Downhole flow switch control method based on vibration signal analysis

Abstract

The present invention relates to the technical field of signal analysis and processing, and further to a downhole flow switch control method based on vibration signal analysis. The method comprises: step 1: collecting the vibration signal of the pump through a three-axis vibration sensor to obtain the acceleration time domain signal in the three-axis direction; performing multi-dimensional vibration spectrum component decoupling on the acceleration time domain signal to obtain the time-frequency characteristic matrix of the three-axis vibration; step 2: calculating the Reynolds stress tensor based on the turbulence intensity; calculating the flow state transition criterion value according to the turbulence intensity and the Reynolds stress tensor, and establishing a flow estimation model; step 3: generating the dynamic response of the downhole flow switch control according to the flow estimation model; generating the adaptive control law of the downhole flow switch control according to the dynamic response using an adaptive control method. The present invention effectively overcomes the limitations of traditional pressure sensing and flow sensing technologies in complex downhole flow states, and significantly improves the real-time, accuracy and environmental adaptability of flow control.

Description

Technical Field

[0001] The invention belongs to the technical field of signal analysis and processing, and in particular relates to a downhole flow switch control method based on vibration signal analysis. Background Art

[0002] Fluid transport systems play a vital role in industrial production and energy extraction. Especially in underground mining fields such as oil, natural gas and geothermal, precise control of fluid flow directly affects the safety and efficiency of equipment operation and the economy of resource extraction. In these scenarios, downhole flow switches are important equipment for dynamic regulation and safety control of fluid transport, and their performance is critical to the stability and reliability of the overall system. However, due to the complexity of the underground environment, such as high pressure, high temperature and multiphase fluid, extremely high requirements are placed on the control technology of flow switches.

[0003] Existing downhole flow control technologies can be roughly divided into control methods based on pressure sensing, control based on flow sensing, and control methods based on fluid dynamics modeling. Traditional flow control mainly relies on pressure sensors to collect pressure signals in pipelines. By measuring pressure changes, combining the Bernoulli equation and the theoretical relationship between flow and pressure difference, the dynamic changes of flow are inferred. For example, some literature discloses real-time monitoring of fluid pressure through wellhead or downhole pressure sensors, and adjusting the opening of the flow switch according to pressure changes, thereby achieving dynamic regulation of flow. The advantages of this type of method are simple implementation, less hardware and computing resources required, and suitable for simple working conditions of single fluid flow. Pressure signals are susceptible to interference under complex working conditions. For example, in multiphase fluid or turbulent conditions, pressure fluctuations cannot accurately reflect the actual changes in flow. The indirect inference of flow by pressure measurement relies on a series of assumptions (such as fluid uniformity, laminar flow conditions, etc.). When turbulent or frequent changes in flow state occur, the deviations of these assumptions will lead to inaccurate inference results. In order to overcome the limitations of indirect inference of pressure signals, some existing technologies have introduced direct control methods based on flow sensors. For example, an ultrasonic flowmeter or turbine flowmeter installed in a pipeline can be used to collect fluid flow data in real time, and use it as a feedback signal for the controller to adjust the state of the flow switch. This type of method can directly obtain flow information and improve measurement accuracy, especially under uniform flow conditions. In an underground environment, flow sensors are difficult to install and maintain, especially in high pressure, high temperature, and highly corrosive environments, where the reliability and life of the sensors are significantly limited. The flow data directly measured by the sensor is not sensitive enough to changes in flow states, and it is difficult to capture complex dynamic characteristics such as turbulence and flow state transitions. The high cost of high-performance flow sensors limits their economic feasibility in large-scale underground applications. Summary of the invention

[0004] The main purpose of the present invention is to provide a downhole flow switch control method based on vibration signal analysis, which effectively overcomes the limitations of traditional pressure sensing and flow sensing technologies in complex downhole flow states and significantly improves the real-time, accuracy and environmental adaptability of flow control.

[0005] In order to solve the above problems, the technical solution of the present invention is achieved as follows:

[0006] A downhole flow switch control method based on vibration signal analysis, the method comprising:

[0007] Step 1: Collect the vibration signal of the pump through a three-axis vibration sensor to obtain the acceleration time domain signal in the three-axis direction; decouple the acceleration time domain signal by multi-dimensional vibration spectrum components to obtain the time-frequency characteristic matrix of the three-axis vibration; calculate the fluid pressure fluctuation characteristics based on the time-frequency characteristic matrix; calculate the turbulence intensity based on the time-frequency characteristic matrix and the fluid pressure fluctuation characteristics;

[0008] Step 2: Based on the turbulence intensity, calculate the Reynolds stress tensor; based on the turbulence intensity and the Reynolds stress tensor, calculate the flow transition criterion value and establish a flow estimation model;

[0009] Step 3: Generate a dynamic response of the downhole flow switch control based on the flow estimation model; and generate an adaptive control law of the downhole flow switch control using an adaptive control method based on the dynamic response.

[0010] Furthermore, when the vibration signal of the pump is collected by the three-axis vibration sensor, the collection frequency is higher than twice the vibration frequency of the vibration signal to satisfy the Nyquist sampling theorem.

[0011] Furthermore, in step 1, the time-frequency characteristic matrix of the triaxial vibration is expressed using the following formula:

[0012] ;

[0013] in, is the time-frequency characteristic matrix of triaxial vibration, reflecting the pump at the current time and frequency Vibration characteristics under Indicates The acceleration time domain signal of the axis; is the imaginary number symbol; is a function of the change in volume of the fluid in the pump, constructed by collecting historical fluid volume data in the pump; is a function of the fluid pressure variation in the pump, constructed by collecting historical fluid pressure data in the pump; For historical time; is the historical time integration variable.

[0014] Furthermore, in step 1, the fluid pressure fluctuation characteristics are calculated based on the time-frequency characteristic matrix by the following formula:

[0015] ;

[0016] in, For current time Fluid pressure fluctuation characteristics when is the fluid density; is the acceleration due to gravity; For current time Liquid level height at is the fluid dynamic viscosity; is the pipe diameter; is the elastic modulus of the pipe; is the speed of sound.

[0017] Furthermore, in step 1, the turbulence intensity is calculated according to the time-frequency characteristic matrix and the fluid pressure fluctuation characteristics by the following formula:

[0018] ;

[0019] in, is the turbulence intensity, describing the radial distance in the pipe. and the current time Turbulent pulsation characteristics under For current time The Reynolds number under , which describes the ratio of inertia to viscosity of the fluid flow; is the critical Reynolds number, which indicates the critical value of the fluid transition from laminar flow to turbulent flow; is the radial distance in the pipeline, which means the radial distance from the center of the pipeline to a certain point; is the pipeline radius, indicating the maximum radial distance of the pipeline; is the preset vibration correction factor; is the vibration characteristic frequency, indicating the main frequency of the vibration signal of the pump; is the vibration period; is the radial distribution function, which describes the variation of turbulence intensity with pipe radius; The radial distance inside the pipe is and the current time The turbulent kinetic energy under ;in, is the average pulsating velocity component of the first axis extracted from the vibration signal of the pump; is the average pulsating velocity component of the second axis extracted from the vibration signal of the pump; It is the average pulsating velocity component of the third axis extracted from the vibration signal of the pump.

[0020] Furthermore, in step 2, the Reynolds stress tensor is calculated based on the turbulence intensity using the following formula:

[0021] ;

[0022] in, A coordinate variable indicating the direction of the first axis; A coordinate variable indicating the direction of the second axis; A coordinate variable indicating the direction of the third axis; represents the turbulent viscosity of the fluid; Indicates the radial distance inside the pipe is and the current time The Reynolds stress tensor under .

[0023] Furthermore, in step 2, the flow transition criterion value is calculated based on the turbulence intensity and the Reynolds stress tensor using the following formula:

[0024] ;

[0025] in, For current time The flow transition criterion at ; is the preset critical turbulence intensity; For current time The Weber number at ; is the critical Weber number; is the preset periodic item weight; is the preset pressure fluctuation weight.

[0026] Furthermore, in step 2, the following formula is used to establish a flow estimation model:

[0027] ;

[0028] in, For current time Flow estimation at time For current time The pressure change value when is the critical flow transition criterion value; is the preset flow coefficient.

[0029] Furthermore, in step 3, the following formula is used to generate the dynamic response of the downhole flow switch control according to the flow estimation model:

[0030] ;

[0031] in, is the Laplace variable; is the expected flow in the form of Laplace variables; is the natural frequency; is the damping ratio; is the cut-off frequency; for The corresponding Laplace variable form; for The corresponding Laplace variable form.

[0032] Furthermore, in step 3, the following formula is used to generate an adaptive control law for downhole flow switch control based on the dynamic response using an adaptive control method:

[0033] ;

[0034] in, The adaptive control law for the generated downhole flow switch control; is the adaptive gain; is the expected flow in the form of time variable; is the static gain; for The frequency domain form of is the expected flow in the form of historical time-integrated variable; It is the flow estimation in the form of historical time integrated variable.

[0035] The downhole flow switch control method based on vibration signal analysis of the present invention has the following beneficial effects:

[0036] Traditional pressure sensor and flow sensor technologies are difficult to effectively capture the complex dynamic behaviors of turbulence characteristics, flow transition and multiphase flow in the downhole fluid environment. The present invention directly uses the vibration signal of the pump to characterize the fluid state by introducing three-axis vibration signal acquisition and time-frequency feature analysis technology. The vibration signal not only reflects the mechanical vibration characteristics of the pump, but also captures the dynamic characteristics of turbulence intensity, flow transition and pressure fluctuation through the coupling effect between the fluid and the pump.

[0037] By constructing a turbulence intensity model and Reynolds stress tensor based on vibration signals, the present invention can sensitively respond to dynamic changes in flow states, thereby achieving efficient monitoring and control of complex flow states. The present invention effectively solves the problem of disconnection between flow estimation and flow dynamic behavior in the prior art by introducing turbulence intensity, Reynolds stress tensor and flow transition criterion value into the flow estimation model. Turbulence intensity reflects the energy distribution of velocity fluctuations in the fluid, while the Reynolds stress tensor characterizes the impact of turbulence on momentum exchange. These key parameters are obtained through vibration signal processing and combined with fluid pressure fluctuations and pipeline parameters to achieve a comprehensive description of flow changes. In particular, by constructing a dynamic response model that includes flow transition criterion values, the present invention can timely adjust the flow estimation results when the turbulence state is significantly enhanced or the flow state undergoes a sudden change, thereby ensuring the accuracy and real-time performance of flow estimation.

[0038] The complexity of the underground environment (such as high pressure, high temperature, multiphase fluid, etc.) places stringent requirements on the flow control system. The present invention effectively avoids the performance degradation problem of traditional sensors in extreme environments through non-contact acquisition of vibration signals and multi-dimensional signal processing methods. In addition, by introducing flow transition criterion values ​​and dynamic response models, the present invention can maintain the stability and reliability of system control when the flow state changes frequently or the flow fluctuates violently. Especially under conditions of enhanced turbulence or significant fluid pressure fluctuations, the system can quickly adjust the control strategy to avoid failure of the flow switch or system overload, ensuring the long-term stable operation of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic diagram of a method flow chart of a downhole flow switch control method based on vibration signal analysis provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0041] Example 1, reference Figure 1 : A downhole flow switch control method based on vibration signal analysis, the method comprising:

[0042] Step 1: Collect the vibration signal of the pump through a three-axis vibration sensor to obtain the acceleration time domain signal in the three-axis direction; decouple the acceleration time domain signal by multi-dimensional vibration spectrum components to obtain the time-frequency characteristic matrix of the three-axis vibration; calculate the fluid pressure fluctuation characteristics based on the time-frequency characteristic matrix; calculate the turbulence intensity based on the time-frequency characteristic matrix and the fluid pressure fluctuation characteristics;

[0043] The triaxial vibration sensor is used to capture the acceleration signals in three directions during the operation of the pump, which are , and Acceleration in the direction. The time domain signal of acceleration directly reflects the instantaneous change of the vibration intensity of the pump at different time points. However, time domain data alone cannot fully reveal the frequency components in the vibration signal, and frequency information is crucial for the study of fluid pressure fluctuations. This is because the turbulent state and pressure fluctuations of fluid flow often manifest as periodic or quasi-periodic disturbances, which propagate in the form of vibrations and manifest as specific frequency components in the frequency domain of the vibration signal. Therefore, converting the time domain signal into frequency domain or time-frequency domain form is a key step in analyzing vibration signals. In the specific analysis process, the time domain signal is processed using short-time Fourier transform (STFT) or wavelet transform to obtain the time-frequency feature matrix of the vibration signal in each direction. For example, for Directional acceleration signal , the result of its time-frequency transformation is a two-dimensional function ,in It's time. is the frequency, Indicates time Time at frequency The vibration intensity at . Similarly, we can get and Directional time-frequency matrix and Finally, the time-frequency information of these three directions is combined into the time-frequency feature matrix of triaxial vibration , which completely describes the dynamic distribution of the vibration signal in the time and frequency domain. The construction of the time-frequency feature matrix provides a basis for the decoupling of the multidimensional components of the vibration signal. Since vibrations in different directions may be coupled with each other during the operation of the pump, for example, the vibration caused by fluid flow may be superimposed on the mechanical vibration, resulting in mixed signals, it is necessary to separate these mixed signals into their own independent components. This decoupling process is usually based on signal processing algorithms, such as independent component analysis (ICA) or principal component analysis (PCA), which achieve signal separation by finding the statistical independence of the signal or the direction of maximum variance. After component decoupling, the vibration signal in each direction can be used separately to analyze its association with fluid pressure fluctuations.

[0044] The time-frequency feature matrix contains a lot of energy distribution information of vibration signals, and the characteristics of fluid pressure fluctuations can often be extracted through these energy characteristics. Specifically, when the fluid flow state changes, such as from laminar flow to turbulent flow, the pressure disturbance caused by it will be manifested in the time-frequency matrix as an energy peak enhancement or attenuation within a specific frequency range. In order to capture these changing characteristics, the energy spectrum analysis method of the signal can be used. For example, by summing the frequency components of each time slice in the time-frequency matrix, the total energy change at each time point can be obtained, thereby identifying the instantaneous intensity of the pressure fluctuation. In addition, the characteristic quantity of the pressure fluctuation can be calculated by extracting the local amplitude change of the time-frequency matrix. Hilbert transform is a commonly used method that can calculate the instantaneous amplitude and phase of the signal, thereby providing richer dynamic characteristics than simple energy statistics. These characteristics reflect the non-stationarity of fluid pressure disturbances and can further reveal the instantaneous dynamic behavior of the fluid flow state. From the perspective of fluid mechanics, the pressure fluctuation of the fluid is an important manifestation of the turbulent characteristics of the fluid, and turbulence is essentially a complex flow state dominated by nonlinear effects. In the downhole environment, since the fluid movement is restricted by the pipeline boundary and pressure gradient, the turbulent characteristics are more significant and directly affect the operation state of the pump. As an indirect representation of this turbulent state, the frequency components and amplitude changes in the time-frequency characteristic matrix of the vibration signal reflect the pressure pulsation characteristics in the turbulent field. Therefore, by analyzing the time-frequency characteristics of the vibration signal, the characteristic quantities directly related to the pressure fluctuation can be extracted from it, laying the foundation for further analysis of the turbulence intensity. The signal processing performed in step 1 actually realizes a conversion process from mechanical vibration to fluid pressure fluctuation. The acceleration signal acquisition is used as input, and the time-frequency characteristic matrix closely related to the fluid characteristics is constructed through time-frequency transformation and component decoupling, and the analysis of this matrix outputs the characteristic information of pressure fluctuation. The core principle of this process is to use the dynamic characteristics in the vibration signal to indirectly reflect the pressure change of the fluid, because the vibration signal and pressure fluctuation are essentially different manifestations of the interaction between the fluid and the mechanical system. Through this processing process, the dynamic characteristics of the fluid can be accurately derived without directly measuring the pressure fluctuation.

[0045] Step 2: Based on the turbulence intensity, calculate the Reynolds stress tensor; based on the turbulence intensity and the Reynolds stress tensor, calculate the flow transition criterion value and establish a flow estimation model;

[0046] Turbulence intensity is usually defined as the ratio of the root mean square value of fluid velocity fluctuation to the average flow velocity, and is an important indicator for measuring the intensity of velocity disturbance in the fluid. In the downhole environment, the strength of turbulence directly reflects the stability of the flow state because the fluid is affected by the combined effects of pipe wall friction, pressure gradient and the viscosity of the fluid itself. The calculation of turbulence intensity is based on the pressure fluctuation characteristics, because pressure fluctuation is an indirect manifestation of fluid velocity fluctuation. By establishing the relationship between pressure fluctuation characteristics and velocity disturbance, the results of vibration signal analysis can be mapped to the core dynamic quantity of turbulence intensity. For example, when the pressure fluctuation amplitude increases significantly, it indicates that the velocity fluctuation inside the fluid is intensified, which usually corresponds to the enhancement of turbulence intensity. Next, the Reynolds stress tensor can be further calculated based on the results of turbulence intensity. The Reynolds stress tensor is an important parameter for describing momentum exchange in turbulence, and its physical meaning is the covariance between the fluctuations of velocity components in all directions of the fluid. Specifically, the components of the Reynolds stress tensor represent the contribution of velocity fluctuations in different directions to the average momentum. The calculation of the Reynolds stress tensor requires the combination of the turbulence intensity and the relevant frequency components in the vibration signal, because these frequency components can indirectly reflect the synergy of the velocity fluctuation. In the present invention, through the in-depth analysis of the time-frequency characteristic matrix, the characteristic frequency and energy distribution corresponding to the velocity fluctuation can be extracted, thereby deriving the component values ​​of the Reynolds stress tensor. This calculation process further extends the results of vibration signal analysis to the important parameters that describe the internal dynamic characteristics of the fluid.

[0047] After calculating the turbulence intensity and Reynolds stress tensor, these parameters can be used to construct the flow state transition criterion value. The flow state transition criterion value is used to judge the critical state of the transition of the fluid from laminar flow to turbulence, and is an important concept in fluid dynamics research. For complex fluid environments downhole, the construction of the transition criterion value is particularly important because the operating efficiency and stability of the pump are closely related to the fluid flow state. If the fluid is in a laminar state, the workload of the pump is relatively low, and when the fluid enters a turbulent state, the additional resistance and pressure pulsation caused by the turbulence may cause the performance of the pump to deteriorate or even fail. Therefore, accurately judging the flow state transition is crucial for controlling the operating state of the pump. In the present invention, the calculation of the flow state transition criterion value is based on the combined characteristics of the turbulence intensity and the Reynolds stress tensor. For example, the critical conditions for the transition can be extracted by analyzing the relationship between the rate of change of certain components in the Reynolds stress tensor and the turbulence intensity. This criterion value establishes a quantitative connection between the vibration signal characteristics and the fluid transition behavior, so that the flow state changes can be indirectly monitored through the vibration signal. After completing the calculation of the flow transition criterion value, the next step is to establish a flow estimation model. The core of the flow estimation model is to establish a mapping relationship between the characteristic quantity extracted from the vibration signal and the actual flow of the fluid. In an underground environment, direct flow measurement is often difficult and costly, so indirect estimation through vibration signals is an efficient solution. Turbulence intensity and Reynolds stress tensor, as core dynamic parameters of fluid flow, can establish a quantitative relationship with the flow rate. For example, under turbulent conditions, changes in turbulence intensity often show a certain linear or nonlinear relationship with changes in flow, and this relationship can be calibrated through experimental or simulation data. In the present invention, the flow estimation model constructed using turbulence intensity and Reynolds stress tensor can not only reflect the overall trend of the flow, but also capture the flow fluctuation characteristics caused by turbulent instability.

[0048] Step 3: Generate a dynamic response of the downhole flow switch control based on the flow estimation model; and generate an adaptive control law of the downhole flow switch control using an adaptive control method based on the dynamic response.

[0049] The generation of dynamic response is the first link of step 3. Its principle is to use the real-time flow information provided by the flow estimation model to generate a control response signal for the flow switch according to the change trend of the fluid state. In the flow estimation model, the mapping relationship between parameters such as turbulence intensity and Reynolds stress tensor and flow has been established. Therefore, when the dynamic characteristics in the vibration signal reflect fluid pressure fluctuations or flow state changes, this change will be quickly mapped to the estimated value of the flow through the model. For example, when the turbulence intensity increases significantly, the flow estimation model will determine that the fluid flow state may enter the unstable turbulence zone, thereby deriving the fluctuation amplitude and change rate of the flow. This information is used to generate dynamic response. The role of dynamic response is to provide real-time adjustment control signals based on the flow estimation results, such as opening or closing the flow switch, or adjusting the operating parameters such as the opening angle of the flow switch. This dynamic response mechanism ensures that the system can quickly perceive the changes in the fluid state and make timely adjustments to avoid the decrease in pump operation efficiency or equipment damage due to sudden changes in the flow state. After generating the dynamic response, the second link of step 3 is to design an adaptive control law through an adaptive control method to achieve optimal control of the downhole flow switch. The core principle of adaptive control is to adjust the control strategy according to the real-time changes of the system state, so that the controller can always maintain efficient operation in a changing environment. In the complex fluid environment downhole, the changes in fluid flow state are often random and nonlinear. Traditional fixed control strategies are difficult to cope with these changes, so it is necessary to introduce adaptive control methods. The design of the adaptive control law is based on dynamic response, and adapts to changes in flow and flow state by adjusting control parameters in real time. For example, when the dynamic response signal indicates that the flow fluctuation amplitude exceeds the normal range, the adaptive control law will automatically adjust the control gain of the flow switch to increase the sensitivity of the system, thereby responding to changes in flow more quickly. Conversely, when the flow fluctuation tends to be stable, the adaptive control law will reduce the control gain to avoid oscillation or increased energy consumption caused by excessive system response.

[0050] The implementation of adaptive control law usually combines two strategies: predictive control and feedback control. Predictive control uses the dynamic characteristics of the flow estimation model to determine the change trend of the flow in advance, thereby providing prior information for control decisions, while feedback control corrects the possible deviations of the prediction model by real-time monitoring of the state of the flow switch and the actual flow of the fluid. In the present invention, vibration signal analysis provides accurate input data for the adaptive control law, so that the controller can respond quickly and accurately to the changes in the downhole flow. For example, when the flow estimation model predicts that the flow will increase significantly, the control law will send a signal in advance to adjust the switch state to adapt to the increase in flow, and when the feedback information indicates that there is a deviation between the predicted value and the actual value, the control law will immediately correct the control strategy to achieve closed-loop control. This adaptive control method combining prediction and feedback can effectively cope with the dynamic changes of the downhole fluid environment and ensure that the operation of the flow switch is always in the optimal state. In addition, the adaptive control method also needs to consider the particularity of the downhole environment, such as high pressure, high temperature, and possible particulate matter in the fluid. These factors may lead to non-ideal operation of the control system, such as actuator hysteresis or noise interference of vibration signals. In the present invention, the adaptive control law solves these problems by adding robust design, that is, fully considering the interference and uncertainty that the system may be subject to when designing the control strategy. For example, when the noise level in the vibration signal increases, the adaptive control law will adjust the filter parameters to improve the accuracy of signal processing, thereby ensuring the reliability of dynamic response. On the other hand, the adaptive control law can also dynamically optimize the control parameters based on the system's operating history data to further improve the control performance. This optimization process based on historical data combines the idea of ​​machine learning. By analyzing the system's past operating status and continuously improving the control strategy, the controller can continuously improve efficiency and stability in long-term operation.

[0051] Embodiment 2: When collecting the vibration signal of the pump by means of a three-axis vibration sensor, the collection frequency is higher than twice the vibration frequency of the vibration signal to satisfy the Nyquist sampling theorem.

[0052] Specifically, the Nyquist sampling theorem states that in order to fully reconstruct the original signal, the sampling frequency must be at least twice the highest frequency of the signal. This requirement comes from the way the signal is represented in the frequency domain. When a continuous-time signal is discretely sampled, the spectrum of the signal will repeat periodically in the frequency domain. If the sampling frequency is not enough to cover the highest frequency of the original signal, it will cause the spectrum to overlap, i.e., "aliasing". The aliasing effect will introduce pseudo signals, making the sampled discrete signal unable to correctly represent the original signal. Therefore, in the process of vibration signal acquisition, ensuring that the sampling frequency satisfies the Nyquist theorem is the basic premise to avoid aliasing. In the vibration signal acquisition of downhole pumps, the frequency range of the vibration signal is usually determined by the operating state of the pump, the fluid characteristics, and the environmental conditions. The operating frequency of the pump and the pressure fluctuation frequency of the fluid constitute the main frequency components of the vibration signal, while the high-frequency components caused by turbulence determine the upper limit of the signal spectrum. In order to accurately capture these features, the sampling frequency not only needs to be higher than twice the frequency of the vibration signal, but also needs to reserve a certain safety margin in practical applications. For example, if the maximum frequency of the vibration signal of the pump is 1000Hz, then the sampling frequency needs to be set to at least 2000Hz, but considering the possible high-frequency interference and nonlinear changes in the signal boundary, the actual sampling frequency is usually set to 2500Hz or even higher. This high-frequency sampling setting is of great significance for the feature extraction and analysis of downhole vibration signals. First, a sampling frequency higher than twice can ensure that the vibration signal retains complete frequency information after discretization, providing a reliable data basis for subsequent time-frequency analysis. In particular, in the calculation of turbulence intensity and the solution of the Reynolds stress tensor, the construction of the time-frequency feature matrix depends on the complete frequency spectrum information of the signal. If the sampling frequency is insufficient, the high-frequency components in the signal will be distorted due to aliasing, thus affecting the accurate extraction of time-frequency features. Secondly, the reasonable setting of the sampling frequency can also improve the time domain resolution of the signal, that is, to capture the changes in the vibration signal more finely in time. This high resolution is particularly critical for monitoring the dynamic changes of fluid pressure fluctuations and turbulence intensity, because these changes often have a short time scale, and only high-frequency sampling can ensure that these rapid changes are accurately recorded. In addition, the selection of the sampling frequency also needs to balance the real-time performance of signal processing and the consumption of system resources. In underground environments, due to the limitations of data transmission bandwidth and processing power, excessively high sampling frequencies may lead to a surge in data volume, thereby increasing the burden of signal processing. Therefore, in practical applications, it is necessary to comprehensively consider the frequency range of vibration signals, system processing capabilities, and real-time requirements, and select an appropriate sampling frequency to achieve performance and resource utilization optimization.

[0053] Embodiment 3: In step 1, the time-frequency characteristic matrix of the three-axis vibration is expressed using the following formula:

[0054] ;

[0055] in, is the time-frequency characteristic matrix of triaxial vibration, reflecting the pump at the current time and frequency Vibration characteristics under Indicates The acceleration time domain signal of the axis; is the imaginary number symbol; is a function of the change in volume of the fluid in the pump, constructed by collecting historical fluid volume data in the pump; is a function of the fluid pressure variation in the pump, constructed by collecting historical fluid pressure data in the pump; For historical time; is the historical time integration variable.

[0056] Specifically, the formula is based on the triaxial vibration signal is the basic input, representing the pump , , The acceleration signals in three directions change with time. These signals directly reflect the vibration force on the pump, which contains the superposition information of mechanical vibration and fluid disturbance. In the complex downhole environment, the vibration signal of the pump is not only affected by mechanical factors, such as bearing wear and rotor imbalance, but also closely related to the turbulent state, pressure fluctuations and volume changes of the fluid. Through the time-frequency domain analysis of these signals, the dynamic characteristics of the pump can be freed from the limitations of the time domain, revealing the distribution characteristics of its frequency components and the law of change over time, thereby comprehensively describing the coupled vibration behavior between the pump and the fluid. The time variable is used in the formula The integral form of this means that the vibration state at the current moment is not only related to the current signal The integral form reflects an important feature of fluid dynamics, namely the non-instantaneous nature of the fluid state. Specifically, the pressure fluctuations and volume changes of the fluid in the pump have inertia and hysteresis effects, and their effects will continue to manifest over a period of time. Therefore, the characteristics of the vibration signal cannot be determined only by the data at the current moment, but the cumulative contribution over the historical time period must be considered. By introducing the integral term, the formula realizes the dynamic memory of the vibration signal and provides theoretical support for describing the long-term change trend of the vibration signal. In the core part of the formula, a frequency domain transformation factor is included , which is derived from the basic principle of Fourier transform, is used to transform time domain signals into frequency domain expressions. The physical meaning of Fourier transform is to decompose complex time domain signals into superpositions of different frequency components, thereby revealing the frequency characteristics of the signal. In this formula, the transform factor allows the time domain signal is mapped into frequency space so that a specific frequency The vibration intensity on the pump can be accurately captured. This frequency domain information is crucial in vibration signal analysis because the operating state of the pump is often manifested by vibration characteristics of specific frequencies. For example, the enhancement of fluid turbulence may lead to a significant amplification of certain high-frequency components, while the laminar state is more concentrated in the low-frequency range. Through frequency domain transformation, the changes in these specific frequency components can be intuitively analyzed and corresponded to the fluid state.

[0057] The formula also introduces two functions related to fluid properties, namely the fluid pressure change function and the fluid volume change function . These two functions are the core parameters of fluid dynamics, which respectively reflect the pressure fluctuation and volume change of the fluid in the pump during the historical time period. The pressure fluctuation is directly related to the turbulent state of the fluid, while the volume change reflects the compressibility characteristics of the fluid flow. These two parameters are obtained by collecting and modeling the historical data of the fluid in the pump. Their role in the formula is to introduce the modulation effect of the fluid state on the vibration signal. Specifically, the frequency characteristics of the vibration signal are not only determined by the mechanical vibration, but also affected by the dynamic characteristics of the fluid pressure and volume. For example, when the amplitude of the pressure fluctuation in the pump increases, its modulation effect on the vibration signal will be more significant, resulting in the enhancement of the high-frequency components; and when the volume change tends to be stable, the low-frequency components of the vibration signal may dominate. By introducing and , the formula realizes the deep coupling of vibration signal and fluid dynamic state, so as to more comprehensively characterize the dynamic characteristics of vibration signal. The formula also contains a square root term , this ratio reflects the dynamic equilibrium relationship between the fluid pressure change and the volume change. This equilibrium relationship is an important feature of fluid dynamics in the pump, which directly affects the amplitude and frequency characteristics of the vibration signal. For example, when the pressure fluctuation is significantly greater than the volume change, the vibration signal of the pump may show a stronger high-frequency component, and when the pressure fluctuation and volume change are close to equilibrium, the frequency distribution of the vibration signal may be more uniform. By introducing this ratio, the formula can capture subtle changes in the modulation effect of the fluid state on the vibration signal, thereby further improving the accuracy and resolution of the time-frequency feature matrix.

[0058] Embodiment 4: In step 1, the fluid pressure fluctuation characteristics are calculated based on the time-frequency characteristic matrix by the following formula:

[0059] ;

[0060] in, For current time Fluid pressure fluctuation characteristics when is the fluid density; is the acceleration due to gravity; For current time Liquid level height at is the fluid dynamic viscosity; is the pipe diameter; is the elastic modulus of the pipe; is the speed of sound.

[0061] Specifically, the first part of the formula is Expresses the static pressure characteristics of the fluid, which is determined by the liquid level height The direct contribution of gravity to the fluid pressure is determined by and the acceleration due to gravity is a physical constant, and the liquid level It changes dynamically over time. In the operating environment of a downhole pump, the fluctuation of the liquid level reflects the unbalanced state of fluid supply and discharge in the system, and the rise and fall of its height directly changes the baseline value of the static pressure. For example, when the liquid level in the pump rises, the static pressure in the system increases accordingly. This pressure change will have a direct impact on the operating state of the pump. The static pressure part provides the formula with a baseline value for pressure fluctuations, so that the superposition of dynamic fluctuations can accurately reflect the true fluid pressure state. However, the static pressure part only describes the basic contribution of the liquid level to the pressure. The more complex and more important pressure changes come from the dynamic fluctuation part. This part is composed of the time-frequency feature matrix The time derivative of Drive, directly capture the rate of change of the vibration signal over time. In dynamic systems, rapid changes in vibration signals usually correspond to violent fluctuations in fluid pressure. For example, when the pump operation causes enhanced turbulence, the vibration signal will produce a significant increase in high-frequency components, and this change is clearly reflected in the time derivative. By squaring the time derivative, the formula further amplifies the impact of high-rate-of-change signals, thereby emphasizing the severity of dynamic fluctuations. This dynamic pressure feature is an important representation of turbulent properties. Its amplitude and frequency are directly related to the instability of the flow state and can provide key information for the diagnosis of fluid state.

[0062] In describing the dynamic pressure fluctuations, the formula also introduces an exponential decay factor This factor reflects the natural dissipation of pressure fluctuations by the viscosity of the fluid. Dynamic viscosity It is an important property of the fluid, which determines the rate at which the internal friction of the fluid dissipates the energy of the fluctuation. The decay form used in the formula reflects the gradual decay of the fluctuation amplitude over time. For example, in a high viscosity fluid, the fluctuation energy will be dissipated faster, and the rate of decrease of the fluctuation amplitude will be more obvious in this case. On the other hand, the pipe diameter It also has a direct impact on the attenuation rate: a smaller diameter pipe will increase the viscous damping due to the stronger shearing effect between the fluid and the pipe wall, thereby accelerating the attenuation of fluctuations. Through this attenuation factor, the formula can effectively adapt to different fluid and pipeline conditions and truly reflect the changing law of pressure fluctuations in the system. In addition, the formula also combines the elastic modulus Speed ​​of sound Correction of the propagation characteristics of pressure fluctuations. This part is achieved by the factor Characterizes the regulation of pipe elasticity and fluid acoustic properties on pressure fluctuations. Describes the speed at which pressure disturbances propagate in a fluid. In a fluid with a higher speed of sound, pressure fluctuations can diffuse quickly, while in a fluid with a lower speed of sound, the propagation of fluctuations is more localized. It reflects the responsiveness of the pipeline material to pressure fluctuations. A higher elastic modulus can more effectively suppress the fluctuation amplitude, while a lower elastic modulus may amplify the propagation effect of pressure fluctuations. This correction term unifies the fluid characteristics and pipeline parameters, making the formula not only suitable for the analysis of fluid state, but also able to reflect the overall regulatory effect of the system structure on fluctuations. Through the multiple combination of static pressure, dynamic pressure, viscous damping and pipeline correction, the formula achieves a comprehensive description of the characteristics of fluid pressure fluctuations. The static pressure part provides a stable pressure reference, while the dynamic pressure part captures the instantaneous fluctuations of the fluid state through the time change of the time-frequency characteristic matrix. The exponential decay factor and acoustic correction term further improve the adaptability of the formula to actual downhole working conditions, ensuring that it can be accurately modeled under a variety of complex conditions. In the context of downhole pump flow control, the extraction of pressure fluctuation characteristics provides a key dynamic indicator for the system, which can directly reflect the changes in fluid flow state and provide reliable support for subsequent turbulence intensity calculation, flow state transition judgment and dynamic control of flow switches.

[0063] Embodiment 5: In step 1, the turbulence intensity is calculated according to the time-frequency characteristic matrix and the fluid pressure fluctuation characteristics by the following formula:

[0064] ;

[0065] in, is the turbulence intensity, describing the radial distance in the pipe. and the current time Turbulent pulsation characteristics under For current time The Reynolds number under , which describes the ratio of inertia to viscosity of the fluid flow; is the critical Reynolds number, which indicates the critical value of the fluid transition from laminar flow to turbulent flow; is the radial distance in the pipeline, which means the radial distance from the center of the pipeline to a certain point; is the pipeline radius, indicating the maximum radial distance of the pipeline; is the preset vibration correction factor; is the vibration characteristic frequency, indicating the main frequency of the vibration signal of the pump; is the vibration period; is the radial distribution function, which describes the variation of turbulence intensity with pipe radius; The radial distance inside the pipe is and the current time The turbulent kinetic energy under ;in, is the average pulsating velocity component of the first axis extracted from the vibration signal of the pump; is the average pulsating velocity component of the second axis extracted from the vibration signal of the pump; It is the average pulsating velocity component of the third axis extracted from the vibration signal of the pump.

[0066] Specifically, the turbulence intensity The calculation of turbulent kinetic energy As the core, the first part of the formula is The fundamental contribution of turbulent kinetic energy to turbulence intensity is introduced. Turbulent kinetic energy is essentially the energy density of velocity fluctuations in the fluid, which is defined as the sum of the square means of the three-axis velocity fluctuation components. By extracting , and , can be obtained respectively , and The average pulsating velocity components in three directions. These components directly reflect the turbulent fluctuation characteristics of the fluid in different directions. The vibration signal of the pump contains dynamic information about the coupling between the fluid and the mechanical system. By extracting and calculating these pulsating velocity components, the vibration signal can be converted into a quantitative representation of the turbulent kinetic energy. The square root of the turbulent kinetic energy is proportional to the turbulence intensity. This relationship reflects the direct connection between the turbulence intensity and the velocity fluctuation amplitude. The greater the velocity fluctuation amplitude, the higher the turbulence intensity, and the square root form of the turbulent kinetic energy smoothes possible local extremes, making the calculation results more stable. Through this part, the formula can capture the energy characteristics of the turbulent state of the fluid, providing a basis for analyzing the local intensity and overall distribution of turbulence. The second part of the formula converts the fluid pressure fluctuation characteristics Introduced into the calculation of turbulence intensity, through Describes the driving effect of pressure fluctuations on turbulent pulsations. Pressure fluctuations are an important source of turbulent states, and changes in their amplitude directly reflect the fluctuations in turbulent energy. , the formula eliminates the difference due to fluid density Speed ​​of sound The formula is more adaptable to different fluid conditions because it can avoid the deviation of the calculation results caused by different Reynolds number ratios. For example, in high-density fluids (such as downhole mud), the influence of pressure fluctuations on turbulence intensity is more significant, while in low-density fluids (such as gas), the contribution of pressure fluctuations is relatively small. The formula is standardized to ensure the universality of the calculation of turbulence intensity. It is another key component of the formula, reflecting the regulating effect of the fluid turbulence state on the turbulence intensity. The Reynolds number is an important dimensionless parameter in fluid dynamics, describing the ratio between the fluid inertia force and the viscous force. Above the critical Reynolds number When the Reynolds number is close to or lower than The formula links the change of fluid flow state with turbulence intensity through the Reynolds number ratio, so that the calculation of turbulence intensity can dynamically reflect the process of fluid transition from laminar flow to turbulence. For example, when the flow rate of the downhole pump increases, the Reynolds number As the radial distribution function increases, the Reynolds number ratio part of the formula will decrease, thereby improving the calculation result of the turbulence intensity, reflecting the direct influence of fluid velocity on turbulence characteristics. The formula describes the distribution of turbulence intensity on the pipe cross section. The turbulence intensity is usually highest at the center of the pipe and gradually decreases toward the pipe wall. This distribution characteristic is due to the shear effect of the fluid and the viscous damping of the pipe wall. The formula captures this characteristic in the form of a Gaussian distribution, where the radial distance is the distance from the center of the pipe to the target location, and the pipe radius This defines the normalized scale of the distribution. near When , the radial distribution function quickly approaches zero, reflecting the significant reduction of turbulence intensity near the pipe wall. Through this part, the formula can provide the detailed distribution of turbulence intensity on the pipe cross section, providing theoretical support for analyzing the scouring effect of turbulence on the pipe wall and the local characteristics of fluid energy dissipation. Vibration correction term The formula further enriches its ability to describe the dynamic changes of turbulence intensity. is the vibration correction factor, is the main frequency of the vibration signal, is the vibration period. The vibration correction term reflects the periodic effect of the mechanical vibration of the pump on the turbulent state by introducing sinusoidal modulation. In actual working conditions, the operating frequency of the pump often affects the high-frequency components in the turbulence, and this periodic effect is particularly evident in the main frequency of the vibration signal. Through this correction term, the formula can capture the periodic fluctuations in turbulence intensity caused by pump vibration, thereby enhancing the ability to describe the dynamic characteristics of turbulence.

[0067] Example 6: In step 2, the Reynolds stress tensor is calculated based on the turbulence intensity using the following formula:

[0068] ;

[0069] in, A coordinate variable indicating the direction of the first axis; A coordinate variable indicating the direction of the second axis; A coordinate variable indicating the direction of the third axis; represents the turbulent viscosity of the fluid; Indicates the radial distance inside the pipe is and the current time The Reynolds stress tensor under .

[0070] Specifically, the Reynolds stress tensor The calculation formula is based on the turbulence intensity and velocity fluctuation derivatives. The core idea of ​​the formula is to use turbulent viscosity The interaction with the velocity pulsation gradient describes the contribution of turbulence to the momentum exchange inside the fluid. Under turbulent conditions, the superposition of velocity pulsations in different directions forms a complex momentum transfer process, and the strength of this momentum transfer is directly related to the flow stability and pressure loss in the pipeline. The first part of the formula introduces turbulent viscosity , which is a key parameter that characterizes the contribution of turbulence to the friction force inside the fluid. Its value is usually much larger than the molecular viscosity, reflecting the amplification effect of the fluid on the shear stress under the turbulent state. The existence of turbulent viscosity enables the Reynolds stress tensor to accurately characterize the turbulent mixing and momentum exchange inside the fluid. The velocity gradient part of the formula is obtained by , , The sum of the three terms describes the velocity fluctuations in , , The rate of change in three directions. Velocity pulsation is the core feature of turbulence, and its rate of change reflects the sensitivity of velocity fluctuations to spatial distribution. By superimposing the velocity pulsation gradients in the three-axis directions, the formula captures the multi-directional characteristics of momentum exchange in turbulence. For example, in downhole fluid systems, there is often a significant difference in turbulence intensity between the center and the wall of the pipe. This difference is manifested as an increase or decrease in local momentum transfer through the velocity pulsation gradient. The formula integrates the complex momentum exchange process in the three-dimensional turbulent state into a tensor quantization framework through the summation of velocity gradients, providing a tool for the all-round analysis of turbulent characteristics.

[0071] The calculation of the Reynolds stress tensor is also related to the turbulence intensity Directly related. Turbulence intensity is an important parameter to measure the fluctuation of fluid turbulence energy, and its size directly affects the strength of turbulence on the momentum exchange inside the fluid. In the formula, turbulence intensity is introduced as a multiplication factor, which amplifies the influence of the turbulence state on the contribution of the velocity gradient. For example, when the turbulence intensity is high, the efficiency of momentum exchange increases significantly, and the value of the Reynolds stress tensor also increases accordingly; when the turbulence intensity decreases, the efficiency of momentum exchange decreases, and the tensor value tends to decrease. The design of this part ensures that the Reynolds stress tensor can dynamically respond to changes in the turbulent state, thereby accurately characterizing the gradual increase or attenuation of momentum exchange during the flow state transition process. The formula also uses the radial position and time Relates the calculation of the Reynolds stress tensor to its temporal and spatial variations. Radial position It represents the distance from the center of the pipe to a certain point. The introduction of this parameter in the formula reflects the uneven distribution characteristics of the turbulent state on the pipe cross section. In the central area of ​​the pipe, the turbulence intensity and momentum exchange are usually high, while near the pipe wall, due to the viscous damping, the turbulence intensity gradually weakens and the momentum exchange efficiency decreases. Time variable The dynamic characteristics of the turbulent state are further introduced. By updating the turbulence intensity and velocity gradient in real time, the formula can accurately capture the changes in turbulence characteristics in the pipeline over time. For example, when the flow increases or the pressure fluctuates, the turbulence intensity may increase instantaneously, and the calculation result of the Reynolds stress tensor also increases accordingly, reflecting the rapid change of the turbulent state.

[0072] Example 7: In step 2, the flow transition criterion value is calculated based on the turbulence intensity and the Reynolds stress tensor using the following formula:

[0073] ;

[0074] in, For current time The flow transition criterion at ; is the preset critical turbulence intensity; For current time The Weber number at ; is the critical Weber number; is the preset periodic item weight; is the preset pressure fluctuation weight.

[0075] Specifically, the first part of the formula is expressed by The Reynolds stress tensor The density of the fluid and dynamic viscosity Combined with the Reynolds stress tensor, it is used to describe the relative size of the shear stress in the fluid. The Reynolds stress tensor reflects the intensity of momentum exchange under turbulent conditions and indicates the disturbing effect of turbulence on the average flow, while density and viscosity are the basic properties of fluid dynamics, characterizing the characteristics of fluid inertia and internal friction, respectively. Through this calculation, the formula can quantify the influence of turbulent shear intensity on the physical parameters of the fluid, thereby providing basic information for the judgment of flow state transition. For example, when the absolute value of the Reynolds stress tensor is high, it indicates that the turbulent momentum exchange is strong and the fluid is closer to a turbulent state; otherwise, it is closer to a laminar state. Through normalization, this part effectively eliminates the calculation deviation caused by differences in fluid properties (such as density or viscosity), making the formula more universal under different fluid conditions. The second part of the formula The turbulence intensity The calculation of flow transition criterion value is introduced, and the critical turbulence intensity is compared with the critical turbulence intensity. The square of the ratio amplifies the effect of turbulence intensity on the transition criterion value. Turbulence intensity is a direct representation of the turbulent state and describes the relative amplitude of fluid velocity fluctuations. Through the square form, the formula further emphasizes the nonlinear contribution of turbulence intensity to the transition process. For example, when the turbulence intensity approaches or exceeds the critical value, its increment to the criterion value increases significantly, which is consistent with the rapid enhancement trend of the turbulent state during the actual flow state transition process. This part ensures that the formula can sensitively capture the changes in turbulent characteristics and provides a highly dynamic analysis capability for flow state discrimination.

[0076] The third part is through index terms Weber number The Weber number is a dimensionless parameter that describes the ratio between the surface tension and inertial force of the fluid. Its current value is and critical Weber number The ratio reflects the inhibitory effect of surface tension on the turbulent state. When the Weber number is low, the surface tension plays a dominant role, the turbulent state is suppressed, and the transition process is delayed; when the Weber number is high, the inertial force plays a dominant role, the turbulent state is easier to form, and the transition process is accelerated. The exponential decay term can accurately capture this characteristic and optimize the calculation results of the criterion value through the nonlinear influence of the Weber number on the transition process. This part is particularly suitable for describing the complexity of the transition process in downhole multiphase fluids (such as liquid-gas mixed flow). In addition, the formula is passed The introduction of corrections to the periodic term and pressure fluctuation term further improves the dynamic adaptability of the flow transition criterion value. It is used to reflect the periodic modulation effect of the mechanical vibration of the pump on the turbulent state, where is the preset weight, is the main frequency of vibration. This part shows that the main frequency of the vibration signal in the operation of the pump can have a direct impact on the flow state transition. For example, when the main frequency is high, it may stimulate turbulent pulsation in the fluid, thereby accelerating the transition of the flow state. Pressure fluctuation term The pressure fluctuation characteristics The calculation of the criterion value is included, and the driving effect of pressure fluctuations on the turbulent state is reflected by normalizing with density and sound speed. This section emphasizes the important influence of internal pressure changes in the fluid on the turbulent formation and transition process. For example, under high-pressure fluctuation conditions, the disturbance inside the fluid is intensified, and the turbulent state is more likely to form, while low-pressure fluctuations may delay the transition.

[0077] Example 8: In step 2, the flow estimation model is established using the following formula:

[0078] ;

[0079] in, For current time Flow estimation at time For current time The pressure change value when is the critical flow transition criterion value; is the preset flow coefficient.

[0080] Specifically, the core of the formula lies in the flow calculation framework based on the Bernoulli equation, where describes the fluid flow distribution in the pipe under ideal conditions. Here, is the current time The pressure change value at the time of the flow reflects the driving force of the fluid in the pipeline, while the fluid density This part provides the inertial property. Through this part, the formula captures the nonlinear relationship between flow and pressure difference, that is, when the pressure change value increases, the flow increases in the form of square root. This relationship conforms to the basic theory of fluid mechanics and can accurately reflect the macroscopic trend of fluid flow. At the same time, Indicates the cross-sectional area of ​​the pipe, converts the linear velocity caused by the pressure difference into volume flow, thus realizing the conversion from physical driving force to flow quantification. Based on the ideal flow, the formula further introduces the flow coefficient , which is used to correct the deviation between the actual flow rate and the ideal flow rate. The flow coefficient is an empirical parameter that depends on the geometry of the pipeline, the physical properties of the fluid, and the specific conditions of the system operation. Due to the influencing factors such as turbulence, friction loss, and pipeline irregularities that may exist in the downhole fluid system, the actual flow rate is often lower than the ideal flow rate. The introduction of the flow coefficient can effectively make up for this gap. For example, in the case of large pipeline roughness, the flow coefficient will be less than 1 to reflect the inhibitory effect of friction on flow. With this parameter, the formula has a wider applicability and can meet the flow estimation needs under different pipeline and fluid conditions.

[0081] The dynamic adjustment ability of the formula is reflected in the exponential decay factor Flow transition criterion value It is an important indicator of the transition of fluid from laminar flow to turbulent flow, and its magnitude directly reflects the impact of turbulent state on flow rate. The reference point of the transition process is defined to determine whether the flow state has changed significantly. The formula describes the nonlinear attenuation relationship of flow rate with the change of turbulence state in exponential form: Close to or exceed When , the turbulent state significantly increases the inhibitory effect on the flow rate, resulting in a decrease in the estimated flow rate. This part enables the formula to dynamically adapt to changes in flow regimes, especially in complex downhole environments, where the impact of flow regime transitions on flow changes is often of great significance. The formula also uses the correction term Introducing vibration signal characteristics and liquid level height into the flow estimation model further improves the model's ability to respond to real-time fluid conditions. is the time-frequency characteristic matrix of the vibration signal at the main frequency The value at reflects the dynamic characteristics of the vibration signal during the operation of the pump. describes the liquid level Static contribution to flow. The higher the liquid level, the greater the static pressure, and the driving force of the flow increases accordingly; while the dominant frequency characteristics of the vibration signal reflect the regulating effect of the mechanical properties of the pump on the flow. Through this correction term, the formula can capture the coupling effect between fluid dynamics and vibration dynamics. For example, when the dominant frequency of the pump vibration signal increases, the contribution of the correction term increases, indicating that the influence of vibration drive on flow is more significant.

[0082] Example 9: In step 3, the following formula is used to generate the dynamic response of the downhole flow switch control according to the flow estimation model:

[0083] ;

[0084] in, is the Laplace variable; is the expected flow in the form of Laplace variables; is the natural frequency; is the damping ratio; is the cut-off frequency; for The corresponding Laplace variable form; for The corresponding Laplace variable form.

[0085] Specifically, the dynamic response function in the formula is the actual flow With expected flow The ratio of describes the real-time adjustment capability of the flow switch to flow changes. In the Laplace domain, this ratio can reveal the transfer characteristics of the control system to the input flow signal. The first part of the formula is It is a typical second-order system transfer function, reflecting the inherent dynamic characteristics of the system. Natural frequency Indicates the natural oscillation frequency of the system, which determines the basic response speed of the flow switch to flow changes; damping ratio Describes the degree to which the system suppresses oscillations. When , the system is in a critical damping state and can respond quickly to input without overshoot; when When , the system appears underdamped and may experience response overshoot; When the system is overdamped, the response speed is slow. This part of the design ensures that the flow switch can quickly and stably adjust the operating state according to the inherent characteristics of the system. The second part of the formula Is an exponential decay term used to describe the cutoff characteristics of the system under high-frequency signals. The system sensitivity to high-frequency input signals is defined. Its physical meaning is to suppress the interference of high-frequency noise on the control response. In the downhole fluid environment, the vibration signal may contain higher-frequency random disturbances, which may have an adverse effect on the control accuracy of the flow switch. Through exponential decay, the formula effectively filters out the influence of high-frequency components, making the dynamic response more concentrated in the main frequency range of the flow signal. For example, when the main frequency of the flow signal is lower than When the frequency is higher than , the response amplitude decreases rapidly, thus avoiding the interference of high-frequency noise.

[0086] The third part of the formula The flow state transition criterion value is introduced into the dynamic response model, which reflects the direct regulatory effect of the turbulent state on the flow switch control. Defines the benchmark for the turbulence state to the system response, and the current criterion value It describes the strength of the real-time turbulence state. Close to or below When , the turbulence has little effect on flow changes, and the system responds more sensitively; Exceed , the turbulence state intensifies and the system response gradually weakens. This part of the design ensures that the flow switch can dynamically adjust the control strength according to the changes in the turbulence state. For example, when the turbulence state is strong, the control response of the flow switch will be appropriately slowed down to avoid over-adjustment or instability of the system. Overall, this formula constructs a dynamic response model of flow switch control through the coupling of inherent dynamics, frequency characteristics and turbulence state. This model can fully reflect the dynamic characteristics of complex fluid systems downhole, especially under conditions of frequent changes in flow state, its dynamic adaptability is particularly important. In practical applications, the dynamic response function It can be used to adjust the control strategy of the flow switch so that it can make accurate real-time adjustments to the input signal under different flow change conditions. For example, when the flow estimation model indicates that the system has a large flow change, the dynamic response function can quickly amplify the response to the input signal, thereby achieving rapid adjustment of the flow switch; and when the turbulent state increases or the input signal contains more high-frequency noise, the response function will attenuate these components to avoid instability caused by overshoot or frequency coupling in the control system.

[0087] Embodiment 10: In step 3, the following formula is used to generate an adaptive control law for downhole flow switch control using an adaptive control method according to the dynamic response:

[0088] ;

[0089] in, The adaptive control law for the generated downhole flow switch control; is the adaptive gain; is the expected flow in the form of time variable; is the static gain; for The frequency domain form of is the expected flow in the form of historical time-integrated variable; It is the flow estimation in the form of historical time integrated variable.

[0090] Specifically, the first term of the formula Is the proportional control part, which directly describes the desired flow The actual estimated flow The difference between the control output Here, is the proportional gain factor, which is used to adjust the control system’s sensitivity to flow deviation. When it is larger, the control system responds more quickly to flow deviation, but may introduce oscillation; When it is smaller, the system response is relatively smooth, but the adjustment to flow changes may be delayed. The proportional control part is the core of the control law, which ensures that the system can quickly respond to the deviation between the actual flow and the expected flow, thereby maintaining the target state of the flow. The second term of the formula is It is the integral control part, which dynamically modifies the control law based on the change rate of historical flow deviation. Critical criterion value The ratio of , weights the contribution of the historical deviation change rate, thus reflecting the dynamic regulation of the turbulent state on the control output. Close to or exceed ), the weight of the integral term increases, making the impact of historical deviation on the control output more significant. This mechanism can enhance the adaptability of the control law to turbulent conditions, especially in downhole environments where the flow state changes frequently. The integral control part can effectively compensate for the long-term deviation of the system through cumulative effects, thereby improving the stability and accuracy of control.

[0091] Deviation change rate in the integral control part It provides dynamic information about the flow deviation over time. By integrating the rate of change over time, the control law can capture the trend of the flow deviation and adjust the control output according to the cumulative effect of the deviation change. For example, when the actual flow rate is continuously lower than the expected flow rate, the output of the integral term gradually increases, thereby guiding the flow switch to adjust to a higher flow state; conversely, when the actual flow rate is higher than the expected flow rate, the contribution of the integral term gradually decreases. The third term of the formula It is the differential control part, based on the dynamic response function The frequency domain characteristics of the control law are used to quickly adjust the control law. is the normalized form of the dynamic response function, which is used to describe the system dynamic behavior in the frequency domain, while It is a real-time estimated flow rate. The differential control part directly reflects the instantaneous characteristics of flow changes by deriving the dynamic response multiplied by the rate of change of real-time flow. Since differential control can provide a quick response to the trend of flow changes, this part is particularly important when the system needs to be adjusted quickly. For example, when the flow signal rises or falls rapidly, the differential control part can provide immediate control adjustments to avoid delays or overshoots in the system. The introduction of the dynamic response function further enhances the control law's ability to adapt to the system's frequency characteristics. By converting the frequency domain form of the dynamic response Incorporating the differential control part, the formula can effectively filter out the interference of high-frequency noise on the control output, while amplifying the response to the flow change in the target frequency band. This design ensures that the control system can accurately respond to the dynamic changes of the flow signal in a complex downhole environment, especially in conditions with turbulent interference or high-frequency vibration. The differential control part can significantly improve the sensitivity and anti-interference ability of the control. Overall, the adaptive control law constructs a highly dynamic control strategy through the synergistic effect of the proportional, integral and differential parts. The proportional part provides a direct response to the real-time flow deviation to ensure the rapidity of the system; the integral part enhances the long-term stability of the control by accumulating the dynamic influence of historical deviations and turbulent states; the differential part provides the system with additional sensitivity and anti-interference ability by capturing the instantaneous characteristics of flow changes. In addition, the introduction of the flow transition criterion value and the dynamic response function enables the control law to be adaptively adjusted according to the turbulent state and the frequency characteristics of the system, thereby further improving the control accuracy and adaptability.

[0092] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A downhole flow switch control method based on vibration signal analysis, characterized in that: The method comprises: Step 1: Collect the vibration signal of the pump through a three-axis vibration sensor to obtain the acceleration time domain signal in the three-axis direction; decouple the acceleration time domain signal by multi-dimensional vibration spectrum components to obtain the time-frequency characteristic matrix of the three-axis vibration; calculate the fluid pressure fluctuation characteristics based on the time-frequency characteristic matrix; calculate the turbulence intensity based on the time-frequency characteristic matrix and the fluid pressure fluctuation characteristics; Step 2: Based on the turbulence intensity, calculate the Reynolds stress tensor; based on the turbulence intensity and the Reynolds stress tensor, calculate the flow transition criterion value and establish a flow estimation model; Step 3: Generate a dynamic response of the downhole flow switch control according to the flow estimation model; and generate an adaptive control law of the downhole flow switch control using an adaptive control method according to the dynamic response; In step 1, the time-frequency characteristic matrix of triaxial vibration is expressed using the following formula: ； in, is the time-frequency characteristic matrix of triaxial vibration, reflecting the pump at the current time and frequency Vibration characteristics under Indicates The acceleration time domain signal of the axis; is the imaginary number symbol; is a function of the change in volume of the fluid in the pump, constructed by collecting historical fluid volume data in the pump; is a function of the fluid pressure variation in the pump, constructed by collecting historical fluid pressure data in the pump; For historical time; is the historical time integration variable; In step 1, the fluid pressure fluctuation characteristics are calculated based on the time-frequency characteristic matrix using the following formula: ； in, For current time Fluid pressure fluctuation characteristics when is the fluid density; is the acceleration due to gravity; For current time Liquid level height at is the fluid dynamic viscosity; is the pipe diameter; is the elastic modulus of the pipe; is the speed of sound; In step 1, the turbulence intensity is calculated according to the time-frequency characteristic matrix and the fluid pressure fluctuation characteristics using the following formula: ； in, is the turbulence intensity, describing the radial distance in the pipe. and the current time Turbulent pulsation characteristics under For current time The Reynolds number under , which describes the ratio of inertia to viscosity of the fluid flow; is the critical Reynolds number, which indicates the critical value of the fluid transition from laminar flow to turbulent flow; is the radial distance in the pipeline, which means the radial distance from the center of the pipeline to a certain point; is the pipeline radius, indicating the maximum radial distance of the pipeline; is the preset vibration correction factor; is the vibration characteristic frequency, indicating the main frequency of the vibration signal of the pump; is the vibration period; is the radial distribution function, which describes the variation of turbulence intensity with pipe radius; The radial distance inside the pipe is and the current time The turbulent kinetic energy under ;in, is the average pulsating velocity component of the first axis extracted from the vibration signal of the pump; is the average pulsating velocity component of the second axis extracted from the vibration signal of the pump; It is the average pulsating velocity component of the third axis extracted from the vibration signal of the pump.

2. The downhole flow switch control method based on vibration signal analysis according to claim 1, characterized in that: When the vibration signal of the pump is collected by a three-axis vibration sensor, the collection frequency is higher than twice the vibration frequency of the vibration signal to meet the Nyquist sampling theorem.

3. The downhole flow switch control method based on vibration signal analysis according to claim 2, characterized in that: In step 2, the Reynolds stress tensor is calculated based on the turbulence intensity using the following formula: ； in, A coordinate variable indicating the direction of the first axis; A coordinate variable indicating the direction of the second axis; Coordinate variable indicating the direction of the third axis; represents the turbulent viscosity of the fluid; Indicates the radial distance inside the pipe is and the current time The Reynolds stress tensor under .

4. The downhole flow switch control method based on vibration signal analysis according to claim 3, characterized in that: In step 2, the flow transition criterion value is calculated based on the turbulence intensity and the Reynolds stress tensor using the following formula: ； in, For current time The flow transition criterion at ; is the preset critical turbulence intensity; For current time The Weber number at ; is the critical Weber number; is the preset periodic item weight; is the preset pressure fluctuation weight.

5. The downhole flow switch control method based on vibration signal analysis according to claim 4, characterized in that: In step 2, the flow estimation model is established using the following formula: ； in, For current time Flow estimation at time For current time The pressure change value when is the critical flow transition criterion value; is the preset flow coefficient.

6. The downhole flow switch control method based on vibration signal analysis according to claim 5, characterized in that: In step 3, the dynamic response of the downhole flow switch control is generated according to the flow estimation model using the following formula: ； in, is the Laplace variable; is the expected flow in the form of Laplace variables; is the natural frequency; is the damping ratio; is the cut-off frequency; for The corresponding Laplace variable form; for The corresponding Laplace variable form.

7. The downhole flow switch control method based on vibration signal analysis according to claim 6, characterized in that: In step 3, the following formula is used to generate the adaptive control law of the downhole flow switch control based on the dynamic response using the adaptive control method: ； in, The adaptive control law for the generated downhole flow switch control; is the adaptive gain; is the expected flow in the form of time variable; is the static gain; for The frequency domain form of is the expected flow in the form of historical time-integrated variable; It is the flow estimation in the form of historical time integrated variable.

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