Flotation equipment optimization method and system based on pressure pulsation wavelet analysis

Abstract

The present invention relates to a flotation equipment optimization method and system based on pressure pulsation wavelet analysis, belonging to the technical field of flotation equipment design and optimization, comprising: obtaining flotation equipment structural parameters and pressure pulsation signals; performing continuous wavelet transform processing on the pressure pulsation signals, calculating wavelet coefficients and converting them into wavelet transform coefficients, then calculating the frequency energy spectrum density corresponding to the pressure pulsation signal frequency, and obtaining turbulence characteristic parameters from the average energy spectrum density; constructing a mapping relationship model between the flotation equipment structural parameters and the turbulence characteristic parameters, and obtaining the optimal flotation equipment structural parameters by reversely optimizing and solving the mapping relationship model. The present invention realizes quantitative optimization of turbulence structure in flotation equipment by constructing a mapping relationship model between the flotation equipment structural parameters and the turbulence characteristic parameters and performing reverse optimization and solution, and is used to guide the design and development of large-scale flotation equipment.

Description

Technical Field

[0001] The present invention relates to the technical field of flotation equipment design and optimization, and in particular to a flotation equipment optimization method and system based on pressure pulsation wavelet analysis. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Flotation is one of the most sophisticated separation methods in mineral processing, playing a central role in the recovery of coal, nonferrous metals, and rare earth elements. With the dual demands of reducing resource grade and increasing processing capacity, existing flotation equipment is developing towards larger-scale, more efficient, and more intelligent systems.

[0004] During flotation, slurry modification and effective collision, adhesion, and entrainment of bubbles and mineral particles are key microscopic mechanisms determining flotation efficiency. Microscale turbulence, the physical foundation that underpins this mechanism, not only promotes frequent disturbances and collisions between particles and bubbles but also plays a regulatory role in suppressing bubble aggregation and particle desorption. Therefore, turbulence control has become one of the most critical performance parameters in flotation equipment design.

[0005] The development of existing flotation equipment suffers from numerous drawbacks when it comes to turbulence optimization. For one thing, existing flotation equipment designs generally rely on empirical rules or structural analogies. Improvements primarily rely on multiple rounds of experimental optimization through trial-and-error strategies, such as changing the impeller and stator configuration and altering the aeration method. Furthermore, while existing technologies involve structural optimization or cell improvements, they lack a physical basis for measurement. This results in improvements that, while somewhat feasible, suffer from long development cycles, low efficiency, and a lack of quantitative evidence and predictability.

[0006] On the other hand, in recent years, CFD (computational fluid dynamics) numerical simulation methods have been widely used to predict the flow field of flotation equipment and to optimize the impeller structure and tank layout. However, research has found that this method has the following problems: 1. The model scale does not match the actual equipment scale, and the amplification effect is significant; 2. The ability to simulate turbulent non-steady-state and multi-scale characteristics is limited; 3. There is a lack of experimental data support, and the problem of model closure is prominent.

[0007] Meanwhile, while existing experimental measurement methods such as PIV, LDV, and CTA offer high accuracy, their reliance on transparent media and optical paths makes them difficult to apply to complex multiphase systems within flotation cells, particularly in industrial environments with high solids concentrations, dense bubbles, and particle obstruction. Furthermore, their high cost and deployment difficulties limit their widespread deployment in engineering practice. Summary of the Invention

[0008] In order to solve the above problems, the present invention proposes a flotation equipment optimization method and system based on pressure pulsation wavelet analysis. By constructing a mapping relationship model between the structural parameters of the flotation equipment and the turbulence characteristic parameters and performing reverse optimization and solution, the quantitative optimization of the turbulence structure in the flotation equipment is achieved, which is used to guide the design and development of large-scale flotation equipment.

[0009] In order to achieve the above object, the present invention adopts the following technical solutions:

[0010] In a first aspect, the present invention provides a flotation equipment optimization method based on pressure pulsation wavelet analysis, comprising:

[0011] Obtaining structural parameters of the flotation equipment, and placing pressure sensors in the turbulent area of ​​the flotation equipment tank to obtain pressure pulsation signals based on the structural parameters of the flotation equipment;

[0012] The acquired pressure pulsation signal is processed by continuous wavelet transform, and the wavelet coefficients are calculated and converted into wavelet transform coefficients; the frequency energy spectral density corresponding to the pressure pulsation signal frequency is calculated based on the wavelet transform coefficients, and the turbulence characteristic parameters are obtained from the frequency energy spectral density;

[0013] A mapping relationship model between the structural parameters of the flotation equipment and the turbulence characteristic parameters is constructed, the target turbulence characteristic parameters are determined, and the optimal flotation equipment structural parameters are obtained by reverse optimization of the mapping relationship model.

[0014] According to a further technical solution, the structural parameters of the flotation equipment include the number of impeller blades, impeller diameter, stator spacing, rotation speed, and inflation volume; the turbulence characteristic parameters include main frequency, main frequency energy, high frequency energy ratio, energy spectrum width, total turbulence energy, and turbulence intermittency coefficient.

[0015] A further technical solution is that the wavelet transform process uses the Morlet mother wavelet, and the formula for calculating the wavelet coefficient is:

[0016] ;in, represents the wavelet coefficients, Indicates the pressure pulsation signal, represents the wavelet scale parameter, represents the translation parameter, Indicates the sampling time, represents the conjugate of the Morlet mother wavelet;

[0017] The wavelet scale parameter The translation parameter is converted into the physical frequency of the pressure pulsation signal through the scale-frequency conversion formula. Replace with sampling time , get the wavelet transform coefficients , the scale-frequency conversion formula is: ;in, Indicates the physical frequency of the pressure pulsation signal, Represents the dimensionless center frequency of the Morlet mother wavelet.

[0018] In a further technical solution, the formula for calculating the frequency energy spectrum density corresponding to the pressure pulsation signal frequency is:

[0019] ;

[0020] in, represents the frequency energy spectral density, Indicates the sampling duration, Represents the wavelet transform coefficients.

[0021] A further technical solution is to construct a mapping relationship model between the structural parameters of the flotation equipment and the turbulence characteristic parameters, including: adjusting the structural parameters of the flotation equipment, obtaining different turbulence characteristic parameters under different combinations of the structural parameters of the flotation equipment, and forming a data set, defining the form of the mapping relationship model according to the data set, first using a multiple linear regression model to fit the turbulence characteristic parameters, if the fitting goodness of the multiple linear regression model is lower than the design threshold, then using a nonlinear regression model, and taking the model with the best fitting goodness as the mapping relationship model.

[0022] In a further technical solution, the multiple linear regression model is expressed as:

[0023] ;in, represents the turbulence characteristic parameter, represents the fitting coefficient, Indicates the number of impeller blades, Indicates the impeller diameter, represents the stator spacing, Indicates the speed, Indicates the amount of inflation. represents the fitting residual term.

[0024] In a further technical solution, the nonlinear regression model adopts a support vector regression model, wherein the kernel function adopts a radial basis function, which is specifically expressed as: ;in, represents the radial basis function, Indicates the structural parameters of the flotation equipment, Indicates the Structural parameters of flotation equipment under group working conditions, is the support vector weight coefficient corresponding to the j-th turbulence characteristic parameter, Represents the bias term of the j-th turbulence characteristic parameter.

[0025] In a second aspect, the present invention provides a flotation equipment optimization system based on pressure pulsation wavelet analysis, comprising:

[0026] The data acquisition module is configured to: acquire structural parameters of the flotation device, and arrange pressure sensors in the turbulent area of ​​the flotation device tank to acquire pressure pulsation signals based on the structural parameters of the flotation device;

[0027] The wavelet analysis module is configured to: perform continuous wavelet transform processing on the acquired pressure pulsation signal, calculate the wavelet coefficients and convert them into wavelet transform coefficients; calculate the frequency energy spectral density corresponding to the frequency of the pressure pulsation signal based on the wavelet transform coefficients, and obtain turbulence characteristic parameters from the frequency energy spectral density;

[0028] The parameter optimization module is configured to: construct a mapping relationship model between the flotation equipment structural parameters and the turbulence characteristic parameters, determine the target turbulence characteristic parameters, and obtain the optimal flotation equipment structural parameters by performing reverse optimization on the mapping relationship model.

[0029] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0030] The present invention performs continuous wavelet transform processing on the pressure pulsation signal, uses wavelet analysis to effectively decompose the non-steady-state signal, and extracts the turbulence energy changes at different time scales, with high time-frequency resolution. In combination with the constructed mapping relationship model, the optimal flotation equipment structural parameters are reversely solved according to the target turbulence characteristic parameters, which significantly shortens the development cycle, improves efficiency, reduces structural trial and error, and realizes the quantitative optimization of the turbulence structure in the flotation equipment, which is used to guide the design and development of large-scale flotation equipment.

[0031] The present invention arranges a pressure sensor in the turbulent area of ​​the flotation equipment tank, is applicable to industrial flotation equipment with opaque and high solid content systems, and solves the problem that optical measurement means cannot be deployed. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their description are used to explain the present invention but do not constitute a limitation of the present invention.

[0033] Figure 1 1 is a flow chart of a flotation equipment optimization method based on pressure pulsation wavelet analysis in Example 1 of the present invention;

[0034] Figure 2 Schematic diagram of the structure of a flotation equipment optimization system based on pressure pulsation wavelet analysis in Example 2 of the present invention;

[0035] Among them, 1. Flotation tank; 2. Impeller assembly; 3. Slurry; 4. Pressure sensor; 5. Data acquisition module; 6. Wavelet analysis and processing module. DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0038] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0039] Example 1

[0040] This embodiment proposes a flotation equipment optimization method based on pressure pulsation wavelet analysis, such as Figure 1 As shown,

[0041] The specific technical solutions include the following:

[0042] First, the structural parameters of the flotation equipment are obtained and designed, including the number of impeller blades, impeller diameter, stator spacing, rotational speed, and aeration volume. As an implementation method, the number of impeller blades is designed to be 4, 5, and 6, the impeller diameter is designed to be 300 mm, 350 mm, and 400 mm, the stator spacing is designed to be 20 mm and 30 mm, the rotational speed is designed to be 500 rpm, 600 rpm, and 700 rpm, and the aeration volume is designed to be 0.8 m3 / h, 1.0 m3 / h, and 1.2 m3 / h.

[0043] Then, if Figure 2 As shown, pressure sensors 4 are arranged in the turbulent area of ​​the flotation device tank body. Specifically, six high-frequency dynamic pressure sensors are arranged at typical locations of the impeller assembly 2 (impeller outlet area, stator outer edge area) and the tank wall of the flotation device. The frequency response range of the high-frequency dynamic pressure sensor is 10-15 kHz, the sampling frequency is not less than 20 kHz, and this embodiment is set to 20 kHz. The sampling time is not less than 60 s, and this embodiment is set to 60 s. The pressure pulsation signal of each measuring point is collected by a 16-channel synchronous data acquisition module. .

[0044] Then, the pressure pulsation signal obtained Perform continuous wavelet transform processing, where the wavelet transform processing uses Morlet mother wavelet, and the formula for calculating the wavelet coefficient is:

[0045] ;

[0046] in, represents the wavelet coefficients, Indicates the pressure pulsation signal, represents the wavelet scale parameter, represents the translation parameter, Indicates the sampling time, represents the conjugate of the Morlet mother wavelet.

[0047] Then the wavelet scale parameter The translation parameter is converted into the physical frequency of the pressure pulsation signal through the scale-frequency conversion formula. Replace with sampling time , get the wavelet transform coefficients , where the scale-frequency conversion formula is:

[0048] ;

[0049] above Indicates the physical frequency of the pressure pulsation signal, Represents the dimensionless center frequency of the Morlet mother wavelet.

[0050] Then, the frequency energy spectrum density corresponding to the pressure pulsation signal frequency is calculated based on the wavelet transform coefficients , and obtain the turbulence characteristic parameters in the frequency energy spectrum density. The formula for calculating the frequency energy spectrum density corresponding to the pressure pulsation signal frequency is:

[0051] ;

[0052] in, represents the frequency energy spectral density, Indicates the sampling duration.

[0053] In this embodiment, the acquired turbulence characteristic parameters include the main frequency f p , main frequency energy E p , high frequency energy ratio R hf , energy spectrum width Δf, total turbulent energy E total , turbulence intermittency coefficient I t .

[0054] The above process is repeated for the designed flotation equipment structural parameter X to obtain the corresponding turbulence characteristic parameter Y and form a data set for constructing a mapping relationship model between the flotation equipment structural parameter and the turbulence characteristic parameter.

[0055] Then, a mapping relationship model between the structural parameters of the flotation equipment and the turbulence characteristic parameters is constructed. The specific steps are as follows:

[0056] 1. Adjust the structural parameters of the flotation equipment. Under different combinations of flotation equipment structural parameters, obtain different turbulence characteristic parameters to form n groups of (Xi, Yi) data samples as the model training set.

[0057] 2. Define the mapping relationship model based on the data set. First, use the multivariate linear regression model to calculate each turbulence characteristic parameter (including the main frequency f p , main frequency energy E p , high frequency energy ratio R hf , energy spectrum width Δf, total turbulent energy E total , turbulence intermittency coefficient I t ) is fitted, where the multiple linear regression model is expressed as:

[0058] ;

[0059] in, represents the turbulence characteristic parameter, represents the fitting coefficient, Indicates the number of impeller blades, Indicates the impeller diameter, represents the stator spacing, Indicates the speed, Indicates the amount of inflation. represents the fitting residual term.

[0060] 3. If the goodness of fit of the multiple linear regression model If the value is lower than the design threshold (0.9), a nonlinear regression model is further adopted. In this embodiment, the nonlinear regression model adopts a support vector regression model, wherein the kernel function adopts a radial basis function, which is specifically expressed as:

[0061] ;

[0062] in, represents the radial basis function, Indicates the structural parameters of the flotation equipment, Indicates the Structural parameters of flotation equipment under group working conditions, is the support vector weight coefficient corresponding to the j-th turbulence characteristic parameter, Represents the bias term of the j-th turbulence characteristic parameter.

[0063] 4. After training is completed, retain the goodness of fit The optimal model is used as the final mapping relationship model for subsequent reverse optimization design.

[0064] Then, based on the flotation equipment optimization design objectives, the target turbulence characteristic parameters were determined. Based on these target turbulence characteristic parameters, the mapping relationship model was reversely optimized and solved using genetic algorithms and particle swarm optimization algorithms to obtain the optimal flotation equipment structural parameter combination that meets the target turbulence characteristics. The optimized design results were verified, completing the closed-loop process of equipment optimization design.

[0065] Example 2

[0066] This embodiment provides a flotation equipment optimization system based on pressure pulsation wavelet analysis, which specifically includes the following modules:

[0067] The data acquisition module is configured to: acquire structural parameters of the flotation device, and arrange pressure sensors in the turbulent area of ​​the flotation device tank to acquire pressure pulsation signals based on the structural parameters of the flotation device;

[0068] The wavelet analysis module is configured to: perform continuous wavelet transform processing on the acquired pressure pulsation signal, calculate the wavelet coefficients and convert them into wavelet transform coefficients; calculate the frequency energy spectral density corresponding to the frequency of the pressure pulsation signal based on the wavelet transform coefficients, and obtain turbulence characteristic parameters from the frequency energy spectral density;

[0069] The parameter optimization module is configured to: construct a mapping relationship model between the flotation equipment structural parameters and the turbulence characteristic parameters, determine the target turbulence characteristic parameters, and obtain the optimal flotation equipment structural parameters by performing reverse optimization on the mapping relationship model.

[0070] The implementation of the specific modules in this embodiment refers to the steps of the flotation equipment optimization method based on pressure pulsation wavelet analysis described in the first embodiment, and will not be described in detail here.

[0071] The above-described embodiments merely illustrate several embodiments of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A flotation equipment optimization method based on pressure pulsation wavelet analysis, characterized in that: include: Obtaining structural parameters of the flotation equipment, and placing pressure sensors in the turbulent area of ​​the flotation equipment tank to obtain pressure pulsation signals based on the structural parameters of the flotation equipment; The acquired pressure pulsation signal is processed by continuous wavelet transform, and the wavelet coefficients are calculated and converted into wavelet transform coefficients; the frequency energy spectral density corresponding to the pressure pulsation signal frequency is calculated based on the wavelet transform coefficients, and the turbulence characteristic parameters are obtained from the frequency energy spectral density; Construct a mapping relationship model between the structural parameters of the flotation equipment and the turbulence characteristic parameters, determine the target turbulence characteristic parameters, and obtain the optimal flotation equipment structural parameters by performing reverse optimization on the mapping relationship model; The process of constructing a mapping relationship model between flotation device structural parameters and turbulence characteristic parameters includes: adjusting the flotation device structural parameters, obtaining different turbulence characteristic parameters under different flotation device structural parameter combinations, and forming a data set; defining a form of the mapping relationship model based on the data set; first, fitting the turbulence characteristic parameters using a multiple linear regression model; if the goodness of fit of the multiple linear regression model is lower than a design threshold, then using a nonlinear regression model; and selecting the model with the best goodness of fit as the mapping relationship model; The multiple linear regression model is expressed as: ;in, represents the turbulence characteristic parameter, represents the fitting coefficient, Indicates the number of impeller blades, Indicates the impeller diameter, represents the stator spacing, Indicates the speed, Indicates the amount of inflation. represents the fitting residual term; The nonlinear regression model adopts the support vector regression model, wherein the kernel function adopts the radial basis function, which is specifically expressed as: ;in, represents the radial basis function, Indicates the structural parameters of the flotation equipment, Indicates the Structural parameters of flotation equipment under group working conditions, is the support vector weight coefficient corresponding to the j-th turbulence characteristic parameter, Represents the bias term of the j-th turbulence characteristic parameter.

2. The flotation equipment optimization method based on pressure pulsation wavelet analysis according to claim 1, characterized in that: The structural parameters of the flotation equipment include the number of impeller blades, impeller diameter, stator spacing, rotation speed, and inflation volume; the turbulence characteristic parameters include main frequency, main frequency energy, high frequency energy ratio, energy spectrum width, total turbulence energy, and turbulence intermittency coefficient.

3. The flotation equipment optimization method based on pressure pulsation wavelet analysis according to claim 1, characterized in that: The wavelet transform process uses the Morlet mother wavelet, and the formula for calculating the wavelet coefficient is: ;in, represents the wavelet coefficients, Indicates the pressure pulsation signal, represents the wavelet scale parameter, represents the translation parameter, Indicates the sampling time, represents the conjugate of the Morlet mother wavelet; The wavelet scale parameter The translation parameter is converted into the physical frequency of the pressure pulsation signal through the scale-frequency conversion formula. Replace with sampling time , and get the wavelet transform coefficients , the scale-frequency conversion formula is: ;in, Indicates the physical frequency of the pressure pulsation signal, Represents the dimensionless center frequency of the Morlet mother wavelet.

4. The flotation equipment optimization method based on pressure pulsation wavelet analysis according to claim 1, characterized in that: The formula for calculating the frequency energy spectrum density corresponding to the pressure pulsation signal frequency is: ； in, represents the frequency energy spectral density, Indicates the sampling duration, Represents the wavelet transform coefficients.

5. The flotation equipment optimization system based on pressure pulsation wavelet analysis is characterized by: include: The data acquisition module is configured to: acquire structural parameters of the flotation device, and arrange pressure sensors in the turbulent area of ​​the flotation device tank to acquire pressure pulsation signals based on the structural parameters of the flotation device; The wavelet analysis module is configured to: perform continuous wavelet transform processing on the acquired pressure pulsation signal, calculate the wavelet coefficients and convert them into wavelet transform coefficients; calculate the energy spectrum density corresponding to the frequency of the pressure pulsation signal based on the wavelet transform coefficients, and obtain turbulence characteristic parameters from the frequency energy spectrum density; The parameter optimization module is configured to: construct a mapping relationship model between the structural parameters of the flotation equipment and the turbulence characteristic parameters, determine the target turbulence characteristic parameters, and obtain the optimal flotation equipment structural parameters by performing reverse optimization on the mapping relationship model; The process of constructing a mapping relationship model between flotation device structural parameters and turbulence characteristic parameters includes: adjusting the flotation device structural parameters, obtaining different turbulence characteristic parameters under different flotation device structural parameter combinations, and forming a data set; defining a form of the mapping relationship model based on the data set; first, fitting the turbulence characteristic parameters using a multiple linear regression model; if the goodness of fit of the multiple linear regression model is lower than a design threshold, then using a nonlinear regression model; and selecting the model with the best goodness of fit as the mapping relationship model; The multiple linear regression model is expressed as: ;in, represents the turbulence characteristic parameter, represents the fitting coefficient, Indicates the number of impeller blades, Indicates the impeller diameter, represents the stator spacing, Indicates the speed, Indicates the amount of inflation. represents the fitting residual term; The nonlinear regression model adopts the support vector regression model, wherein the kernel function adopts the radial basis function, which is specifically expressed as: ;in, represents the radial basis function, Indicates the structural parameters of the flotation equipment, Indicates the Structural parameters of flotation equipment under group working conditions, is the support vector weight coefficient corresponding to the j-th turbulence characteristic parameter, Represents the bias term of the j-th turbulence characteristic parameter.

6. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the flotation equipment optimization method based on pressure pulsation wavelet analysis as described in any one of claims 1 to 4 are implemented.

7. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the flotation equipment optimization method based on pressure pulsation wavelet analysis according to any one of claims 1 to 4 are implemented.

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