A shock wave signal resonance denoising method based on sparrow search algorithm optimization VMD

Abstract

The present application belongs to the technical field of communication signal processing, and in particular to a shock wave signal resonance denoising method based on sparrow search algorithm optimization VMD, the main steps of the method comprising: step one: analyzing the shock wave signal collected by the pressure sensor, and optimizing the two important parameters of VMD, the decomposition mode number and the penalty factor, according to the sparrow search algorithm to obtain the optimal parameter combination; step two: decomposing the shock wave signal collected by the pressure sensor by the parameter optimization VMD algorithm; step three: clustering the decomposition mode by the resonance energy loss ratio formula; step four: reconstructing the signal component to obtain the denoised shock wave signal. The shock wave signal resonance denoising method based on sparrow search algorithm optimization VMD provided by the present application reduces the interference of resonance noise on the shock wave signal. Considering the influence of the decomposition mode number and the penalty factor of the VMD algorithm on the decomposition effect, the VMD is optimized by the SSA algorithm, the robustness of the VMD algorithm is improved, and the algorithm is more suitable for popularization and use.

Description

Technical Field

[0001] This invention relates to the field of communication signal processing technology, specifically to a method for resonant noise reduction of shock wave signals based on the sparrow search algorithm to optimize VMD. Background Technology

[0002] This invention primarily targets the processing of shock wave signals. Shock wave signals are characterized by short duration, strong time-varying nature, and wide frequency spectrum. During the acquisition of shock wave signals, the effective operating bandwidth of the pressure sensor itself cannot fully cover the frequency domain information of the signal, leading to the introduction of resonance noise. Currently, shock wave resonance noise reduction mainly employs two types of methods. One is a dynamic compensation method, including swarm intelligence global optimization and deep learning. This method uses algorithms to compensate the shock tube test signal acquired by the pressure sensor to establish a dynamic compensation model for the pressure sensor, and then applies the dynamic compensation model to the shock wave signal acquired by the corresponding pressure sensor to reduce the impact of resonance noise. The other method directly decomposes the shock wave signal using signal processing algorithms to separate the resonance noise component and obtain the denoised shock wave signal. These algorithms mainly include wavelet transform, empirical mode decomposition (EMD), related improved algorithms of EMD, and variational mode decomposition (VMD).

[0003] The first type of dynamic compensation algorithm requires a shock tube system for auxiliary testing. Besides being affected by resonant noise, the shock tube test signal is inevitably interfered with by the testing environment itself, such as gas viscosity, the degree of diaphragm rupture, and vibration. However, in actual shock wave signal testing, due to the excessive energy of the shock wave signal, the main noise originates from the resonant noise introduced by the pressure sensor system. Therefore, applying the dynamic compensation method obtained by dynamically compensating the pressure sensor using the shock tube system and then applying it to the shock wave signal for resonant noise reduction will lose some important information about the shock wave signal.

[0004] In the second type of signal processing algorithm, wavelet transform requires the selection of appropriate wavelet basis functions, which places high demands on prior knowledge of the signal. EMD suffers from a lack of rigorous mathematical proof and modal aliasing issues. Algorithms improved upon EMD also exhibit some modal aliasing problems. VMD, based on variational thinking, decomposes signals, achieving frequency division and effective separation, and possesses a complete mathematical theory. It effectively avoids the modal aliasing problem in EMD. However, avoiding modal aliasing depends on setting appropriate input parameters. The key parameters are the number of decomposed modes and the penalty factor, which determine the decomposition effect of VMD. Too few decomposed modes will result in frequency aliasing between modal components, while too many will cause over-decomposition and spurious components. The penalty factor determines the bandwidth of each mode; too small a factor will lead to excessively large bandwidths for each mode, resulting in the loss of important signal information. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a shock wave signal resonance noise reduction method based on the Sparrow Search Algorithm (SSA) to optimize VMD. The Sparrow Search Algorithm (SSA) solves the parameter selection problem in the VMD decomposition of shock wave signals, effectively decomposes the resonance noise component corresponding to the shock wave signal, and uses the resonance energy loss ratio formula to complete the reconstruction of the signal after removing the resonance component, thereby reducing the impact of resonance noise on the shock wave signal.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention specifically adopts the following technical solution:

[0009] A shock wave signal resonance denoising method based on sparrow search algorithm to optimize VMD is proposed, which is applicable to the denoising of shock wave signals in environments with a large amount of resonance noise. The main steps of this method include:

[0010] Step 1: Analyze the shock wave signal collected by the pressure sensor, and optimize the optimal parameter combination by using the sparrow search algorithm to decompose the two important parameters of VMD: mode number and penalty factor;

[0011] Step 2: Substitute the obtained optimal parameter combination into the VMD input parameters and decompose the shock wave signal collected by the pressure sensor to obtain IMF components containing information on different center frequencies.

[0012] Step 3: Calculate the resonant energy loss ratio formula for each order IMF component, and cluster the components according to the magnitude of the resonant energy loss ratio of the IMF components, dividing them into signal components and resonant components.

[0013] Step 4: Reconstruct the signal components to obtain the noise-reduced shock wave signal.

[0014] Furthermore, the specific implementation steps of the sparrow search algorithm to optimize VMD are as follows:

[0015] Initialize the sparrow population by randomly generating a set of initial solutions as the starting population; calculate the initial fitness function value for each sparrow, and use the minimum envelope entropy value as the fitness function to evaluate the optimization effect. The envelope entropy formula is:

[0016]

[0017]

[0018] Where: K represents the number of modal components in VMD decomposition; E n (i) represents the total envelope entropy of the K IMF components; Hen (i) is the envelope entropy value of the i-th BIMF component; L represents the number of sampling points; m i represents the envelope signal obtained by modulating the component IMF(i) through Hilbert transform; p i represents the normalization process of m i .

[0019] Simulate the foraging, predator avoidance, reproduction, search and other behaviors of sparrows. Sparrows with higher fitness values obtain higher priorities and are called discoverers, while other sparrows with lower fitness values are called followers. The discoverer leads the followers to search for the easiest solutions. When the fitness value corresponding to the position information of each sparrow is less than the previous fitness value, the corresponding optimal parameter combination information is updated. The expression for updating the position of the discoverer is:

[0020]

[0021] where: t represents the current iteration level; j = 1, 2,..., d. represents the value of the j-th dimension of the i-th sparrow at the t-th iteration; iter max represents the constant with the most iterations; α ∈ (0, 1] is a random number; R2 (R2 ∈ [0, 1]) and ST (ST ∈ [0.5, 1.0]) respectively represent the alarm value and the safety threshold; Q is a random number subject to a normal distribution; L represents a 1×d matrix with all elements being 1. When R2 < ST, it proves that there are no natural enemies around the discoverer and it is in a safe search mode. When R2 > ST, it means that a sparrow has discovered a natural enemy and all sparrows need to quickly move away from this area.

[0022] When searching in other spaces, the followers can obtain energy to improve their fitness values, or they can follow the discoverer and snatch the energy of the discoverer to increase their own energy. The expression for updating the position of the followers is:

[0023]

[0024] where: X p represents the optimal position occupied by the discoverer; X worst represents the current globally worst position; A represents a 1×d matrix, and each element in the matrix is randomly assigned as 1 or -1, while satisfying A + = A T (AA T ) -1 . When i > n / 2, it means that the i-th follower with a lower fitness value may be in a hungry state.

[0025] By limiting the speed and activity range of each sparrow, the population is prevented from escaping the search space; the speed and position of the sparrows are updated based on the positions of the current optimal solution and the global optimal solution, causing the population to move towards the direction of the optimal solution for VMD parameters; warning sparrows are set up to detect predators, and the initial positions of these warning sparrows are randomly generated, with the expression for their position update being:

[0026]

[0027] Where: X best β represents the current global optimal position; β is the step size control parameter of a random normal distribution with a mean of 0 and a variance of 1; K is a random number in K∈[-1,1]; f i This represents the current fitness value of the sparrow; f g and f w These represent the current globally optimal fitness value and the worst fitness value, respectively; ε is a minimal constant to avoid division by zero errors; f i >f g This indicates that the sparrow is currently on the edge of the sparrow colony; f i =f g This indicates that a sparrow in the middle of a flock of sparrows has detected danger and needs to move closer to other sparrows; K is the step size control coefficient, used to indicate the direction of the sparrow's movement.

[0028] Furthermore, the specific implementation steps of the SSA-VMD algorithm for decomposing shock wave signals are as follows:

[0029] Based on the optimal combination of decomposed modes and penalty factors obtained from the above sparrow search optimization VMD, VMD decomposition is performed on the shock wave signal to establish a constrained variational model. The signal is decomposed into a set of sparse IMF components by searching for the optimal solution of the constrained variational model. A constrained variational model is established with the constraint that the sum of all IMF components equals the original shock wave signal, and the objective function is to minimize the sum of the bandwidths of all IMF components. Then, based on the penalty factor, the constrained variational model is continuously updated and optimized using the Lagrange multiplier method and the alternating direction multiplier method until a feasible solution satisfying the constraints is obtained as the final IMF components.

[0030] The resonant energy loss ratio of each order IMF component of the shock wave signal is calculated separately. Based on the obtained resonant energy loss ratio values ​​of each IMF component, the IMF components are clustered into signal components and resonant components. The remaining signal components are then reconstructed to obtain the denoised shock wave signal. The formula for the resonant energy loss ratio is:

[0031]

[0032] Where: e k The resonant energy loss ratio, and These are shock wave signals and IMFs, respectively. k The spectral amplitude at the resonant frequency.

[0033] (III) Beneficial Effects

[0034] Compared with existing technologies, this invention provides a shock wave signal resonance noise reduction method based on the sparrow search algorithm to optimize VMD, which has the following beneficial effects:

[0035] This invention addresses the issue of significant resonant noise interference introduced during shock wave acquisition due to insufficient dynamic characteristics of pressure sensors. It proposes an SSA-VMD algorithm that optimizes the decomposition mode number and penalty factor parameters of the VMD algorithm using SSA, thereby decomposing the shock wave signal into different frequency signal components with a certain bandwidth (determined by the penalty factor) (the number of components is determined by the decomposition mode number).

[0036] This invention calculates the resonant energy loss ratio of each signal component, sets a threshold for the resonant energy loss ratio, clusters signal components with a resonant energy loss ratio greater than the threshold as resonant components, and clusters the remaining signal components as shock wave signal components, thereby reconstructing the shock wave signal components to reduce resonant noise interference.

[0037] The shock wave signal resonance noise reduction method based on sparrow search optimization VMD provided by this invention reduces the resonance noise interference caused by the acquisition system itself. Considering the influence of the number of decomposition modes and the penalty factor of the VMD algorithm on the decomposition effect, the SSA algorithm is used to optimize the parameters and find the optimal parameter combination, thereby improving the robustness of VMD decomposition and facilitating the widespread use of the algorithm. Attached Figure Description

[0038] Figure 1 This is a complete flowchart of the shock wave resonance noise reduction method based on the sparrow search algorithm to optimize VMD as described in this invention;

[0039] Figure 2 The time domain and corresponding spectrum diagram of the test signal of the shock tube used in the example of this invention;

[0040] Figure 3 The graph shows the fitness function curve obtained by the sparrow search optimization algorithm for VMD parameter optimization in the example.

[0041] Figure 4 The time-domain and frequency-domain plots of each IMF component obtained by decomposing the shock tube test signal using the VMD algorithm optimized by the sparrow search in the example;

[0042] Figure 5 The noise reduction effect of the shock tube test signal processed by the method of this invention is shown in the example. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] Example

[0045] like Figure 1-5 As shown, an embodiment of the present invention proposes a method for resonant noise reduction of shock wave signals based on the sparrow search algorithm to optimize VMD;

[0046] Step 1: Analyze the shock wave signal collected by the pressure sensor, and optimize the optimal parameter combination by using the sparrow search algorithm to decompose the two important parameters of VMD: mode number and penalty factor;

[0047] Specifically, time-domain and frequency-domain analyses were performed on the shock tube test signal acquired by a certain type of pressure sensor to analyze the main components of the signal:

[0048] Class A: Shock wave signal generated by a shock tube;

[0049] Class B: Resonant noise introduced by the pressure sensor in the acquisition system;

[0050] The time domain and corresponding spectrum of the signal are as follows: Figure 2 As shown, Figure 2 The vertical axis represents the signal amplitude, and the horizontal axis represents time and frequency, respectively. For ease of subsequent calculations, the shock tube signal was center-normalized.

[0051] The specific implementation steps of the sparrow search algorithm to optimize VMD are as follows:

[0052] Initialize the sparrow population by randomly generating a set of initial solutions as the starting population; calculate the initial fitness function value for each sparrow, and use the minimum envelope entropy value as the fitness function to evaluate the optimization effect. The envelope entropy formula is:

[0053]

[0054]

[0055] Where: K represents the number of modal components in VMD decomposition; E n (i) represents the total envelope entropy of the K IMF components; H en (i) represents the envelope entropy value of the i-th BIMF component; L represents the number of sampling points; mi denotes the envelope signal obtained by performing Hilbert transform modulation on the component IMF(i); p i denotes the i normalization process of m

[0056] Simulate the foraging, predator avoidance, reproduction, search and other behaviors of sparrows. Sparrows with higher fitness values obtain higher priorities and are called discoverers, while other sparrows with lower fitness values are called followers. The discoverers lead the followers to search for the easiest solutions. When the fitness value corresponding to the position information of each sparrow is less than the previous fitness value, the corresponding optimal parameter combination information is updated. The expression for updating the position of the discoverer is:

[0057]

[0058] where: t represents the current iteration level; j = 1, 2, …, d. denotes the value of the j-th dimension of the i-th sparrow at the t-th iteration; iter max denotes the constant with the most iterations; α ∈ (0, 1] is a random number; R2 (R2 ∈ [0, 1]) and ST (ST ∈ [0.5, 1.0]) represent the alarm value and the safety threshold respectively; Q is a random number subject to a normal distribution; L represents a 1×d matrix with all elements being 1. When R2 < ST, it proves that there are no natural enemies around the discoverer and it is in a safe search mode. When R2 > ST, it means that a sparrow has discovered a natural enemy and all sparrows need to quickly move away from this area;

[0059] When searching in other spaces, the followers can obtain energy to improve their fitness values, or they can follow the discoverers and snatch the energy of the discoverers to increase their own energy. The expression for updating the position of the followers is:

[0060]

[0061] where: X p denotes the optimal position occupied by the discoverer; X worst denotes the current globally worst position; A represents a 1×d matrix, and each element in the matrix is randomly assigned as 1 or -1, while satisfying A + = A T (AA T ) -1 . When i > n / 2, it means that the i-th follower with a lower fitness value may be in a hungry state;

[0062] By limiting the speed and activity range of each sparrow, the population is prevented from escaping the search space; the speed and position of the sparrows are updated based on the positions of the current optimal solution and the global optimal solution, causing the population to move towards the direction of the optimal solution for VMD parameters; warning sparrows are set up to detect predators, and the initial positions of these warning sparrows are randomly generated, with the expression for their position update being:

[0063]

[0064] Where: X best β represents the current global optimal position; β is the step size control parameter of a random normal distribution with a mean of 0 and a variance of 1; K is a random number in K∈[-1,1]; f i This represents the current fitness value of the sparrow; f g and f w These represent the current globally optimal fitness value and the worst fitness value, respectively; ε is a minimal constant to avoid division by zero errors; f i >f g This indicates that the sparrow is currently on the edge of the sparrow colony; f i =f g This indicates that a sparrow in the middle of a flock of sparrows has detected danger and needs to move closer to other sparrows; K is the step size control coefficient, used to indicate the direction of the sparrow's movement.

[0065] The fitness function curve obtained by optimizing VMD using the sparrow search algorithm is shown below. Figure 3 As shown, Figure 3 After the 63rd iteration, the optimal parameter combination for VMD is (75, 15), and the fitness function value is 6.7366, which is the minimum value.

[0066] Step 2: Substitute the obtained optimal parameter combination into the VMD input parameters and decompose the shock wave signal collected by the pressure sensor to obtain IMF components containing information on different center frequencies.

[0067] Furthermore, the specific implementation steps of the parameter-optimized VMD algorithm for decomposing shock wave signals are as follows:

[0068] Based on the optimal combination of decomposed modes and penalty factors obtained from the above sparrow search optimization VMD, VMD decomposition is performed on the shock wave signal to establish a constrained variational model. The signal is decomposed into a set of sparse IMF components by searching for the optimal solution of the constrained variational model. A constrained variational model is established with the constraint that the sum of all IMF components equals the original shock wave signal, and the objective function is to minimize the sum of the bandwidths of all IMF components. Then, based on the penalty factor, the constrained variational model is continuously updated and optimized using the Lagrange multiplier method and the alternating direction multiplier method until a feasible solution satisfying the constraints is obtained as the final IMF components.

[0069] The results of decomposing the shock wave signal using the parameter-optimized VMD algorithm are as follows: Figure 4 As shown, Figure 4 The left side shows the time-domain waveform of the decomposed IMF components, and the right side shows the frequency-domain waveform of each IMF. From top to bottom, they are IMF1-IMF15. It can be clearly observed that the signal is decomposed into signals with different center frequencies.

[0070] Step 3: Calculate the resonant energy loss ratio formula for each order IMF component, and cluster the components according to the magnitude of the resonant energy loss ratio of the IMF components, dividing them into signal components and resonant components.

[0071] The resonant energy loss ratio of each order IMF component of the shock wave signal is calculated separately. Based on the obtained resonant energy loss ratio values ​​of each IMF component, the IMF components are clustered into signal components and resonant components. The remaining signal components are then reconstructed to obtain the denoised shock wave signal. The formula for the resonant energy loss ratio is:

[0072]

[0073] Where: e k The resonant energy loss ratio, and These are shock wave signals and IMFs, respectively. k The spectral amplitude at the resonant frequency.

[0074] Clustering the IMF components according to the resonant energy loss ratio formula, it was found that the resonant components are mainly concentrated in IMF8, IMF9 and IMF10.

[0075] Step 4: Reconstruct the signal components to obtain the denoised shock wave signal;

[0076] After removing the resonant component and reconstructing the remaining signal components, the resulting shock wave signal after noise reduction is as follows: Figure 5 As shown.

[0077] The shock wave signal generated by the shock tube testing system can be evaluated using overshoot and rise time as indicators. After noise reduction, the overshoot of the shock wave signal was reduced from 141% to 39%, and the rise time was increased to 5µs. This effectively preserved the characteristics of the shock wave signal itself while effectively reducing the impact of resonant noise on the shock wave signal generated by the shock tube.

[0078] Overshoot is the percentage difference between the maximum response of a pressure sensor and its final steady-state response, expressed by the formula:

[0079]

[0080] Where: H(t) pH(∞) represents the maximum response of the signal, and H(∞) represents the response of the signal in its final stationary state.

[0081] The rise time is based on the response value at which the signal finally reaches a steady state. The rise time is the time it takes for the steady state to rise from 0.1 to 0.9, and the formula is:

[0082] t r =t 90％*H(∞) -t 10％*H(∞)

[0083] Where: t 10％*H(∞) The time when it reaches 10% of the H(∞) response value is t 90％*H(∞) The difference t between the two values ​​corresponds to the moment when the response reaches 90% of H(∞). r This refers to the rising time.

[0084] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for resonant noise reduction of shock wave signals based on sparrow search algorithm to optimize VMD, characterized in that: The main steps of this method include: Step 1: Analyze the shock wave signal collected by the pressure sensor, and optimize the optimal parameter combination by using the sparrow search algorithm to decompose the two important parameters of VMD: mode number and penalty factor; Step 2: Substitute the obtained optimal parameter combination into the VMD input parameters and decompose the shock wave signal collected by the pressure sensor to obtain IMF components containing information on different center frequencies. Step 3: Calculate the resonant energy loss ratio formula for each order IMF component, and cluster the components according to the magnitude of the resonant energy loss ratio of the IMF components, dividing them into signal components and resonant components. The specific implementation steps of the VMD algorithm for parameter optimization in steps two and three to decompose the shock wave signal are as follows: Based on the optimal combination of decomposed modes and penalty factor obtained by optimizing VMD using the above sparrow search algorithm, VMD decomposition is performed on the shock wave signal to establish a constrained variational model. By searching for the optimal solution of the constrained variational model, the signal is decomposed into a set of sparsity IMF components. A constrained variational model is established with the constraint that the sum of each order of IMF components is equal to the original shock wave signal and the objective function is to minimize the sum of the bandwidths of each order of IMF components. Then, based on the penalty factor, the constrained variational model is continuously updated and optimized using the Lagrange multiplier method and the alternating direction multiplier method until a feasible solution that satisfies the constraint conditions is obtained as the final IMF component. The resonant energy loss ratio of each order IMF component of the shock wave signal is calculated separately. Based on the obtained resonant energy loss ratio of each IMF component, the IMF components are clustered into signal components and resonant components. The remaining signal components are then reconstructed to obtain the denoised shock wave signal. The formula for the resonant energy loss ratio is as follows: ; in: The resonant energy loss ratio, and These are shock wave signals and sub-signals. The spectral amplitude at the resonant frequency; Step 4: Reconstruct the signal components to obtain the noise-reduced shock wave signal.

2. The shock wave signal resonance noise reduction method based on sparrow search algorithm to optimize VMD according to claim 1, characterized in that: The specific implementation steps for optimizing VMD parameters using the sparrow search algorithm in step one are as follows: Initialize the sparrow population by randomly generating a set of initial solutions as the starting population; calculate the initial fitness function value for each sparrow, and use the minimum envelope entropy value as the fitness function to evaluate the optimization effect. The envelope entropy formula is: ; ; in: Represents the number of modal components in VMD decomposition; express The total envelope entropy of each IMF component; For the first Envelope entropy values ​​of each BIMF component; Indicates the number of sampling points; Representing components The envelope signal obtained by Hilbert transform modulation; Indicates to Normalization processing; Simulating the foraging, predator avoidance, breeding, and searching behaviors of sparrows, sparrows with higher fitness values ​​are given higher priority and are called discoverers, while other sparrows with lower fitness values ​​are called followers. Discoverers guide followers to find the easiest solution. When the fitness value corresponding to each sparrow's position information is less than the previous fitness value, the corresponding optimal parameter combination information is updated. The expression for updating the discoverer's position is: ; in: Indicates the current iteration level; ; Indicates the first Only sparrows in the first The first iteration Values ​​in each dimension; The constant representing the number of iterations; It is a random number; and These represent the alarm value and the safety threshold, respectively. These are random numbers that follow a normal distribution. This represents a set of elements that are all equal to 1. Matrix, when This proves that the discoverer had no natural enemies nearby and was in a safe search mode. When this occurs, it indicates that a sparrow has spotted a predator, and all sparrows need to quickly move away from this area; Followers can gain energy to increase their fitness value while searching in other spaces. They can also follow discoverers and steal their energy to increase their own. The expression for updating the follower's position is: ; in: This indicates the optimal position occupied by the discoverer; This indicates the worst position globally at present; Represent a A matrix, in which each element is randomly assigned either 1 or -1, while satisfying the following conditions: ;when When, it indicates the first A follower with a low fitness value may be in a state of starvation; By limiting the speed and activity range of each sparrow, the population is prevented from escaping the search space; the speed and position of the sparrows are updated based on the positions of the current optimal solution and the global optimal solution, causing the population to move towards the direction of the optimal solution for VMD parameters; warning sparrows are set up to detect predators, and the initial positions of these warning sparrows are randomly generated, with the expression for their position update being: ; in: This indicates the current global optimal position; The step size control parameter is a random normal distribution with a mean of 0 and a variance of 1. yes A random number; This represents the current fitness value of the sparrow. and These represent the current globally optimal fitness value and the worst fitness value, respectively. It is the smallest constant, avoiding the error of division by zero; This indicates that the sparrow is currently on the edge of the sparrow colony; This indicates that a sparrow in the middle of a flock of sparrows has detected danger and needs to approach the other sparrows; It is the step size control coefficient, used to indicate the direction of the sparrow's movement.

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