JP4696243B2 - Young's modulus estimation method, Young's modulus estimation program, and Young's modulus estimation apparatus - Google Patents

Description

  The present invention relates to a Young's modulus estimation method, a Young's modulus estimation program, and a Young's modulus estimation apparatus for estimating the Young's modulus of a member such as wood.

For example, it is necessary to know the strength performance of the structural member in order to determine whether it can be used continuously or reused in repairing / reconstructing / reconstructing a wooden building. Conventionally, the determination is often made by subjective evaluation based on the experience of a skilled carpenter and the like, and it is required to objectively evaluate the strength strength performance of the structural member, that is, numerically.
As a method for numerically evaluating the strength strength performance of the structural member as described above, for example, there are the following methods.
(1) “Load method”: A method in which a static load such as compression, tension, or bending is applied to a structural member to obtain a proportional constant in the relationship between the load and the deformation of the structural member.
(2) “Frequency analysis method (striking method)”: striking a structural member with a hammer, collecting impact sound with a microphone, obtaining a natural frequency using a frequency analyzer, and calculating the weight and volume of the structural member. A method of measuring and calculating Young's modulus by a predetermined relational expression (see Patent Document 1 below).
(3) “Ultrasonic method”: The ultrasonic velocity in the structural member is measured by an ultrasonic sensor, the density of the structural member is measured, and the Young's modulus is calculated from the ultrasonic velocity and density of the ultrasonic wave according to a predetermined relational expression. How to calculate
(4) “Stress wave method”: A stress wave propagation velocity measuring device is used to measure the stress wave propagation velocity in the structural member, and the density of the structural member is measured. A method of calculating Young's modulus by a relational expression (see Patent Document 2 below).
Japanese Examined Patent Publication No. 6-78974 Japanese Patent Publication No. 40-18194

  However, in the load method, it is necessary to specify the cross-sectional shape of the structural member, and there is a problem that accurate numerical measurement is difficult for a structural member having an indefinite cross-sectional shape. On the other hand, in the conventional frequency analysis method, ultrasonic method and stress wave method described above, it is necessary to grasp the density of the structural member, and in particular, the strength strength performance of the structural member is evaluated while being incorporated in the wooden building. There is a problem that it is difficult. In the ultrasonic method, since the ultrasonic wave attenuates in accordance with the degree of adhesion between the structural member and the ultrasonic sensor, the adhesion between the two becomes a problem, and has not yet exceeded the laboratory level and lacks practicality.

  The present invention has been completed based on the above circumstances, and its purpose is Young's modulus that makes it possible to objectively evaluate retained strength performance without directly measuring the density of a member to be measured. An estimation method, a Young's modulus estimation program, and a Young's modulus estimation apparatus are provided.

As a means for achieving the above object, the Young's modulus estimation method according to the invention of claim 1 measures the stress wave propagation velocity of the member to be measured, and falls within the range of the measured database of the Young's modulus-density relationship of the member. A plurality of first densities that may exist are extracted regularly or irregularly, and the following steps (A) to (C) are repeated for each first density, thereby corresponding to the stress wave propagation velocity. The Young's modulus of the member to be measured is estimated.
(A) A Young's modulus extraction step of extracting a Young's modulus based on the regression line of the actual measurement database and the first density;
(B) a density calculating step for calculating a second density corresponding to the extracted Young's modulus extracted in the Young's modulus extracting step and the stress wave propagation velocity based on a predetermined first relational expression;
(C) An estimated Young's modulus determining step for determining the extracted Young's modulus as an estimated Young's modulus on the condition that an error between the first density and the second density is within a setting allowable range.
In the present invention, “regularly extracted” means extracting in a predetermined order, and “irregularly extracted” means arbitrarily extracting randomly using, for example, a random number generation method. To do.

The Young's modulus estimation method according to the invention of claim 2 measures the length and natural frequency of a member to be measured, and determines a plurality of first densities that may exist within the range of an actual measurement database of the Young's modulus-density relationship of the member. The measurement corresponding to the length and the natural frequency of the member to be measured is performed by regularly or irregularly extracting sequentially and repeating the following steps (A) to (C) for each first density. The Young's modulus of the target member is estimated.
(A) A Young's modulus extraction step of extracting a Young's modulus based on the regression line of the actual measurement database and the first density;
(B) a density calculating step for calculating a second density corresponding to the extracted Young's modulus extracted in the Young's modulus extracting step, the length, and the natural frequency based on a predetermined second relational expression;
(C) An estimated Young's modulus determining step for determining the extracted Young's modulus as an estimated Young's modulus on the condition that an error between the first density and the second density is within a setting allowable range.

The Young's modulus estimation program according to the invention of claim 3 is actually measured with respect to an actual measurement database of the Young's modulus-density relationship of members and a measurement target member by causing a computer to execute the following processes (A) to (D). The Young's modulus of the measurement target member is estimated based on the measured stress wave propagation velocity.
(A) a density extraction process for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database;
(B) For each first density extracted in the density extraction process, a Young's modulus extraction process for extracting each Young's modulus based on the regression line information of the actual measurement database stored in the memory and each first density;
(C) For each extracted Young's modulus extracted in the Young's modulus extraction process, density calculation for calculating each extracted Young's modulus and each second density corresponding to the stress wave propagation velocity based on a predetermined first relational expression. processing,
(D) For each of the second densities, when an error from the corresponding first density is within a setting allowable range, the extracted Young's modulus corresponding to the second density is determined as an estimated Young's modulus Young's modulus determination process.

The Young's modulus estimation program according to the invention of claim 4 causes the computer to execute the following processes (A) to (D), thereby measuring the measured database of the Young's modulus-density relationship of the member and the measurement target member. The Young's modulus of the measurement target member is estimated based on the measured length and the natural frequency.
(A) a density extraction process for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database;
(B) For each first density extracted in the density extraction process, a Young's modulus extraction process for extracting each Young's modulus based on the regression line information of the actual measurement database stored in the memory and each first density;
(C) For each extracted Young's modulus extracted in the Young's modulus extraction process, each second density corresponding to each extracted Young's modulus, the length, and the natural frequency is calculated based on a predetermined second relational expression. Density calculation processing,
(D) For each of the second densities, when an error from the corresponding first density is within a setting allowable range, the extracted Young's modulus corresponding to the second density is determined as an estimated Young's modulus. Estimated Young's modulus determination process.

  According to a fifth aspect of the present invention, in the program for estimating the Young's modulus according to the third or fourth aspect, the density extraction processing extracts the first density according to a probability distribution of the density in the actual measurement database by a Monte Carlo simulation method. It is processing to do.

  The invention of claim 6 is the Young's modulus estimation program according to any one of claims 3 to 5, wherein the Young's modulus extraction processing is an average for obtaining an average Young's modulus corresponding to the first density on the regression line. A Young's modulus calculation process; and a correction process for correcting the average Young's modulus based on a variation in Young's modulus corresponding to the first density in the actual measurement database to obtain the extracted Young's modulus.

  A seventh aspect of the invention is the Young's modulus estimation program according to any one of the third to fifth aspects, wherein the Young's modulus extraction process is an average for obtaining an average Young's modulus corresponding to the first density on the regression line. A Young's modulus calculation process, a regression residual extraction process for extracting a regression residual for the average Young's modulus according to a normal distribution by the Monte Carlo simulation method, and correcting the average Young's modulus according to the extracted regression residual Correction processing to obtain the extracted Young's modulus.

  The invention of claim 8 is the Young's modulus estimation program according to claim 7, wherein the regression residual extraction process generates a uniform random number, calculates a standard normal random variable based on the uniform random number, The regression residual is obtained by multiplying the random variable by the standard deviation of Young's modulus corresponding to the first density in the actual measurement database.

  The invention of claim 9 is the Young's modulus estimation program according to any one of claims 3 to 8, wherein the program is based on a plurality of types of measured databases classified based on at least one of the type of member and the environment. A specification process for specifying a specific actual measurement database is further included, and the processes (A) to (D) are executed based on the actual measurement database specified in the specification process.

  According to a tenth aspect of the present invention, there is provided an Young's modulus estimation apparatus that stores acquisition means for acquiring a stress wave propagation velocity of a measurement target member, and regression line information and density information of an actual measurement database of the Young's modulus-density relationship of the member. Means, a density extracting means for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database based on the density information, and each first density extracted by the density extracting means. The Young's modulus extracting means for extracting each Young's modulus based on the regression line information and each of the first densities, and each extracted Young's modulus extracted by the Young's modulus extracting means in a predetermined first relational expression Based on the extracted Young's modulus and the density calculation means for calculating the second density corresponding to the stress wave propagation velocity, an error between the second density and the first density corresponding to the second density is set. If within the allowable range, comprising the estimated Young's modulus determination means for determining the extraction Young's modulus corresponding to the second density as the estimated Young's modulus, the.

  The Young's modulus estimation apparatus according to the invention of claim 11 stores acquisition means for acquiring the length and natural frequency of the measurement target member, and regression line information and density information of an actual measurement database of the Young's modulus-density relationship of the member. Storage means, density extraction means for regularly or irregularly extracting a plurality of first densities that may exist in the range of the actual measurement database based on the density information, and each of the first extractions extracted by the density extraction means. For one density, Young's modulus extraction means for extracting each Young's modulus based on the regression line information and each first density, and a predetermined second relationship for each extracted Young's modulus extracted by the Young's modulus extraction means Based on the equation, density calculating means for calculating each second density corresponding to each extracted Young's modulus, the length, and the natural frequency, and each first density corresponding to each second density, If the error is within the allowable setting range, comprising the estimated Young's modulus determination means for determining the extraction Young's modulus corresponding to the a second density as the estimated Young's modulus, the.

  According to a twelfth aspect of the present invention, in the Young's modulus estimation apparatus according to the tenth or the eleventh aspect, the density extraction unit extracts the first density according to a probability distribution regarding the density in the actual measurement database by a Monte Carlo simulation method. To do.

  According to a thirteenth aspect of the present invention, in the Young's modulus estimation apparatus according to any one of the tenth to twelfth aspects, the Young's modulus extraction means calculates an average for obtaining an average Young's modulus corresponding to the first density on the regression line. Young's modulus calculation means, and correction means for correcting the average Young's modulus based on a variation in Young's modulus corresponding to the first density in the actual measurement database to obtain the extracted Young's modulus.

  According to a fourteenth aspect of the present invention, in the Young's modulus estimation apparatus according to any one of the tenth to twelfth aspects, the Young's modulus extraction means calculates an average for obtaining an average Young's modulus corresponding to the first density on the regression line. A Young's modulus calculating means, a regression residual extracting means for extracting a regression residual with respect to the average Young's modulus according to a normal distribution by a Monte Carlo simulation method, and correcting the average Young's modulus according to the extracted regression residual Correction means for obtaining the extracted Young's modulus.

  According to a fifteenth aspect of the present invention, in the Young's modulus estimation apparatus according to the fourteenth aspect, the regression residual extracting means generates a uniform random number, calculates a standard normal random variable based on the uniform random number, and The regression residual is obtained by multiplying the random variable by the standard deviation of Young's modulus corresponding to the first density in the actual measurement database.

  A sixteenth aspect of the present invention is the Young's modulus estimation apparatus according to any one of the tenth to fifteenth aspects, wherein the storage means includes a plurality of types classified based on at least one of a member type and an environment. The regression line information and the density information of the actual measurement database are stored, and includes a designation means for designating a specific actual measurement database from the plurality of types of the actual measurement databases, and the density extraction means and the Young's modulus extraction means include The processing is executed based on the regression line information and density information of the actual measurement database designated by the designation means.

<Invention of claims 1, 3 and 10>
According to this configuration, the first density (not only the actual measurement value but also the actual measurement value group) that can exist within the range of the actual measurement database of the Young's modulus-density relationship of the various members in each environment collected experimentally in advance. (It may be a simulated value that may exist from the probability distribution), and the Young's modulus is extracted based on this and the regression line of the actual measurement database. Then, a second density satisfying a predetermined first relational expression is calculated backward based on the extracted Young's modulus and the stress wave propagation velocity actually measured for the measurement target member. Here, if the density error between the second density and the first density is large, it means that there is a low possibility that the combination of the extracted Young's modulus and the second density exists within the range of the measured database. Therefore, this extracted Young's modulus cannot be adopted as the estimated Young's modulus of the measurement target member. Conversely, when the density error between the second density and the first density is small, it means that the combination of the extracted Young's modulus and the second density is likely to exist within the range of the measured database. This extracted Young's modulus can be adopted as the estimated Young's modulus of the member to be measured.

  In this configuration, the above steps (processing, means) are repeated for a plurality of first densities that are sequentially extracted, and the extracted Young's modulus in which the density error is within the set allowable range, that is, the actually measured stress. A Young's modulus that is highly likely to satisfy the predetermined first relational expression between the wave propagation velocity and the density that can exist within the range of the actual measurement database is determined as the estimated Young's modulus. Therefore, the actual Young's modulus of the measurement target member can be estimated from the determined estimated Young's modulus (or estimated Young's modulus group).

  As described above, according to this configuration, the strength strength performance of the measurement target member is scientifically quantified and objectively evaluated by measuring the stress wave propagation velocity without measuring the density of the measurement target member. be able to. Further, it has been experimentally confirmed that the stress wave propagation velocity does not affect the difference in the support method of the measurement target member. Therefore, in the present configuration employing the stress wave method, even if the measurement target member is incorporated as, for example, a structure of a building, the retained strength performance can be evaluated as it is without breaking.

<Invention of Claims 2, 4 and 11>
According to this configuration, the first density (not only the actual measurement value but also the actual measurement value group) that can exist within the range of the actual measurement database of the Young's modulus-density relationship of the various members in each environment collected experimentally in advance. (It may be a simulated value that may exist from the probability distribution), and the Young's modulus is extracted based on this and the regression line of the actual measurement database. Then, a second density satisfying a predetermined second relational expression is calculated backward based on the extracted Young's modulus, the length actually measured for the measurement target member, and the natural frequency. Here, when the density error between the second density and the first density is large, it means that there is a low possibility that the combination of the extracted Young's modulus and the second density exists in the range of the measured database. Therefore, this extracted Young's modulus cannot be adopted as the estimated Young's modulus of the measurement target member. Conversely, when the density error between the second density and the first density is small, it means that the combination of the extracted Young's modulus and the second density is likely to exist within the range of the measured database. This extracted Young's modulus can be adopted as the estimated Young's modulus of the member to be measured.

In this configuration, the above steps (processing) are repeatedly performed on a plurality of first densities that are sequentially extracted, and the extracted Young's modulus in which the density error is within the set allowable range, that is, the actually measured length and A Young's modulus that is highly likely to satisfy the predetermined second relational expression between the natural frequency and a density that may exist within the range of the actual measurement database is determined as an estimated Young's modulus. Therefore, the actual Young's modulus of the measurement target member can be estimated from the determined estimated Young's modulus (or estimated Young's modulus group).
As described above, according to the present configuration, the holding strength performance of the measurement target member is scientifically quantified objectively by measuring the length and the natural frequency without measuring the density of the measurement target member. Can be evaluated.

<Invention of claims 5 and 12>
According to this configuration, the frequency based on the actual probability distribution (data variation, cumulative frequency (probability density) curve) even if the probability distribution of density in the measurement database of Young's modulus-density relationship is not uniform. Thus, the first density can be extracted, and the Young's modulus more suitable for the measured database of the Young's modulus-density relationship can be estimated.

<Inventions of Claims 6 and 13>
According to this configuration, the average Young's modulus corresponding to the first density on the regression line is extracted by correcting the Young's modulus corresponding to the first density (for example, standard deviation, maximum and minimum Young's modulus). Extract as Young's modulus. Therefore, it is possible to estimate the Young's modulus more suitable for the actual measurement database.

<Invention of Claims 7 and 14>
According to this configuration, the regression residual can be extracted with a frequency based on the actual probability distribution of the Young's modulus corresponding to the extracted density data in the measured data group of the Young's modulus-density relationship, and the accuracy of the Young's modulus estimation simulation is further improved. be able to.

<Inventions of Claims 8 and 15>
According to this configuration, it is possible to extract an arbitrary regression residual in accordance with the probability distribution in the actual measurement database using uniform random numbers.

<Invention of Claims 9 and 16>
According to this configuration, for example, if the type and environment of the measurement target member are known in advance, the Young's modulus can be estimated with higher accuracy by designating the corresponding measurement database.

従って、測定対象木材Ｗのヤング率は、その測定対象木材Ｗについて密度ρと応力波伝播速度ｖとを測定すれば上記数式１から求めることができる。しかしながら、測定対象木材Ｗの密度ρを測定するには、その測定対象木材Ｗ自体の重量や体積を測定する必要があり容易なことではない。特に、測定対象木材Ｗが例えば木造建築物の構造体として組み込まれたものである場合には、そのままの状態で密度ρを正確に測定することは極めて困難である。 A first embodiment of the present invention will be described with reference to FIGS.
1. Outline of the present embodiment In this embodiment, wood is used as a measurement target member (hereinafter referred to as “measurement target wood W”), and the holding strength (Young's modulus) is evaluated non-destructively using a stress wave method. It is about the method. Here, between the Young's modulus E [Pa] of the material, the density ρ [kg / m ³ ], and the stress wave propagation velocity v [m / s], the following formula 1 (the “first” Equivalent to “relational expression”).

Therefore, the Young's modulus of the measurement target wood W can be obtained from Equation 1 above by measuring the density ρ and the stress wave propagation velocity v for the measurement target wood W. However, in order to measure the density ρ of the measurement target wood W, it is necessary to measure the weight and volume of the measurement target wood W itself, which is not easy. In particular, when the measurement target wood W is incorporated as, for example, a structure of a wooden building, it is extremely difficult to accurately measure the density ρ as it is.

  By the way, an actual measurement database of (bending) Young's modulus-density relationship for wood under each tree species and in each environment is currently open to the public by each research institution. However, as can be seen from these measured databases, the Young's modulus-density relationship differs easily depending on the period of use and usage environment, not to mention the case where the wood species (characteristics) differ. It is difficult to rule.

  Therefore, in the present embodiment, only the stress wave propagation velocity v of the measurement target wood W is measured, and the combination of “Young's modulus and density” in which the above Equation 1 holds between the stress wave propagation velocity v is the above-described research. Based on the accumulated "measurement database of Young's modulus-density relationship", it was estimated by the Monte Carlo simulation method.

2. Young's modulus estimator for wood (1) Overall configuration In the following, the wood Young's modulus estimator 10 will be described as an example. This wood Young's modulus estimation apparatus 10 is configured, for example, by incorporating the configuration of the Young's modulus estimation function of the present invention into a known stress wave propagation velocity measuring device.

  Specifically, as shown in FIG. 1, the wood Young's modulus estimating apparatus 10 has a pair of sensor units 11 and 11 led out from one end surface of a main body case 12 having a rectangular box shape as a whole. It has a configuration. A needle is provided at the tip of each sensor 11, and the pair of sensor portions 11, 11 can be driven into a remote location of the measurement target wood W. When one sensor unit 11 is hit with a hammer or the like (not shown), the time [μs] from when the impact sound is detected by the one sensor unit 11 until the other sensor unit 11 detects the impact sound (hereinafter referred to as “μs”). , “Stress wave propagation time T”). On the surface of the main body case 12, for example, a seven-segment liquid crystal display unit 13, a determination key 14, and an input unit 15 for inputting numerical values and the like are arranged.

  FIG. 2 is a simplified diagram showing the internal configuration of the wood Young's modulus estimation apparatus 10. In the figure, reference numeral 16 denotes a measuring unit provided with an acceleration detection circuit (not shown) connected to each of the sensor units 11. The stress wave propagation time T measured here is A / D converted and the CPU 17. Given to. The display control unit 18 causes the display unit 13 to display a display pattern based on a control signal from the CPU 17. The operation unit 19 gives the CPU 17 a signal corresponding to the input operation at the input unit 15.

  For example, a program storage area, an input data storage area, an actually measured database storage area, and an estimated data storage area are secured in the memory 20 (corresponding to the “storage means” of the present invention). In the program storage area, a Young's modulus estimation program described later is stored. In the input data storage area, data on the stress wave propagation time T from the measurement unit 16, data on the distance L [m] input on the input unit 15, and data on the allowable error R [%] are stored. In the actual measurement database storage area, as described below, data relating to the actual measurement database of the Young's modulus-density relationship of wood as research accumulation is stored. The estimated data storage area stores data such as the estimated Young's modulus extracted by executing the Young's modulus estimation program.

(2) About data regarding measurement database of Young's modulus-density relationship of wood FIG. 3 shows a graph in which a group of actual measurement data of Young's modulus-density relationship for a certain wood is plotted. In the present embodiment, first, a regression line F1 (corresponding to the “regression line” of the present invention) represented by the following formula 2 is obtained by the least square method for the measured value of the Young's modulus-density relationship.
[Equation 2]
E = a · ρ + b
a, b: Regression coefficient If the data distribution of Young's modulus corresponding to each density in the actual measurement database is uneven and it is judged that it is inappropriate to express the Young's modulus-density relationship with a simple regression line In order to correct this, it is desirable to perform processing such as weighted regression analysis (weighted regression analysis).

α：回帰直線Ｆ１の決定係数
このように、図３の実測データベースにおいては、各密度に対応するヤング率のデータ分布は不均一であるが、そのデータ分布（標準偏差）と密度との間にほぼ比例関係をあるとみなすことができるため、上記数式３に示す回帰直線Ｌ２を利用することとした。 In the figure, the distribution of Young's modulus corresponding to the density varies depending on the density, but a certain degree of correlation is recognized between the data distribution and the density. Therefore, in the present embodiment, the image is divided into a plurality of areas according to the density, and the standard deviation of Young's modulus is calculated individually for each divided area. Then, a regression line F2 shown in the following Equation 3 is obtained for the relationship between the standard deviation and the density.
[Equation 3]
SDi = p · ρi + q
SDi: Standard deviation of Young's modulus p, q: Regression coefficient When the data distribution (standard deviation) of Young's modulus corresponding to each density is substantially uniform over the entire density, Equation 3 of the regression line F2 above. Becomes SDi = q (coefficient p is zero), and q is obtained by the following Equation 4.

α: Determinant coefficient of regression line F1 As described above, in the measured database of FIG. 3, the Young's modulus data distribution corresponding to each density is non-uniform, but the data distribution (standard deviation) and the density are between. Since it can be considered that there is a substantially proportional relationship, the regression line L2 shown in Equation 3 is used.

  In the present embodiment, for example, a plurality of Young's modulus-density relationship measurement databases for each tree type of wood, such as cedar and cypress, are prepared in advance, and each of the above-described measurement databases for all tree types and for each tree type corresponds to the above. A cumulative frequency (probability density) curve is calculated for the regression line (F1, F2) and the density in each measured database. These regression line data (F1, F2) and cumulative frequency curve data are stored in advance in the actual measurement database storage area in association with each actual measurement database name. The Young's modulus can be estimated by Monte Carlo simulation based on an actual measurement database arbitrarily selected from the plurality of actual measurement databases.

(3) Processing by Young's Modulus Estimation Program The processing contents by the Young's modulus estimation program will be described with reference to the flowcharts shown in FIGS.

  First, the user drives a pair of sensor units 11 and 11 of the wood Young's modulus estimation device 10 into the measurement target wood W, turns on the wood Young's modulus estimation device 10, and sets one sensor unit 11 with a hammer or the like. Strike with. Then, the CPU 17 reads the stress wave propagation time T in the measurement unit 16 and displays the value on the display unit 13. When the confirmation key 14 is pressed by the user, the CPU 17 stores the data of the stress wave propagation time T in the input data storage area of the memory 20, for example, a message requesting the input of the distance L on the display unit 13. Display. When the distance between the driving positions of the pair of sensor units 11 and 11 is input by an input operation by the user at the input unit 15 and the enter key 14 is pressed, the CPU 17 stores the data of the distance L. Store in the input data storage area. The distance L divided by the stress wave propagation time T is the stress wave propagation velocity v of the measurement target wood W. Therefore, the measurement unit 16 and the input unit 15 correspond to the “acquisition unit” of the present invention.

  Thereafter, the CPU 17 displays, for example, a message requesting the input of the allowable error R on the display unit 13, and when the user performs an input operation and presses the enter key 14, the data of the allowable error R is stored in the input data storage area. Remember. Subsequently, the CPU 17 causes the display unit 13 to display a message for designating a desired one from the above-described various Young's modulus-density relationship measurement databases. Here, if the tree species of the measurement target wood W cannot be specified, the user designates an actual measurement database of the Young's modulus-density relationship of all tree species. On the other hand, if the tree species of the measurement target wood W can be specified, a more accurate estimated Young's modulus can be calculated by designating an actual measurement database of Young's modulus-density relationship of the tree species.

  When the measurement database is designated by the user and the confirmation key 14 is pressed, the CPU 17 reads the Young's modulus estimation program from the program storage area and executes the processing shown in the flowchart of FIG. First, the CPU 17 reads cumulative frequency curve data corresponding to the designated actual measurement database from the actual measurement database storage area of the memory 20 in S1, and accumulates while generating, for example, uniform random numbers in the interval [0, 1] in S2. Arbitrary density (corresponding to “first density” of the present invention, hereinafter referred to as “extraction density ρi”) is extracted by applying to the frequency curve data.

  Here, as can be seen from FIG. 3, the probability distribution of the actually measured density data in the actually measured database varies depending on the value of each density, and this actually exists when the Monte Carlo simulation is executed ignoring this. There is a possibility of extracting even a combination of Young's modulus and density that cannot be obtained. Therefore, as described above, by using the cumulative frequency curve data, the extraction density ρi that can exist in the actual measurement database as research accumulation is extracted according to the probability distribution of the actual measurement database. Therefore, the extracted density ρi extracted here includes not only the actually measured density on the actually measured database but also the pseudo density created according to the probability distribution. In addition, as a random number generation method, a publicly known method such as the Hinaka method or the congruence method can be used. The process at this time corresponds to the “density extraction process” of the present invention, and the CPU 17 functions as the “density extraction means” of the present invention.

  Next, the CPU 17 reads the regression line F1 data corresponding to the designated actual measurement database from the actual measurement database storage area of the memory 20 in S3, and the average Young's modulus Eiave corresponding to the extraction density ρi on the regression line F1. Is calculated. The processing at this time corresponds to “average Young's modulus calculation processing” of the present invention, and the CPU 17 functions as “average Young's modulus calculation means” of the present invention.

  In S4 to S6, an arbitrary Young's modulus (hereinafter referred to as “extracted Young's modulus Ei”) in consideration of the probability distribution (standard deviation) of Young's modulus corresponding to the extraction density ρi in the measured database with respect to the average Young's modulus Eiave. Extract).

Ｖ＝Σｒ
ｒｊ：区間［０，１］の一様乱数 ｎ：標本数であり例えばｎ＝１２
次に、この標準正規確率変数Ｖに上記標準偏差ＳＤｉを乗じて任意の回帰残差（Ｖ・ＳＤｉ）を求め（Ｓ５）、この回帰残差を平均ヤング率Ｅiaveに加算して抽出ヤング率Ｅｉ（＝Ｅiave＋Ｖ・ＳＤｉ）とする（Ｓ６）。これによりに、実測データベース（ヤング率ー密度関係）内において抽出密度ρｉに対応して存在し得るヤング率の中から、抽出ヤング率Ｅｉを正規分布（標準偏差ＳＤｉ）に従って抽出することができる。このときの処理が本発明の「回帰残差抽出処理、補正処理」に相当し、ＣＰＵ１７は本発明の「回帰残差抽出手段、補正手段」として機能する。また、Ｓ３〜Ｓ６までの処理が本発明の「ヤング率抽出ステップ、ヤング率抽出処理」に相当し、ＣＰＵ１７は本発明の「ヤング率抽出手段」として機能する。 Specifically, in this embodiment, with respect to the average Young's modulus Eiave, the regression residual of each Young's modulus corresponding to the extraction density ρi in the actual measurement database (Young's modulus-density relationship) is a normal distribution (in the regression line data F2). It is assumed that it follows the standard deviation SDi) corresponding to the extraction density ρi. Then, the CPU 17 generates a uniform random number, and calculates a standard normal random variable V based on the following formula 5 based on the central limit theorem from the plurality of uniform random numbers (S4). As a method for generating normal random numbers from uniform random numbers, there are, for example, the Box-Muller method and the polar coordinate method in addition to the method using the central limit theorem.

V = Σr
rj: uniform random number in the interval [0, 1] n: number of samples, for example, n = 12
Next, an arbitrary regression residual (V · SDi) is obtained by multiplying the standard normal random variable V by the standard deviation SDi (S5), and this regression residual is added to the average Young's modulus Eiave to extract the extracted Young's modulus Ei. (= Eiave + V · SDi) (S6). Thereby, the extracted Young's modulus Ei can be extracted according to the normal distribution (standard deviation SDi) from the Young's modulus that can exist corresponding to the extracted density ρi in the measured database (Young's modulus-density relationship). The processing at this time corresponds to “regression residual extraction processing and correction processing” of the present invention, and the CPU 17 functions as “regression residual extraction means and correction means” of the present invention. The processing from S3 to S6 corresponds to the “Young's modulus extraction step, Young's modulus extraction processing” of the present invention, and the CPU 17 functions as “Young's modulus extraction means” of the present invention.

  Subsequently, the CPU 17 reads the data of the stress wave propagation time T and the data of the distance L stored in the input data storage area in S7, and the density (this book) satisfies the above-described Equation 1 between these and the extracted Young's modulus Ei. Corresponding to “Second Density” of the Invention Hereinafter, “calculated density ρk”) is calculated. The process at this time corresponds to the “density calculation step, density calculation process” of the present invention, and the CPU 17 functions as the “density calculation means” of the present invention.

  In step S8, the CPU 17 calculates a density error of the calculated density ρk with respect to the extraction density ρi, reads data of the allowable error R, and the ratio of the density error to the extraction density ρi is within an allowable error range (for example, 1%). To determine if it is within.

  If it is determined that the density error is outside the allowable error range (“N” in S8), the combination of the calculated density ρk calculated in the above process and the extracted Young's modulus Ei is stored in the actual measurement database. Therefore, the calculated density ρk and the extracted Young's modulus Ei are not stored in the estimated data storage area. On the other hand, when it is determined that the density error is within the allowable error range (“Y” in S8), there is a high possibility that the combination of the calculated density ρk and the extracted Young's modulus Ei exists in the actual measurement database. That is, the combination of the calculated density ρk and the extracted Young's modulus Ei can be regarded as conforming to the actual measurement database while satisfying Equation 1 between the stress wave propagation time T and the distance L. Therefore, the extracted Young's modulus Ei is set as the estimated Young's modulus and stored in the estimated data storage area together with the extracted density ρi and the calculated density ρk (S9). The process at this time corresponds to the “estimated Young's modulus determining step, estimated Young's modulus determining process” of the present invention, and the CPU 17 functions as “estimated Young's modulus determining means” of the present invention.

  Then, after the processes of S1 to S9 described above are executed a plurality of times (for example, 5000 times in the present embodiment), the process ends (S10). As a result, the Young's modulus of the measurement target wood W can be estimated from one or a plurality of extracted Young's modulus Ei stored in the estimated data storage area as the estimated Young's modulus. In the present embodiment, for example, the maximum value, minimum value, average value, and standard deviation of the extracted Young's modulus Ei as the estimated Young's modulus are displayed on the display unit 13. In addition, the maximum value, the minimum value, the average value, and the standard deviation of the calculated density ρk corresponding to the extracted Young's modulus Ei as the estimated Young's modulus may be displayed. The wood Young's modulus estimation device 10 may have a printing function, and the result data may be printed out on recording paper. Further, the above result data may be output to a terminal device such as a personal computer by a recording medium or communication means.

  In this embodiment, for example, when there is no extracted Young's modulus Ei stored as an estimated Young's modulus in the estimated data storage area, an error message is displayed on the display unit 13. In this case, the Young's modulus estimation program can be executed again by changing the designation of the actual measurement database or expanding the range of the setting allowable error.

  As described above, according to the present embodiment, the measurement target wood W is held by measuring the stress wave propagation velocity v (stress wave propagation time T, distance L) without measuring the density of the measurement target wood W. The strength performance can be scientifically quantified and evaluated objectively. In addition, since the estimated Young's modulus is extracted by Monte Carlo simulation that fully considers the data distribution of the actual measurement database as research accumulation, it is possible to estimate the Young's modulus that is very likely to exist in reality. Further, it has been experimentally confirmed that the stress wave propagation velocity does not affect the difference in the support method of the measurement target member. Therefore, in this embodiment which employs the stress wave method, even if the measurement target member is incorporated as, for example, one structure of a building, the retained strength performance can be evaluated as it is without breaking.

固有振動数を測定する方法としては、例えば特公平６−７８９７４号公報に開示された方法がある。但し、この方法では、測定対象木材が例えば建築物の一構造体として組み込まれた状態では、その固有振動数を測定できないため、非破壊的に保有強度性能を評価するためには、上記実施形態の方法が望ましい。 <Other embodiments>
The present invention is not limited to the embodiments described with reference to the above description and drawings. For example, the following embodiments are also included in the technical scope of the present invention.
(1) In the above embodiment, the method of measuring the stress wave propagation velocity and estimating the Young's modulus by the stress method has been described. However, the natural frequency of the wood to be measured is measured and the Young's modulus is measured by the striking method (natural frequency analysis). May be estimated. In this case, the natural frequency fr is measured instead of the stress wave propagation time T, and the following formula 6 (corresponding to the “second relational expression” of the present invention) is used instead of the formula 1. Will do.

As a method for measuring the natural frequency, for example, there is a method disclosed in Japanese Patent Publication No. 6-78974. However, in this method, since the natural frequency cannot be measured in a state in which the measurement target wood is incorporated as one structure of a building, for example, in order to evaluate the retained strength performance nondestructively, the above embodiment This method is desirable.

  (2) In the above embodiment, the extraction density ρi is irregularly extracted based on random number generation. For example, when the density probability distribution on the actual measurement database is uniform, a predetermined predetermined value is used. Alternatively, the extraction density ρi may be sequentially extracted.

  (3) In the above embodiment, the tree type actual measurement database can be specified. However, in addition to the tree species, for example, a plurality of trees classified as “coniferous tree”, “hardwood”, “tree species”, “new wood”, “old wood”, etc. You may enable it to designate from an actual measurement database.

  (4) In the embodiment described above, the regression residual arbitrarily extracted in consideration of the standard deviation SDi (variation) of the actual Young's modulus on the actual measurement database is added to the average Young's modulus Eiave as the extracted Young's modulus. Not limited to this, for example, regardless of the value of the extraction density ρi, the maximum and minimum Young's modulus shifted by a predetermined allowable amount (for example, 0.3%) from the average Young's modulus Eiave is extracted as the extracted Young's modulus. May be. Furthermore, when it is recognized that the data distribution of the actual measurement database is uniform to some extent, the average Young's modulus Eiave itself may be extracted as the extracted Young's modulus.

  (5) In the above-described embodiment, the wood Young's modulus estimation apparatus 10 including the sensor units 11 and 11 has been described as an example. However, the above-described Young's modulus estimation program is installed in a personal computer, and stress wave propagation is separately performed. The stress wave propagation time T and distance L measured by the velocity measuring device may be input to a personal computer to execute the Young's modulus estimation program.

  (6) In the above-described embodiment, wood has been described as an example of a measurement target member. However, the present invention is not limited to this, and various members that require strength measurement, such as iron and concrete used as a building structure material, By applying the present invention, the same effect as that of the above embodiment can be obtained.

1 is an external view of a Young's modulus estimation device for wood according to an embodiment of the present invention. Simplified diagram showing the internal structure of the Young's modulus estimation device for wood Graph plotting measured data group of Young's modulus-density relationship Flow chart showing processing contents of Young's modulus estimation program

Explanation of symbols

10 ... Wood Young's modulus estimation device 15 ... Input unit (acquisition means)
16 ... Measurement unit (acquisition means)
17 ... CPU (computer)
20 ... Memory (storage means)
F1 ... regression line (regression line)
Eiave ... Average Young's modulus Ei ... Extracted Young's modulus W ... Measurement target wood ρi ... Extraction density (first density)
ρk ... Calculated density (second density)
v ... Stress wave propagation velocity

Claims (16)

By measuring the stress wave propagation velocity of the measurement target member, a plurality of first densities that may exist within the range of the measured database of the Young's modulus-density relationship of the member are regularly or irregularly extracted, and each of the first densities is extracted. A Young's modulus estimation method for estimating the Young's modulus of the measurement target member corresponding to the stress wave propagation velocity by repeatedly performing the following steps (A) to (C).
(A) A Young's modulus extraction step of extracting a Young's modulus based on the regression line of the actual measurement database and the first density;
(B) a density calculating step for calculating a second density corresponding to the extracted Young's modulus extracted in the Young's modulus extracting step and the stress wave propagation velocity based on a predetermined first relational expression;
(C) An estimated Young's modulus determining step for determining the extracted Young's modulus as an estimated Young's modulus on the condition that an error between the first density and the second density is within a setting allowable range. The length and natural frequency of the member to be measured are measured, and a plurality of first densities that can exist within the range of the measured database of Young's modulus-density relation of the member are regularly or irregularly extracted. A Young's modulus estimation method for estimating the Young's modulus of the measurement target member corresponding to the length and natural frequency of the measurement target member by repeatedly performing the following steps (A) to (C) for each density.
(A) A Young's modulus extraction step of extracting a Young's modulus based on the regression line of the actual measurement database and the first density;
(B) a density calculating step for calculating a second density corresponding to the extracted Young's modulus extracted in the Young's modulus extracting step, the length, and the natural frequency based on a predetermined second relational expression;
(C) An estimated Young's modulus determining step for determining the extracted Young's modulus as an estimated Young's modulus on the condition that an error between the first density and the second density is within a setting allowable range. By causing the computer to execute the following processes (A) to (D), the measurement target member of the measurement target member is measured based on the actual measurement database of the Young's modulus-density relationship of the member and the stress wave propagation velocity actually measured for the measurement target member. A Young's modulus estimation program for estimating Young's modulus.
(A) a density extraction process for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database;
(B) For each first density extracted in the density extraction process, a Young's modulus extraction process for extracting each Young's modulus based on the regression line information of the actual measurement database stored in the memory and each first density;
(C) For each extracted Young's modulus extracted in the Young's modulus extraction process, density calculation for calculating each extracted Young's modulus and each second density corresponding to the stress wave propagation velocity based on a predetermined first relational expression. processing,
(D) For each of the second densities, when an error from the corresponding first density is within a setting allowable range, the extracted Young's modulus corresponding to the second density is determined as an estimated Young's modulus Young's modulus determination process. By causing the computer to execute the following processes (A) to (D), the measurement target is based on the actual measurement database of the Young's modulus-density relationship of the member and the length and natural frequency actually measured for the measurement target member. A Young's modulus estimation program for estimating the Young's modulus of a member.
(A) a density extraction process for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database;
(B) For each first density extracted in the density extraction process, a Young's modulus extraction process for extracting each Young's modulus based on the regression line information of the actual measurement database stored in the memory and each first density;
(C) For each extracted Young's modulus extracted in the Young's modulus extraction process, each second density corresponding to each extracted Young's modulus, the length, and the natural frequency is calculated based on a predetermined second relational expression. Density calculation processing,
(D) For each of the second densities, when an error from the corresponding first density is within a setting allowable range, the extracted Young's modulus corresponding to the second density is determined as an estimated Young's modulus. Estimated Young's modulus determination process. 5. The Young's modulus estimation program according to claim 3, wherein the density extraction process is a process of extracting the first density according to a probability distribution regarding the density in the actual measurement database by a Monte Carlo simulation method. The Young's modulus extraction process includes an average Young's modulus calculation process for obtaining an average Young's modulus corresponding to the first density on the regression line, and the average based on a variation in Young's modulus corresponding to the first density in the actual measurement database. The Young's modulus estimation program according to any one of claims 3 to 5, further comprising correction processing for correcting the Young's modulus to obtain the extracted Young's modulus. The Young's modulus extraction process includes an average Young's modulus calculation process for obtaining an average Young's modulus corresponding to the first density on the regression line, and a regression that extracts a regression residual for the average Young's modulus according to a normal distribution by a Monte Carlo simulation method. 6. The Young's modulus according to claim 3, further comprising: a residual extraction process; and a correction process that corrects the average Young's modulus according to the extracted regression residual to obtain the extracted Young's modulus. Estimation program. In the regression residual extraction process, a uniform random number is generated, a standard normal random variable is calculated based on the uniform random number, and the standard normal random variable is converted into the Young's modulus corresponding to the first density in the actual measurement database. The Young's modulus estimation program according to claim 7, wherein the regression residual is multiplied by a standard deviation. Further including a designation process for designating a specific actual measurement database from a plurality of types of actual measurement databases classified based on at least one of the type of member and the environment,
The Young's modulus estimation program according to any one of claims 3 to 8, wherein the processes (A) to (D) are executed based on an actual measurement database designated in the designation process. Acquisition means for acquiring the stress wave propagation velocity of the measurement target member;
Storage means for storing regression line information and density information of an actual measurement database of Young's modulus-density relationship of members;
Density extraction means for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database based on the density information;
For each first density extracted by the density extraction means, Young's modulus extraction means for extracting each Young's modulus based on the regression line information and each first density;
For each extracted Young's modulus extracted by the Young's modulus extracting means, density calculating means for calculating each second density corresponding to each extracted Young's modulus and the stress wave propagation velocity based on a predetermined first relational expression;
Estimated Young's modulus determination that determines the extracted Young's modulus corresponding to the second density as the estimated Young's modulus when an error from the first density corresponding to each second density is within a setting allowable range. Means for estimating the Young's modulus. Acquisition means for acquiring the length and natural frequency of the member to be measured;
Storage means for storing regression line information and density information of an actual measurement database of Young's modulus-density relationship of members;
Density extraction means for regularly or irregularly extracting a plurality of first densities that may exist within the range of the actual measurement database based on the density information;
For each first density extracted by the density extraction means, Young's modulus extraction means for extracting each Young's modulus based on the regression line information and each first density;
For each extracted Young's modulus extracted by the Young's modulus extracting means, a density calculation for calculating each second density corresponding to each extracted Young's modulus, the length, and the natural frequency based on a predetermined second relational expression. Means,
Estimated Young's modulus determination that determines the extracted Young's modulus corresponding to the second density as the estimated Young's modulus when an error from the first density corresponding to each second density is within a setting allowable range. Means for estimating the Young's modulus. The Young's modulus estimation apparatus according to claim 10 or 11, wherein the density extraction unit extracts the first density according to a probability distribution regarding the density in the actual measurement database by a Monte Carlo simulation method. The Young's modulus extraction means includes an average Young's modulus calculation means for obtaining an average Young's modulus corresponding to the first density on the regression line, and the average based on a variation in Young's modulus corresponding to the first density in the measured database. The Young's modulus estimator according to any one of claims 10 to 12, further comprising correction means for correcting the Young's modulus to obtain the extracted Young's modulus. The Young's modulus extraction means includes an average Young's modulus calculation means for obtaining an average Young's modulus corresponding to the first density on the regression line, and a regression that extracts a regression residual with respect to the average Young's modulus according to a normal distribution by a Monte Carlo simulation method. The Young's modulus according to any one of claims 10 to 12, further comprising: a residual extracting unit; and a correcting unit that corrects the average Young's modulus according to the extracted regression residual to obtain the extracted Young's modulus. Estimating device. The regression residual extracting means generates a uniform random number, calculates a standard normal random variable based on the uniform random number, and sets the standard normal random variable to a Young's modulus corresponding to the first density in the actual measurement database. The Young's modulus estimation apparatus according to claim 14, wherein the regression residual is multiplied by a standard deviation. The storage means stores regression line information and density information of a plurality of types of measurement databases classified based on at least one of the type of member and the environment,
A designation means for designating a specific actual measurement database from the plurality of types of actual measurement databases;
The Young's modulus estimation according to any one of claims 10 to 15, wherein the density extraction unit and the Young's modulus extraction unit execute processing based on regression line information and density information of an actual measurement database designated by the designation unit. apparatus.

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