CN112800615A - Method for predicting residual life of silicon foam material - Google Patents

Method for predicting residual life of silicon foam material Download PDF

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CN112800615A
CN112800615A CN202110157298.7A CN202110157298A CN112800615A CN 112800615 A CN112800615 A CN 112800615A CN 202110157298 A CN202110157298 A CN 202110157298A CN 112800615 A CN112800615 A CN 112800615A
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retention rate
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王九龙
盛俊杰
温金鹏
张思才
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General Engineering Research Institute China Academy of Engineering Physics
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Abstract

The invention discloses a method for predicting the residual life of a silicon foam material, which relates to the field of material life prediction, and comprises the steps of S1 obtaining residual pretightening force data of the silicon foam material and converting the residual pretightening force data into a load retention rate; s2, establishing a basic physical degradation model and superposing test errors; s3, obtaining the prior probability distribution of the load retention rate according to the basic physical degradation model; s4, updating the prior probability distribution to obtain the posterior probability distribution of the load retention rate; s5, predicting the degradation trend and the residual life of the pretightening force of the silicon foam material; a more targeted double-exponential physical model of the stress relaxation of the silicon foam material is provided, based on a digital-analog linkage thought, a Bayesian theory is adopted, a probability density function of a system state is estimated according to observation data of the system, and a degradation trend and a residual life of the pre-tightening force of the silicon foam material are predicted, so that not only is empirical knowledge of a material pre-tightening force decay process considered, but also dynamic information of monitoring data is fused, and the accuracy problem of the physical model based on a model method can be improved.

Description

Method for predicting residual life of silicon foam material
Technical Field
The invention relates to the field of material life prediction, in particular to a method for predicting the residual life of a silicon foam material.
Background
The silicon foam material is a viscoelastic damping material formed by foaming silicon rubber, is widely applied to the fields of heat insulation, packaging and the like due to high temperature resistance, aging resistance and good viscoelastic performance, is filled among multiple layers of structural members and used for compensating interlayer gap change caused by the change of environmental temperature of each layer, and is used as a damping material to absorb energy in the vibration process so as to achieve the purposes of damping and noise control. However, as a typical high polymer material, a silicon foam material can generate a relaxation effect in a long-term use process, and the pretightening force of the silicon foam material is continuously reduced along with the reduction of the stress level, so that the heat insulation and shock absorption effects of the silicon foam material are further weakened, and once the pretightening force between layers is reduced to a certain degree, the whole structure can be caused to loosen. Therefore, for the stress relaxation effect of the silicon foam material, it is necessary to establish a targeted prediction method of the residual life of the pretensioning performance, and the pretensioning performance is replaced in time before the stress level of the pretensioning performance is reduced to a specified threshold value, so that the long-term stable operation of the product is realized.
For residual life prediction, a large number of prediction methods have been proposed by scholars at home and abroad. According to different principles of the method, the existing residual life prediction method can be roughly divided into three categories: model-based methods, data-driven methods, and digital-analog linkage methods. At present, a method based on an exponential model or a logarithmic exponential model is generally adopted for a high polymer material, and a physical model is established according to a failure mechanism of the material to describe the degradation trend of a product, so that the residual life under a specific stress level is predicted. The prior researches show that the failure mechanism of the silicon foam material is different from that of a typical high polymer material, the stress relaxation of the silicon foam material is influenced by two factors of a material cell structure and the material, the early relaxation is mainly physical relaxation caused by compressing the cell structure, and the later relaxation is mainly embodied in chemical relaxation caused by the material. Because the performance parameters and the microscopic stress parameters of the silicon foam material are difficult to obtain accurately and the failure mechanism is not clear enough, no accurate physical degradation model is available at present for describing the stress relaxation degradation process.
Disclosure of Invention
The invention aims to solve the problems and designs a method for predicting the residual life of a silicon foam material.
The invention realizes the purpose through the following technical scheme:
the method for predicting the residual life of the silicon foam material comprises the following steps:
s1, acquiring residual pretightening force data of the silicon foam material, and converting the residual pretightening force data into load retention rate of
Figure BDA0002934221010000021
Wherein FkPre-tightening force of step k, F0For the initial pre-tightening force,
Figure BDA0002934221010000022
is the load retention;
s2, establishing a basic physical degradation model of the silicon foam material, and superposing test errors;
s3, obtaining the prior probability distribution of the load retention rate according to the basic physical degradation model;
s4, updating the prior probability distribution according to the prior probability distribution and the Bayes theory to obtain the posterior probability distribution of the load retention rate;
and S5, predicting the degradation trend and the residual life of the pretightening force of the silicon foam material according to the posterior probability distribution particles.
The invention has the beneficial effects that: a more targeted double-exponential physical model of the stress relaxation of the silicon foam material is provided, the Bayesian theory is adopted based on the digital-analog linkage thought, the prior knowledge of the stress relaxation of the material and the dynamic information of observation data are fused at the same time, the degradation trend and the residual life of the pre-tightening force of the silicon foam material are predicted, the empirical knowledge of the decay process of the material pre-tightening force is considered, the dynamic information of monitoring data is fused, and the accuracy problem of the physical model based on a model method can be improved.
Drawings
FIG. 1 is a schematic flow chart of a method for predicting the remaining life of a silicone foam according to the present invention;
FIG. 2 is a graph showing the degradation tendency of the actually measured load holding rate of the method for predicting the remaining life of a silicon foam of the present invention;
FIG. 3 is a prior probability distribution diagram of the method for predicting the residual life of a silicon foam material according to the present invention;
FIG. 4 is a posterior probability distribution diagram of the method for predicting the remaining life of the silicon foam of the present invention;
FIG. 5 is a graph showing the prediction of the degradation tendency of the method for predicting the remaining life of a silicon foam according to the present invention;
FIG. 6 is a graph showing the prediction of the remaining life of the silicone foam according to the method for predicting the remaining life of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "inside", "outside", "left", "right", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, or the orientations or positional relationships that the products of the present invention are conventionally placed in use, or the orientations or positional relationships that are conventionally understood by those skilled in the art, and are used for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
Furthermore, the terms "first," "second," and the like are used merely to distinguish one description from another, and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it is also to be noted that, unless otherwise explicitly stated or limited, the terms "disposed" and "connected" are to be interpreted broadly, and for example, "connected" may be a fixed connection, a detachable connection, or an integral connection; can be mechanically or electrically connected; the connection may be direct or indirect via an intermediate medium, and may be a communication between the two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
The following detailed description of embodiments of the invention refers to the accompanying drawings.
As shown in fig. 1, the method for predicting the remaining life of a silicon foam material comprises the following steps:
s1, acquiring residual pretightening force data of the silicon foam material, and converting the residual pretightening force data into load retention rate of
Figure BDA0002934221010000041
Wherein FkPre-tightening force of step k, F0For the initial pre-tightening force,
Figure BDA0002934221010000042
the load retention ratio.
And S7, resampling the load retention rate at equal time intervals based on a polynomial interpolation method.
S2, establishing a basic physical degradation model of the silicon foam material, and superposing test errors;
s21, establishing a basic physical degradation model according to double relaxation factors of the silicon foam material
Figure BDA0002934221010000043
S22, unifying the basic physical degradation model and the state transfer function, and superposing the measurement error, wherein the basic physical degradation model is expressed as
Figure BDA0002934221010000044
Wherein ae-btIs a physical relaxation, ce-dtThe method is chemical relaxation, a and c are weights of physical relaxation and chemical relaxation respectively, b and d are relaxation factors, t is time, and theta is a random error obeying normal distribution;
s23, fitting the load retention rate by using a least square method, determining the distribution range of each parameter, initializing each parameter according to the initial distribution type of each parameter, and generating the load retention rate and the probability distribution of each parameter to obtain initial distribution particles; the initial distribution type is
Figure BDA0002934221010000045
Where N (μ, σ) represents a normal distribution subject to a mean μ and a variance σ, the prediction model parameters are determined: the number N of particles used for updating the model is generally between 1000 and 5000, adjustment is carried out according to the prediction situation during actual calculation, the significance level is generally selected from 0.1, 0.05 and 0.025, the failure threshold is determined according to different use requirements, the range is 0 to 1, and the iteration step length is determined according to the prediction object and the use requirements.
S3, obtaining the load retention rate of the k (k ═ 2: n) step and the prior probability distribution of each parameter according to the load retention rate of the k-1(k ═ 2: n) step and the probability distribution of each parameter by combining a basic physical model, wherein the expression is
Figure BDA0002934221010000051
Wherein Dk-1The actual measured value of the load retention rate in the previous k-1 step;
and S4, updating the prior probability distribution according to the measurement value of the k (k is 2: n) th step and based on Bayes theory to obtain the posterior probability distribution of the k (k is 2: n) th step, wherein the expression is
Figure BDA0002934221010000052
Wherein z iskThe measured value is the actual value of the load holding rate in the k-th step.
S6, resampling the particle swarm of the basic physical degradation model aiming at the particle degradation problem in the updating process, copying the particles with large weight, and eliminating the particles with small weight;
s61, obtaining the weight of each particle in the particle swarm according to the cumulative distribution function
Figure BDA0002934221010000053
Wherein j is 1: N, and N is the number of particles;
s62, generating a random number U based on the uniform distribution function U (0, 1), and calculating to satisfy
Figure BDA0002934221010000054
Minimum value of j, let original particle QjAs one of the new particles;
and S63, repeating S62 until N particles are regenerated.
And S5, predicting the degradation trend and the residual life of the pretightening force of the silicon foam material according to the posterior probability distribution particles.
The silicon foam material residual life prediction method provides a more targeted silicon foam material stress relaxation double-exponential physical model, based on a digital-analog linkage thought, adopts a Bayesian theory, and simultaneously fuses the prior knowledge of material stress relaxation and the dynamic information of observation data to predict the silicon foam material pre-tightening force degradation trend and residual life, not only considers the experience knowledge of the material pre-tightening force decay process, but also fuses the dynamic information of monitoring data, thereby improving the accuracy problem of the physical model based on a model method.
In order to unify the pre-tightening force measurement standards of materials with different interlayer structures, use environments, thicknesses and stress levels, the residual pre-tightening force is converted into a load retention rate, as shown in table 1, the load retention rate is used for representing the pre-tightening performance of the materials at a specified time, and the load retention rate is expressed as
Figure BDA0002934221010000061
Wherein FkPre-tightening force of step k, F0For the initial pre-tightening force,
Figure BDA0002934221010000062
is the load retention;
table 1 raw load retention rate observations
Figure BDA0002934221010000063
Meanwhile, in order to unify the observation data format and the data model, the observation data is resampled at equal time intervals based on a polynomial interpolation method, if the original observation data meets the equal time sampling intervals, the step is omitted, and the degradation trend after resampling is shown in figure 2;
establishing a basic physical degradation model aiming at double relaxation factors of the silicon foam material, wherein the basic physical degradation model is expressed as
Figure BDA0002934221010000064
Wherein ae-btIs a physical relaxation, ce-dtThe chemical relaxation is carried out, a and c are weights of physical relaxation and chemical relaxation respectively, b and d are relaxation factors, and t is time;
for unifying the degeneration model and the state transfer function form, the model is expressed as a difference form
Figure BDA0002934221010000065
While taking into account measurement errors as
Figure BDA0002934221010000066
Where θ is the random error obeying a normal distribution;
fitting the acquired load retention rate by adopting a least square function, roughly determining the distribution range of each parameter, initializing each parameter according to the initial distribution type of the parameter, and generating the load retention rate and the probability distribution of each parameter to obtain initial distribution particles; the initial distribution type is
Figure BDA0002934221010000067
Selecting a load retention rate failure threshold value of 0.5, selecting a particle number of 5000, selecting a significance level of 0.1, and setting an iteration step length to be 1 day;
performing iterative update according to the basic physical degradation model and the observation data to obtain prior probability distribution of the k (k is 2: 500), so that observation and comparison are facilitated, the prior probability distribution of the load retention rate at 3 days, 250 days and 500 days is listed, as shown in fig. 3, it can be known from the figure that the load retention rate probability distribution at 3 days, 250 days and 500 days is normal, the distribution mean value is reduced along with the time lapse, and the distribution range is shifted to the zero point;
according to the actual measurement value of the load retention rate in the k step, updating the prior probability distribution to obtain the posterior probability distribution in the k step, and listing the posterior probability distributions of the load retention rate in 3 days, 250 days and 500 days, as shown in fig. 4, it can be known from the figure that compared with the prior probability distribution, the posterior probability distribution also presents a normal distribution form, the distribution range of the posterior probability distribution moves to zero point transition along with time push, but the posterior probability distribution is more concentrated;
resampling the particle swarm, copying particles with large weight, and eliminating particles with small weight; the specific process is to calculate the cumulative distribution function of each particle weight in the particle swarm
Figure BDA0002934221010000071
Wherein j is 1: N, and N is the number of particles; generating a random number U based on a uniformly distributed function U (0, 1), and calculating to satisfy
Figure BDA0002934221010000072
Minimum value of j, let original particle QjAs one of the new particles until the N particles are regenerated;
and predicting the degradation trend of the load retention rate of the silicon foam material and the residual life according to the posterior probability distribution particles after resampling. The load retention rate degradation trend is shown in fig. 5, and it can be known from the graph that within the 90% confidence interval range, the predicted value is more consistent with the actual measured value of the load retention rate, the predicted value of the PF algorithm is more stable, and the error is less than 5%.
At day 250, the remaining life distribution is shown in fig. 6 with the 50% load retention rate as the failure threshold, and the distribution type is normal, and the average life value is about 1280 days.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims (6)

1. The method for predicting the residual life of the silicon foam material is characterized by comprising the following steps of:
s1, acquiring residual pretightening force data of the silicon foam material, and converting the residual pretightening force data into load retention rate of
Figure FDA0002934220000000011
Wherein FkPre-tightening force of step k, F0For the initial pre-tightening force,
Figure FDA0002934220000000012
is the load retention;
s2, establishing a basic physical degradation model of the silicon foam material, and superposing test errors;
s3, obtaining the prior probability distribution of the load retention rate according to the basic physical degradation model;
s4, updating the prior probability distribution according to the prior probability distribution and the Bayes theory to obtain the posterior probability distribution of the load retention rate;
and S5, predicting the degradation trend and the residual life of the pretightening force of the silicon foam material according to the posterior probability distribution particles.
2. The method of predicting remaining life of silicon foam according to claim 1, wherein in S2 comprises:
s21, establishing a basic physical degradation model according to double relaxation factors of the silicon foam material
Figure FDA0002934220000000013
S22, unifying the basic physical degradation model and the state transfer function, and superposing the measurement error, wherein the basic physical degradation model is expressed as
Figure FDA0002934220000000014
Wherein ae-btIs a physical relaxation, ce-dtThe method is chemical relaxation, a and c are weights of physical relaxation and chemical relaxation respectively, b and d are relaxation factors, t is time, and theta is a random error obeying normal distribution;
s23, fitting the load retention rate by using a least square method, determining the distribution range of each parameter, initializing each parameter according to the initial distribution type of each parameter, and generating the load retention rate and the probability distribution of each parameter to obtain initial distribution particles; the initial distribution type is
Figure FDA0002934220000000015
Where N (μ, σ) represents a normal distribution obeying a mean μ and a variance σ.
3. The method of claim 1, wherein in step S3, the load retention rate of step k and the prior probability distribution of each parameter are obtained according to the load retention rate of step k-1 (k-2: n) and the probability distribution of each parameter, and the prior probability distribution is expressed as
Figure FDA0002934220000000021
Wherein Dk-1The actual measurement value of the load retention rate in the previous k-1 step is shown.
4. The method of claim 3, wherein in S4, the prior probability distribution is updated according to the actual measured value of the load-holding ratio in the k-th step to obtain the posterior probability distribution in the k-th step, and the posterior probability distribution is expressed as
Figure FDA0002934220000000022
Wherein z iskThe measured value is the actual value of the load holding rate in the k-th step.
5. The method for predicting the remaining life of the silicon foam material as claimed in any one of claims 1 to 4, further comprising S6 between S4 and S5, resampling the particle group of the basic physical degradation model, specifically:
s61, obtaining the weight of each particle in the particle swarm according to the cumulative distribution function
Figure FDA0002934220000000023
Wherein j is 1: N, and N is the number of particles;
s62, generating a random number U based on the uniform distribution function U (0, 1), and calculating to satisfy
Figure FDA0002934220000000024
Minimum value of j, let original particle QjAs one of the new particles;
and S63, repeating S62 until N particles are regenerated.
6. The method for predicting remaining life of silicone foam according to any one of claims 1-4, further comprising S7 between S1 and S2, and resampling the load holding ratio at equal time intervals based on polynomial interpolation.
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