CN112949184B - A Concrete Freeze-Thaw Life Prediction Method Based on Minimum Sampling Variance Particle Filter - Google Patents

Abstract

The invention relates to a method for predicting the freeze-thaw life of concrete using minimum sampling variance particle filtering. Aiming at the problem of reduced prediction accuracy caused by the lack of particle diversity in the standard particle filter, from the perspective of improving resampling technology, the proposed concrete freeze-thaw life prediction method In the method, the sampling variance is introduced as the cost function, which can minimize the information loss in the resampling process, effectively alleviate the lack of particle diversity, and is suitable for higher-dimensional and more complex state-space models. The standard particle filter algorithm has higher prediction accuracy.

Description

A Method for Concrete Freeze-Thaw Life Prediction Based on Minimum Sampling Variance Particle Filter

technical field

The invention belongs to the field of concrete durability analysis and evaluation, and relates to a concrete freeze-thaw life prediction method based on minimum sampling variance particle filter.

Background technique

The particle filter algorithm can use a large number of "particles" to characterize the deterioration process of freeze-thaw damage under various uncertain factors. It has low requirements for model complexity and does not require a large amount of training data. Correct the forecast results in time. Based on the above advantages, the standard Particle Filter (PF) algorithm has achieved life prediction in the fields of crack growth, concrete freeze-thaw, Li battery, PEM fuel unit, turbine blade, aircraft actuator system and fighter engine, which is different from traditional Compared with the reliability life prediction method, it has higher life prediction accuracy.

Although the standard particle filter algorithm solves the degradation problem through the combination of the suboptimal solution and the resampling algorithm, and the sampling is simple and easy to implement, but it also introduces a new problem, that is, the lack of particle diversity. The lack of particle diversity means that many particles in the original particle swarm have no "offspring" due to their small weights, while a few particles with high weights have many identical "offsprings". The particle swarm after resampling is composed of A large number of repeated particles are formed. With the resampling, the particles with small weights will be discarded with a high probability, so the diversity of the particle group will decrease, and even only one repeated particle will be left in the end. When the number of iterations is large or the number of particles is small, the accuracy of freeze-thaw lifetime prediction will decrease.

One of the ways to solve the lack of particle diversity is to ensure the consistency of particle distribution before and after resampling. Theoretically speaking, in order to ensure the consistency before and after resampling, the number of sampling of the particle with serial number i should be equal to its mathematical expectation, that is, the weighting of the number of particles and the weight. However, since the number of sampling times can only be an integer, this makes the particle distribution unavoidably produce discrete errors before and after resampling, and with the accumulation of resampling times, the information in the resampling process will be gradually lost, making the prediction of freeze-thaw life difficult. The posterior probability is gradually distorted, which eventually leads to a decrease in the accuracy of freeze-thaw lifetime prediction.

Contents of the invention

In order to overcome the lack of particle diversity and improve the accuracy of freeze-thaw life prediction, the present invention proposes a concrete freeze-thaw life prediction method based on minimum sampling variance particle filter.

The technical scheme adopted in the present invention is:

A minimum sampling variance particle filter method for predicting concrete freeze-thaw life, comprising the following steps:

Step 1. Based on the relative dynamic elastic modulus attenuation model of the single-segment mode, construct the state equation and its noise model describing the law of multi-factor freeze-thaw damage degradation;

Step 2. Use the ultrasonic nondestructive testing method to monitor the ultrasonic sound time in the concrete; construct the observation equation through the relationship between the relative dynamic elastic modulus and the ultrasonic sound time; at the same time, combine the state equation in step 1 to construct the description State-space model of freeze-thaw degradation;

Before the start of the multi-factor freeze-thaw cycle, each test piece is subjected to an ultrasonic non-destructive test to collect the reference sound time;

Step 3, judging whether the sound time detection is updated for life prediction;

Initialize the model parameters and particle swarm; during the multi-factor freeze-thaw cycle,

If ultrasonic nondestructive testing is not performed, the particle swarm is substituted into the state equation to generate a priori estimate, and then the prior estimate and particle weights are weighted and summed to obtain the posterior estimate and update the particle swarm. The posterior estimate can be seen in as a predictor of the number of freeze-thaw cycles;

If ultrasonic non-destructive testing is carried out to obtain a new sound-time signal, then the particle swarm at time t is substituted into the state-space model to generate N sound-time prediction values; the difference between the sound-time prediction value and the experimental detection value is assumed to be Gaussian distribution, the normalized weights corresponding to the N sound-time prediction values can be calculated;

Step 4, copy the particles whose particle weight is greater than 1/N, and obtain the copied particle group, whose number of particles is L;

Step 5. After extracting the copied particle swarm from the original particle swarm, calculate the residual particle swarm weight to obtain the residual particle swarm, which is composed of the residual particle swarm and its weight;

Step 6, minimum variance resampling; according to the size of the weight, sort the residual particle swarm, and use the TopRank function to sample N-L particles with the largest weight from the residual particle swarm, that is, MSV particles, and the resampled particles The weight is 1/N;

Step 7. Prediction and update; carry out weighted summation on the copied particle swarm, MSV particle swarm and their corresponding weights to obtain the predicted value of freeze-thaw life; combine the copied particle swarm with the number of particles N-L and the number of MSV particles with the number L Groups are combined to maintain the total number of particles at N, and these two particle groups are used as updated particle groups, and the relative dynamic elastic modulus state value, initial damage velocity, particle weight and particle number are updated at the same time;

Step 8. Use the updated particle swarm as an iterative particle swarm, repeat steps 3 to 7 until the set conditions are reached, and stop the freeze-thaw experiment and prediction process; the total time experienced in the above process is the remaining life of concrete freeze-thaw.

Further, in step 1, the expression of the state equation is:

In formula (1), E _t represents the relative dynamic elastic modulus at time t of the freeze-thaw cycle; C represents the damage acceleration, and A represents the initial damage velocity, both of which can be obtained through experimental fitting; Δt represents time t and time t+1 time interval; ω _t+1 represents additive zero-mean Gaussian white noise, satisfying is the state noise variance.

Further, in step 1, the reference damage acceleration _C0 is defined as a constant, and the reference damage initial velocity _A0 satisfies the Gaussian distribution, as shown in formula (2):

In formula (2), mean(·) represents the mean function, Q represents the number of freeze-thaw test specimens, and Var(·) represents the variance function.

Further, in step 2, the expression of the observation equation is:

In formula (3), T _t represents the ultrasonic sound time at time t of the freeze-thaw cycle, T ₀ represents the reference sound time measured by the ultrasonic method before the freeze-thaw cycle starts; υ _t+1 represents the observation noise, satisfying is the state noise variance, and defines the observation noise υ _t+1 as zero-mean Gaussian white noise;

Combining with formula (1), construct a state space model, as shown in formula (4):

Further, step 3 specifically includes:

For model parameters and particle swarm Initialize, at this time the weight /> N is the number of particles;

At time t+1 of the multi-factor freeze-thaw cycle, if no ultrasonic non-destructive testing is performed, the particle swarm at time t is substituted into the state equation to generate a priori estimation Then the prior estimate and particle weights are weighted and summed, as shown in formula (5), to obtain the posterior estimate > and update iterative particles /> The a posteriori estimate of the relative dynamic modulus can be seen as a predictor of the number of freeze-thaw cycles;

If ultrasonic nondestructive testing is performed at time t+1 of the multi-factor freeze-thaw cycle, and a new ultrasonic sound time T _t+1 is obtained, the particle swarm at time t Substitute into the state space model to generate N ultrasonic sound time prediction values/> Make the difference between the predicted value of sound time and the experimental detection value T _exp , if the difference satisfies the Gaussian distribution /> The normalized weights corresponding to the N acoustic time prediction values can be calculated/>

Further, the particle copying process in step 4 specifically includes:

Copy the particles whose particle weight is greater than 1/N into n _i copies, get copy particle swarm Where L is the number of copied particles, as shown in formula (6);

In the formula, for the rounding operation.

Further, step 5 specifically includes:

Residual Particle Computation from the original particle swarm In , after extracting the copied particle swarm, the weight of the remaining particle swarm will change, and the calculation formula is as follows:

The residual particle swarm and its weight are called the residual particle swarm, namely

Further, the minimum variance resampling process in step 6 specifically includes:

Minimum variance resampling: according to the size of the weight, the residual particle swarm sort, and sample NL particles with the largest weight, which are MSV particles. This process can be characterized by the function TopRank _NL ( ), as shown in formula (8):

Since the sampling process is independent and identically distributed, after resampling, the weights of MSV particles are all 1/N.

Further, the prediction and update process in step 7 specifically includes:

The weighted summation of the copied particle swarm, MSV particle swarm and their corresponding weights, as shown in formula (9), can obtain the predicted value of freeze-thaw life

Combine the copy particle swarm with particle number NL and the MSV particle swarm with the number L to keep the total number of particles at N, and use these two particle swarms as the update particle swarm Simultaneously to the state value of the relative dynamic elastic modulus /> initial damage velocity/> and particle weights to update.

Further, step 8 specifically includes:

Calculate the relative dynamic elastic modulus a posteriori estimated predicted value, as shown in formula (10), meanwhile, let t=t+1, will As an iterative particle swarm, repeat steps 3 to 7 above until the relative dynamic elastic modulus Or the number of freeze-thaw cycles t≥200, stop the freeze-thaw experiment and prediction process; the total time experienced in the above process is the remaining life of concrete freeze-thaw;

The beneficial effects of the present invention are:

Aiming at the lack of particle diversity caused by the traditional resampling method adopted by the standard particle filter algorithm, which cannot guarantee the consistency of particle distribution before and after resampling, a minimum sampling variance particle filter (Minimum Sampling Variance Particle Fitler, MSVPF) concrete freeze-thaw life prediction method, by introducing the sampling variance as the cost function, under the condition of resampling, the TopRank function is used to resample the particle swarm, so that the sampling variance after resampling is the smallest, and the maximum retention The posterior probability distribution, that is to say, minimizes the information loss in the resampling process, which can effectively alleviate the lack of particle diversity and does not lose the characteristics of dimension freedom. Compared with the auxiliary particle filter and the standard particle filter algorithm, With the same number of particles, it has higher precision, which can save a lot of calculation consumption, and is more suitable for the engineering application of online prediction of complex high-dimensional freeze-thaw life prediction state-space model above the third order. It is a deterministic resampling algorithm. Effective complement (comparatively speaking, the deterministic resampling algorithm has higher accuracy).

Description of drawings

Fig. 1 is the block flow diagram of the concrete freeze-thaw life prediction method of minimum sampling variance particle filter of the present invention;

Fig. 2 is the concrete freeze-thaw cycle temperature curve;

Figure 3 is a comparison of the sampling variance between the minimum sampling variance particle filter (MSVPF) and the standard particle filter (PF) algorithm in the process of freeze-thaw life prediction;

Figure 4 is a comparison of the life prediction results of MSVPF, Auxiliary Particle Filter (APF) and PF algorithms;

Figure 5 is a comparison of the life prediction results of MSVPF and deterministic resampling particle filter (DRPF) algorithms.

Detailed ways

The concrete freeze-thaw life prediction method of the minimum sampling variance particle filter of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, a minimum sampling variance particle filter method for predicting concrete freeze-thaw life includes the following steps:

Step 1. Based on the relative dynamic elastic modulus attenuation model of the single-segment mode, construct the state equation and its noise model describing the law of multi-factor freeze-thaw damage degradation;

In step 1, the expression of the state equation is:

In formula (1), E _t represents the relative dynamic elastic modulus at time t of the freeze-thaw cycle; C represents the damage acceleration, and A represents the initial damage velocity, both of which can be obtained through experimental fitting; Δt represents time t and time t+1 time interval; ω _t+1 represents additive zero-mean Gaussian white noise, satisfying is the state noise variance.

The basic attenuation law of the state equation is approximately a parabola, and its uncertainty is mainly related to the damage acceleration C and the damage initial velocity A. Considering the main influencing factors such as material composition and chloride salt concentration, and combining the statistical results of experimental data, the benchmark damage acceleration is defined C ₀ is a constant, and the reference damage initial velocity A ₀ satisfies the Gaussian distribution, as shown in formula (2):

In formula (2), mean(·) represents the mean function, Q represents the number of freeze-thaw test specimens, and Var(·) represents the variance function.

Additive zero-mean Gaussian white noise ω _t+1 represents other uncertain factors except the main influencing factors. The introduction of this noise model can expand the support domain of life prediction. The above-mentioned state equation and noise model contain two noise distributions, which not only consider the uncertainties caused by factors such as material composition and chloride concentration, but also consider other uncertainties in the process of freeze-thaw degradation, and have higher robustness. Stickiness. The state equation is applicable to the influence of various uncertain factors and has universality.

Step 2. Use the ultrasonic non-destructive testing method to monitor the ultrasonic sound time (Ultrasonic Pulse Transmission Time, UPTT, also known as the ultrasonic pulse transmission time) in the concrete; through the relationship between the relative dynamic elastic modulus and the ultrasonic sound time, construct an observation Equation; at the same time, in combination with the state equation in step 1, construct a state-space model describing freeze-thaw degradation;

Before the start of the multi-factor freeze-thaw cycle, each test piece is subjected to an ultrasonic non-destructive test to collect the reference sound time;

In step 2, the expression of the observation equation is:

In formula (3), T _t represents the ultrasonic sound time at time t of the freeze-thaw cycle, T ₀ represents the reference sound time measured by the ultrasonic method before the freeze-thaw cycle starts; υ _t+1 represents the observation noise, which is used to characterize Uncertainty monitoring error of ultrasonic nondestructive testing, which satisfies is the state noise variance, and defines the observation noise υ _t+1 as zero-mean Gaussian white noise;

Combining formula (1) and formula (3), construct a state space model that can describe freeze-thaw degradation, as shown in formula (4):

Step 3, judging whether the sound time detection is updated for life prediction;

Initialize the model parameters and particle swarm; during the multi-factor freeze-thaw cycle,

If ultrasonic nondestructive testing is not performed, the particle swarm is substituted into the state equation to generate a priori estimate, and then the prior estimate and particle weights are weighted and summed to obtain the posterior estimate and update the particle swarm. The posterior estimate can be seen in as a predictor of the number of freeze-thaw cycles;

If ultrasonic nondestructive testing is performed to obtain a new sound-time signal, the current particle swarm is substituted into the state-space model to generate N sound-time prediction values; the difference between the sound-time prediction value and the experimental detection value is made, and if the difference satisfies the Gaussian distribution , the normalized weights corresponding to the N sound-time prediction values can be calculated;

Step 3 specifically includes:

For model parameters and particle swarm Initialize, at this time the weight /> N is the number of particles;

At time t+1 of the multi-factor freeze-thaw cycle, if no ultrasonic non-destructive testing is performed, the particle swarm at time t is substituted into the state equation to generate a priori estimation Then the prior estimate and particle weights are weighted and summed, as shown in formula (5), to obtain the posterior estimate > and update iterative particles /> The a posteriori estimate of the relative dynamic modulus can be seen as a predictor of the number of freeze-thaw cycles;

If ultrasonic nondestructive testing is performed at time t+1 of the multi-factor freeze-thaw cycle, and a new ultrasonic sound time T _t+1 is obtained, the particle swarm at time t Substitute into the state space model to generate N ultrasonic sound time prediction values/> Make the difference between the predicted value of sound time and the experimental detection value T _exp , if the difference satisfies the Gaussian distribution /> The normalized weights corresponding to the N acoustic time prediction values can be calculated/>

Step 4, copy the particles whose particle weight is greater than 1/N, and obtain the copied particle group, whose number of particles is L;

Step 4 specifically includes:

Copy the particles whose particle weight is greater than 1/N into n _i copies, get copy particle swarm Where L is the number of copied particles, as shown in formula (6), the weight of copied particles has not been determined at this time, and it needs to be determined after the particle space sampling process is completed;

In the formula, for the rounding operation.

Step 5. After extracting the copied particle swarm from the original particle swarm, calculate the residual particle swarm weight to obtain the residual particle swarm, which is composed of the residual particle swarm and its weight;

Step 5 specifically includes:

Residual Particle Computation from the original particle swarm In , after extracting the copied particle swarm, the weight of the remaining particle swarm will change, and the calculation formula is as follows:

The residual particle swarm and its weight are called the residual particle swarm, namely

Step 6. Minimum variance resampling. According to the size of the weight, sort the residual particle swarm, and use the TopRank function to sample N-L particles with the largest weight from the residual particle swarm, that is, MSV particles, and the particle weight after resampling is 1/N;

Step 6 specifically includes:

Minimum variance resampling: according to the size of the weight, the residual particle swarm sort, and sample NL particles with the largest weight, which are MSV particles. This process can be characterized by the function TopRank _NL ( ), as shown in formula (8):

Since the sampling process is independent and identically distributed, after resampling, the weights of MSV particles are all 1/N.

Step 7. Prediction and update. The weighted summation of the replicated particle swarm, MSV particle swarm and their corresponding weights can be used to obtain the predicted value of freeze-thaw life. Combine the copy particle swarm with the number of particles N-L and the MSV particle swarm with the number L, so that the total number of particles is maintained at N, and these two particle swarms are used as the update particle swarm, and the relative dynamic elastic modulus state value , damage initial velocity, particle weight and number of particles are updated;

Step 7 specifically includes:

The weighted summation of the copied particle swarm, MSV particle swarm and their corresponding weights, as shown in formula (9), can obtain the predicted value of freeze-thaw life

Combine the copy particle swarm with particle number NL and the MSV particle swarm with the number L to keep the total number of particles at N, and use these two particle swarms as the update particle swarm Simultaneously to the state value of the relative dynamic elastic modulus /> initial damage velocity/> and particle weights to update.

Step 8. Use the updated particle swarm as an iterative particle swarm, repeat steps 3 to 7 until the set conditions are reached, and stop the freeze-thaw experiment and prediction process; the total time experienced in the above process is the remaining life of concrete freeze-thaw.

Step 8 specifically includes:

Calculate the relative dynamic elastic modulus a posteriori estimated predicted value, as shown in formula (10), meanwhile, let t=t+1, will

As an iterative particle swarm, repeat steps 3 to 7 above until the relative dynamic elastic modulus Or the number of freeze-thaw cycles t≥200, stop the freeze-thaw experiment and prediction process; the total time experienced in the above process is the remaining life of concrete freeze-thaw.

In the following, the implementation process of the method of the present invention will be described in detail by taking the freeze-thaw failure experiments of concrete with strength grades C30 and C50 in 3%, 5% and 20% concentration of chloride salt solutions as examples.

The size of the concrete specimen is 40×40×160mm ³ , and three freeze-thaw experiments are carried out under each strength and chloride concentration. There are 18 specimens in total, which are numbered P1A3-1 and P1A3 according to the concrete strength and chloride concentration -2～P2A20-3, where P stands for concrete strength and A stands for chloride concentration.

The freeze-thaw experiment adopts the CDF test machine produced by Schleibinger, Germany, and the salt freeze test system follows the CDF test method proposed by the TC117-FDC Professional Committee of the European International Federation of Materials Laboratories (RILEM), as shown in Figure 2. The method adopts 12 hours as a freeze-thaw cycle period, the initial temperature is 20°C, the temperature is lowered to -20°C within 4 hours at a constant cooling rate (10°C/h) and then kept at a constant temperature for 3 hours; then at a constant heating rate (10°C) °C/h) the temperature was raised to 20 °C for 4 hours, and the temperature was kept constant for 1 hour, and the cycle was carried out in sequence. Remove the mold after 1 day of molding, put it in a standard curing room for 28 days, and then soak it in different concentrations of chlorine salt deicing agent solution for 4 days until saturated; This time is carried out according to GBJ82-85. Before the measurement, clean the scum on the surface of the test piece, wipe off the surface water, and use the NM-4B non-metallic ultrasonic testing analyzer to measure the sound time transmitted by the test piece, and then calculate it based on the known thickness. The speed of sound, comparative analysis of the changes in the relative dynamic elastic modulus of 25, 50, 75, 100, 125, 150, 175, 200 times of freezing and thawing.

Combined with the relative dynamic elastic modulus attenuation model, use the Matlab polynomial fitting toolbox to process the relative dynamic elastic modulus change data of the specimens except P2A3-3, and obtain a curve for each strength and chloride salt concentration, and the damage of each curve The acceleration and initial damage velocity are shown in Table 1.

Table 1 The damage acceleration and initial velocity values of each specimen obtained by Matlab cftool fitting calculation

According to the formula (2), the reference damage acceleration C ₀ is defined as a constant, and its mean value is -1.9294×10 ^-5 , and A ₀ satisfies the Gaussian distribution N(-9.4767×10 ^-5 ,(8.1080×10 ^-4 ) ² ) of random numbers. Assuming that the influence of other non-main factors on the prediction of freeze-thaw life is about 2%, let ω _t+1 ～N(0,0.02 ² ). Finally, the equation of state shown in formula (11) can be constructed, where Δt=1.

Table 2 shows the ultrasonic pulse propagation time and pulse wave velocity of P2A3-3 specimens measured by ultrasonic method under different freeze-thaw cycles. Considering the length measurement error caused by the spalling of the concrete test block during the freeze-thaw experiment, the calculation result of the ultrasonic pulse propagation time can be used as the measurement value of the relative dynamic elastic modulus, and the calculation result of the pulse wave velocity can be used as the measurement value of the relative dynamic elastic modulus. actual value of the quantity. The ultrasonic pulse propagation time accuracy of NM-4B equipment is 0.1μs, and the average sound time of all specimens before freezing and thawing is about 32μs. Assuming that the ultrasonic pulse propagation time error obeys the Gaussian distribution, the observation noise approximately obeys the Gaussian distribution υ _{t+ 1} ～N(0,4.526 ² ). Substituting the above parameters into formula (4), the final state space model constructed is shown in formula (12):

Table 2 UPTT and ultrasonic sound velocity measured by P2A3-3 specimens under different freeze-thaw cycles

In order to compare with the life prediction effect of the traditional reliability algorithm, the relative dynamic elastic modulus attenuation of C50 concrete at 3% concentration was obtained by fitting the experimental data of P2A3-1 and P2A3-2 using the Matlab polynomial fitting toolbox The fitting parameters of the model are shown in P2A3 in Table 1, and the fitting curve represents the effect of the traditional reliability method. The particle number N is selected as 100, and the freeze-thaw cycle iteration interval Δt is 1. When acquiring the acoustic-time signal update of the P2A3-3 specimen, the minimum sampling variance particle filter (MSVPF) and standard particle filter (PF) online prediction algorithms are used respectively , to realize the life prediction of freeze-thaw deterioration of P2A3-3 specimen. Figure 3 shows the comparison of sampling variance between MSVPF and PF algorithms in the process of freeze-thaw life prediction. Aiming at the discrete error problem existing in the PF algorithm in the iterative process, MSVPF uses the TopRank function to resample the particle swarm, so that the sampling variance after resampling is the smallest, and the posterior probability distribution can be preserved to the greatest extent, that is to say Information loss during resampling is minimized. Therefore, it can be seen from Figure 3 that compared with the PF algorithm, the MSVPF algorithm effectively reduces the sampling variance of the particles, and the average sampling variance of the PF algorithm in the life prediction process is 11.1602. The sampling variance has been reduced to 0.8223, an order of magnitude lower sampling variance, minimizing information loss during resampling.

MSVPF, Auxiliary Particle Filter (APF) and PF three algorithms of multi-factor concrete freeze-thaw degradation life prediction results are shown in Figure 4, the root mean square error (Root-Mean-SquareError ,RMSE) as a comparison index of life prediction accuracy, the smaller the RMSE, the higher the accuracy. It can be seen from Figure 4 that compared with the APF and PF life prediction methods, MSVPF minimizes the information loss in the resampling process, effectively It alleviates the lack of particle diversity and has the best prediction effect. Its RMSE is the lowest, which is 0.005050, while the other two are 0.006036 and 0.007883 respectively. At the same time, compared with the APF and PF algorithms, MSVPF uses the same number of particles, but obtains higher prediction accuracy, and the calculation time is similar, which is more suitable for engineering applications of online prediction of concrete freeze-thaw life.

The comparison of multi-factor concrete freeze-thaw degradation life prediction results between MSVPF and deterministic resampling particle filter (Deterministic Resampling Particle Filter, DRPF) algorithm is shown in Figure 5. It can be seen from Figure 5 that the life prediction accuracy of MSVPF and DRPF algorithms are relatively similar, and their RMSE are 0.005050 and 0.003814 respectively. Although the accuracy of the MSVPF algorithm is slightly lower than that of DRPF, the MSVPF algorithm proposed by the present invention does not lose the feature of dimension freedom compared with DRPF, and compared with APF and PF, it has higher precision under the same number of particles, which can save It consumes a lot of calculations and is more suitable for the engineering application of the online prediction of the complex high-dimensional freeze-thaw life prediction state space model above the third order. It is an effective supplement to the DRPF algorithm.

The above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, and any person familiar with the technical field can easily think of replacements or transformations within the scope of the technical methods disclosed in the present invention. methods should be covered within the protection scope of the present invention.

Claims (9)

1. A concrete freeze-thaw life prediction method of minimum sampling variance particle filter, is characterized in that, comprises the steps: Step 1. Based on the relative dynamic elastic modulus attenuation model of the single-segment mode, construct the state equation and its noise model describing the law of multi-factor freeze-thaw damage degradation; Step 2. Use the ultrasonic nondestructive testing method to monitor the ultrasonic sound time in the concrete; construct the observation equation through the relationship between the relative dynamic elastic modulus and the ultrasonic sound time; at the same time, combine the state equation in step 1 to construct the description State-space model of freeze-thaw degradation; Before the start of the multi-factor freeze-thaw cycle, each test piece is subjected to an ultrasonic non-destructive test to collect the reference sound time; Step 3, judging whether the sound time detection is updated for life prediction; Initialize the model parameters and particle swarm; during the multi-factor freeze-thaw cycle, If ultrasonic nondestructive testing is not performed, the particle swarm is substituted into the state equation to generate a priori estimate, and then the prior estimate and particle weights are weighted and summed to obtain the posterior estimate and update the particle swarm. The posterior estimate can be seen in as a predictor of the number of freeze-thaw cycles; If ultrasonic non-destructive testing is carried out to obtain a new sound-time signal, then the particle swarm at time t is substituted into the state-space model to generate N sound-time prediction values; the difference between the sound-time prediction value and the experimental detection value is assumed to be Gaussian distribution, the normalized weights corresponding to the N sound-time prediction values can be calculated; Specifically include: For model parameters and particle swarm Initialize, at this time the weight /> N is the number of particles; At time t+1 of the multi-factor freeze-thaw cycle, if no ultrasonic non-destructive testing is performed, the particle swarm at time t is substituted into the state equation to generate a priori estimation Then the prior estimate and particle weights are weighted and summed, as shown in formula (5), to obtain the posterior estimate > and update iterative particles /> The a posteriori estimate of the relative dynamic modulus can be seen as a predictor of the number of freeze-thaw cycles; If ultrasonic nondestructive testing is performed at time t+1 of the multi-factor freeze-thaw cycle, and a new ultrasonic sound time T _t+1 is obtained, the particle swarm at time t Substitute into the state space model to generate N ultrasonic sound time prediction values/> Make the difference between the predicted value of sound time and the experimental detection value T _exp , if the difference satisfies the Gaussian distribution /> The normalized weights corresponding to the N acoustic time prediction values can be calculated/> Step 4, copy the particles whose particle weight is greater than 1/N, and obtain the copied particle group, whose number of particles is L; Step 5. After extracting the copied particle swarm from the original particle swarm, calculate the residual particle swarm weight to obtain the residual particle swarm, which is composed of the residual particle swarm and its weight; Step 6, minimum variance resampling; according to the size of the weight, sort the residual particle swarm, and use the TopRank function to sample N-L particles with the largest weight from the residual particle swarm, that is, MSV particles, and the resampled particles The weight is 1/N; Step 7. Prediction and update; carry out weighted summation on the copied particle swarm, MSV particle swarm and their corresponding weights to obtain the predicted value of freeze-thaw life; combine the copied particle swarm with the number of particles N-L and the number of MSV particles with the number L Groups are combined to maintain the total number of particles at N, and these two particle groups are used as updated particle groups, and the relative dynamic elastic modulus state value, initial damage velocity, particle weight and particle number are updated at the same time; Step 8. Use the updated particle swarm as an iterative particle swarm, repeat steps 3 to 7 until the set conditions are reached, and stop the freeze-thaw experiment and prediction process; the total time experienced in the above process is the remaining life of concrete freeze-thaw. 2. the concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 1 is characterized in that, in step 1, the expression of state equation is: In formula (1), E _t represents the relative dynamic elastic modulus at time t of the freeze-thaw cycle; C represents the damage acceleration, and A represents the initial damage velocity, both of which can be obtained through experimental fitting; Δt represents time t and time t+1 time interval; ω _tυ1 represents additive zero-mean Gaussian white noise, satisfying is the state noise variance. 3. the concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 2, it is characterized in that, in step 1, define reference damage acceleration C ₀ be constant, reference damage initial velocity A ₀ satisfy Gaussian distribution, such as Formula (2) shows: In formula (2), mean(·) represents the mean function, Q represents the number of freeze-thaw test specimens, and Var(·) represents the variance function. 4. according to claim 2 or the concrete freeze-thaw life prediction method of minimum sampling variance particle filter, it is characterized in that, in step 2, the expression of observation equation is: In formula (3), T _t represents the ultrasonic sound time at time t of the freeze-thaw cycle, T ₀ represents the reference sound time measured by the ultrasonic method before the freeze-thaw cycle starts; υ _t+1 represents the observation noise, satisfying is the state noise variance, and defines the observation noise υ _t+1 as zero-mean Gaussian white noise; Combining with formula (1), construct a state space model, as shown in formula (4): 5. the concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 1, is characterized in that, the particle duplication process of step 4 specifically comprises: Copy the particles whose particle weight is greater than 1/N into n _i copies, get copy particle swarm /> Where L is the number of copied particles, as shown in formula (6); In the formula, for the rounding operation. 6. the concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 5, is characterized in that, step 5 specifically comprises: Residual Particle Computation from the original particle swarm In , after extracting the copied particle swarm, the weight of the remaining particle swarm will change, and the calculation formula is as follows: The residual particle swarm and its weight are called the residual particle swarm, namely 7. the concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 6, is characterized in that, the minimum variance resampling process of step 6 specifically comprises: Minimum variance resampling: according to the size of the weight, the residual particle swarm sort, and sample NL particles with the largest weight, which are MSV particles. This process can be characterized by the function TopRank _NL ( ), as shown in formula (8): Since the sampling process is independent and identically distributed, after resampling, the weights of MSV particles are all 1/N. 8. The concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 7, is characterized in that, the prediction and update process of step 7 specifically comprises: The weighted summation of the copied particle swarm, MSV particle swarm and their corresponding weights, as shown in formula (9), can obtain the predicted value of freeze-thaw life Combine the copy particle swarm with particle number NL and the MSV particle swarm with the number L to keep the total number of particles at N, and use these two particle swarms as the update particle swarm Simultaneously for the state value of the relative dynamic modulus of elasticity initial damage velocity/> and particle weights/> to update. 9. The concrete freeze-thaw life prediction method of minimum sampling variance particle filter according to claim 8, is characterized in that, step 8 specifically comprises: Calculate the relative dynamic elastic modulus a posteriori estimated predicted value, as shown in formula (10), meanwhile, let t=t+1, will As an iterative particle swarm, repeat steps 3 to 7 above until the relative dynamic elastic modulus Or the number of freeze-thaw cycles t≥200, stop the freeze-thaw experiment and prediction process; the total time experienced in the above process is the remaining life of concrete freeze-thaw;