real time and is huge in calculation amount in a traditional algorithm is equivalently replaced with simple multiplication operation through strict mathematical derivation, on the premise that the convergence speed, the steady-state error, the noise reduction amount and other core performance of the traditional narrowband FxLMS algorithm are completely kept, the calculation complexity and memory occupation during operation are greatly reduced, and the method is suitable for large-scale popularization and application. The method is especially suitable for the deployment of an embedded platform with limited computing resources.

Description

Technical Field

[0001] This invention relates to the field of active noise control technology, and more specifically to a narrowband FxLMS active noise reduction method with low computational complexity. Background Technology

[0002] Active noise control (ANC) is a technique that effectively reduces noise by generating secondary sound waves with opposite phase and the same amplitude as the original noise sound waves, thereby achieving destructive interference of sound waves in the target area. For noise generated by rotating machinery (such as engines, fans, propellers, etc.), its spectrum exhibits significant periodicity, with the main energy concentrated at the fundamental frequency and several harmonic frequencies. For this type of noise, the narrowband feedforward FxLMS algorithm is a classic and efficient solution. This algorithm uses a deterministic signal (such as a rotation speed signal) synchronized with the noise source to generate a reference signal, avoiding the problem of acoustic feedback path contamination of the reference signal in traditional broadband ANC systems, thus achieving significant noise reduction.

[0003] However, the traditional narrowband FxLMS algorithm has a significant technical bottleneck: when updating the control filter weights, it requires real-time convolution operations between the reference signal and the estimated model of the secondary path. In practical applications, to accurately model the acoustic path, the order of the secondary path model is often as high as hundreds or even thousands of orders. This results in an exceptionally large computational load for the convolution operation (the computational load is proportional to the model order M), placing extremely high demands on the processor performance of the control system and leading to high power consumption. This greatly limits the application of this algorithm in cost-sensitive, computationally limited embedded platforms (such as automotive active acoustic systems, smart headphones, and online noise reduction in industrial equipment).

[0004] Therefore, there is an urgent need in the field for an improved solution that can significantly reduce the computational complexity and memory resource consumption of the traditional narrowband FxLMS algorithm without sacrificing its denoising performance (such as convergence speed, steady-state error, and denoising amount), so as to promote the widespread application of this technology. Summary of the Invention

[0005] The purpose of this invention is to provide a low computational complexity narrowband FxLMS active noise reduction method. Through rigorous mathematical derivation, the equivalent substitution of the calculation process is achieved, thereby significantly improving the computational efficiency and resource utilization while ensuring that the algorithm performance remains completely unchanged. This overcomes the shortcomings of existing narrowband FxLMS algorithms, such as high computational complexity and large memory consumption.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A low-computational-complexity narrowband FxLMS active noise reduction method includes the following steps:

[0008] S1: Generate a set of synchronous reference signals based on the noise fundamental frequency and its harmonic frequencies;

[0009] S2: Pre-calculate and store the phase offset of the reference signal group after filtering by the secondary path estimation model, release the secondary path model, and initialize the accumulated value;

[0010] S3: Acquire error signals and update the accumulated values ​​related to the reference signal group;

[0011] S4: Calculates the control signal based on the phase offset and accumulated value, outputs it from the secondary sound source, and returns it to S3 to process the next sampling point.

[0012] Furthermore, the reference signal group described in S1 consists of pairs of sine and cosine signals synchronized with the noise fundamental frequency and its harmonic frequencies, expressed as:

[0013] xa q (n)=cos(2πf q nT s )

[0014] xb q (n)=sin(2πf q nT s )

[0015] Among them, f q Let T be the frequency of the qth harmonic, n be the time index, and T be the frequency of the qth harmonic s The sampling period.

[0016] Furthermore, the phase offset is calculated and stored only during the initial stage of system operation;

[0017] The secondary path model and reference signal array do not need to be recalculated or stored during subsequent runtime.

[0018] Furthermore, the phase offset mentioned in S2 includes:

[0019] The phase offset coefficient is expressed as follows:

[0020]

[0021] The derivation coefficient is expressed as follows:

[0022] as′ q =-bs q ,bs′ q =as q

[0023] in, Let ω be the m-th coefficient of the secondary path estimation model. q Let M be the digital angular frequency of the q-th frequency component, and M be the model order.

[0024] Furthermore, the accumulated value mentioned in S3 is expressed as follows:

[0025] λa q (n)=λa q (n-1)+e(n)xa q (n)

[0026] λb q (n)=λb q (n-1)+e(n)xb q (n)

[0027] Where e(n) is the error signal at the current time.

[0028] Furthermore, the control signal described in S4 is expressed as follows:

[0029]

[0030] Where μ is the step size factor.

[0031] Another object of the present invention is to provide a low computational complexity narrowband FxLMS active noise reduction system, which performs the aforementioned low computational complexity narrowband FxLMS active noise reduction method, including:

[0032] Error acquisition module: includes at least one error sensor, whose output is connected to the first input of the signal processing module, and is used to acquire residual noise signals in the target area;

[0033] Reference signal generation module: includes a speed sensor linked to the rotating machinery, whose output is connected to the second input of the signal processing module, used to acquire speed information and generate a set of reference signals synchronized with the noise fundamental frequency and its harmonic frequencies;

[0034] Signal processing module: includes a digital signal processor (DSP), whose output is connected to the input of the secondary sound source module. It is used to receive error signals and reference signal groups, and generate control signals by calculating phase offset and iteratively updating accumulated values.

[0035] Secondary sound source module: contains at least one secondary speaker for outputting noise-resistant waves according to control signals.

[0036] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned low computational complexity narrowband FxLMS active noise reduction method.

[0037] Another object of the present invention is to provide an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the aforementioned low computational complexity narrowband FxLMS active noise reduction method.

[0038] In summary, the present invention has at least one of the following beneficial technical effects:

[0039] 1. Dramatically reduced computational complexity: Through core mathematical derivation, the convolution operation required for each sampling point in traditional algorithms is completely eliminated, transforming it into a one-time calculation during initialization and simple multiplication at runtime. The computational load is reduced from hundreds of millions to tens of thousands, resulting in an efficiency improvement of two orders of magnitude.

[0040] 2. Significantly reduced runtime memory usage: Traditional methods require continuous storage of secondary path models of length M and reference signal arrays of length 2QM, while this invention can release both after initialization, reducing memory usage from the 2QM level to the 2Q level, greatly saving valuable RAM resources of embedded systems;

[0041] 3. No performance loss: This scheme is an exact mathematical equivalent of the traditional algorithm, and maintains consistency in all key performance indicators such as convergence speed, steady-state error and noise reduction, avoiding the drawbacks of other simplified schemes that trade performance for efficiency.

[0042] In summary, this invention achieves a significant improvement in computational efficiency and resource utilization while ensuring that the algorithm performance remains completely unchanged, overcoming the shortcomings of existing narrowband FxLMS algorithms, such as high computational complexity and large memory consumption. Attached Figure Description

[0043] Figure 1 Here is a flowchart of the traditional narrowband FxLMS algorithm;

[0044] Figure 2 This is a flowchart of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0046] This embodiment provides a narrowband FxLMS active noise reduction method with low computational complexity, which optimizes the computational load through the following derivation process.

[0047] Noise generated by rotating machinery exhibits significant periodicity, with its spectral characteristics primarily consisting of the first few harmonic components based on the blade rotation frequency. This fundamental frequency is strictly proportional to the rotor speed and can be directly calculated from the speed parameters. A sinusoidal signal synchronized with the fundamental frequency and low-order harmonic components, generated using a signal generator, can serve as a reference signal for an active noise control (ANC) system. Since this reference signal is not acquired by a microphone, it avoids problems such as external noise interference and acoustic feedback affecting the reference signal quality. Therefore, using this equivalent reference signal to construct a feedforward ANC system for rotating machinery can achieve good noise reduction performance. The algorithm block diagram of the feedforward narrowband FxLMS (Filtered-x LeastMean Square) is shown below. Figure 1 As shown.

[0048] Representing the secondary path, its estimation model uses Let M represent the order and n represent the time step.

[0049] The primary noise signal can be represented as a superposition of a sinusoidal signal and a random signal, as shown in equation (1):

[0050]

[0051] Where ν(n) is random noise, a q and b q These are the Discrete Fourier Coefficients (DFCs) of the corresponding frequencies in the signal.

[0052] The reference signal is represented as:

[0053] x(n) = [xa1(n), xb1(n), ..., xa q (n),xb q (n),...,xa Q (n),xb Q (n)] T

[0054] Where, xa q (n)=cos(ω q n), xb q (n)=sin(ω q n).

[0055] The k-th error signal is:

[0056]

[0057] Where * represents convolution operation, and d(n) is primary noise.

[0058] The secondary sound source control signal can be represented as:

[0059]

[0060] Among them, wa q (n) and wb q (n) represents the control filter coefficients, which are essentially the coefficients of the DFC, i.e., a. q and b q The estimate.

[0061] The objective function of the Least Mean Square (LMS) algorithm is the sum of the mean squares of the error signals:

[0062] J(n)=E[e 2 (n)](4)

[0063] Taking the gradient of w(n) yields:

[0064]

[0065] Using the classic steepest descent method, the iterative formula for the weight coefficients can be expressed as:

[0066]

[0067] In the formula, μ is called the convergence factor or step size, which is used to adjust the iteration step size. However, since it is impossible to obtain the accurate gradient at every step during the iteration process, the instantaneous square value of the error signal at each iteration is used instead of its mean square value, and the gradient is estimated using this value, denoted as μ.

[0068]

[0069] w(n+1)=w(n)+μe(n)x′(n) (8)

[0070] in Specifically, each element in w(n) can be represented as:

[0071] wa q (n+1)=wa q (n)+μe(n)ra q (n)(9)

[0072] wb q (n+1)=wb q (n)+μe(n)rb q (n)(10)

[0073] in:

[0074]

[0075] Due to xa q (n) and xbq (n) is a sinusoidal signal. Assuming that the secondary path remains unchanged or its change is negligible, equations (11) and (12) can be converted to

[0076]

[0077] Among them, as′ q =-bs q ,bs′ q =as q , and as q and bs q The results are obtained from equations (15) and (16):

[0078]

[0079]

[0080] Normally wa q (0)=0,wb q (0) = 0, equations (9) and (10) can be transformed into:

[0081]

[0082] but

[0083]

[0084] make Equation (19) then transforms into:

[0085] ya q (n)=μ·xa q (n)[as q ·λa q (n)+bs q ·λb q (n)](20)

[0086] Similarly:

[0087]

[0088] but

[0089]

[0090] Equations (13) and (14) show that complex convolution operations can be equivalently replaced by simple multiplication operations, and the computational complexity of reference signal filtering is greatly reduced. Considering that the order M of the secondary path model is usually hundreds or even thousands of orders in practical applications, the reduction in computational complexity brought about by this improvement is extremely considerable. This is the theoretical basis for the present invention to reduce computational complexity.

[0091] Based on the above deduction, this embodiment includes the following steps ( Figure 2 ):

[0092] S1: Generate a set of synchronous reference signals based on the noise fundamental frequency and its harmonic frequencies;

[0093] S2: Pre-calculate and store the phase offset of the reference signal group after filtering by the secondary path estimation model, release the secondary path model, and initialize the accumulated value;

[0094] S3: Acquire error signals and update the accumulated values ​​related to the reference signal group;

[0095] S4: Calculates the control signal based on the phase offset and accumulated value, outputs it from the secondary sound source, and returns it to S3 to process the next sampling point.

[0096] The following is a detailed description with reference to specific embodiments.

[0097] S1: Generate a set of synchronous reference signals based on the noise fundamental frequency and its harmonic frequencies.

[0098] 1. The rotational speed signal of rotating machinery is acquired in real time by a speed sensor, usually a photoelectric encoder or a Hall sensor.

[0099] 2. The processor calculates the harmonic frequency f based on the real-time rotational speed of the rotating machinery. q .

[0100] Calculate the fundamental frequency based on the rotational speed R:

[0101]

[0102] Where, N blades This refers to the number of leaves.

[0103] Rotating machinery noise includes not only the fundamental frequency but also frequency components that are integer multiples of the fundamental frequency, i.e., harmonics. The formula for calculating the frequency of the q-th harmonic is:

[0104] f q =q×f0

[0105] Where q = 1, 2, 3..., usually taking the first few orders such as 1 (fundamental frequency itself), 2, 3, etc. is sufficient to cover the main noise energy.

[0106] 3. Generate a set of synchronization reference signals:

[0107] xa q (n)=cos(2πf q nT s )

[0108] xb q (n)=sin(2πf q nTs )

[0109] Among them, f q Let T be the frequency of the qth harmonic, n be the time index, and T be the frequency of the qth harmonic s The sampling period.

[0110] S2: Pre-calculate and store the phase offset of the reference signal group after filtering by the secondary path estimation model, release the secondary path model, and initialize the accumulated value.

[0111] First, the phase offset is pre-calculated and stored in memory.

[0112] Load the pre-identified secondary path model The expression is:

[0113]

[0114] Where the order is M, and n represents time.

[0115] For each frequency component f q Calculate its angular frequency ω q =2πf q .

[0116] Calculate the phase offset coefficient and derivation coefficient for each frequency.

[0117] The phase offset coefficient is expressed as follows:

[0118]

[0119] The derivation coefficient is expressed as follows:

[0120] as′ q =-bs q ,bs′ q =as q

[0121] in, Let ω be the m-th coefficient of the secondary path estimation model. q Let M be the digital angular frequency of the q-th frequency component, and M be the model order.

[0122] The aforementioned phase offset is calculated and stored only during the initial stage of system operation.

[0123] Secondly, release the secondary path model. After pre-computation, the large array of secondary path models will be released. By freeing them from memory, subsequent calculations no longer require them, thus significantly reducing runtime memory usage. The secondary path model and reference signal array do not need to be recalculated or stored during subsequent runs.

[0124] Finally, initialize the accumulated values. Set the accumulated values ​​corresponding to all frequency components to zero, i.e., the initial value λa. q (0) and λb q (0) is 0.

[0125] S3: Acquire error signals and update the accumulated values ​​associated with the reference signal group.

[0126] First, error signal acquisition is performed. The error microphone signal e(n) is read through an analog-to-digital converter (ADC), gain adjustment and DC bias correction are applied, and a 50Hz power frequency notch filter is used to eliminate power supply interference before updating the accumulated value. An iterative update method is adopted, which greatly reduces the computational load.

[0127] λa q (n)=λa q (n-1)+e(n)xa q (n)

[0128] λb q (n)=λb q (n-1)+e(n)xb q (n)

[0129] Wherein, the initial value λa q (0) and λb q (0) is 0, and e(n) is the error signal at the current time.

[0130] S4: Calculates the control signal based on the phase offset and accumulated value, outputs it from the secondary sound source, and returns it to S3 to process the next sampling point.

[0131] First, the phase offset of S2 and the accumulated value of S3 are integrated to synthesize the final control signal, which is expressed as follows:

[0132]

[0133] Where μ is the step size factor.

[0134] Finally, y(n) is converted by a digital-to-analog converter (DAC) and then driven by a power amplifier to output the secondary speaker, thereby reducing noise. After completion, the process returns to S3 to process the next sampling point n+1.

[0135] In summary, this embodiment changes the problem-solving path through mathematical derivation, replacing a continuously expensive computational path (traditional convolution) with a new path that is expensive once but continuously inexpensive (pre-computation + multiplication), thereby achieving a significant performance improvement in the field of digital signal processing and having great industrial application value.

[0136] This invention, through mathematical derivation, completely eliminates the convolution operation required for each sampling point in the traditional narrowband FxLMS algorithm. Instead, it replaces this with a one-time calculation during initialization and simple multiplication during runtime, reducing the computational load from hundreds of millions to tens of thousands of times, thus improving efficiency by two orders of magnitude. Simultaneously, the lengthy secondary path model and reference signal array are released from memory immediately after initialization, significantly saving RAM resources in embedded systems. This optimization is a precise mathematical equivalent of the traditional algorithm, without any loss in key performance aspects such as convergence speed, steady-state error, and noise reduction, successfully overcoming the shortcomings of high computational complexity and large memory consumption inherent in traditional algorithms.

[0137] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0138] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0139] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0140] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0141] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A low-computational-complexity narrowband FxLMS active noise reduction method, characterized in that, Includes the following steps: S1: Generate a set of synchronous reference signals based on the noise fundamental frequency and its harmonic frequencies; S2: Pre-calculate and store the phase offset of the reference signal group after filtering by the secondary path estimation model, release the secondary path model, and initialize the accumulated value; S3: Acquire error signals and update the accumulated values ​​related to the reference signal group; S4: Calculates the control signal based on the phase offset and accumulated value, outputs it from the secondary sound source, and returns it to S3 to process the next sampling point.

2. The low computational complexity narrowband FxLMS active noise reduction method according to claim 1, characterized in that, The reference signal group described in S1 consists of pairs of sine and cosine signals synchronized with the noise fundamental frequency and its harmonic frequencies, expressed as: x q (n)=cos(2πf q nT s ) xb q (n)=sin(2πf q nT s ) Among them, f q Let T be the frequency of the qth harmonic, and n be the time index. s The sampling period.

3. The low computational complexity narrowband FxLMS active noise reduction method according to claim 1, characterized in that: The phase offset is calculated and stored only during the initial stage of system operation; The secondary path model and reference signal array do not need to be recalculated or stored during subsequent runtime.

4. The low computational complexity narrowband FxLMS active noise reduction method according to claim 1, characterized in that, The phase offset mentioned in S2 includes: The phase offset coefficient is expressed as follows: The derivation coefficient is expressed as follows: as′ q =-bs q ,bs′ q =as q in, Let ω be the m-th coefficient of the secondary path estimation model. q Let M be the digital angular frequency of the q-th frequency component, and M be the model order.

5. The low computational complexity narrowband FxLMS active noise reduction method according to claim 1, characterized in that, The accumulated value mentioned in S3 is expressed as follows: λa q (n)=λa q (n-1)+e(n)xa q (n) λb q (n)=λb q (n-1)+e(n)xb q (n) Where e(n) is the error signal at the current time.

6. The low computational complexity narrowband FxLMS active noise reduction method according to claim 1, characterized in that, The control signal mentioned in S4 is expressed as follows: Where μ is the step size factor.

7. A narrowband FxLMS active noise reduction system with low computational complexity, characterized in that, The system performs a low computational complexity narrowband FxLMS active noise reduction method as described in any one of claims 1-6, comprising: Error acquisition module: includes at least one error sensor, whose output is connected to the first input of the signal processing module, and is used to acquire residual noise signals in the target area; Reference signal generation module: includes a speed sensor linked to the rotating machinery, whose output is connected to the second input of the signal processing module, used to acquire speed information and generate a set of reference signals synchronized with the noise fundamental frequency and its harmonic frequencies; Signal processing module: includes a digital signal processor (DSP), whose output is connected to the input of the secondary sound source module. It is used to receive error signals and reference signal groups, and generate control signals by calculating phase offset and iteratively updating accumulated values. Secondary sound source module: contains at least one secondary speaker for outputting noise-resistant waves according to control signals.

8. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements a low computational complexity narrowband FxLMS active noise reduction method according to any one of claims 1-6.

9. An electronic device, characterized in that, It includes a memory and a processor, the memory being used to store computer programs, and the processor running the computer programs to cause the electronic device to perform a low computational complexity narrowband FxLMS active noise reduction method according to any one of claims 1-6.

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