Method for measuring porosity of magnesium oxide coating

Abstract

The present application relates to the technical field of coating detection, and discloses a method for detecting the porosity of a magnesium oxide coating. The method comprises: applying a detection gas pressure and collecting pressure response data; establishing a gas permeation response model and characterizing it according to the coupling relationship between open pores and closed pores in response to pressure; separating the pressure response data according to the difference in time constant between open pores and closed pores, obtaining an open pore permeation response component and a closed pore retention response component, and extracting permeation characteristic parameters and retention characteristic parameters, respectively; determining the coupling influence degree of closed pores on the permeation behavior of open pores according to the retention characteristic parameters, and correcting the permeation characteristic parameters using the coupling influence degree; calculating the density of the magnesium oxide coating according to the corrected permeation characteristic parameters; and determining the total porosity of the magnesium oxide coating according to the density of the magnesium oxide coating. The present application effectively reduces the coupling influence of closed pores on the permeation behavior of open pores, and improves the accuracy and consistency of the detection of the density and porosity of the magnesium oxide coating.

Description

Technical Field

[0001] This invention relates to the field of coating inspection technology, and in particular to a method for measuring the density and porosity of magnesium oxide coatings by pressure. Background Technology

[0002] Silicon steel is the preferred material for manufacturing low-energy-consumption transformer cores. The density and porosity of its surface magnesium oxide coating directly determine the quality of the magnesium silicate insulation underlayer after high-temperature annealing, thus affecting the magnetic properties and lamination quality of the product. Therefore, accurately detecting the density and porosity of the magnesium oxide coating on the silicon steel surface is crucial for controlling coating quality.

[0003] Several methods for detecting coating porosity exist in the prior art. For example, Chinese patent CN120890972B discloses a system and method for testing the performance of magnesium oxide coatings based on curing degree analysis. This method evaluates the performance of magnesium oxide coatings through curing degree analysis, thereby achieving the detection of magnesium oxide coating quality. Furthermore, mercury intrusion porosimetry is a commonly used method for determining the porosity and pore size distribution of porous materials and has been applied in fields such as ceramic coatings. However, after coating, magnesium oxide coatings on silicon steel surfaces contain pores with different interconnected states, such as open pores and closed pores. Most existing pressure testing methods, such as mercury intrusion porosimetry, assume that the pressure response is only related to the overall porosity of the coating, without considering the differences in the influence of different interconnected pore states within the coating on the gas permeation process. Since the gas being detected mainly permeates through open pores and other connected pores, while closed pores and other non-connected pores are difficult to participate in gas transport, the pressure response characteristics of magnesium oxide coatings with similar overall porosity but different proportions of open and closed pores are significantly different. This makes it difficult for existing detection results to accurately reflect the true density of magnesium oxide coatings. At the same time, the pressure response information generated by pores in different connected states is superimposed. Existing methods lack the means to separate the permeation characteristics of open pores from the retention effect of closed pores from the superimposed response, and cannot effectively distinguish the contribution of each type of pore to the pressure response, resulting in low accuracy in the detection of the density of magnesium oxide coatings.

[0004] The existing technologies have the following problems: the existing magnesium oxide coating pressure testing methods do not incorporate the differentiated contributions of open pores and closed pores to the gas permeation process into the pressure response analysis, do not consider the interference of changes in the proportion of open pores and closed pores on the pressure response characteristics, and do not establish a means to effectively separate the open pore permeation response and closed pore retention response signals from the superimposed pressure response information. They cannot distinguish the contribution of the permeation response of connected pores and the retention effect of non-connected pores to the pressure response, and are difficult to meet the accuracy requirements of online detection of magnesium oxide coating density and porosity. Summary of the Invention

[0005] This invention aims to overcome the shortcomings of the prior art and provide a method and system for measuring the density and porosity of magnesium oxide coatings. By establishing a gas permeation response model under the condition of coexistence of open and closed pores, and by using response separation and coupling correction, the density and total porosity of magnesium oxide coatings can be accurately detected, reducing the coupling influence of closed pores on the permeation behavior of open pores and improving the accuracy and consistency of the detection results.

[0006] In a first aspect, the present invention provides a method for measuring the density and porosity of magnesium oxide coatings by pressure, comprising: A pressure measuring device was used to apply a detection pressure to the surface of the magnesium oxide coating, and pressure response data of the magnesium oxide coating were collected during the detection process. Based on the coupling relationship between the open pore permeation behavior and the closed pore retention behavior of the magnesium oxide coating and the pressure response, a gas permeation response model of the magnesium oxide coating is established, and the pressure response data is characterized based on the gas permeation response model. Based on the response characteristic characterization results, and according to the difference in time constant between the rapid decay of open pores and the slow decay of closed pores, the pressure response data is separated to obtain the open pore permeation response component and the closed pore retention response component, and the permeation characteristic parameters characterizing the open pore permeation behavior and the retention characteristic parameters characterizing the closed pore retention behavior are extracted respectively. The degree of coupling influence of closed pores on the permeation behavior of open pores is determined based on the retention characteristic parameters, and the permeation characteristic parameters are corrected using the degree of coupling influence. The density of the magnesium oxide coating was calculated based on the corrected permeation characteristic parameters; The total porosity is determined based on the density of the magnesium oxide coating.

[0007] Furthermore, the establishment of a gas permeation response model for the magnesium oxide coating, and the characterization of the pressure response data based on the gas permeation response model, includes: Based on the coupling effect of open-pore permeation behavior and closed-pore retention behavior on pressure response, the pressure response process is divided into open-pore rapid permeation response and closed-pore slow retention response. A double exponential pressure decay model is used to describe the overall pressure response. The double exponential pressure decay model contains two exponential decay terms with different time constants: the first time constant corresponds to the rapid permeation response of open pores and the second time constant corresponds to the slow retention response of closed pores. The overall pressure response is composed of the superposition of the open pore permeation response term and the closed pore retention response term to establish a gas permeation response model for magnesium oxide coating. The gas permeation response model outputs the first time constant and the second time constant. The pressure response data is fitted with a nonlinear least squares fitting algorithm. Based on the numerical difference between the first time constant and the second time constant, the open orifice response coefficient, the open orifice response time constant, the closed orifice response coefficient, and the closed orifice response time constant are obtained respectively. The pressure response data are characterized by the response characteristics based on the open orifice response coefficient, open orifice response time constant, closed orifice response coefficient, and closed orifice response time constant.

[0008] Furthermore, the step of performing response separation on the pressure response data and extracting permeation characteristic parameters and retention characteristic parameters includes: Based on the response feature characterization results, obtain the response curves corresponding to the open-pore fast response term and the closed-pore slow response term, respectively. The first time constant and the second time constant in the gas permeation response model are obtained, and the open pore fast response term and the closed pore slow response term are decoupled according to the difference between the first time constant and the second time constant on the time scale, so as to obtain the open pore permeation response component and the closed pore retention response component respectively. The initial pressure drop rate and steady-state pressure change of the open orifice are calculated based on the open orifice permeation response components and used as the permeation characteristic parameters. The closed-hole pressure retention amount and closed-hole pressure recovery rate are calculated based on the closed-hole retention response components and used as the retention characteristic parameters.

[0009] Furthermore, the degree of coupling influence of the closed pore on the permeation behavior of the open pore includes: The effect of local structural deformation in the closed-hole region on the effective cross-sectional area of ​​the open-hole channel; Local structural deformation includes: local compression deformation of the skeleton around the closed hole under the action of detection air pressure, and changes in the effective pore diameter of the open hole channel in the region adjacent to the closed hole; The degree of coupling influence is determined based on the retention characteristic parameters, which establish the influence coefficient of the closed pore on the effective cross-sectional area of ​​the open pore channel. The influence coefficient is a value greater than 0. When the influence coefficient is less than 1, it indicates that the closed pore leads to a decrease in the effective cross-sectional area of ​​the open pore channel; when the influence coefficient is equal to 1, it indicates that the closed pore has no effect on the effective cross-sectional area of ​​the open pore channel; and when the influence coefficient is greater than 1, it indicates that the closed pore leads to an increase in the effective cross-sectional area of ​​the open pore channel. The degree of coupling influence is determined by using the retention characteristic parameters of multiple magnesium oxide coating calibration samples as input variables and the measured influence degree of the closed pore on the effective cross-sectional area of ​​the open pore channel in the calibration samples as the output variable. A mapping relationship between the retention characteristic parameters and the degree of coupling influence is established. The retention characteristic parameters of the sample to be tested are substituted into the mapping relationship to calculate the corresponding degree of coupling influence.

[0010] Furthermore, the step of determining the degree of coupling influence between closed pores and open pore permeation behavior based on the retention characteristic parameters, and using the degree of coupling influence to correct the permeation characteristic parameters, includes: Obtain the retention characteristic parameters and the permeation characteristic parameters; Establish the correspondence between retention characteristic parameters and the degree of coupling influence; The degree of coupling influence of closed pores on the permeation behavior of open pores is determined based on the correspondence, and the degree of coupling influence reflects the impact of local structural deformation caused by closed pores on the effective cross-sectional area of ​​open pore channels; The product obtained by multiplying the permeation characteristic parameter by the influence coefficient corresponding to the degree of coupling influence is used as the corrected permeation characteristic parameter.

[0011] Furthermore, the calculation of the magnesium oxide coating density based on the corrected permeation characteristic parameters includes: The corrected initial pressure drop rate of the open orifice and the steady-state pressure change of the open orifice are normalized respectively, and the values ​​obtained after normalization are used as normalized characteristic values. Establish a multiple linear regression calibration relationship between the normalized initial pressure drop rate of the open pores and the normalized steady-state pressure change of the open pores and the density of the magnesium oxide coating; The normalized initial pressure drop rate of the open pores and the normalized steady-state pressure change of the open pores in the magnesium oxide coating to be tested are substituted into the calibration relationship to obtain the values ​​as the density of the magnesium oxide coating to be tested.

[0012] Furthermore, determining the total porosity based on the density of the magnesium oxide coating includes: The total porosity is the sum of the open pore porosity and the closed pore porosity, and the difference between the value of 1 and the density of the magnesium oxide coating is taken as the total porosity.

[0013] Secondly, the present invention provides a pressure testing system for measuring the density and porosity of magnesium oxide coatings, comprising: The pressure measuring device module is used to apply a detection gas pressure to the surface of the magnesium oxide coating; The data acquisition module is used to collect pressure response data of the magnesium oxide coating during the testing process; The model building and characterization module is used to establish a gas permeation response model of the magnesium oxide coating based on the coupling relationship between the open pore permeation behavior and the closed pore retention behavior inside the magnesium oxide coating and the pressure response, and to characterize the pressure response data based on the gas permeation response model. The response separation and feature extraction module is used to perform response separation on the pressure response data based on the response feature characterization results, obtain the open pore permeation response component and the closed pore retention response component, and extract the permeation feature parameters characterizing the open pore permeation behavior and the retention feature parameters characterizing the closed pore retention behavior, respectively. The coupling correction module is used to determine the degree of coupling influence of the closed pore on the permeation behavior of the open pore based on the retention characteristic parameters, and to correct the permeation characteristic parameters using the degree of coupling influence. The density calculation module is used to calculate the density of the magnesium oxide coating based on the corrected permeation characteristic parameters. The total porosity calculation module is used to determine the total porosity based on the density of the magnesium oxide coating.

[0014] Thirdly, the present invention provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-mentioned method for measuring the density and porosity of magnesium oxide coatings by pressure.

[0015] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) This invention establishes a gas permeation response model based on the coupling relationship between the permeation behavior of open pores and the retention behavior of closed pores in the magnesium oxide coating and the pressure response. Based on the difference in the time constant between the rapid decay of open pores and the slow decay of closed pores, the pressure response data is separated to obtain the permeation response component of open pores and the retention response component of closed pores. This overcomes the technical difficulty of existing methods in distinguishing the contribution of the two types of pores to the pressure response, and provides a reliable data basis for the accurate calculation of the density and porosity of magnesium oxide coatings.

[0016] (2) The present invention determines the degree of coupling influence of closed pores on the permeation behavior of open pores based on retention characteristic parameters, and uses the degree of coupling influence to correct the permeation characteristic parameters, effectively reducing the coupling influence of closed pores on the permeation behavior of open pores, and significantly improving the accuracy and consistency of magnesium oxide coating density detection.

[0017] (3) This invention directly determines the density of the magnesium oxide coating based on the corrected permeation characteristic parameters, and determines the total porosity based on the density of the magnesium oxide coating. This enables the simultaneous acquisition of two key quality indicators, the density of the magnesium oxide coating and the total porosity, in a single pressure test. This overcomes the problem of the two indicators needing to be tested separately and the low efficiency in the prior art, and provides a reliable technical means for the rapid evaluation of the quality of magnesium oxide coatings. Attached Figure Description

[0018] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the overall process for measuring the density and porosity of magnesium oxide coating according to the present invention. Figure 2 This is a flowchart of the response separation and feature extraction process of the present invention; Figure 3 This is a flowchart of the coupling correction and magnesium oxide coating density calculation of the present invention; Figure 4 This is a schematic diagram of the structure of the magnesium oxide coating density and porosity pressure testing system of the present invention. Detailed Implementation

[0019] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, all terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention pertains. It should be understood that the term "comprising" as used in the specification and drawings of the present invention means the presence of the stated features, steps, operations and / or components, but does not exclude the presence or addition of one or more other features, steps, operations, components and / or combinations thereof.

[0020] Example 1 Please see Figure 1 , Figure 1 This is a schematic diagram of the overall process of the magnesium oxide coating density and porosity pressure testing method provided in this embodiment of the invention, which specifically includes the following steps: S1. Apply a detection pressure to the surface of the magnesium oxide coating using a pressure measuring device, and collect the pressure response data of the magnesium oxide coating during the detection process; In this embodiment, the pressure measuring device includes a sealed detection chamber, a gas supply unit, a pressure sensor, and a data acquisition unit. The sealed detection chamber is used to cover the surface of the magnesium oxide coating to be tested, forming a relatively closed detection space. The gas supply unit is used to fill the sealed detection chamber with detection gas. The pressure sensor is used to detect the pressure change in the sealed detection chamber in real time. The data acquisition unit is used to collect the pressure signal output by the pressure sensor and generate pressure response data. The preset detection pressure is determined based on the maximum non-destructive testing pressure that the magnesium oxide coating can withstand. Specifically, this includes: obtaining the thickness, compressive strength, and elastic modulus of the magnesium oxide coating; calculating the allowable detection pressure based on the stress state of the magnesium oxide coating under the detection pressure; and taking 80% to 90% of the allowable detection pressure as the preset detection pressure to ensure that the detection gas can enter the open hole without damaging the magnesium oxide coating structure.

[0021] Specifically, the silicon steel sample to be tested is fixed on the testing platform, with the magnesium oxide coating facing the sealed testing chamber. Then, the sealed testing chamber is controlled to adhere to the surface of the magnesium oxide coating to form a sealed testing space. Testing gas is then introduced into the sealed testing chamber through the gas supply unit until the pressure in the testing chamber reaches the preset testing pressure.

[0022] During the testing process, the pressure sensor continuously collects the pressure value inside the sealed testing chamber according to a fixed sampling period and records the corresponding sampling time. The sampling period is determined based on the time constant of the rapid permeation response of the open hole. Before the formal testing, the magnitude of this time constant is roughly measured through a pre-experiment, and the sampling period is set to less than 1 / 10 of this time constant to ensure that the signal characteristics of the rapid decay process can be completely collected. When effective rough measurement results cannot be obtained in the pre-experiment, the highest sampling rate of the pressure sensor is used as the default sampling period. The continuously collected pressure values ​​are arranged in time sequence to form a pressure-time response curve, which reflects the entire process of the pressure change of the sealed testing chamber with time during the entry of the detection gas into the magnesium oxide coating.

[0023] To eliminate the influence of pressure sensor noise and gas source fluctuations on the detection results, the pressure-time response curve is digitally filtered. A low-pass filter is used, with the cutoff frequency determined based on the pressure sensor's response bandwidth and sampling frequency. According to the Nyquist sampling theorem, half the sampling frequency is the highest frequency at which the signal can be reconstructed. However, the effective components of the pressure response signal are mainly concentrated in the low-frequency band, and its energy percentage decreases sharply with increasing frequency. Based on the analysis of the pressure response signal power spectrum, more than 95% of the signal energy is concentrated in the frequency band below 1 / 5 of the sampling frequency. Therefore, setting the cutoff frequency to 1 / 5 of the sampling frequency can filter out high-frequency noise while retaining more than 95% of the effective signal energy. When the pressure sensor's response bandwidth is lower than 1 / 5 of the sampling frequency, the sensor's response bandwidth is used as the cutoff frequency to avoid introducing invalid signals exceeding the sensor's response capability. For cases where abnormal jump points still exist after filtering, median filtering is used for secondary processing, replacing the value of the current point with the median of the two sampling points before and after it. The filtered pressure-time response curve is then used as pressure response data input for subsequent steps in constructing the gas permeation response model.

[0024] S2. Based on the coupling relationship between the open pore permeation behavior and the closed pore retention behavior inside the magnesium oxide coating and the pressure response, a gas permeation response model of the magnesium oxide coating is established, and the pressure response data is characterized based on the gas permeation response model. In this embodiment, the coupling relationship between open-pore permeation behavior and closed-pore retention behavior in the pressure response refers to the following: open pores act as permeation channels for the detection gas to enter the coating, and the pressure inside the coating decreases rapidly when the gas permeates along the open pores; closed pores, as non-connected pores, hinder the entry of the detection gas, and the pressure inside the coating decreases slowly when the gas accumulates and compresses at the closed pores; local structural deformation in the area where the closed pores are located (including local compression deformation of the skeleton around the closed pores under the action of the detection gas pressure, and changes in the effective pore diameter of the open pore channels in the adjacent closed pore areas) will change the effective cross-sectional area of ​​the open pore channels, so that the permeation response of the open pores is indirectly affected by the retention behavior of the closed pores, and the two are superimposed to form the overall pressure response.

[0025] Specifically, based on the above coupling relationship, the pressure response process is divided into open-pore rapid permeation response and closed-pore slow retention response. The open-pore response corresponds to the rapid transport process of the detection gas in the connected pores, while the closed-pore response corresponds to the slow decay process of the detection gas near the non-connected pores. The two types of responses together constitute the complete pressure response.

[0026] Furthermore, to simultaneously describe the coupled process of rapid decay in open pores and slow decay in closed pores, a bi-exponential pressure decay model is used to establish a gas permeation response model for the magnesium oxide coating. The overall pressure response is expressed as: Where P(t) represents the pressure in the chamber at time t. Indicates steady-state pressure. Indicates the open hole response coefficient. Indicates the open orifice response time constant. Indicates the closed-hole response coefficient. This represents the closed-pore response time constant; the overall pressure response is determined by the open-pore permeation response term. With closed-pore retention response term It is composed of superposition.

[0027] Since the gas transmission velocity inside the open orifice is significantly faster than the gas pressure decay rate near the closed orifice, it satisfies... When the fitting process occurs When the open-hole response term and the closed-hole response term are exchanged, the two time constants and their corresponding response coefficients are reordered so that the smaller time constant corresponds to the open-hole response term and the larger time constant corresponds to the closed-hole response term. When the difference between the two fitted time constants is less than 10% of the smaller of the two time constants, they are considered to be approximately equal, and the model is degenerated into a single exponential model for processing to ensure that the physical meaning of the model remains consistent. The 10% threshold is determined based on the measurement accuracy of the pressure sensor and the numerical stability of the fitting algorithm. This ratio can effectively identify the situation where the time constants converge, and will not mistakenly degenerate the separable double exponential model into a single exponential model due to an excessively large threshold.

[0028] The pressure response data obtained above were input into the aforementioned double exponential pressure decay model. A nonlinear least squares fitting algorithm was used to fit the parameters of the pressure response data. The fitting objective was to minimize the sum of squared residuals between the measured pressure values ​​and the model calculated values. Specifically, the Levenberg-Marquardt algorithm was used for iterative solution. The initial values ​​for iteration were set in the following manner and based on the following: The average value of each sampling point in the last 20% interval of the pressure response curve is taken. Since the pressure change in the last segment has tended to stabilize, its average value can be used as a reasonable estimate of the steady-state pressure. Take initial pressure and 80% of the difference Take initial pressure and The difference of 20% is because in actual testing, the open orifice contributes 70% to 90% to the pressure decay, while the closed orifice contributes 10% to 30%. Allocating 80% to the initial value of the open orifice response coefficient and 20% to the initial value of the closed orifice response coefficient allows the algorithm to search for the optimal solution within a reasonable range. The characteristic time corresponding to the time required for the pressure response curve to drop to 1 / e of its initial amplitude from the initial moment is taken. The characteristic time from the end of the first part to the point where the curve tends to stabilize is taken from the middle and later part of the pressure response curve. The former reflects the time scale of rapid permeation in open pores, while the latter reflects the time scale of slow retention in closed pores.

[0029] The iteration terminates when the number of iterations exceeds the maximum number of iterations or the sum of squared residuals is less than the convergence tolerance. The maximum number of iterations is set to 1000, which is sufficient to ensure convergence in most cases while avoiding infinite loops. The convergence tolerance is determined based on the measurement accuracy of the pressure sensor, and is set to 0.1% of the sensor's full scale. This threshold is on the same order of magnitude as the sensor's quantization error, ensuring that the fitting accuracy matches the measurement accuracy. If the fitting algorithm fails to converge, the initial value is randomly perturbed within a reasonable range and the iteration is repeated up to 3 times. If convergence is still not achieved, the measurement is deemed invalid and a prompt to re-acquire data is displayed.

[0030] According to the first time constant With the second time constant The numerical differences yielded the open-pore response coefficients. Open hole response time constant Closed-pore response coefficient and closed-hole response time constant The four parameters mentioned above, along with their corresponding bi-exponential model expressions, together constitute the response characteristic representation of the pressure response data. and The numerical difference is the physical basis for subsequent response separation operations. and The amplitude and velocity characteristics of the open-pore permeation response are described. and The amplitude and velocity characteristics of the closed-pore retention response are described; based on the double-exponential model expression, at the initial time t=0, the open-pore permeability response term... The value is Closed-pore retention response term The value is ,Right now and These correspond to the amplitudes of the two types of pore responses at the initial moment; the response characteristic characterization results are input into the subsequent response separation step as the parameter basis for distinguishing between open pore responses and closed pore responses.

[0031] S3. Based on the response characteristic characterization results, and according to the difference in time constant between the rapid decay of open pores and the slow decay of closed pores, the pressure response data is separated to obtain the open pore permeation response component and the closed pore retention response component, and the permeation characteristic parameters characterizing the open pore permeation behavior and the retention characteristic parameters characterizing the closed pore retention behavior are extracted respectively. Please see Figure 2 , Figure 2 This is a flowchart of the response separation and feature extraction process of the present invention; specifically, it reads the response feature characterization results, including the double exponential pressure decay model and the open pore response coefficient. Open hole response time constant Closed-pore response coefficient and the closed-hole response time constant The open-pore permeability response term in the double-exponential pressure decay model. With closed-pore retention response term The pressure variation patterns contributed by each pore were described, but not yet independently separated from the measured superimposed data. This step uses a decoupling operation to transform these two components into open-pore permeation response components and closed-pore retention response components with clear numerical correspondences. Because open pores connect to the outside, the detected gas can permeate rapidly, thus corresponding to a smaller time constant. Closed pores cannot be directly connected to the outside world; they can only transmit pressure slowly through the surrounding material. Therefore, closed pores correspond to a relatively large time constant. . use Less than The timescale differences reflected are used as the basis for response separation to decouple the overall pressure response, obtaining the open-pore permeability response component and the closed-pore retention response component. Decoupling means splitting the superimposed signal into two independent exponential decay processes according to their respective time constants. The decoupled open-pore permeability response component is expressed as follows: The closed-pore retention response component is expressed as Both satisfy ,in The steady-state pressure constant term of the overall response does not contribute to any single component, thereby achieving the separation of the overall pressure response into open-pore and closed-pore responses.

[0032] when and When the difference is less than the time constant separation threshold, it indicates that there is a large overlap between the open-hole response and the closed-hole response, which does not meet the decoupling condition. Therefore, it indicates that the measurement data is not suitable for double exponential separation and terminates the current detection process. The time constant separation threshold is determined based on the sampling frequency of the pressure sensor. According to the Nyquist sampling theorem, the sampling frequency must be at least twice the highest frequency of the signal, that is, at least two sampling points are required. To ensure sufficient signal reconstruction accuracy, three sampling points are taken as the minimum requirement. When the sampling frequency is 100Hz, the sampling interval is 10ms, and the three sampling periods correspond to 30ms. This value is used as the time constant separation threshold.

[0033] The initial pressure drop rate and steady-state pressure change of the open orifice are calculated based on the open orifice permeability response components as permeability characteristic parameters. The initial pressure drop rate is the slope of the tangent line to the open orifice response curve at the initial moment, obtained by least-squares linear fitting of the first five sampling points of the open orifice response curve. The steady-state pressure change is taken as the pressure value at the initial moment of the open orifice response component (this value is the open orifice response coefficient in the aforementioned response characteristic characterization results). The stable pressure value is the difference between the open-pore permeation response component (at t=0) and the steady-state pressure value. The steady-state pressure value is the pressure value at the end of a time interval after the rate of pressure change in adjacent time intervals of the response curve has been continuously less than 5% of the maximum rate of change. This 5% threshold is determined based on the resolution of the pressure sensor and the measurement noise level. When the pressure change is below this threshold, the sensor noise is on the same order of magnitude and can be considered to have stabilized. When the above-mentioned criteria for determining the steady-state pressure value cannot be met within the entire fitting time window, the pressure value at the end of the fitting time window is taken as the steady-state pressure value. The fitting time window is the time range required from the initial moment to the pressure response curve decaying to 5% of the initial pressure value. This range covers the main decay process of the pressure response, and the end pressure value is used as an estimate of the steady-state pressure value.

[0034] The closed-hole pressure retention amount and closed-hole pressure recovery rate are calculated based on the closed-hole retention response components as retention characteristic parameters. The closed-hole pressure retention amount is taken as the pressure value at the initial moment of the closed-hole response component (this value is the closed-hole response coefficient in the aforementioned response characteristic characterization results). The pressure recovery rate is the difference between the amplitude of the closed-pore retention response component at t=0 and the steady-state pressure value. The closed-pore pressure recovery rate is the ratio of the steady-state pressure value of the closed-pore response component to the initial pressure value. When the initial pressure value is less than the pressure sensor resolution, the closed-pore response is deemed nonexistent, and the closed-pore pressure recovery rate is set to zero. These permeability and retention characteristic parameters are input into the subsequent coupling correction step as input data for calculating the degree of coupling influence and correcting the permeability characteristic parameters.

[0035] S4. Determine the degree of coupling influence of closed pores on the permeation behavior of open pores based on the retention characteristic parameters, and use the degree of coupling influence to correct the permeation characteristic parameters; Please see Figure 3 , Figure 3 This is a flowchart of the coupling correction and magnesium oxide coating density calculation of the present invention. In this step, the retention characteristic parameters and permeation characteristic parameters obtained in the previous steps are read. It should be noted that the retention characteristic parameters extracted in the previous steps describe the pressure response behavior of the closed pore itself, while this step needs to convert them into the degree of coupling influence of the closed pore on the permeation behavior of the open pore. This conversion is achieved by establishing a correspondence between the retention characteristic parameters and the degree of coupling influence.

[0036] The correspondence between retention characteristic parameters and the degree of coupling influence is established as follows: Multiple magnesium oxide coating calibration samples are used to obtain the retention characteristic parameters of each sample. At the same time, the measured influence of closed pores on the effective cross-sectional area of ​​open pore channels in each sample is obtained through microstructural characterization methods (such as scanning electron microscopy combined with image analysis). This measured influence is used as the benchmark value of the degree of coupling influence. With the retention characteristic parameters as input variables and the benchmark value of the degree of coupling influence as output variables, the least squares method is used for linear regression fitting to obtain the mapping relationship between the retention characteristic parameters and the degree of coupling influence. When the number of calibration samples is less than 3 groups, an effective mapping relationship cannot be established, and additional calibration samples are required to bring the total to no less than 3 groups. When the number of calibration samples is 3 groups, linear interpolation is used to establish a piecewise mapping relationship. When the number of calibration samples is greater than 3 groups, least squares linear regression fitting is used.

[0037] Based on the above correspondence, the retention characteristic parameters of the sample to be tested are substituted into the mapping relationship to calculate the corresponding coupling influence degree. This coupling influence degree reflects the impact of local structural deformation caused by the closed hole on the effective cross-sectional area of ​​the open hole channel. The coupling influence degree is expressed in the form of an influence coefficient, which is a value greater than 0. The influence coefficient is calculated as follows: the maximum and minimum values ​​of the mapping relationship output value in the calibration sample are used as boundaries to linearly map the mapping relationship output value of the sample to be tested to the interval between 0 and 1. When the mapping relationship output value exceeds the range of the calibration sample, the maximum and minimum values ​​of the mapping relationship output value in the calibration sample are used as boundaries for truncation.

[0038] The permeability characteristic parameters are corrected using the aforementioned coupling effect. The correction method is as follows: the initial pressure drop rate and steady-state pressure change of the open pores in the permeability characteristic parameters are multiplied by an influence coefficient, and the product is used as the corrected permeability characteristic parameter. To ensure that the influence coefficient reflects the two opposite directions of weakening and strengthening, the linearly mapped value to the 0-1 interval is shifted, changing the center of the mapping interval from 0.5 to 1, so that the influence coefficient is distributed between 0.5 and 1.5 with 1 as the center of symmetry. When the influence coefficient is less than 1, the permeability characteristic parameter is weakened, indicating that the closure of the pore leads to a decrease in the effective cross-sectional area of ​​the open pore channel and a decrease in the permeability of the open pore. When the influence coefficient is greater than 1, the permeability characteristic parameter is strengthened, indicating that the closure of the pore leads to an increase in the effective cross-sectional area of ​​the open pore channel and an increase in the permeability of the open pore. When the influence coefficient equals 1, the permeability characteristic parameter remains unchanged. The corrected permeability characteristic parameters are then input into the subsequent magnesium oxide coating density calculation step as input data for the magnesium oxide coating density calculation.

[0039] S5. Calculate the density of the magnesium oxide coating based on the corrected penetration characteristic parameters; Specifically, the permeability characteristic parameters obtained in the aforementioned steps are read, including the initial pressure drop rate of the open pore and the steady-state pressure change of the open pore. To eliminate the influence of differences in the dimensions and numerical ranges of different characteristic parameters on the fusion calculation results, each permeability characteristic parameter is normalized so that each normalized characteristic value is mapped to the interval between 0 and 1. The normalization adopts a linear normalization method, using the maximum and minimum values ​​of the characteristic parameter in multiple magnesium oxide coating calibration samples as boundaries. The normalization formula is: ,in These are the feature parameter values ​​of the sample to be tested. and These are the maximum and minimum values ​​of the feature parameter in the calibration samples, respectively. The value is the normalized feature value. When the maximum and minimum values ​​of the feature parameter are equal, it means that the feature is not different in all the calibrated samples, and the corresponding normalized feature value is directly set to 1.

[0040] A calibration relationship was established between the corrected permeability characteristic parameters and the density of the magnesium oxide coating. Using the same set of magnesium oxide coating calibration samples as in S4, the normalized initial pressure drop rate and normalized steady-state pressure change of the open pores were used as input variables, and the actual magnesium oxide coating density measured by the benchmark method was used as the output variable. Least squares multivariate linear regression was employed to fit the calibration relationship. After fitting, the coefficient of determination was calculated to evaluate the accuracy of the calibration relationship. The coefficient of determination was calculated as follows: the coefficient of determination equals 1 minus the ratio of the sum of squares of the residuals to the sum of squares of the total deviations. The sum of squares of the residuals is the sum of squares of the differences between the actual magnesium oxide coating density of each calibration sample and the predicted value of the fitted curve; the sum of squares of the total deviations is the sum of squares of the differences between the actual magnesium oxide coating density of each calibration sample and the average actual magnesium oxide coating density. The closer the coefficient of determination is to 1, the higher the explanatory power of the calibration relationship on the data. When the coefficient of determination reaches 0.90 or higher, the accuracy of the calibration relationship is considered to meet the requirements; when the coefficient of determination is greater than or equal to 0 and less than 1, the accuracy is considered to meet the requirements. A coefficient of determination of 0.90 indicates insufficient accuracy in the calibration relationship. The fitting and coefficient of determination evaluation process needs to be repeated after increasing the number of calibration samples. The threshold of 0.90 is based on the following: a coefficient of determination of 0.90 or higher means that the calibration relationship can explain more than 90% of the data variation, with the remaining less than 10% attributed to measurement noise and individual sample differences. This threshold aligns with the general principle in engineering practice of controlling measurement errors within 10%. A coefficient of determination below 0 indicates that the fitted curve's predictive performance is inferior to directly averaging the data, and the calibration relationship is completely invalid. The calibration data needs to be re-examined or the fitting model replaced. When the coefficient of determination reaches 0.90 or higher, the accuracy of the calibration relationship meets the requirements. The normalized initial pressure drop rate and the normalized steady-state pressure change of the open pores are substituted into the calibration relationship, and the corresponding magnesium oxide coating density value is calculated using a multiple linear regression equation. This magnesium oxide coating density is calculated based on the open pore permeability characteristics. This magnesium oxide coating density is then input into the subsequent total porosity calculation step as input data for calculating the total porosity.

[0041] S6. Determine the total porosity based on the density of the magnesium oxide coating.

[0042] In this step, the density of the magnesium oxide coating calculated in the previous steps is read. Total porosity is the sum of open-pore porosity and closed-pore porosity, and its physical meaning is the proportion of the total volume of all pores in the magnesium oxide coating to the total volume of the coating. The density of the magnesium oxide coating is the proportion of the volume of solid matter in the coating to the total volume of the coating; the sum of the two is equal to 1. Therefore, total porosity equals 1 minus the density of the magnesium oxide coating. Substituting the density of the magnesium oxide coating obtained in the previous steps into this formula, the total porosity is calculated. When the density of the magnesium oxide coating is less than 0 or greater than 1, it indicates an error in the calculation process. In this case, the measurement result is deemed invalid and a retest is prompted. When the density of the magnesium oxide coating is within the range of 0 to 1, the total porosity is calculated as 1 minus the density of the magnesium oxide coating, and the calculated total porosity is output as the final test result.

[0043] Example 2 Please see Figure 4 , Figure 4 This is a schematic diagram of the structure of the magnesium oxide coating density and porosity pressure testing system provided in an embodiment of the present invention. The magnesium oxide coating density and porosity pressure testing system includes a pressure testing device module, a data acquisition module, a model construction and characterization module, a response separation and feature extraction module, a coupling correction module, a density calculation module, and a total porosity calculation module.

[0044] The pressure measuring device module is used to apply a detection gas pressure to the surface of the magnesium oxide coating. Its specific implementation method corresponds to the pressure measuring device setting method and detection gas pressure application method in step S1 of Example 1, and will not be described again here.

[0045] The data acquisition module is used to collect the pressure response data of the magnesium oxide coating during the detection process. Its specific implementation method corresponds to the pressure response data acquisition and filtering method in step S1 of Example 1, and will not be described again here.

[0046] The model construction and characterization module is used to establish a gas permeation response model of the magnesium oxide coating based on the coupling relationship between the open pore permeation behavior and the closed pore retention behavior inside the magnesium oxide coating and the pressure response. Based on the gas permeation response model, the pressure response data is characterized by response features. The specific implementation method corresponds to the coupling relationship definition, double exponential model establishment, parameter fitting and response feature characterization method in step S2 of Example 1, and will not be repeated here.

[0047] The response separation and feature extraction module is used to separate the pressure response data based on the response feature characterization results, obtain the open pore permeation response component and the closed pore retention response component, and extract the permeation feature parameters characterizing the open pore permeation behavior and the retention feature parameters characterizing the closed pore retention behavior, respectively. Its specific implementation method corresponds to the decoupling separation and feature parameter extraction method in step S3 of Example 1, and will not be described again here.

[0048] The coupling correction module is used to determine the degree of coupling influence of the closed pore on the permeation behavior of the open pore based on the retention characteristic parameters, and to correct the permeation characteristic parameters using the degree of coupling influence. Its specific implementation method corresponds to the mapping relationship establishment, coupling influence determination and permeation characteristic parameter correction method in step S4 of Example 1, and will not be described again here.

[0049] The density calculation module is used to calculate the density of the magnesium oxide coating based on the corrected penetration characteristic parameters. Its specific implementation method corresponds to the normalization process, calibration relationship establishment and substitution calculation method in step S5 of Example 1.

[0050] The total porosity calculation module is used to determine the total porosity based on the density of the magnesium oxide coating. Its specific implementation method corresponds to the total porosity calculation method in step S6 of Example 1, and will not be repeated here.

[0051] Example 3 This embodiment provides an electronic device, including a processor and a memory. The memory stores a computer program, and when the processor executes the computer program, it implements the magnesium oxide coating density and porosity pressure measurement method as described in Embodiment 1.

[0052] Specifically, the electronic device can be an industrial computer or an embedded industrial control computer with the following hardware configuration: an Intel Core i7-10700 CPU (8 cores and 16 threads), 16GB DDR4 memory, a Windows 10 IoT Enterprise operating system, an NI data acquisition card for data acquisition, and signal processing algorithms implemented based on Python 3.8. The electronic device connects to the pressure sensor of the pressure measuring device via a wired network or serial communication, and after receiving the pressure response data, it performs data preprocessing, gas permeation response model construction, response separation and feature extraction, coupling correction, and calculation of magnesium oxide coating density and total porosity.

[0053] This embodiment also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the above-described method for measuring the density and porosity of magnesium oxide coatings. The computer-readable storage medium can be any tangible medium containing or storing a program, such as a read-only memory, random access memory, disk, optical disk, USB flash drive, solid-state drive, etc.

[0054] The above description is merely a specific embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring the density and porosity of magnesium oxide coatings under pressure, characterized in that, Includes the following steps: A pressure measuring device was used to apply a detection pressure to the surface of the magnesium oxide coating, and pressure response data of the magnesium oxide coating were collected during the detection process. Based on the coupling relationship between the open pore permeation behavior and the closed pore retention behavior of the magnesium oxide coating and the pressure response, a gas permeation response model of the magnesium oxide coating is established, and the pressure response data are characterized based on the gas permeation response model. Based on the response characteristic characterization results, and according to the difference in time constant between the rapid decay of open pores and the slow decay of closed pores, the pressure response data is separated to obtain the open pore permeation response component and the closed pore retention response component, and the permeation characteristic parameters characterizing the open pore permeation behavior and the retention characteristic parameters characterizing the closed pore retention behavior are extracted respectively. The degree of coupling influence of closed pores on the permeation behavior of open pores is determined based on the retention characteristic parameters, and the permeation characteristic parameters are corrected using the degree of coupling influence. The density of the magnesium oxide coating was calculated based on the corrected permeation characteristic parameters; The total porosity was determined based on the density of the magnesium oxide coating. The process of establishing a gas permeation response model for the magnesium oxide coating and characterizing the pressure response data based on the gas permeation response model includes: Based on the coupling effect of open-pore permeation behavior and closed-pore retention behavior on pressure response, the pressure response process is divided into open-pore rapid permeation response and closed-pore slow retention response. A double exponential pressure decay model is used to describe the overall pressure response. The double exponential pressure decay model contains two exponential decay terms with different time constants: the first time constant corresponds to the rapid permeation response of open pores and the second time constant corresponds to the slow retention response of closed pores. The overall pressure response is composed of the superposition of the open pore permeation response term and the closed pore retention response term to establish a gas permeation response model for magnesium oxide coating. The gas permeation response model outputs the first time constant and the second time constant. The pressure response data were fitted using a nonlinear least squares fitting algorithm. Based on the numerical difference between the first time constant and the second time constant, the open orifice response coefficient, the open orifice response time constant, the closed orifice response coefficient, and the closed orifice response time constant were obtained respectively. The pressure response data are characterized based on the open orifice response coefficient, open orifice response time constant, closed orifice response coefficient, and closed orifice response time constant. The process of separating the pressure response data and extracting permeability and retention characteristic parameters includes: Based on the response characteristic characterization results, obtain the response curves corresponding to the fast response term of the open orifice and the slow response term of the closed orifice. The first and second time constants in the gas permeation response model are obtained, and the open-pore fast response term and the closed-pore slow response term are decoupled based on the difference between the first and second time constants on the time scale, so as to obtain the open-pore permeation response component and the closed-pore retention response component respectively. The initial pressure drop rate and steady-state pressure change of the open orifice are calculated based on the open orifice permeation response components and used as permeation characteristic parameters. The closed-hole pressure retention amount and closed-hole pressure recovery rate are calculated based on the closed-hole retention response components and used as retention characteristic parameters. The determination of the degree of coupling influence of closed pores on the permeation behavior of open pores includes: constructing a magnesium oxide coating calibration sample, using the retention characteristic parameters of the magnesium oxide coating calibration sample as input variables, using the measured influence degree of closed pores on the effective cross-sectional area of ​​open pore channels in the magnesium oxide coating calibration sample as output variables, establishing a mapping relationship between retention characteristic parameters and the degree of coupling influence, substituting the retention characteristic parameters of the sample to be tested into the mapping relationship, and calculating the corresponding degree of coupling influence; The process of determining the degree of coupling influence of closed pores on open pore permeation behavior based on retention characteristic parameters, and then using this degree of coupling influence to correct the permeation characteristic parameters, includes: Obtain retention and permeation characteristic parameters; Establish the correspondence between retention characteristic parameters and the degree of coupling influence; The degree of coupling influence of closed pores on the permeation behavior of open pores is determined based on the correspondence. The degree of coupling influence reflects the impact of local structural deformation caused by closed pores on the effective cross-sectional area of ​​open pore channels. The product of the permeability characteristic parameter and the influence coefficient corresponding to the degree of coupling effect is used as the corrected permeability characteristic parameter. The calculation of the magnesium oxide coating density based on the corrected permeation characteristic parameters includes: The corrected initial pressure drop rate and steady-state pressure change of the open orifice were normalized, and the values ​​obtained after normalization were used as normalized characteristic values. Establish a multiple linear regression calibration relationship between the normalized initial pressure drop rate of the open pores and the normalized steady-state pressure change of the open pores and the density of the magnesium oxide coating; The normalized initial pressure drop rate of the open pores and the normalized steady-state pressure change of the open pores in the magnesium oxide coating to be tested are substituted into the multivariate linear regression calibration relationship to obtain the values ​​as the magnesium oxide coating density. The determination of total porosity based on the density of the magnesium oxide coating includes: The total porosity is the sum of the open pore porosity and the closed pore porosity. The total porosity is the difference between the value of 1 and the density of the magnesium oxide coating.

2. A pressure testing system for measuring the density and porosity of magnesium oxide coatings, used to implement the method described in claim 1, characterized in that, include: The pressure measuring device module is used to apply a detection gas pressure to the surface of the magnesium oxide coating; The data acquisition module is used to collect pressure response data of the magnesium oxide coating during the testing process; The model building and characterization module is used to establish a gas permeation response model of the magnesium oxide coating based on the coupling relationship between the open pore permeation behavior and the closed pore retention behavior inside the magnesium oxide coating and the pressure response, and to characterize the response features of the pressure response data based on the gas permeation response model. The response separation and feature extraction module is used to separate the pressure response data based on the response feature characterization results, obtain the open pore permeation response component and the closed pore retention response component, and extract the permeation feature parameters characterizing the open pore permeation behavior and the retention feature parameters characterizing the closed pore retention behavior, respectively. The coupling correction module is used to determine the degree of coupling influence of closed pores on the permeation behavior of open pores based on the retention characteristic parameters, and to correct the permeation characteristic parameters using the degree of coupling influence. The density calculation module is used to calculate the density of the magnesium oxide coating based on the corrected permeation characteristic parameters. The total porosity calculation module is used to determine the total porosity based on the density of the magnesium oxide coating.

3. An electronic device comprising a processor and a memory, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the pressure measurement and detection method for the density and porosity of magnesium oxide coating as described in claim 1.

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