CN112949184B - Concrete freeze-thawing life prediction method by minimum sampling variance particle filtering - Google Patents
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Abstract
The invention relates to a concrete freeze-thawing life prediction method of minimum sampling variance particle filtering, which aims at the problem of prediction precision reduction caused by the lack of particle diversity in standard particle filtering, and is provided with higher prediction precision compared with an auxiliary particle filtering algorithm and a standard particle filtering algorithm by introducing sampling variance as a cost function in the concrete freeze-thawing life prediction method, so that the information loss in the resampling process can be reduced to the greatest extent, the lack of particle diversity can be effectively relieved, and the method is suitable for a higher-dimensional and more complex state space model.
Description
Technical Field
The invention belongs to the field of concrete durability analysis and evaluation, and relates to a concrete freeze-thawing life prediction method by minimum sampling variance particle filtering.
Background
The particle filtering algorithm can represent the degradation process of freeze thawing damage under various uncertain factors through a large number of particles, has low requirements on model complexity, does not need a large amount of training data, and can correct a prediction result in time by combining with a proper observation means. Based on the above advantages, standard Particle Filter (PF) algorithms have realized life prediction in the areas of crack propagation, concrete freeze thawing, li batteries, PEM fuel cells, turbine blades, aircraft actuator systems, and fighter engines, etc., and have higher life prediction accuracy compared to conventional reliable life prediction methods.
Although the standard particle filtering algorithm solves the degradation problem by combining the suboptimal solution with the resampling algorithm, the sampling is simple and easy to realize, and a new problem, namely the phenomenon of particle diversity shortage, is introduced. The phenomenon of lack of particle diversity refers to that a lot of particles in the original particle swarm have no 'offspring' due to the fact that the weight of the particles is too small, a few particles with higher weight of the particles have the same 'offspring', the particle swarm after resampling consists of a large number of repeated particles, and as resampling is carried out, the particles with small weight are discarded with high probability, so that the diversity of the particle swarm is reduced, and even only one repeated particle is remained finally. When the number of iterations is large or the number of particles is small, the accuracy of freeze-thawing life prediction will be reduced.
One of the methods for solving the shortage of particle diversity is to ensure the consistency of particle distribution before and after resampling. Theoretically, to ensure consistency before and after resampling, the number of samples of particles with a sequence number i should be equal to the mathematical expectation, i.e. the weighting of the number of particles and the weight. However, the sampling times can only be integers, so that the particle distribution inevitably generates discrete errors before and after resampling, and the information in the resampling process is gradually lost along with the accumulation of the resampling times, so that the posterior probability of the freeze-thawing life prediction is gradually distorted, and finally the precision of the freeze-thawing life prediction is reduced.
Disclosure of Invention
In order to overcome the phenomenon of lack of particle diversity and improve the accuracy of freeze-thawing life prediction, the invention provides a concrete freeze-thawing life prediction method by minimum sampling variance particle filtering.
The technical scheme adopted by the invention is as follows:
a concrete freeze-thawing life prediction method of minimum sampling variance particle filtering comprises the following steps:
step 1, constructing a state equation and a noise model thereof for describing a multi-factor freeze-thawing damage degradation rule based on a relative dynamic elastic modulus attenuation model in a single-segment mode;
step 2, monitoring ultrasonic sound in the concrete by adopting an ultrasonic nondestructive detection method; an observation equation is constructed through the relation between the relative dynamic elastic modulus and the ultrasonic sound time; meanwhile, a state space model describing freeze thawing degradation is constructed by combining the state equation in the step 1;
before the multi-factor freeze thawing cycle starts, each test piece is subjected to ultrasonic nondestructive testing once, and reference sound is acquired;
step 3, judging whether the sound detection is updated or not so as to predict the service life;
initializing model parameters and particle swarms; during the multi-factor freeze-thaw cycle,
if the ultrasonic nondestructive testing is not performed, substituting the particle swarm into a state equation to generate a priori estimate, and then carrying out weighted summation on the priori estimate and the particle weight to obtain a posterior estimate, and updating the particle swarm, wherein the posterior estimate can be regarded as a predicted value of the freeze-thawing cycle times;
if ultrasonic nondestructive testing is carried out, a new sound time signal is obtained, substituting a particle swarm at the time t into a state space model, and generating N sound time predicted values; making the sound time predicted value and the experimental detection value differ, and calculating to obtain normalized weights corresponding to the N sound time predicted values under the assumption that the difference value meets Gaussian distribution;
step 4, copying particles with particle weights larger than 1/N to obtain a complex particle swarm, wherein the particle number of the complex particle swarm is L;
step 5, after extracting complex particle swarm from the original particle swarm, calculating the weight of the residual particle swarm to obtain residual particle swarm, wherein the residual particle swarm consists of the residual particle swarm and the weight thereof;
step 6, resampling the minimum variance; sequencing the residual particle swarm according to the weight, sampling N-L particles with the largest weight, namely MSV particles, from the residual particle swarm by utilizing a TopRank function, wherein the weight of the resampled particles is 1/N;
step 7, predicting and updating; weighting and summing the complex particle swarm, the MSV particle swarm and the corresponding weights to obtain a freeze-thawing life prediction value; combining a replication particle group with the number of N-L particles with an MSV particle group with the number of L particles, keeping the total number of the particles as N particles, taking the two particle groups as updated particle groups, and updating the relative dynamic elastic modulus state value, the initial damage speed, the particle weight and the number of the particles;
step 8, taking the updated particle swarm as an iterative particle swarm, repeating the steps 3 to 7 until the set condition is reached, and stopping the freezing and thawing experiment and prediction process; the total time of the process is the residual life of the concrete after freezing and thawing.
Further, in step 1, the expression of the state equation is:
in the formula (1), E t The relative dynamic elastic modulus at the time t of the freeze thawing cycle is shown; c represents the damage acceleration, A represents the initial damage speed, and the two can be obtained through experimental fitting; Δt represents a time interval between time t and time t+1; omega t+1 Zero mean Gaussian white noise representing additive, satisfies Is the state noise variance.
Further, in step 1, a reference lesion acceleration C is defined 0 Constant, reference initial injury velocity A 0 The gaussian distribution is satisfied as shown in formula (2):
in the formula (2), mean (·) represents a mean function, Q represents the number of test pieces for freeze thawing experiments, and Var (·) represents a variance function.
Further, in step 2, the expression of the observation equation is:
in the formula (3), T t When representing ultrasonic sound at time T of freeze thawing cycle, T 0 Representing the reference sound time measured by an ultrasonic method before the freeze-thawing cycle starts; upsilon (v) t+1 Represents observation noise, satisfies For the state noise variance, define the observation noise v t+1 Zero mean gaussian white noise;
in combination with the formula (1), a state space model is constructed as shown in the formula (4):
further, the step 3 specifically includes:
model parameters and particle populationsInitializing, wherein the weight is->N is the number of particles;
at time t+1 of the multi-factor freeze thawing cycle, substituting the particle swarm at time t into a state equation to generate prior estimation if ultrasonic nondestructive testing is not performedThen the prior estimation and the particle weight are weighted and summed to obtain posterior estimation +.>And update the iterative particle->The posterior estimate of the relative dynamic elastic modulus can be considered as a predictor of the number of freeze-thaw cycles;
if multi-factor freeze thawing cycle t+1 is performed with ultrasonic nondestructive test, a new ultrasonic time T is obtained t+1 Then the particle swarm at the time t is selectedSubstituting into state space model, generating N ultrasonic prediction values +.>Let the predicted value and experimental detection value T at sound time exp Difference is made if the difference satisfies Gaussian distribution +.>The normalized weight corresponding to the predicted values of N voices can be calculated>
Further, the particle replication process of step 4 specifically includes:
copying particles with the particle weight being greater than 1/N into N i The weight of the components is calculated by the weight,obtaining a population of replicating particlesWherein L is the number of replicative particles, as shown in formula (6);
in the method, in the process of the invention,is a rounding operation.
Further, step 5 specifically includes:
residual particle calculation from raw particle swarmAfter the complex particle swarm is extracted, the weight of the residual particle swarm is changed, and the calculation formula is as follows:
the residual particle group and its weight are called residual particle group, i.e
Further, the minimum variance resampling process of step 6 specifically includes:
minimum variance resampling: according to the weight, for the residual particle groupSequencing and sampling N-L particles with the largest weight value to obtain MSV particles, wherein the process can be realized through a function TopRank N-L (. Cndot.) characterization is performed as shown in formula (8):
because the sampling process is independent and distributed, the MSV particle weight is 1/N after resampling.
Further, the predicting and updating process in step 7 specifically includes:
weighting and summing the complex particle swarm, MSV particle swarm and the corresponding weight values, as shown in formula (9), to obtain the freeze-thawing life prediction value
Combining a copy particle group with the number of N-L particles with an MSV particle group with the number of L particles to maintain the total number of the particles as N, and taking the two particle groups as update particle groupsAt the same time for the state value of the relative dynamic elastic modulus +.>First-speed of injury->Particle weightAnd updating.
Further, the step 8 specifically includes:
calculating a predicted value of the posterior estimation of the relative dynamic elastic modulus as shown in the formula (10), and simultaneously, let t=t+1 to beRepeating the steps 3 to 7 until the relative dynamic elastic modulus is +.>Or the number of freeze thawing cycles t is more than or equal to 200, and stopping the freeze thawing experiment and prediction process; the total time of the process is the residual life of the concrete after freezing and thawing;
the invention has the beneficial effects that:
according to the concrete freeze-thawing life prediction method for the minimum sampling variance particle filtering (Minimum Sampling Variance Particle Fitler, MSVPF), which is provided by the invention, aiming at the phenomenon of particle diversity deficiency caused by the consistency of particle distribution before and after resampling, the traditional resampling method adopted by the standard particle filtering algorithm is unable to ensure that the sampling variance is introduced as a cost function, and under the condition that resampling is established, a TopRank function is utilized to resample a particle swarm, so that the sampling variance after resampling is minimum, posterior probability distribution can be reserved to the greatest extent, that is, information loss in the resampling process is reduced to the greatest extent, the phenomenon of particle diversity deficiency can be effectively relieved, the characteristic of dimensional freedom is not lost, and compared with an auxiliary particle filtering algorithm and a standard particle filtering algorithm, the concrete freeze-thawing life prediction method for the minimum sampling variance particle filtering (Minimum Sampling Variance Particle Fitler, MSVPF) has higher precision under the condition of the same particle number, can save a large amount of calculation consumption, is more suitable for the engineering application of online prediction of a complex high-dimensional freeze-thawing life prediction state space model with more than three-order, and is effective supplement to a deterministic resampling algorithm (relatively speaking, the deterministic resampling algorithm has higher precision).
Drawings
FIG. 1 is a block flow diagram of a method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to the present invention;
FIG. 2 is a graph of the concrete freeze-thaw cycle temperature;
FIG. 3 is a sample variance comparison of Minimum Sample Variance Particle Filter (MSVPF) and standard Particle Filter (PF) algorithms during freeze-thaw life prediction;
FIG. 4 is a comparison of lifetime prediction results of MSVPF, auxiliary Particle Filter (APF) and PF algorithms;
fig. 5 is a comparison of lifetime prediction results of an MSVPF and a Deterministic Resampling Particle Filter (DRPF) algorithm.
Detailed Description
The concrete freeze-thaw life prediction method of the minimum sampling variance particle filter of the present invention is described in further detail below with reference to the accompanying drawings and specific examples.
As shown in fig. 1, a method for predicting the freeze-thawing life of concrete by minimum sampling variance particle filtering comprises the following steps:
step 1, constructing a state equation and a noise model thereof for describing a multi-factor freeze-thawing damage degradation rule based on a relative dynamic elastic modulus attenuation model in a single-segment mode;
in step 1, the expression of the state equation is:
in the formula (1), E t The relative dynamic elastic modulus at the time t of the freeze thawing cycle is shown; c represents the damage acceleration, A represents the initial damage speed, and the two can be obtained through experimental fitting; Δt represents a time interval between time t and time t+1; omega t+1 Zero mean Gaussian white noise representing additive, satisfies Is the state noise variance.
The basic attenuation rule of the state equation is approximately parabolic, the uncertainty of the state equation is mainly related to the damage acceleration C and the damage initial speed A, the main influencing factors such as material composition, chloride salt concentration and the like are considered, and the reference damage acceleration C is defined by combining the statistical result of experimental data 0 Constant, reference initial injury velocity A 0 The gaussian distribution is satisfied as shown in formula (2):
in the formula (2), mean (·) represents a mean function, Q represents the number of test pieces for freeze thawing experiments, and Var (·) represents a variance function.
Additive zero-mean Gaussian white noise omega t+1 The noise model is introduced to expand the support domain of life prediction. The state equation and the noise model comprise two noise distributions, not only consider uncertainty caused by factors such as material composition, chloride concentration and the like, but also consider other uncertainty in the freeze thawing degradation process, and have higher robustness. The state equation is applicable to the influence of various uncertain factors and has universality.
Step 2, monitoring ultrasonic sound time (Ultrasonic Pulse Transmission Time, UPTT, also called ultrasonic pulse propagation time) in the concrete by adopting an ultrasonic nondestructive testing method; an observation equation is constructed through the relation between the relative dynamic elastic modulus and the ultrasonic sound time; meanwhile, a state space model describing freeze thawing degradation is constructed by combining the state equation in the step 1;
before the multi-factor freeze thawing cycle starts, each test piece is subjected to ultrasonic nondestructive testing once, and reference sound is acquired;
in step 2, the expression of the observation equation is:
in the formula (3), T t When representing ultrasonic sound at time T of freeze thawing cycle, T 0 Representing the reference sound time measured by an ultrasonic method before the freeze-thawing cycle starts; upsilon (v) t+1 Represents observation noise, is used for representing uncertainty monitoring errors of ultrasonic nondestructive detection, and meets the following requirements For the state noise variance, define the observation noise v t+1 Zero mean gaussian white noise;
combining equation (1) and equation (3), constructing a state space model that can be constructed to describe freeze-thaw degradation, as shown in equation (4):
step 3, judging whether the sound detection is updated or not so as to predict the service life;
initializing model parameters and particle swarms; during the multi-factor freeze-thaw cycle,
if the ultrasonic nondestructive testing is not performed, substituting the particle swarm into a state equation to generate a priori estimate, and then carrying out weighted summation on the priori estimate and the particle weight to obtain a posterior estimate, and updating the particle swarm, wherein the posterior estimate can be regarded as a predicted value of the freeze-thawing cycle times;
if the ultrasonic nondestructive testing is carried out, a new sound time signal is obtained, the current particle swarm is substituted into the state space model, and N sound time predicted values are generated; making the sound time predicted value and the experimental detection value different, and if the difference value meets Gaussian distribution, calculating to obtain normalized weights corresponding to the N sound time predicted values;
the step 3 specifically comprises the following steps:
model parameters and particle populationsInitializing, wherein the weight is->N is the number of particles;
at time t+1 of the multi-factor freeze thawing cycle, substituting the particle swarm at time t into a state equation to generate prior estimation if ultrasonic nondestructive testing is not performedThen the prior estimation is carried outWeighted summation with particle weights, as shown in equation (5), to obtain a posterior estimate +.>And update the iterative particle->The posterior estimate of the relative dynamic elastic modulus can be considered as a predictor of the number of freeze-thaw cycles;
if multi-factor freeze thawing cycle t+1 is performed with ultrasonic nondestructive test, a new ultrasonic time T is obtained t+1 Then the particle swarm at the time t is selectedSubstituting into state space model, generating N ultrasonic prediction values +.>Let the predicted value and experimental detection value T at sound time exp Difference is made if the difference satisfies Gaussian distribution +.>The normalized weight corresponding to the predicted values of N voices can be calculated>
Step 4, copying particles with particle weights larger than 1/N to obtain a complex particle swarm, wherein the particle number of the complex particle swarm is L;
the step 4 specifically comprises the following steps:
copying particles with the particle weight being greater than 1/N into N i The weight of the components is calculated by the weight,obtaining a population of replicating particlesWherein L is the number of the copied particles, as shown in the formula (6), the weight of the copied particles is not determined at the moment, and the weight is determined after the particle space sampling process is finished;
in the method, in the process of the invention,is a rounding operation.
Step 5, after extracting complex particle swarm from the original particle swarm, calculating the weight of the residual particle swarm to obtain residual particle swarm, wherein the residual particle swarm consists of the residual particle swarm and the weight thereof;
the step 5 specifically comprises the following steps:
residual particle calculation from raw particle swarmAfter the complex particle swarm is extracted, the weight of the residual particle swarm is changed, and the calculation formula is as follows:
the residual particle group and its weight are called residual particle group, i.e
And 6, resampling the minimum variance. Sequencing the residual particle swarm according to the weight, sampling N-L particles with the largest weight, namely MSV particles, from the residual particle swarm by utilizing a TopRank function, wherein the weight of the resampled particles is 1/N;
the step 6 specifically comprises the following steps:
minimum variance resampling: according to the weight, for the residual particle groupSequencing and sampling N-L particles with the largest weight value to obtain MSV particles, wherein the process can be realized through a function TopRank N-L (. Cndot.) characterization is performed as shown in formula (8):
because the sampling process is independent and distributed, the MSV particle weight is 1/N after resampling.
And 7, predicting and updating. And carrying out weighted summation on the complex particle swarm, the MSV particle swarm and the corresponding weights, and obtaining the freeze-thawing life prediction value. Combining a replication particle group with the number of N-L particles with an MSV particle group with the number of L particles, keeping the total number of the particles as N particles, taking the two particle groups as updated particle groups, and updating the relative dynamic elastic modulus state value, the initial damage speed, the particle weight and the number of the particles;
the step 7 specifically comprises the following steps:
weighting and summing the complex particle swarm, MSV particle swarm and the corresponding weight values, as shown in formula (9), to obtain the freeze-thawing life prediction value
Combining a copy particle group with the number of N-L particles with an MSV particle group with the number of L particles to maintain the total number of the particles as N, and taking the two particle groups as update particle groupsAt the same time for the state value of the relative dynamic elastic modulus +.>First-speed of injury->Particle weightAnd updating.
Step 8, taking the updated particle swarm as an iterative particle swarm, repeating the steps 3 to 7 until the set condition is reached, and stopping the freeze thawing experiment and prediction process; the total time of the process is the residual life of the concrete after freezing and thawing.
The step 8 specifically comprises the following steps:
calculating a predicted value of the posterior estimation of the relative dynamic elastic modulus as shown in the formula (10), and simultaneously, let t=t+1 to be
Repeating the steps 3 to 7 until the relative dynamic elastic modulus is reached as an iterative particle groupOr the number of freeze thawing cycles t is more than or equal to 200, and stopping the freeze thawing experiment and prediction process; the total time of the process is the residual life of the concrete after freezing and thawing.
In the following, the implementation of the method according to the invention will be described in detail by taking as an example freeze-thaw damage experiments for strength grade C30 and C50 concrete in chloride salt solutions of 3%, 5% and 20% concentration.
The concrete test piece size is 40×40×160mm 3 3 freeze thawing experiments are respectively carried out under each strength and chloride concentration, 18 test pieces are added, and the test pieces are numbered as P1A3-1, P1A 3-2-P2A 20-3 according to the concrete strength and the chloride concentration, wherein P represents the concrete strength, and A represents the chloride concentration.
The freeze thawing test was carried out using a CDF tester manufactured by Schleinger, germany, and the salt freezing test system was according to the CDF test method proposed by the European International Association of materials laboratories (RILEM) TC117-FDC professional Commission, as shown in FIG. 2. The method adopts a freeze thawing cycle period of 12 hours, the initial temperature is 20 ℃, and the temperature is kept constant for 3 hours after the temperature is reduced to-20 ℃ at a constant temperature reduction rate (10 ℃/h) within 4 hours; then heating for 4 hours to 20 ℃ at a constant heating rate (10 ℃/h), and keeping the temperature for 1 hour, and sequentially and circularly carrying out. Removing the mould after molding for 1 day, putting the mould into a standard curing room for curing for 28 days, and then putting the mould into chlorine salt snow-melting agent solutions with different concentrations for soaking for 4 days until the mould is saturated; and then quick freeze thawing is carried out in a corresponding chloride solution for 200 times, each freeze thawing is carried out for 25 times according to GBJ82-85, scum on the surface of a test piece is cleaned before measurement, surface water is wiped off, when sound propagated by the test piece is measured by adopting an NM-4B nonmetal ultrasonic detection analyzer, and then the change of relative dynamic elastic modulus of the freeze thawing for 25, 50, 75, 100, 125, 150, 175 and 200 times is compared and analyzed according to sound velocity calculated under the condition of known thickness.
And (3) combining a relative dynamic elastic modulus attenuation model, processing relative dynamic elastic modulus change data of the test piece except the P2A3-3 by utilizing a Matlab polynomial fitting tool box, and respectively obtaining a curve for each strength and chloride salt concentration, wherein the damage acceleration and the damage initial speed of each curve are shown in a table 1.
TABLE 1 Matlab cftool fitting calculation of the damaged acceleration and initial velocity values for each test piece
According to the formula (2), the reference damage acceleration C 0 Defined as a constant, the average value of which is-1.9294 ×10 -5 ，A 0 To satisfy the Gaussian distribution N (-9.4767 ×10) -5 ,(8.1080×10 -4 ) 2 ) Is a random number of (a) in the memory. Assuming that the influence of other non-main factors on the prediction of the freeze-thawing life is about 2%, let ω t+1 ～N(0,0.02 2 ). Finally, a state equation can be constructed as shown in equation (11), where Δt=1.
The ultrasonic pulse propagation time and pulse wave velocity of the P2A3-3 test piece under different freeze-thawing cycles measured by the ultrasonic method are shown in table 2. Considering the length measurement error caused by the concrete block flaking phenomenon in the freeze thawing test process, 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 true value of the relative dynamic elastic modulus. The ultrasonic pulse propagation time precision of NM-4B type equipment is 0.1 mu s, the acoustic time mean value of all test pieces before freezing and thawing is about 32 mu s, and if the ultrasonic pulse propagation time error is subject to Gaussian distribution, the observed noise is approximately subject to Gaussian distribution upsilon t+1 ～N(0,4.526 2 ). Substituting the parameters into the formula (4), the finally constructed state space model is shown as the formula (12):
TABLE 2 UPTT and ultrasonic Sound velocity measured for P2A3-3 test pieces at different freeze thawing cycle times
For comparison with the life prediction effect of the traditional reliability algorithm, experimental data of P2A3-1 and P2A3-2 are firstly used for fitting by using a Matlab polynomial fitting tool box to obtain a relative dynamic elastic modulus attenuation model of C50 concrete at 3% concentration, fitting parameters are shown as P2A3 in table 1, and a fitting curve represents the effect of the traditional reliability method. And selecting a particle number N as 100, and setting a freeze-thawing cycle iteration interval delta t as 1, and respectively utilizing a Minimum Sampling Variance Particle Filter (MSVPF) and a standard Particle Filter (PF) online prediction algorithm to realize freeze-thawing degradation life prediction of the P2A3-3 test piece when the acoustic signals of the P2A3-3 test piece are updated. The sampling variance comparison of the MSVPF and PF algorithms during freeze-thaw life prediction is shown in FIG. 3. Aiming at the problem of discrete errors of the PF algorithm in the iterative process, the MSVPF resamples the particle swarm by using the TopRank function, so that the sampling variance after resampling is minimum, posterior probability distribution can be reserved to the greatest extent, that is, information loss in the resampling process is reduced to the greatest extent. Thus, as can be seen from fig. 3, compared with the PF algorithm, the MSVPF algorithm effectively reduces the sampling variance of particles, the average sampling variance of the PF algorithm in the life prediction process is 11.1602, and after the topmannk function processing, the sampling variance of the MSVPF algorithm has been reduced to 0.8223, the sampling variance is reduced by one order of magnitude, and the information loss in the resampling process is reduced to the greatest extent.
As shown in FIG. 4, the prediction results of the multi-factor concrete freeze-thawing degradation life of the MSVPF, the auxiliary particle filtering (Auxiliary Particle Filter, APF) and the PF algorithm take Root Mean square error (Root Mean-bean-SquareError, RMSE) of the prediction value and the experimental value as the comparison index of the life prediction precision, the smaller the RMSE is, the higher the precision is, and as can be seen from FIG. 4, compared with the APF and PF life prediction method, the MSVPF reduces the information loss in the resampling process to the greatest extent, effectively relieves the particle diversity shortage phenomenon, has the optimal prediction effect, and has the lowest RMSE of 0.005050 and 0.006036 and 0.007883 respectively. Meanwhile, compared with APF and PF algorithms, MSVPF adopts the same particle number, but obtains higher prediction precision, and the calculation time is similar, so that the method is more suitable for engineering application of online prediction of concrete freeze-thawing life.
The multi-factor concrete freeze-thaw degradation lifetime prediction result pair of MSVPF and deterministic resampling particle filtering (Deterministic Resampling Particle Filter, DRPF) algorithm is shown in fig. 5. As can be seen from fig. 5, the life prediction accuracy of the MSVPF and DRPF algorithms has been relatively close, and RMSE is 0.005050 and 0.003814, respectively. Although the accuracy of the MSVPF algorithm is slightly lower than that of the DRPF, the MSVPF algorithm provided by the invention has the characteristics that the dimension freedom is not lost compared with the DRPF, and compared with the APF and the PF, the MSVPF algorithm has higher accuracy under the condition of the same particle number, can save a large amount of calculation consumption, is more suitable for the engineering application of the on-line prediction of a complex high-dimensional freeze-thawing life prediction state space model with more than three orders, and is an effective supplement to the DRPF algorithm.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any alternatives or modifications, which are easily conceivable by those skilled in the art within the scope of the present invention, should be included in the scope of the present invention.
Claims (9)
1. The concrete freeze-thawing life prediction method of the minimum sampling variance particle filter is characterized by comprising the following steps of:
step 1, constructing a state equation and a noise model thereof for describing a multi-factor freeze-thawing damage degradation rule based on a relative dynamic elastic modulus attenuation model in a single-segment mode;
step 2, monitoring ultrasonic sound in the concrete by adopting an ultrasonic nondestructive detection method; an observation equation is constructed through the relation between the relative dynamic elastic modulus and the ultrasonic sound time; meanwhile, a state space model describing freeze thawing degradation is constructed by combining the state equation in the step 1;
before the multi-factor freeze thawing cycle starts, each test piece is subjected to ultrasonic nondestructive testing once, and reference sound is acquired;
step 3, judging whether the sound detection is updated or not so as to predict the service life;
initializing model parameters and particle swarms; during the multi-factor freeze-thaw cycle,
if the ultrasonic nondestructive testing is not performed, substituting the particle swarm into a state equation to generate a priori estimate, and then carrying out weighted summation on the priori estimate and the particle weight to obtain a posterior estimate, and updating the particle swarm, wherein the posterior estimate can be regarded as a predicted value of the freeze-thawing cycle times;
if ultrasonic nondestructive testing is carried out, a new sound time signal is obtained, substituting a particle swarm at the time t into a state space model, and generating N sound time predicted values; making the sound time predicted value and the experimental detection value differ, and calculating to obtain normalized weights corresponding to the N sound time predicted values under the assumption that the difference value meets Gaussian distribution;
the method specifically comprises the following steps:
model parameters and particle populationsInitializing, wherein the weight is->N is the number of particles;
at time t+1 of the multi-factor freeze thawing cycle, substituting the particle swarm at time t into a state equation to generate prior estimation if ultrasonic nondestructive testing is not performedThen the prior estimation and the particle weight are weighted and summed to obtain posterior estimation +.>And update the iterative particle->The posterior estimate of the relative dynamic elastic modulus can be considered as a predictor of the number of freeze-thaw cycles;
if multi-factor freeze thawing cycle t+1 is performed with ultrasonic nondestructive test, a new ultrasonic time T is obtained t+1 Then the particle swarm at the time t is selectedSubstituting into state space model, generating N ultrasonic prediction values +.>Let the predicted value and experimental detection value T at sound time exp The difference is made and the difference is made,if the difference satisfies the Gaussian distribution->The normalized weight corresponding to the predicted values of N voices can be calculated>
Step 4, copying particles with particle weights larger than 1/N to obtain a complex particle swarm, wherein the particle number of the complex particle swarm is L;
step 5, after extracting complex particle swarm from the original particle swarm, calculating the weight of the residual particle swarm to obtain residual particle swarm, wherein the residual particle swarm consists of the residual particle swarm and the weight thereof;
step 6, resampling the minimum variance; sequencing the residual particle swarm according to the weight, sampling N-L particles with the largest weight, namely MSV particles, from the residual particle swarm by utilizing a TopRank function, wherein the weight of the resampled particles is 1/N;
step 7, predicting and updating; weighting and summing the complex particle swarm, the MSV particle swarm and the corresponding weights to obtain a freeze-thawing life prediction value; combining a replication particle group with the number of N-L particles with an MSV particle group with the number of L particles, keeping the total number of the particles as N particles, taking the two particle groups as updated particle groups, and updating the relative dynamic elastic modulus state value, the initial damage speed, the particle weight and the number of the particles;
step 8, taking the updated particle swarm as an iterative particle swarm, repeating the steps 3 to 7 until the set condition is reached, and stopping the freezing and thawing experiment and prediction process; the total time of the process is the residual life of the concrete after freezing and thawing.
2. The method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 1, wherein in step 1, the expression of the state equation is:
in the formula (1), E t The relative dynamic elastic modulus at the time t of the freeze thawing cycle is shown; c represents the damage acceleration, A represents the initial damage speed, and the two can be obtained through experimental fitting; Δt represents a time interval between time t and time t+1; omega tυ1 Zero mean Gaussian white noise representing additive, satisfies Is the state noise variance.
3. The method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 2, wherein in step 1, a reference damage acceleration C is defined 0 Constant, reference initial injury velocity A 0 The gaussian distribution is satisfied as shown in formula (2):
in the formula (2), mean (·) represents a mean function, Q represents the number of test pieces for freeze thawing experiments, and Var (·) represents a variance function.
4. A method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 2 or 3, wherein in step 2, the expression of the observation equation is:
in the formula (3), T t When representing ultrasonic sound at time T of freeze thawing cycle, T 0 Representing the reference sound time measured by an ultrasonic method before the freeze-thawing cycle starts; upsilon (v) t+1 Represents observation noise, satisfies For the state noise variance, define the observation noise v t+1 Zero mean gaussian white noise;
in combination with the formula (1), a state space model is constructed as shown in the formula (4):
5. the method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 1, wherein the particle replication process of step 4 specifically comprises:
copying particles with the particle weight being greater than 1/N into N i The weight of the components is calculated by the weight,obtaining complex particle swarm->Wherein L is the number of replicative particles, as shown in formula (6);
in the method, in the process of the invention,is a rounding operation.
6. The method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 5, wherein step 5 specifically comprises:
residual particle calculation from raw particle swarmAfter the complex particle swarm is extracted, the weight of the residual particle swarm is changed, and the calculation formula is as follows:
the residual particle group and its weight are called residual particle group, i.e
7. The method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 6, wherein the minimum variance resampling process of step 6 specifically comprises:
minimum variance resampling: according to the weight, for the residual particle groupSequencing and sampling N-L particles with the largest weight value to obtain MSV particles, wherein the process can be realized through a function TopRank N-L (. Cndot.) characterization is performed as shown in formula (8):
because the sampling process is independent and distributed, the MSV particle weight is 1/N after resampling.
8. The method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 7, wherein the predicting and updating process of step 7 specifically comprises:
weighting and summing the complex particle swarm, MSV particle swarm and the corresponding weight values, as shown in formula (9), to obtain the freeze-thawing life prediction value
Combining a copy particle group with the number of N-L particles with an MSV particle group with the number of L particles to maintain the total number of the particles as N, and taking the two particle groups as update particle groupsAt the same time for the relative dynamic elastic modulus state valueFirst-speed of injury->Particle weight->And updating.
9. The method for predicting the freeze-thaw life of concrete by minimum sampling variance particle filtering according to claim 8, wherein step 8 specifically comprises:
calculating a predicted value of the posterior estimation of the relative dynamic elastic modulus as shown in the formula (10), and simultaneously, let t=t+1 to beRepeating the steps 3 to 7 until the relative dynamic elastic modulus is +.>Or the number of freeze thawing cycles t is more than or equal to 200, and stopping the freeze thawing experiment and prediction process; the total time of the process is the residual life of the concrete after freezing and thawing;
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