CN114528706B - Method for evaluating effective stress distribution of prestressed concrete structure based on limited data - Google Patents
Method for evaluating effective stress distribution of prestressed concrete structure based on limited data Download PDFInfo
- Publication number
- CN114528706B CN114528706B CN202210159864.2A CN202210159864A CN114528706B CN 114528706 B CN114528706 B CN 114528706B CN 202210159864 A CN202210159864 A CN 202210159864A CN 114528706 B CN114528706 B CN 114528706B
- Authority
- CN
- China
- Prior art keywords
- effective stress
- prestressed
- value
- tendon
- distribution
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Geometry (AREA)
- Data Mining & Analysis (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Evolutionary Computation (AREA)
- Mathematical Physics (AREA)
- Evolutionary Biology (AREA)
- Life Sciences & Earth Sciences (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Bioinformatics & Computational Biology (AREA)
- Architecture (AREA)
- Structural Engineering (AREA)
- Operations Research (AREA)
- Probability & Statistics with Applications (AREA)
- Algebra (AREA)
- Civil Engineering (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
Abstract
The invention discloses a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps of: calculating the theoretical distribution characteristic of the effective stress probability of the ith prestressed tendon of the existing concrete structure; the probability of the effective stress of the ith prestressed tendon is centralized; establishing a Gaussian mixture model; calculating skewness and kurtosis of the Gaussian mixture model; carrying out normal significance test and detection range determination on the Gaussian mixture model; detecting the effective stress value of the prestressed tendon of the existing structure; estimating the effective stress probability of the prestressed component lumped body; and estimating the effective stress probability of each component of the prestressed tendon.
Description
Technical Field
The invention relates to the technical field of prestressed concrete structures, in particular to a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data.
Background
The effective stress of the prestressed concrete structure is the residual stress value of the stress at the instantaneous tension end before the prestressed tendon is anchored after deducting all prestress losses, and the stress level is the premise of normal operation and maintenance and safe service of the structure and is one of the key indexes for evaluating the service performance of the existing structure.
A prestress loss certainty calculation method considering influences of anchoring instant and long-term service is provided in structural specifications of buildings, bridges and the like. However, the prestressed tendon is influenced by the randomness of parameters such as construction, materials, design and the like in the tensioning and service processes, so that the real effective stress of the prestressed tendon has uncertainty, and the deviation between the effective stress of the prestressed tendon and a theoretical value is large when the existing structure is actually detected. In addition, the prestressed system of the prestressed concrete frame structure is often composed of thousands or even tens of thousands of prestressed tendons, each prestressed tendon is influenced by design factors such as length, reinforcement ratio, concrete cross-sectional area and the like, so that stress loss of different degrees is caused, and effective stress distribution of the prestressed concrete frame structure has certain uneven characteristics.
The prestressed tendons of the post-tensioned prestressed concrete frame structure are numerous, the effective stress is uncertain and the distribution is uneven. And the effective stress of all the prestressed tendons of the structure cannot be comprehensively evaluated even after sampling detection. The existing method for evaluating the effective force based on the mean value has certain potential safety hazards. Therefore, how to provide a calculation method for the effective stress probability of the prestressed concrete structure based on the detection data, and further accurately calculate the effective stress probability distribution interval of each prestressed tendon of the existing prestressed concrete structure, so as to determine the prestress value applicable to safety evaluation of the existing structure, which is a problem that needs to be solved by the technical staff in the field.
Disclosure of Invention
In view of the above, the present invention provides a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data, so as to solve the potential safety hazard existing in the method for evaluating the effective stress by using a mean value.
In order to achieve the purpose of the invention, the following technical scheme is adopted in the application:
the invention relates to a method for evaluating the effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps:
(I) calculating theoretical distribution characteristics of the effective stress probability of the ith prestressed tendon of the existing concrete structure
Selecting an ith prestressed tendon from an existing concrete structure, wherein the calculation of the effective stress of the ith prestressed tendon comprises the following 12 uncertain parameters: stress sigma of tension control con Friction coefficient mu, pipeline deviation coefficient k, anchor deformation and prestress retraction value a, beam length l and prestress rib elastic modulus E p Compressive strength f ptk Concrete strength σ 'when prestressing force is applied' pc Beam cross-section net cross-sectional area A n Distance e from center of gravity of cross section to acting point of pre-applied force pn Prestressed tendon cross-sectional area A p And the section area A of the common steel bar s Based on the existing statistical results, the distribution probability of the 12 parameters conforms to normal distribution, a numerical value is randomly generated from each parameter according to the probability distribution characteristics of the parameters to form an array, and the effective stress of the prestressed tendon under the array is calculated according to each prestress loss theoretical calculation formula specified in section 7.2 of chapter 7, appendix J and appendix K of concrete structure design Specification GB 50010-2015; repeating the above operation to generate N arrays of the i-th prestressed tendon, wherein N is more than or equal to 10 ten thousand, respectively calculating the effective stress of the prestressed tendon under the N arrays to obtain N effective stress values in total, and taking the N effective stress values as a set F i Analyzing the probability distribution and calculating to obtain the average value u of N effective stresses of the prestressed tendon i Standard deviation σ i And variance
Calculating the probability density p of the normal distribution formula (1) i (x),
x is effective stress, u i Effective stress set F for the ith tendon i Mean value of (a) i Is the ith prestressed tendon effective stress set F i The standard deviation of (a) is determined,
effective stress set F for the ith tendon i The variance of (a);
probability centralization of effective stress of (II) th prestressed tendon
In order to eliminate the nonuniformity of the effective stress distribution, the effective stress value set F obtained in the step (I) needs to be subjected to centralization treatment based on the probability density average value of each prestressed tendon i The mean u of each effective stress minus the collective effective stress i Form a new set F i ', the set F i ' also have N values, with each element in the set being the set F i Of each effective stress value and set F i Mean value u i Difference, set F i 'has a mean value of u' i =0, standard deviation σ i And variance
The method is equivalent to translating the normal distribution curve of the ith prestressed tendon to the left to 0 point, keeping the effective stress distribution variance and the linear shape unchanged, and calculating the probability density p 'after the center of the prestressed tendon is changed by the formula (2)' i (x)：
Equation (2) represents that the mean is at 0, σ i Is the ith prestressed tendon effective stress set F i The standard deviation of the' is that of,
is the ith prestressed tendon effective stress set F i ' variance;
(III) establishing a Gaussian mixture model
Repeating the step (I) to the step (II) to obtain the probability density p 'of all n prestressed tendons in the structure' i (x) The weight omega of n prestressed tendons in the structure of each prestressed tendon i =1/n, the probability density p 'of each tendon' i (x) Adding as sub-distribution to form a Gaussian mixture model, calculating the effective stress probability density P (x) of the existing structure prestressed tendon aggregate by using a formula (3),
(IV) calculating skewness and kurtosis of the Gaussian mixture model
The k-order moment of the effective stress of the ith prestressed tendon (k =2,3,4) is obtained by the formula (4),
wherein k and r in the formula (4) are orders, E (X) r ) Is the r-th order origin moment of the standard normal distribution, and E (X) when r is odd number r ) 0,r even number E (X) r )＝(r-1)(r-3)···3·1，u′ i Centering the effective stress of the ith heel rib F i ' mean of set, σ i Is a set F i ' the standard deviation of the equation (4) is used to derive the second-order origin moment E of the effective stress of the ith prestressed tendon in the equation (5) i (x 2 ) Third order origin moment E i (x 3 ) And fourth order origin moment E i (x 4 )，
The second order origin moment, the third order origin moment and the fourth order origin moment of the total effective stress probability density P (x) in the structure of the formula (6) are obtained by superposing the second order origin moment, the third order origin moment and the fourth order origin moment of each prestressed tendon;
mean value of Gaussian mixture model
Is obtained by multiplying the mean value of each sub-division by the weight omega i Is added later to obtain
As can be seen from the formula (2), after the centering treatment, all the sub-parts p 'of the Gaussian mixture model' i (x) Of u's mean value' i Is 0, so the mean of the Gaussian mixture model
Variance of effective stress probability density P (x) of structural prestressed tendon lumped body
Equal to the second-order origin moment of the gaussian mixture model,
calculating skewness and kurtosis according to the definition of skewness and kurtosis by simplified formula (7),
substituting equation (6) into equation (7) to obtain equation (8)
Skewness: s =0
Kurtosis:
(V) Gaussian mixture model normal significance test and detection range determination
If the skewness value of the random variable probability density is in a range of-0.2, and the kurtosis value is in a range of [3,3.7], considering that the overall effective stress distribution of the structural prestressed tendon set obeys normal distribution, wherein the skewness value of the centralized Gaussian mixture model calculated in the step (IV) is 0, the kurtosis value is calculated by a formula (8), and for more accuracy, the normal distribution is used for estimating the overall effective stress of the structural prestressed tendon set, of which the kurtosis value is in a range of [3,3.5 ]; if the kurtosis value is larger than 3.5, arranging the variances of all the prestressed tendons from large to small, removing the prestressed tendons with the maximum variance and the minimum variance in the arrangement, then calculating the kurtosis value by using a formula (8), and if the kurtosis value is positioned between [3,3.5], estimating the total effective stress of the structural prestressed tendon set by using normal distribution; collecting the total effective stress of the prestressed tendons with the kurtosis value still larger than 3.5, and repeating the steps until the kurtosis value is smaller than 3.5;
(VI) detecting the effective stress value of the prestressed tendon of the existing structure
And (5) for the structural prestressed tendon aggregate with the obvious normal characteristic in the step (five), adopting a prestress effective stress detection method, randomly extracting at least more than 100 prestressed tendons in the structure to detect prestress effective stress values, and detecting each detection value F pe Subtracting the theoretical average value u of the prestressed tendon calculated in the step (I) of the detected prestressed tendon i Forming centralized sample data;
(VII) estimation of effective stress probability of prestressed component lump body
Calculating the mean value of the centralized sample data in the step (VI)
And standard deviation of
Forming a normal distribution curve by taking the normal distribution as a basic parameter, wherein the normal distribution curve of the formula (9) is adopted to estimate the total probability density distribution of the real-time effective stress of the existing structure after the structure is centralized according to the characteristic of the normal distribution, wherein
It is the probability density of the overall effective stress of the existing structure;
(VIII) effective stress probability estimation of each component of prestressed tendon
Returning the theoretical mean value of each prestressed tendon according to the probability distribution of the overall sample, and expressing the probability distribution forming each prestressed tendon by (10)
Selecting a guarantee value with 95% of possibility as an effective stress value of the prestressed tendon to evaluate the service state of the structure, and expressing the value by a formula (11), wherein 1.645 is an estimation coefficient of normally distributing the 95% guarantee rate to obtain the minimum effective stress F with 95% of possibility pe_L
The invention relates to a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps: in the step (five), if the number of the removed prestressed tendons is more than 1/10 of the total number of the prestressed tendons in the structure, the removed prestressed tendons are arranged from large to small in variance, then the removed prestressed tendons are divided into a plurality of groups according to the order of the variance, the difference value between the maximum variance and the minimum variance of each group of prestressed tendons is not more than 1000, then the step (three), the step (four) and the step (five) are repeated to calculate each group of prestressed tendons, the kurtosis value of a Gaussian mixture model of each group of prestressed tendons is between [3,3.5], and then the step (six) is carried out.
The invention relates to a method for evaluating the effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps: in the step (v), if the number of the removed prestressed tendons is less than 1/10 of the total number of the prestressed tendons in the structure, according to the importance degree of the removed prestressed tendons in the structure, if the prestressed tendons are prestressed tendons in the main stressed member, the effective stress values of the prestressed tendons need to be detected separately, and if the prestressed tendons are prestressed tendons in a general stressed member, the effective stress values of the prestressed tendons can be ignored.
The invention relates to a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps: in the step (VI), the effective prestress stress detection method is a pull-off method or a stress release method.
The invention relates to a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps: the primary stressed member is one that will itself fail causing other members to fail and endanger the safety of the load bearing structural system, or one that directly affects the operation of the production facility.
The invention relates to a method for evaluating effective stress distribution of a prestressed concrete structure based on limited data, which comprises the following steps: the general stressed component is a component which can be used for realizing the isolated event of the failure of the general stressed component, can not cause the failure of other components and can not directly influence the operation of the production equipment.
Compared with the existing mean value evaluation method, the effective stress distribution evaluation method of the prestressed concrete structure based on the limited data has the following advantages:
1) The method carries out probability estimation on the effective stress of each prestressed tendon of the prestressed concrete structure based on an uncertain analysis method, and solves the problems that the number of the prestressed tendons of the structure is large, the effective stress is uncertain and strong, the distribution is uneven, the effective stress of all the prestressed tendons of the structure cannot be comprehensively estimated after sampling detection, and the like.
2) The method can estimate the effective stress of the structural prestressed tendon based on limited data, and can remarkably improve the accuracy and the scientificity of the estimation of the effective stress of the existing structure on the basis of reducing the detection and evaluation cost.
3) The method can calculate the effective stress value with 95% of guarantee rate based on probability distribution characteristics, and compared with the average value (50% of guarantee rate), the effective stress value with 95% of guarantee rate reasonably considers the influence of uncertainty of each parameter, so that the safety of service performance evaluation of the existing prestressed concrete structure is improved.
Drawings
FIG. 1 is a schematic diagram of normal distribution of the probability density of effective stress of the ith prestressed tendon
FIG. 2 is a schematic diagram of the distribution of the effective stress probability density of each tendon
FIG. 3 is a schematic diagram of probability density distribution of each prestressed tendon and probability density distribution of a Gaussian mixture model after centralization;
FIG. 4 is a schematic diagram of the effective stress of normally distributed tendons under a condition with 95% assurance rate;
fig. 5 is a plan view of an actual engineering primary floor.
Detailed description of the preferred embodiments
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.
The effective stress distribution evaluation method of the prestressed concrete structure based on the limited data takes a certain 19-year-in-service project as an example: the construction area of a certain project is about 4.3 ten thousand square meters, 2 underground layers, 9 above-ground layers, a top plate of an underground layer and beam plates of an upper layer all adopt the unbonded prestressed concrete technology, the project is planned to be reinforced and transformed after the service of the project is about 20 years, and the current situation of the structural prestress of the project needs to be evaluated. The engineering prestressed tendon selects 1570MPa steel strand, the tension control stress is 70%, the strength of the concrete beam is C35, most beam members are concrete wide flat beams, and the prestressed arrangement diagram of the first layer beam is shown in figure 5; the method comprises the following steps:
(I) calculating theoretical distribution characteristics of the effective stress probability of the ith prestressed tendon of the existing concrete structure
The Monte Carlo numerical simulation method described in section 19.1 of statistical learning method (author Li Hang) published by Qinghua university Press (2019), 2 nd edition, selects the influence parameters as random variables to sample, and carries out Monte Carlo simulation on the effective stress of the prestressed tendons, and the specific operation is as follows:
selecting an ith prestressed tendon from an existing concrete structure, wherein the calculation of the effective stress of the ith prestressed tendon comprises the following 12 uncertain parameters: stress sigma of tension control con Friction coefficient mu, pipeline deviation coefficient k, anchor deformation and prestress retraction value a, beam length l and prestress rib elastic modulus E p Compressive strength f ptk Concrete Strength σ 'when prestressed' pc Beam cross-section net cross-sectional area A n Distance e from center of gravity of cross section to acting point of pre-applied force pn Prestressed tendon cross-sectional area A p And the section area A of the common steel bar s Table 1 shows statistical characteristics of the loss-related parameters, as shown in the statistical results in table 1: the distribution probability of the 12 parameters accords with normal distribution, a numerical value is randomly generated from each parameter to form an array according to the probability distribution characteristics of the parameters, and the effective stress of the prestressed tendon under the array is calculated according to each prestress loss theoretical calculation formula specified in table 10.2.1, formula (10.2.4), formula (10.2.5-3), formula (J.0.1-1-J.0.1-5) in appendix J and formula (K.0.1-1) in appendix K in chapter 10.2 of GB50010-2015, and formula (J.0.1-3) in appendix K, wherein the effective stress is the tension control stress sigma con Subtracting the combination of the prestress loss values of each stage (see section 10.2 of Table 10.2.7 in chapter 10 of GB50010-2015 concrete structure design Specification); repeating the above operation to generate N arrays of the i-th prestressed tendon, wherein N is more than or equal to 10 ten thousand, respectively calculating the effective stress of the prestressed tendon under the N arrays to obtain N effective stress values in total, and taking the N effective stress values as a set F i Respectively calculating the effective stress probability distribution of each rib according to the probability distribution of the basic stress of the PCI Journal,1995,40 (6): 76-8]The normal distribution formula is adopted to fit the effective stress probability density of the steel bar (the author is STEINBERG E P.), and if the normal distribution formula is adopted to fit the normal distribution of the ith bar effective stress probability density into a curve p shown in figure 1 by using the formula (1) i (x)，
x is effective stress, u i Effective stress set F for the ith tendon i Mean value of (a) i Is the ith prestressed tendon effective stress set F i The standard deviation of (a) is determined,
effective stress set F for the ith tendon i The variance of (a);
| design value/mean value | Coefficient of variation (standard deviation/mean) | Type of | |
| σ | |||
| con | 1 | 0.0365 | Normal (normal) |
| |
1 | 0.216 | Normal (normal) |
| |
1 | 0.256 | Normal (normal) |
| a | 1 | 0.005 | Normal (normal) |
| |
1 | 0.020 | |
| E | |||
| p | 1 | 0.020 | Normal (normal) |
| f ptk | 1.08 | 0.0378 | Normal (normal) |
| f′ cu | 1.36 | 0.13 | Normal (normal) |
| |
1 | 0.0125 | |
| A | |||
| s | 1 | 0.035 | Normal (normal) |
| |
1 | 0.08 | Normal (normal) |
| |
1 | 0.01 | Normal (normal) |
TABLE 1
Probability centralization of effective stress of (II) th prestressed tendon
In order to eliminate the nonuniformity of the effective stress distribution, the effective stress value set F obtained in the step (I) needs to be subjected to centralization treatment based on the probability density average value of each prestressed tendon i The mean value u of each effective stress minus the collective effective stress i Form a new set F i ', the set F i ' also have N values, each element in the set being a set F i Of each effective stress value and set F i Mean value u i Difference, a set F is obtained i 'has a mean value of u' i =0, standard deviation σ i And variance
The method is unchanged, namely, the normal distribution curve of the ith prestressed tendon is translated to the 0 point to the left, the effective stress distribution variance and the linear shape are unchanged, and the centralization is calculated by the following formula (2)Probability density of rear p' i (x)：
Equation (2) represents that the mean is at 0, σ i Is the ith prestressed tendon effective stress set F i The standard deviation of the' is that of,
is the ith prestressed tendon effective stress set F i ' variance;
(III) establishing a Gaussian mixture model
According to the related content of the Gaussian mixture model in section 9.3.1 of the statistical learning method 2 (author Li Hang) published by Qinghua university Press (2019), the effective stress of all the prestressed tendons in the structure is taken as a total limited sample, and the proportion weight omega of each prestressed tendon in the total number n of all the prestressed tendons in the structure is considered i =1/n, repeating the steps (one) to (two), and calculating the probability density p of each prestressed tendon (n =1460 prestressed tendons) i (x) Adding as sub-distribution to form Gaussian mixture model, calculating the effective stress probability density P (x) of the existing structure prestressed tendon aggregate by the following formula (3),
respectively calculating the effective stress probability distribution of each tendon through Monte Carlo simulation, fitting the effective stress probability density of each prestressed tendon by adopting a normal distribution formula, wherein the effective stress and probability distribution curve of each prestressed tendon before centralization are shown in figure 2, and the theoretical calculation mean value and variance of the effective stress of each prestressed tendon are shown in table 2; the effective stress and probability distribution curves of the prestressed tendons after centralization are shown in fig. 3, and it can be known from fig. 3 that the effective stress probability density curves have smaller difference after centralization because the variances of the prestressed tendons are relatively close. Namely, the probability density curve of the Gaussian mixture model is taken as the center, and the probability distribution of each rib fluctuates slightly around the center.
TABLE 2
(IV) calculating skewness and kurtosis of the Gaussian mixture model
According to the university of Chongqing university of Industrial and Industrial sciences report (Nature science edition), 2014,31 (9), 1-5: "calculation of high-order origin moments of several probability distributions [ J ] (Jiang Peihua by author), the following formula (4) can be obtained:
the k-order moment of the effective stress of the ith prestressed tendon (k =2,3,4) is obtained by the formula (4),
wherein k and r in the formula (4) are orders, E (X) r ) Is the origin moment of the standard normal distribution in order r, and E (X) when r is odd r ) 0,r even number E (X) r )＝(r-1)(r-3)···3·1，u′ i Centering the effective stress of the ith following rib F i ' mean of set, σ i Is a set F i ' the standard deviation of the equation (4) is used to derive the second-order origin moment E of the effective stress of the ith prestressed tendon in the equation (5) i (x 2 ) Third order origin moment E i (x 3 ) And fourth order origin moment E i (x 4 )，
The second order origin moment, the third order origin moment and the fourth order origin moment of the total effective stress probability density P (x) in the structure of the formula (6) are obtained by superposing the second order origin moment, the third order origin moment and the fourth order origin moment of each prestressed tendon;
mean of Gaussian mixture model
Is obtained by multiplying the mean value of each sub-division by the weight omega i Is added later to obtain
As can be seen from the formula (2), after the centering treatment, all the sub-parts p 'of the Gaussian mixture model' i (x) Of u's mean value' i Is 0, so the mean of the Gaussian mixture model
Variance of effective stress probability density P (x) of structural prestressed tendon lumped body
Equal to the second-order origin moment of the gaussian mixture model,
the skewness and kurtosis were calculated using simplified equation (7) according to the definitions of skewness and kurtosis in the analysis of underwater vehicle cavitation noise [ J ] (authors Zhang Jun, wang Mingzhou, hu Youfeng) by Acoustic techniques 2021,40 (6), 757-762,
substituting formula (6) into formula (7) to obtain formula (8)
Skewness: s =0
Kurtosis:
(V) Gaussian mixture model normal significance test and detection range determination
According to the article entitled "non-gaussian characteristics of wind pressure pulsation of large span roof structure" J "(authors Sun Ying, wu Yue, lin Zhixing, etc.) in civil engineering report 2007 (04): 1-5, it is pointed out that: if the skewness value of the random variable probability density is in the range of-0.2 and the kurtosis value is in the range of [3,3.7], considering that the random variable obeys normal distribution, the skewness value of the centralized Gaussian mixture model calculated in the step (IV) is 0, the kurtosis value is calculated by the formula (8), and for more accuracy, selecting the structural prestressed tendon set total effective stress with the kurtosis value between [3,3.5] to estimate by normal distribution; the skewness value of the Gaussian mixture model of the total effective stress of the structural prestressed tendon is calculated to be 0, the numerical values in the table 2 are substituted into the formula (8), the kurtosis K is obtained to be 3.048 (< 3.5), and the estimation can be carried out by adopting normal distribution,
substituting the numerical values in Table 2 into the above formula (3) to obtain the following formula
If the kurtosis value is larger than 3.5, arranging the variances of all the prestressed tendons from large to small, removing the prestressed tendons with the maximum variance and the minimum variance in the arrangement, then calculating the kurtosis value by using a formula (8), and if the kurtosis value is positioned between [3,3.5], estimating the total effective stress of the structural prestressed tendon set by using normal distribution; collecting the total effective stress of the prestressed tendons with the kurtosis value still larger than 3.5, and repeating the steps until the kurtosis value is smaller than 3.5;
if the number of the removed prestressed tendons is more than 1/10 of the total number of the prestressed tendons in the structure, arranging the variances from large to small, dividing the variances into a plurality of groups according to the magnitude sequence of the variances, enabling the difference value between the maximum variance and the minimum variance of each group of prestressed tendons to be not more than 1000, then repeating the step (three), the step (four) and the step (five) to calculate each group of prestressed tendons, enabling the kurtosis value of a Gaussian mixture model of each group of prestressed tendons to be between 3,3.5, and then performing the step (six);
if the number of the removed prestressed tendons is less than 1/10 of the total number of the prestressed tendons in the structure, different treatments are carried out according to the importance degree of the removed prestressed tendons in the structure, if the number of the removed prestressed tendons is the number of the prestressed tendons in the main stressed member, the effective stress value of the prestressed tendons needs to be independently detected, if the number of the removed prestressed tendons in the main stressed member is the number of the prestressed tendons in the general stressed member, the effective stress value of the prestressed tendons can be ignored, and if the number of the removed prestressed tendons in the general stressed member is the number of the prestressed tendons in the general stressed member, the main stressed member is a member which can cause other members to fail and endanger the safety of a bearing structure system due to self failure or a member which directly influences the operation of production equipment; the general stressed component is a component which has the self failure as an isolated event, can not cause the failure of other components and does not directly influence the operation of production equipment;
sixthly, detecting the effective stress value of the prestressed tendon with the existing structure
And (5) adopting a prestress effective stress detection method for the structural prestressed tendon aggregate with the obvious normal characteristic in the step (five), for example: detecting the effective prestress value by a pull-off method or a stress release method, randomly extracting at least more than 100 prestressed tendons in the structure to detect the effective prestress value, and detecting each detection value F pe Subtracting the theoretical mean value u of the prestressed tendon calculated in the step (I) from the detected prestressed tendon i Forming centralized sample data;
(VII) estimation of effective stress probability of prestressed component lump body
Calculating the mean value of the centralized sample data in the step (six)
And standard deviation of
Forming a normal distribution curve by taking the normal distribution as a basic parameter, wherein the normal distribution curve of the formula (9) is adopted to estimate the total probability density distribution of the real-time effective stress of the existing structure after the centering of the structure according to the characteristic of the normal distribution
It is the probability density of the overall effective stress of the existing structure;
mean value of centered sample data
Sum variance
Performing calculation to obtain
Forming a normal distribution curve by taking the normal distribution curve as a basic parameter, and substituting the probability distribution of the total effective stress of the structure after the centralization treatment into the formula (9) to obtain the following formula:
(eight) estimation of effective stress probability of each component of prestressed tendon
Returning the theoretical mean value of each prestressed tendon according to the probability distribution of the overall sample, and expressing the probability distribution of each prestressed tendon by a formula (10)
Mean value of sample data to be centralized
Sum variance
Namely, it is
Substituting equation (10) results in the following equation:
as shown in fig. 4, a guarantee value with 95% of possibility is selected as an effective stress value of the prestressed tendon to evaluate the service state of the structure, and the minimum effective stress F with 95% of possibility is obtained by referring to a calculation formula (3.5.10-2) of the guarantee rate in chapter 3.5 of technical standard for building structure detection GB/T50344-2019, and expressed by a formula (11), wherein 1.645 is an estimation coefficient of the normal distribution 95% of guarantee rate, and pe_L
the effective stress F of each prestressed tendon of the existing structure with the minimum effective stress with the 95 percent guarantee value in the table 3 is obtained pe_L 。
TABLE 3
The foregoing description is illustrative of the present invention and is not to be construed as limiting thereof, the scope of the invention being defined by the appended claims, which may be modified in any manner without departing from the spirit of the invention.
Claims (6)
1. A prestressed concrete structure effective stress distribution evaluation method based on limited data comprises the following steps:
(I) calculating theoretical distribution characteristics of i-th prestressed tendon effective stress probability of existing concrete structure
Selecting an ith prestressed tendon from an existing concrete structure, wherein the calculation of the effective stress of the ith prestressed tendon comprises the following 12 uncertain parameters: stress sigma of tension control con Friction coefficient mu, pipeline deviation coefficient k, anchor deformation and prestress retraction value a and beam length lModulus of elasticity E of tendon p Compressive strength f ptk Concrete Strength σ 'when prestressed' pc Beam cross-section net cross-sectional area A n Distance e from center of gravity of cross section to acting point of prestressing force pn Prestressed tendon cross-sectional area A p And the cross-sectional area A of the common steel bar s Based on the existing statistical results, the distribution probability of the 12 parameters conforms to normal distribution, a numerical value is randomly generated from each parameter according to the probability distribution characteristics of the parameters to form an array, and the effective stress of the prestressed tendon under the array is calculated according to each prestress loss theoretical calculation formula specified in section 7.2 of chapter 7, appendix J and appendix K of concrete structure design Specification GB 50010-2015; repeating the above operation to generate N arrays of the i-th prestressed tendon, wherein N is more than or equal to 10 ten thousand, respectively calculating the effective stress of the prestressed tendon under the N arrays to obtain N effective stress values in total, and taking the N effective stress values as a set F i Analyzing the probability distribution and calculating to obtain the average value u of N effective stresses of the prestressed tendon i Standard deviation σ i And variance
Calculating the probability density p of the normal distribution formula (1) i (x),
x is effective stress, u i Is the effective stress set F of the ith prestressed tendon i Mean value of (a) i Is the ith prestressed tendon effective stress set F i The standard deviation of (a) is determined,
effective stress set F for the ith tendon i The variance of (a);
probability centralization of effective stress of (II) th prestressed tendon
To eliminate effectivenessThe nonuniformity of stress distribution needs to be centered based on the probability density mean value of each prestressed tendon, and the effective stress value set F obtained in the step (one) is collected i The mean u of each effective stress minus the collective effective stress i Form a new set F i ', the set F i ' also have N values, each element in the set being a set F i Of each effective stress value and set F i Mean value u i Difference, set F i 'has a mean value of u' i =0, standard deviation σ i And variance
The method is unchanged, namely translating the normal distribution curve of the ith prestressed tendon to the 0 point leftwards, keeping the effective stress distribution variance and the linearity unchanged, and calculating the probability density p after the centralization through a formula (2) i ′(x)：
The formula (2) represents that the mean value is at 0, σ i Is the ith prestressed tendon effective stress set F i The standard deviation of the' is that of,
is the ith prestressed tendon effective stress set F i ' variance;
(III) establishing a Gaussian mixture model
Repeating the steps (I) to (II) to obtain the probability density p 'of all n prestressed tendons in the structure' i (x) The weight omega of n prestressed tendons in the structure of each prestressed tendon i =1/n, the probability density p 'of each tendon' i (x) Adding as sub-distribution to form a Gaussian mixture model, calculating the effective stress probability density P (x) of the existing structure prestressed tendon aggregate by using a formula (3),
(IV) calculating skewness and kurtosis of the Gaussian mixture model
Obtaining k-order moment of the effective stress of the ith prestressed tendon through a formula (4), wherein k =2,3 and 4,
wherein k and r in formula (4) are the order, E (X) r ) Is the r-th order origin moment of the standard normal distribution, and E (X) when r is odd number r ) E (X) when =0,r is even number r )＝(r-1)(r-3)···3·1；u′ i F after the effective stress of the ith rib is centralized i ' mean of set, σ i Is a set F i ' standard deviation; deducing a second-order origin moment E of the effective stress of the ith prestressed tendon of the formula (5) from the formula (4) i (x 2 ) Third order origin moment E i (x 3 ) And fourth order origin moment E i (x 4 )，
Superposing the second order origin moment, the third order origin moment and the fourth order origin moment of each prestressed tendon to obtain the second order origin moment, the third order origin moment and the fourth order origin moment of the total effective stress probability density P (x) in the structure of the formula (6);
mean value of Gaussian mixture model
Is obtained by multiplying the mean value of each sub-division by the weight omega i Is added later to obtain
As can be seen from the formula (2), after the centering treatment, all the sub-parts p 'of the Gaussian mixture model' i (x) Of u's mean value' i Is 0, so the mean of the Gaussian mixture model
Variance of effective stress probability density P (x) of structural prestressed tendon lumped body
Equal to the second-order origin moment of the gaussian mixture model,
calculating skewness and kurtosis according to the definition of skewness and kurtosis by simplified formula (7),
substituting equation (6) into equation (7) to obtain equation (8)
Skewness: s =0
Kurtosis:
(V) Gaussian mixture model normal significance test and detection range determination
If the skewness value of the random variable probability density is in the range of-0.2 and the kurtosis value is in the range of [3,3.7], considering that the total effective stress distribution of the structural prestressed tendon set is in accordance with normal distribution, the skewness value of the centralized Gaussian mixture model calculated in the step (IV) is 0, the kurtosis value is calculated by the formula (8), and for higher accuracy, the total effective stress of the structural prestressed tendon set with the kurtosis value between [3,3.5] is selected and estimated by the normal distribution; if the kurtosis value is larger than 3.5, arranging the variances of all the prestressed tendons from large to small, removing the prestressed tendons with the maximum variance and the minimum variance in the arrangement, then calculating the kurtosis value by using a formula (8), and if the kurtosis value is positioned between [3,3.5], estimating the total effective stress of the structural prestressed tendon set by using normal distribution; collecting the total effective stress of the prestressed tendons with the kurtosis value still larger than 3.5, and repeating the steps until the kurtosis value is smaller than 3.5;
(VI) detecting the effective stress value of the prestressed tendon of the existing structure
Adopting a prestress effective stress detection method to the structural prestressed tendon set total with the obvious normal characteristic in the step (five), randomly extracting at least more than 100 prestressed tendons in the structure to detect the prestress effective stress value, and carrying out detection on each detection value F pe Subtracting the theoretical average value u of the prestressed tendon calculated in the step (I) of the detected prestressed tendon i Forming centralized sample data;
(VII) estimation of effective stress probability of prestressed component lump body
Calculating the mean value of the centralized sample data in the step (six)
And standard deviation of
Forming a normal distribution curve by taking the normal distribution as a basic parameter, wherein the normal distribution curve of the formula (9) is adopted to estimate the total probability density distribution of the real-time effective stress of the existing structure after the structure is centralized according to the characteristic of the normal distribution, wherein
It is the probability density of the overall effective stress of the existing structure;
(eight) estimation of effective stress probability of each component of prestressed tendon
Returning the theoretical mean value of each prestressed tendon according to the probability distribution of the overall sample, and expressing the probability distribution forming each prestressed tendon by (10)
Selecting a guarantee value with 95% of possibility as an effective stress value of the prestressed tendon to evaluate the service state of the structure, and expressing the value by a formula (11), wherein 1.645 is an estimation coefficient of a normal distribution 95% guarantee rate to obtain a minimum effective stress F with 95% of possibility pe_L
2. The limited-data-based effective stress distribution evaluation method of a prestressed concrete structure according to claim 1, characterized in that: in the step (five), if the number of the removed prestressed tendons is more than 1/10 of the total number of the prestressed tendons in the structure, the removed prestressed tendons are arranged from large to small in variance, then the removed prestressed tendons are divided into a plurality of groups according to the order of the variance, the difference value between the maximum variance and the minimum variance of each group of prestressed tendons is not more than 1000, then the step (three), the step (four) and the step (five) are repeated to calculate each group of prestressed tendons, the kurtosis value of a Gaussian mixture model of each group of prestressed tendons is between [3,3.5], and then the step (six) is carried out.
3. The limited-data-based effective stress distribution evaluation method for prestressed concrete structures according to claim 1 or 2, characterized in that: in the step (five), if the number of the removed prestressed tendons is less than 1/10 of the total number of the prestressed tendons in the structure, according to the importance degree of the removed prestressed tendons in the structure, if the removed prestressed tendons are the prestressed tendons in the main stressed member, the effective stress values of the prestressed tendons need to be detected separately, and if the removed prestressed tendons are the prestressed tendons in the general stressed member, the effective stress values of the prestressed tendons are ignored.
4. The limited-data-based effective stress distribution evaluation method for prestressed concrete structures according to claim 3, characterized in that: in the step (VI), the effective prestress stress detection method is a pull-off method or a stress release method.
5. The limited-data-based effective stress distribution evaluation method for prestressed concrete structures according to claim 4, characterized in that: the primary stressed member is one that will itself fail causing other members to fail and endanger the safety of the load bearing structural system, or one that directly affects the operation of the production facility.
6. The limited-data-based effective stress distribution evaluation method for prestressed concrete structures according to claim 4, characterized in that: the general stressed component is a component which can be used for realizing the isolated event of the failure of the general stressed component, can not cause the failure of other components and can not directly influence the operation of the production equipment.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210159864.2A CN114528706B (en) | 2022-02-22 | 2022-02-22 | Method for evaluating effective stress distribution of prestressed concrete structure based on limited data |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210159864.2A CN114528706B (en) | 2022-02-22 | 2022-02-22 | Method for evaluating effective stress distribution of prestressed concrete structure based on limited data |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114528706A CN114528706A (en) | 2022-05-24 |
| CN114528706B true CN114528706B (en) | 2022-11-18 |
Family
ID=81625399
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210159864.2A Active CN114528706B (en) | 2022-02-22 | 2022-02-22 | Method for evaluating effective stress distribution of prestressed concrete structure based on limited data |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114528706B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117114436B (en) * | 2023-07-27 | 2024-07-09 | 中冶建筑研究总院有限公司 | Existing prestressed concrete member performance evaluation method based on measured data |
| CN117235862B (en) * | 2023-10-08 | 2024-05-14 | 中冶建筑研究总院有限公司 | Concrete structure effective prestress estimation and evaluation characteristic value calculation method |
| CN117591791A (en) * | 2023-12-08 | 2024-02-23 | 中冶建筑研究总院有限公司 | Dichotomy-based prestress rib retraction loss along-path distribution calculation method |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2008268123A (en) * | 2007-04-24 | 2008-11-06 | Oriental Shiraishi Corp | System and method for measuring stress of reinforced concrete member |
| CN102651042A (en) * | 2011-12-28 | 2012-08-29 | 上海同吉建筑工程设计有限公司 | Prestressed pull rod foundation design method for large-span space structure |
| CN112461407A (en) * | 2020-09-29 | 2021-03-09 | 河南牛帕力学工程研究院 | Stress detection method for prestressed tendon |
| CN112683425A (en) * | 2021-01-21 | 2021-04-20 | 交通运输部公路科学研究所 | Method for detecting effective stress of longitudinal prestressed tendon in bridge body |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102651041B (en) * | 2011-12-28 | 2016-12-28 | 同济大学 | Prestressed cable basic engineering method in large-span space structure |
-
2022
- 2022-02-22 CN CN202210159864.2A patent/CN114528706B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2008268123A (en) * | 2007-04-24 | 2008-11-06 | Oriental Shiraishi Corp | System and method for measuring stress of reinforced concrete member |
| CN102651042A (en) * | 2011-12-28 | 2012-08-29 | 上海同吉建筑工程设计有限公司 | Prestressed pull rod foundation design method for large-span space structure |
| CN112461407A (en) * | 2020-09-29 | 2021-03-09 | 河南牛帕力学工程研究院 | Stress detection method for prestressed tendon |
| CN112683425A (en) * | 2021-01-21 | 2021-04-20 | 交通运输部公路科学研究所 | Method for detecting effective stress of longitudinal prestressed tendon in bridge body |
Non-Patent Citations (4)
| Title |
|---|
| Live-load strain evaluation of the prestressed concrete box-girder bridge using deep learning and clustering;Hanwei Zhao等;《Structural Health Monitoring》;20190923;第19卷(第4期);全文 * |
| 基于振动法检测预应力混凝土梁有效应力的实验研究及有限元分析;徐满意等;《水道港口》;20081215;第29卷(第6期);全文 * |
| 基于等效质量法的梁板有效预应力值测试研究;王清洲等;《中外公路》;20180228;第38卷(第1期);全文 * |
| 预应力混凝土结构钢绞线有效应力测量与评估方法;戎芹等;《建筑结构学报》;20200831;第41卷(第08期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114528706A (en) | 2022-05-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN114528706B (en) | Method for evaluating effective stress distribution of prestressed concrete structure based on limited data | |
| Pavlović et al. | Bolted shear connectors vs. headed studs behaviour in push-out tests | |
| Jalayer et al. | Structural modeling uncertainties and their influence on seismic assessment of existing RC structures | |
| Ma et al. | Fatigue life prediction for aging RC beams considering corrosive environments | |
| Darmawan et al. | Effect of pitting corrosion on capacity of prestressing wires | |
| Ramirez et al. | Fragility functions for pre-Northridge welded steel moment-resisting beam-to-column connections | |
| CN103018063B (en) | Bridge random fatigue life prediction method based on Mittag-Leffler distribution | |
| Torres et al. | Structural reliability evaluation considering capacity degradation over time | |
| CN112541286A (en) | Tunnel earthquake vulnerability analysis method based on incremental dynamic analysis method | |
| CN114329709A (en) | Method for rapidly diagnosing service performance and predicting development trend of shield tunnel | |
| Ha | Reliability assessment of frame steel considering semi-rigid connections | |
| Li et al. | Reliability-based investigation into the duration of load effect for the design of timber structures based on Chinese standard | |
| Rahgozar et al. | Performance evaluation of self-centring steel-braced frame | |
| Song et al. | Experimental investigation of ultra-low-cycle fatigue behaviors of plate bearings in spatial grid structures | |
| Deng et al. | Monitoring damage evolution of steel strand using acoustic emission technique and rate process theory | |
| Creagh et al. | Seismic performance of concrete special boundary element | |
| Nugraha et al. | Reliability evaluation of steel truss bridge due to traffic load based on bridge weigh-in-motion measurement | |
| Yan et al. | Analysis of the importance coefficient of offshore bridges under earthquakes based on seismic fragility and incremental dynamic analysis | |
| CN110261051B (en) | Method for calculating section bending moment of prestressed concrete structure based on structural deformation | |
| CN105701333B (en) | A kind of space prestressed cable-strut system overall security evaluation method | |
| Campbell et al. | Steel moment frame damage predictions using low-cycle fatigue | |
| Bai et al. | Experimental study on seismic performance and deformation damage of loose dovetail-tenon joints in ancient timber structures | |
| Wang et al. | The effects of uniform temperature and bolts fracture on the behaviour of high strength bolted frictional steel connection in Dashegnguan Railway Bridge. | |
| CN109840389B (en) | Bayes and GARCH-based prestress prediction method | |
| CN117235862B (en) | Concrete structure effective prestress estimation and evaluation characteristic value calculation method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |