A method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation

Abstract

This invention discloses a method for predicting the lifetime of organic coatings by jointly modeling the pre-change-point distribution and random degradation, belonging to the field of organic coating monitoring technology. The method includes the following steps: preprocessing and stage identification of coating electrochemical impedance data; first-stage pre-change-point distribution modeling; second-stage random degradation modeling; combined two-stage lifetime distribution modeling; and coating reliability assessment. This invention, employing the above-mentioned method for predicting the lifetime of organic coatings by jointly modeling the pre-change-point distribution and random degradation, solves the problems of distinguishing the stage characteristics of the organic coating degradation process, describing the randomness of the degradation amount, and quantitatively assessing the reliability of organic coatings under actual working conditions. This method is scientifically effective, easy to operate, and has broad application value.

Description

Technical Field

[0001] This invention relates to the field of organic coating monitoring technology, and in particular to a method for predicting the lifetime of organic coatings by jointly modeling the distribution before change point and random degradation. Background Technology

[0002] When organic coatings are exposed to seawater corrosion for extended periods, their corrosion resistance decreases due to factors such as temperature, salinity, and ultraviolet radiation. Degradation phenomena such as blistering, cracking, and peeling occur, rendering the coatings ineffective at blocking seawater and weakening their protective ability against the metal substrate. Among these factors: increased temperature accelerates seawater convection and diffusion, increases seawater conductivity, and speeds up the anodic and cathodic reactions in the electrochemical corrosion process, thus increasing the corrosion rate; regarding salinity, as salinity increases within a certain range, the concentration of chloride ions in seawater increases, increasing conductivity and accelerating the movement of ions and electrons, thereby accelerating the electrochemical corrosion reaction; ultraviolet radiation provides high radiation energy, causing photochemical reactions in organic polymers, leading to the loss of stable polymer structures and photodegradation. To reduce the degree of seawater corrosion on the metal materials of ships in near-shore fully submerged areas, organic coatings are the first line of defense, and their performance degradation directly affects the overall reliability and service life of the ship.

[0003] Currently, various methods exist both domestically and internationally for evaluating the corrosion resistance of organic coatings, such as measuring physical properties like gloss, gloss loss rate, and color difference, as well as observing coating damage morphology. In recent years, methods for evaluating the performance of organic coatings based on electrochemical principles have developed rapidly. Among these, electrochemical impedance spectroscopy (EIS) has become the main electrochemical method for evaluating the corrosion resistance of organic coatings due to its advantages of minimal interference with the organic coating-metal system, readily available experimental results, and sufficient information acquisition. Low-frequency impedance modulus is one of the electrochemical characteristic parameters of coatings that EIS focuses on, with well-established evaluation standards and corresponding models describing the changes in low-frequency impedance modulus during coating degradation. However, existing models rarely consider the stage characteristics of the coating degradation process and the randomness of the degradation amount, and also fail to address the reliability of organic coatings. Further improvements are urgently needed to more accurately reflect the degradation process of organic coatings.

[0004] Based on the above ideas, this invention provides an organic coating lifetime prediction method that uses joint modeling of pre-variable point distribution and random degradation. It selects the low-frequency impedance modulus as an indicator to evaluate the anti-corrosion performance of the coating and constructs a two-stage degradation model of the coating that considers environmental effects. This allows for reliability assessment and reliable lifetime prediction of the coating, effectively solving the problems of describing the stage characteristics and randomness of the degradation process, as well as assessing the reliability of the coating. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the lifetime of organic coatings by jointly modeling the pre-degradation distribution and random degradation. This method addresses the problems of existing coating degradation models based on low-frequency impedance modulus values, which do not adequately consider the stage characteristics and randomness of degradation, and pay little attention to the reliability of the coating. By performing preliminary processing, stage division, and separate modeling of the low-frequency impedance modulus data of epoxy acrylic coatings, the lifetime distribution of the coating is obtained, and the reliability assessment of the coating under different ultraviolet irradiation intensities is finally achieved.

[0006] To achieve the above objectives, this invention provides a method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation, comprising the following steps:

[0007] Step S1, coating electrochemical impedance data preprocessing and stage identification, specifically includes:

[0008] Step S11: Standardize the coating electrochemical impedance data;

[0009] Step S12: Identify the failure stage;

[0010] Step S13: Use the moving median method to remove outliers;

[0011] Step S2: First-stage distribution modeling before the point change;

[0012] Step S3: Second-stage stochastic degradation modeling;

[0013] Step S4: Two-stage combined lifetime distribution modeling;

[0014] Step S5: Conduct a coating reliability assessment.

[0015] Preferably, step S11 specifically includes:

[0016] The directly measured low-frequency impedance modulus data of the coating |Z| 初 Multiplied by the effective area of ​​the coating (cm) 2 The corresponding value is obtained in Ω·cm 2 The standard impedance modulus |Z| is expressed in units of 标 ;

[0017] Let the diameter of the bottom surface of the sample be d, then |Z| 初 With |Z| 标 The conversion relationship is as follows:

[0018]

[0019] The standard impedance modulus data |Z| 标 Taking the natural logarithm, we obtain the logarithmic impedance magnitude data ln|Z| 标 .

[0020] Preferably, in step S12, the maximum likelihood change point detection method is used to divide the process into a first stage and a second stage. The initial immersion stage of the coating system is classified as the first stage, which is the stage where the impedance modulus remains basically unchanged in the early stage of the test. The middle stage and the later stage are classified as the second stage, which is the stage where the impedance modulus decreases.

[0021] Preferably, the steps of the moving median method in step S13 are as follows:

[0022] The data sequence after removing outliers is y1, y2, ..., y n Let n0 be the range for outlier detection (n0 is odd and n0≤n), and let median(A) be the median of all elements in set A. For data y i ,if Among these n0 data points, any data y j The data should be removed if the following condition is met:

[0023] |y j -median(Y i )|≥-3c·median(|Y i -median(Y i )|);

[0024] In the formula, Y i -median(Y i (Refers to set Y) i The difference between each element and the median is calculated, with parameter c ≈ -0.4769;

[0025] An outlier value ln|Z| in logarithmic impedance data i After being removed, it is replaced with the average of the two logarithmic impedance data:

[0026]

[0027] The corresponding standard impedance data without taking the logarithm is as follows:

[0028]

[0029] Preferably, step S2 includes the following specific steps:

[0030] Assuming the end time of the first stage follows an exponential distribution, the failure distribution function and probability density function are:

[0031]

[0032] In the formula, θ is the parameter of the exponential distribution, which represents the mean of the lifetime, and here it represents the mean of the end time of the first stage, and t represents time.

[0033] n0 samples under the same environmental conditions, until the end of the test at time t s So far, a total of r0 samples have entered the second stage, while the first stage for n0-r0 samples is still ongoing; the times when r0 samples entered the second stage are t... (1) ≤t (2) ≤…≤t (r) ≤t s Then the maximum likelihood estimate of the parameter θ is:

[0034]

[0035] At the same time, the maximum likelihood estimate of the failure rate λ is obtained as follows:

[0036]

[0037] Different groups of samples The value is linked to the ultraviolet irradiance level, establishing the ultraviolet irradiance S UV Model of the impact of exponential distribution failure rate λ:

[0038] 10 4 λ=pS UV +q;

[0039] In the formula, p and q are the parameters of the regression line, and p > 0. The estimated value is obtained by least squares estimation. and

[0040] Preferably, in step S3, the second-stage coating degradation model is established as shown in the following equation:

[0041] X(t)=aS UV g ·t r +σB(t r );

[0042] In the formula, a and g are the parameters to be estimated, and S UV X(t) represents the ultraviolet radiation intensity, X(t) represents the product degradation path as a function of time t, B(·) is the standard Brownian motion, and the diffusion parameter σ reflects the fluctuation of performance degradation.

[0043] Preferably, step S4 includes the following specific steps:

[0044] The coating lifetime T is the sum of the first arrival time of the coating's low-frequency impedance modulus failure, the end time of the first stage, and the first arrival time of the second stage, T = T1 + T2;

[0045] Based on the assumption that the two-stage degradation processes are independent, the distribution of T is obtained, and its failure distribution is calculated using the convolution formula:

[0046]

[0047]

[0048] In the formula, f T (t) is the failure distribution function of the coating, F T (t) is the probability density function of the coating lifetime, with parameter λ = pS UV +q, parameter μ = aS UV g All are determined by the ultraviolet radiation intensity S under actual working conditions. UV Decide.

[0049] Therefore, the present invention adopts the above-mentioned method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation, which solves the problems of distinguishing the stage characteristics of the degradation process of organic coatings, describing the randomness of the degradation amount of organic coatings, and quantitatively evaluating the reliability of organic coatings in actual working environments. This method is scientific, effective, easy to operate, and has broad application value.

[0050] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0051] Figure 1 A flowchart illustrating an embodiment of the organic coating lifetime prediction method based on joint modeling of pre-variant distribution and random degradation of the present invention;

[0052] Figure 2 This is a graph showing the low-frequency impedance modulus-time relationship of each sample in this invention;

[0053] Figure 3 These are the standard impedance moduli of samples 1 to 4 of the present invention;

[0054] Figure 4 This is a diagram showing the outlier removal results for sample 2 of the present invention;

[0055] Figure 5 This is the failure distribution function of the coating of the present invention;

[0056] Figure 6 Let be the probability density function of the coating lifetime of this invention. Detailed Implementation

[0057] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0059] Example

[0060] Please see Figure 1-6 This invention provides a method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation. This method requires the following basic settings:

[0061] Setting 1: Based on the composition of the anti-corrosion organic coating, design a batch of organic coating-metal system samples and fabricate an electrochemical detection probe; design a degradation test according to the actual working temperature and seawater salinity of the organic coating, arrange multiple different ultraviolet irradiation intensity levels, and set a certain number of parallel samples at each level, for a total of N samples; when carrying out the degradation test, use the electrochemical testing system to monitor the low-frequency impedance modulus of the sample every 1 hour, and record the test conditions and test duration for each sample.

[0062] Setting 2: Take the natural logarithm of the low-frequency impedance modulus data of the sample to obtain the logarithmic impedance modulus, and then calculate the increment of the next data relative to the previous one. Assume that these increments can be divided into two groups, which come from two different normal populations. The logarithmic impedance modulus data can be divided into two stages based on the test results, and the two degradation stages are independent of each other.

[0063] Setting 3: After dividing into stages, assume that the end time of the first stage follows an exponential distribution, and the logarithmic impedance magnitude degradation of the second stage follows a Wiener process.

[0064] The above-mentioned method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation specifically includes the following steps:

[0065] Step S1: Preprocessing and stage identification of coating electrochemical impedance data. This specifically includes the following steps:

[0066] Step S11: Standardize the coating electrochemical impedance data.

[0067] The directly measured low-frequency impedance modulus data of the coating |Z| 初 Multiplied by the effective area of ​​the coating (cm) 2 The corresponding value is obtained in Ω·cm 2 The standard impedance modulus |Z| is expressed in units of 标 ;

[0068] Let the diameter of the bottom surface of the sample be d, then |Z| 初 With |Z| 标 The conversion relationship is as follows:

[0069]

[0070] The standard impedance modulus data |Z| 标 Taking the natural logarithm, we obtain the logarithmic impedance magnitude data ln|Z| 标 .

[0071] Step S12: Identify the failure stage.

[0072] The initial immersion period of the coating system is classified as the first stage, which is the stage in which the impedance modulus remains basically unchanged at the beginning of the test; the middle and subsequent immersion periods are classified as the second stage, which is the stage in which the impedance modulus decreases.

[0073] The maximum likelihood transformation point detection method accurately divides the first and second stages. Maximum likelihood transformation point detection treats transformation points as parameters and estimates these parameters by finding the maximum value of the maximum likelihood function. The mean transformation point model is as follows: Samples X1, X2, ..., X... n They are ordered and independent of each other, assuming they come from two different normal populations and belong to two groups: Where m, μ1, μ2, All parameters are unknown, and 2≤m≤n-1.

[0074] X1,X2,…,X n The likelihood function is:

[0075]

[0076] In the formula, S1 represents the sample X1, X2, ..., X... m The sum of squared deviations, S2 represents the sample X m+1 ,X m+2 ,…,X n The sum of squared deviations.

[0077] For the likelihood function Iterate through each m (m = 2, 3, ..., n-1) and calculate the corresponding likelihood function value. Given μ1 when m is known... μ2, Substituting the maximum likelihood estimate into the unknown value, we get:

[0078]

[0079] After being replaced by the maximum likelihood estimate, the likelihood function With only one variable m, it simplifies to:

[0080]

[0081] In the formula, and These are the maximum likelihood estimates of the variances of the first and second halves of the data, respectively, both changing with m; C1 is a constant. Calculate the log-likelihood function to observe the peak point of L(m):

[0082]

[0083] Make L(m) the largest That is, the point of change.

[0084] When applying the above method, take the logarithm of n consecutive standard impedance magnitude data, and treat the increment of each data point relative to the previous data point as an independent normal sample:

[0085] X i =ln|Z| i -ln|Z| i-1 (i = 2, 3, ..., n) (6)

[0086] By defining X1 = 0, we obtain the sample sequence X1, X2, ..., X n Iterate through each m (m = 2, 3, ..., n-1) and calculate the value of lnL(m) in equation (5) for each m. Finally, find the value that maximizes lnL(m). Therefore, the standard electrochemical impedance data is determined to be in At (i.e., in the trial) A phase transition occurred at the moment h ended. This is the first phase. This is the second phase.

[0087] Based on the maximum likelihood transition point detection method, the timing of the transition point is identified, and the coating failure process is divided into two main stages. This allows for the extraction of coating performance parameters for the second stage, characterizing its degradation process. Furthermore, it is stipulated that for a given sample, if the determined stage transition point... or If a very small number of data points at the beginning or end are classified into the same stage, it is considered that the sample does not have a reasonable stage division scheme, and all impedance data are in the first stage.

[0088] Step S13: Use the moving median method to remove outliers.

[0089] Due to fluctuations in environmental factors, individual differences in samples, and measurement errors of impedance detectors, a small number of impedance modulus values ​​deviate significantly from the surrounding data. It is necessary to use the moving median method to remove these outliers.

[0090] The moving median method is as follows: The data sequence to be removed from outliers is y1, y2, ..., y n Let n0 be the range for outlier detection (n0 is odd and n0≤n), and let median(A) be the median of all elements in set A. For data y i ,if Among these n0 data points, any data y j The data should be removed if the following condition is met:

[0091] |y j -median(Y i )|≥-3c·median(|Y i -median(Y i )|) (7)

[0092] In the formula, Y i -median(Y i (Refers to set Y) i The difference between each element and the median is calculated, and the parameter c is the solution of equation (8).

[0093]

[0094] Based on the above formula, we can obtain c≈-0.4769.

[0095] An outlier value ln|Z| in logarithmic impedance data i After being removed, it is replaced with the average of the two logarithmic impedance data:

[0096]

[0097] The corresponding standard impedance data without taking the logarithm is as follows:

[0098]

[0099] Step S2: First stage distribution modeling before the change point.

[0100] A pre-change point distribution model is established for the end time of the first stage. Assuming the pre-change point distribution is an exponential distribution, its failure distribution function and probability density function are as follows:

[0101]

[0102] In the formula, θ is the parameter of the exponential distribution, which represents the mean of the lifetime, and in this case, it represents the mean of the end time of the first stage, and t represents time.

[0103] Some samples may not complete the first stage, which is equivalent to truncated data. Therefore, maximum likelihood estimation of truncated data without replacement is used. For n0 samples under the same environmental conditions, the time to the end of the experiment is t... s So far, a total of r0 samples have entered the second stage, while the first stage for n0-r0 samples is still ongoing. The times when r0 samples entered the second stage are t1 and t2 respectively. (1) ≤t (2) ≤…≤t (r) ≤t s Then the maximum likelihood estimate of parameter θ is:

[0104]

[0105] At the same time, the maximum likelihood estimate of the failure rate λ is obtained as follows:

[0106]

[0107] Different groups of samples The value is linked to the ultraviolet irradiance level, establishing the ultraviolet irradiance S UV Model of the impact of exponential distribution failure rate λ:

[0108] 10 4 λ=pS UV +q (14)

[0109] In the formula, p and q are the parameters of the regression line, and p > 0. The estimated value is obtained by least squares estimation. and

[0110] Step S3: Second stage of random degradation modeling.

[0111] In the second stage, it is assumed that the degradation of the logarithmic impedance modulus of the epoxy-acrylic coating follows a stochastic process, namely a Wiener process. The degradation path X(t) is defined as: the decrease in the logarithmic impedance modulus of the coating at time t in the second stage relative to the logarithmic impedance modulus at the beginning of the second stage, i.e.:

[0112]

[0113] In the formula, ln|Z| t This represents the logarithmic impedance modulus of the coating at time t. This indicates the decrease in the logarithmic impedance magnitude at the beginning of the second stage;

[0114] Wiener's process degradation model is as follows:

[0115] X(t)=μΛ(t)+σB(Λ(t)) (16)

[0116] In the formula, X(t) represents the product degradation path changing with time t, and X(0) = 0; the drift parameter μ reflects the performance degradation rate; the diffusion parameter σ reflects the fluctuation of performance degradation; Λ(t) is a monotonically increasing time scale transformation function, and Λ(0) = 0; B(·) is standard Brownian motion, reflecting stochastic dynamics. Assume that Λ(t) is a power function:

[0117] Λ(t)=t r (17)

[0118] In the formula, r represents the exponent of the power function, and r > 0.

[0119] The drift parameter μ characterizes the degradation rate and is related to environmental conditions, namely the ultraviolet radiation intensity S. UV (μW / cm 2 )related:

[0120] μ=aS UV g (18)

[0121] In the formula, a and g are the parameters to be estimated, and a>0.

[0122] Therefore, the second-stage coating degradation model is shown in the following equation:

[0123] X(t)=aS UV g ·t r +σB(t r (19)

[0124] In the formula, S UV X(t) represents the ultraviolet radiation intensity, X(t) represents the product degradation path as a function of time t, B(·) is the standard Brownian motion, and the diffusion parameter σ reflects the fluctuation of performance degradation.

[0125] The number of coating samples entering the second stage is N, and the corresponding ultraviolet irradiation intensities are S, respectively. UV1 ,S UV2 ,…,S UV,N Among them, the nth sample underwent (m) tests in the second stage. n +1) Secondary impedance data monitoring, the decrease in logarithmic impedance modulus is as follows: The monitoring times are respectively Where n = 1, 2, ..., N, X n,0 =0. The two stages are independent of each other, so the second stage restarts the time calculation, i.e., t. n,0 =0.

[0126] With ΔX n,j =X n,j -X n,j-1 Δt represents the degradation increment of the Wiener process. n,j =t n,j -t n,j-1 Indicates the time increment, ΔΛ n,j =Λ(t) n,j )-Λ(t n,j-1 () represents the increment of the time-scale transformation function. If the coating performance degradation follows a standard Wiener process, then each degradation increment... Obey m n The distribution follows a normal distribution, assuming that each degradation increment is independent. It is known that ΔX... n The mean and variance are:

[0127] μ n =aS UV g I n Ω n =σ 2 I n (20)

[0128] Where: μ n Represents ΔX n The mean vector, I n Ω represents the vector formed by the increments of the time-scale transformation function Λ(t). n Represents ΔX n The variance vector;

[0129] in:

[0130]

[0131] All the parameters to be estimated in the model are denoted as Θ=(a,g,σ) 2 ,r) T The likelihood function of Θ is:

[0132]

[0133] In the formula, n,j represent the subscripts of the product operation, and σ represents the diffusion parameter;

[0134] Therefore, the log-likelihood function is:

[0135]

[0136] Then, the maximum likelihood estimation method is used for parameter estimation. The partial derivatives of ln L(Θ|ΔX) with respect to Θ are calculated, and by setting all partial derivatives to zero, the following system of likelihood equations is obtained:

[0137]

[0138] In the formula, m n This indicates that the number of impedance data monitoring times in the second stage is reduced by 1, which is the degradation increment ΔX. n dimensionality and It is the time scale transformation function Λ(t) n,j ) and Λ(t n,j-1 );

[0139] The above system of equations cannot be solved analytically directly, but by solving them numerically, a, g, and σ can be obtained. 2 The maximum likelihood estimate of r;

[0140] Finally, the threshold d for the degradation increment is determined. The logarithmic impedance magnitude of all samples at the last moment of the first stage is taken (if there is a stage transition point, the logarithmic impedance magnitude at that point is taken). If the first stage is not completed, the average value of the logarithmic impedance modulus at the end of the experiment shall be taken as the initial state of the second stage:

[0141]

[0142] in This represents the impedance modulus at the last moment of the first stage of the nth sample; N0 is the total number of samples. When evaluating organic coating failure using an impedance modulus of 0.01 Hz, 10 is commonly chosen. 6 Ω·cm 2 Therefore, 10 is chosen as the failure threshold. 6 Ω·cm 2 The logarithm of the logarithmic impedance magnitude is used as the failure criterion: X F =ln 10 6 The difference between the two is taken as the threshold d for the decrease in the logarithmic impedance magnitude:

[0143]

[0144] Based on the above analysis, it is determined that the first arrival time T2 in the second stage follows an inverse Gaussian distribution, and its failure distribution function and probability density function are as follows:

[0145]

[0146] In the formula, Φ(·) is the cumulative distribution function of the standard normal distribution, and S UV The intensity of ultraviolet radiation in the environment (μW / cm²) 2The remaining parameters are either known or have been estimated.

[0147] Step S4: Two-stage combined lifetime distribution modeling. Specific steps include:

[0148] The coating lifetime T is the sum of the first arrival time of the coating's low-frequency impedance modulus failure, the end time of the first stage, and the first arrival time of the second stage, T = T1 + T2.

[0149] Based on the assumption that the two-stage degradation processes are independent, the distribution of T is obtained, and its failure distribution is calculated using the convolution formula:

[0150]

[0151] In the formula, f T (t) is the failure distribution function of the coating, F T (t) is the probability density function of the coating lifetime, with parameter λ = pS UV +q, parameter μ = aS UV g All are determined by the ultraviolet radiation intensity S under actual working conditions. UV Decide.

[0152] Step S5: Conduct a coating reliability assessment.

[0153] By obtaining the ultraviolet irradiation intensity data of the coating under actual working environment, the parameters λ and μ are calculated according to the models of Equations (14) and (18), and then substituted into Equation (28) to obtain the failure distribution function and probability density function of the coating lifetime.

[0154] The following will provide a more detailed explanation of this technical solution with examples.

[0155] The test specimen mainly consists of a metal substrate and an organic coating, and is connected to an electrochemical impedance spectroscopy instrument by wires; the metal substrate is 945 steel, a steel commonly used in ship structures; the organic coating is an epoxy acrylic coating system composed of H44-61 modified thick epoxy anti-rust paint, HB53-3 epoxy bonding paint and B40-AFB2 antifouling paint.

[0156] A degradation test was designed based on the working temperature (40℃) and seawater salinity (5%) of the organic coating. Three different UV irradiation intensity levels were arranged, with four parallel samples set at each level, for a total of 12 samples. The low-frequency impedance modulus of the samples was monitored every 1 hour using an electrochemical testing system, and the test conditions and test duration for each sample were recorded.

[0157] Table 1 shows the arrangement of ultraviolet radiation intensity for the three groups of samples; Table 2 shows the partial low-frequency impedance modulus data for sample 1.

[0158] Table 1. Arrangement of ultraviolet radiation intensity of the samples

[0159]

[0160] Table 2. Low-frequency impedance modulus data for sample 1.

[0161]

[0162] This invention provides a method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation, the process of which is as follows: Figure 1 As shown, this can be achieved through the following steps:

[0163] Step S1: Preprocessing and stage identification of coating electrochemical impedance data. The specific steps are as follows:

[0164] Step S11: Standardization of coating electrochemical impedance data.

[0165] In this specimen design, the bottom diameter of the 945 steel substrate covered by the coating is d = 2.7 cm, therefore |Z| 初 With |Z| 标 The conversion relationship is as follows:

[0166]

[0167] Taking samples 1 to 4 as examples, the standard impedance modulus |Z| 标 like Figure 3 As shown, this is also presented on a logarithmic scale. The standard impedance modulus data |Z| is used. 标 Taking the natural logarithm, we obtain the logarithmic impedance magnitude data ln|Z| 标 .

[0168] Step S12: Failure Stage Identification.

[0169] Based on Equation (5) and the corresponding maximum likelihood change point detection method, the first stage and the second stage are divided, and the results are shown in Table 3.

[0170] Table 3 Results of failure stage classification of the samples

[0171]

[0172]

[0173] Note: "*" indicates that the experiment is still in the first stage until the end.

[0174] Step S13: Removal of outliers.

[0175] Due to fluctuations in environmental factors, individual differences in samples, and measurement errors in the impedance detector, a small number of impedance modulus values ​​deviated significantly from the surrounding data. These outliers were removed using the moving median method. Taking sample 2 from the first group of experiments as an example, the second-stage electrochemical impedance data of sample 2 was extracted. With n0 = 21, the moving median method was used to remove outliers, as shown below. Figure 4 As shown.

[0176] Step S2: First stage distribution modeling before the change point.

[0177] The model is established according to the method in step S2 of the technical solution. Table 3 shows that for the first and third groups of tests, n0 = r0 = 4; for the second group of tests, r0 = 1 and n0 = 4. Substituting the failure stage classification data of the three groups of samples sequentially, the corresponding... and The values ​​are shown in Table 4.

[0178] Table 4. Estimation of exponential distribution parameters for the end time of the first stage.

[0179]

[0180] The least squares estimates of the parameters p and q are as follows: The goodness-of-fit r = 0.927, which is close to 1, indicating a good fit. The distribution function and probability density function for the end time T1 of the first stage are obtained as follows:

[0181]

[0182] Step S3: Second stage of random degradation modeling.

[0183] Based on the method determined in step S3 of the technical solution, a, g, and σ are obtained. 2 The maximum likelihood estimates of r are shown in Table 5.

[0184] Table 5. Parameter estimation of the Wiener process degradation model in the second stage.

[0185] Parameters to be estimated a g <![CDATA[σ 2 ]]> r estimated value <![CDATA[3.6148×10 -2 ]]> 0.3382 0.9850 0.3557

[0186] Finally, the threshold d for the degradation increment was determined. Based on equations (25) and (26) of the technical solution, and combined with the data from this experiment, X0 = 16.6285 and d = 2.8130 were calculated.

[0187] Based on the above analysis, it is determined that the first arrival time T2 in the second stage follows an inverse Gaussian distribution, and its failure distribution function and probability density function are shown in equation (27).

[0188] Step S4: Two-stage combined lifetime distribution modeling.

[0189] The parameters in the coating lifetime T distribution model of equation (28) are shown in Table 6 below.

[0190] Table 6 Parameters of Coating Lifetime Distribution Model

[0191]

[0192] Step S5: Coating Reliability Assessment

[0193] By obtaining ultraviolet irradiance data under the actual working environment of the coating, and calculating parameters λ and μ according to the models in equations (14) and (18), and then substituting them into equation (28), the failure distribution function and probability density function of the coating lifetime are obtained. Using S... UV =16, S UV =35, S UV =67 (μW / cm) 2 Taking three ultraviolet irradiation intensities as examples, numerical integration was performed using a computer to plot the probability density function and failure distribution function of the coating lifetime T(h), as follows: Figure 5 , Figure 6 As shown.

[0194] Therefore, the present invention adopts the above-mentioned method for predicting the lifetime of organic coatings by jointly modeling the pre-change distribution and random degradation, which solves the problems of distinguishing the stage characteristics of the degradation process of organic coatings, describing the randomness of the degradation amount of organic coatings, and quantitatively evaluating the reliability of organic coatings in actual working environments. This method is scientific, effective, easy to operate, and has broad application value.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the lifetime of an organic coating layer by combining the variable point prior distribution with random degradation, characterized in that, The method comprises the following steps: Step S1, coating electrochemical impedance data preprocessing and stage identification, specifically comprising: Step S11, standardization processing of coating electrochemical impedance data is performed; Step S12, failure stage identification is performed; Step S13, outlier is removed by using moving median method; Step S2, first stage pre-distribution modeling; Step S3, second stage random degradation modeling; Step S4, two-stage combined life distribution modeling; Step S5, coating reliability evaluation is performed; The specific steps of step S2 comprise: Supposing that the end time of the first stage obeys exponential distribution, the failure distribution function and the probability density function are as follows: ； ； wherein is the parameter of the exponential distribution, representing the mean of the lifetime, here the mean of the end time of the first phase, denotes time; Under the same environmental conditions The total number of samples entering the second stage is The total number of samples entering the second stage is The total number of samples entering the second stage is The total number of samples entering the second stage is The total number of samples entering the second stage is The maximum likelihood estimate of the parameter is ； The maximum likelihood estimate of the failure rate is obtained simultaneously as ； The different groups of samples The values are linked to the UV irradiance level to establish a UV irradiance Effect model on the exponential distribution failure rate ​ ； wherein p and q are parameters of the regression line, and are obtained by least square estimation and ; In step S3, the established second stage coating degradation model is as follows: ； In the formula, a and g are the parameters to be estimated. Indicates ultraviolet radiation intensity. Indicates time Changing product degradation paths It is standard Brownian motion, diffusion parameters Fluctuations reflecting performance degradation Let represent the exponent of the power function, and >0; The specific steps of step S4 comprise: Coating lifetime T is the failure first passage time of the coating low frequency impedance modulus value, the sum of the first stage end time and the second stage first passage time, ; According to the assumption that the degradation processes of the two stages are independent, the distribution of T is obtained, and the failure distribution is obtained by convolution formula: ； ； In the formula, is the failure distribution function of the coating, is the probability density function of the coating life, parameter The expression of , parameter , is determined by the ultraviolet radiation intensity in the actual working environment, is the threshold value of the logarithmic impedance modulus reduction amount.

2. The method of claim 1, wherein, Step S11 specifically comprises: The directly measured coating low frequency impedance modulus data is multiplied by the effective area of the coating in cm 2 , resulting in a normalized impedance modulus in units of Ω·cm 2 ;​ The bottom surface diameter of the test sample is set to 50 mm d Then The conversion relationship with is: ； Standard impedance modulus data Taking natural logarithm, logarithmic impedance modulus data is obtained .

3. The method of claim 2, wherein: In step S12, the maximum likelihood change point detection method is used to divide the first stage and the second stage, the initial stage of the coating system is divided into the first stage, the impedance modulus of the first stage is basically unchanged in the initial stage of the test, and the middle stage and the later stage are divided into the second stage, and the second stage is a stage in which the impedance modulus decreases.

4. The method of claim 1, wherein, In step S13, the steps of the moving median method are as follows: The data sequence with outliers removed is , the selected outlier determination range , is odd and , record the set The median of all elements is For data If This Among the data, any one data Satisfies the following conditions: ； In the formula, Point to the set Difference of each element from the median, parameter ; Certain outliers of log impedance data After being removed, replaced by the average of the two log impedance data before and after: ； The corresponding standard impedance data without logarithm is as follows: 。

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