JP6723605B2 - Measuring method of Young's modulus of wood and its equipment - Google Patents

Description

The present invention relates to a Young's modulus estimation method and apparatus for estimating the Young's modulus of wood or the like.

From the viewpoint of conservation of forest resources, promotion of effective use of domestic timber as a structural member for wooden houses is desired. In the case of using new wood in a new house, it is necessary to evaluate the strength of wood, which is a biological material to be used, one by one, and a simpler method for evaluating the strength of wood will become more important in the future. It becomes an issue.

When repairing, reconstructing or rebuilding a wooden building, it is necessary to determine whether or not the structural members used can be used or reused, and it is necessary to know the strength performance of the structural members. .. In the past, the judgment was often made by a subjective evaluation based on the experience of a skilled carpenter, but it is required to evaluate the strength of the structural member objectively, that is, numerically.

Young's modulus is one of the indexes for evaluating the deformation strength of wood. That is, it is expressed as the ratio of the deformation per unit length to the applied force per unit area. There are various devices for measuring the Young's modulus, which are commercially available, but for measuring the Young's modulus of the wood of the structural member, or for measuring the Young's modulus of the wood before shipping, a simple device is required, Various methods have been proposed in an attempt to meet the demand.

(1) "Frequency analysis method (striking method)": striking a structural member with a hammer, collecting impact sound with a microphone, measuring a natural frequency using a frequency analyzer, and measuring the weight and volume of the other structural member. Is calculated, the density is determined from this, and the Young's modulus is calculated by a predetermined relational expression (see Patent Document 1 below).

(2) "Ultrasonic method": The ultrasonic sensor is used to measure the sound velocity of ultrasonic waves in the structural member, the density of the structural member is measured, the density is determined from this, and a predetermined value is determined from the sound velocity and density of these ultrasonic waves. A method of calculating Young's modulus by the relational expression of.

(3) "Stress wave method": A stress wave propagation velocity measuring instrument is used to measure the stress wave propagation velocity in a structural member, and the density of the structural member is measured. A method of calculating Young's modulus from speed and density by a predetermined relational expression (see Patent Document 2 below).

(4) A method of estimating Young's modulus and density by Monte Carlo simulation using the measured stress wave propagation velocity (JP 2007-232698 A).

Japanese Patent Publication No. 6-78974 Japanese Examined Patent Publication No. 40-18194 JP, 2007-232698, A

By the way, in the above-mentioned conventional frequency analysis method, ultrasonic method, and stress wave method (1) to (3), it is necessary to grasp the density of structural members. However, measuring the density is not always easy. For example, when there are many objects to be measured, the weight measurement requires a lot of labor. Further, when measuring members in a building, it is almost impossible to measure the density while maintaining the structure.

Further, in the ultrasonic method, the ultrasonic waves are attenuated according to the degree of adhesion between the structural member and the ultrasonic sensor, and thus the adhesion between the two becomes a problem, and it does not exceed the laboratory level and is not practical.

Furthermore, the method using the Monte Carlo simulation method is a method of estimating the Young's modulus and the density without measuring the density, but it is impossible to obtain information on the estimation accuracy, and the calculation is too complicated to understand. There is a difficulty, and it will require a considerable cost to incorporate the calculation software into the CPU.

The present invention has been proposed based on the above circumstances, and an object thereof is to provide a method and apparatus for estimating the Young's modulus of wood by a simple method.

The present invention employs the following means in order to achieve the above object.

From the database of Young's modulus and density of wood, the parameters of the equation (bivariate normal distribution) representing the probability distribution curved surface with the probability density as the vertical axis are obtained on the Young's modulus-density coordinate plane.

In the above state, the stress wave propagation velocity v of the wood to be measured is obtained in advance, and the straight line of E=ρv ² on the Young's modulus (E)-density (ρ) coordinate plane is obtained from the stress wave propagation velocity. ..

Estimated points of Young's modulus and density are obtained from a peak p obtained from a curve (hereinafter referred to as an intersection curve) generated by the intersection of a plane perpendicular to the coordinate plane corresponding to the straight line and the probability distribution curved surface. In this case, the estimated point is obtained by calculation from the equation expressing the probability distribution curved surface and the equation of the straight line.

The equation representing the probability distribution surface is expressed as the equation (2) described below assuming a bivariate normal distribution, and each parameter in the equation is obtained by Bayesian statistics, for example, the Hamiltonian Monte Carlo method (HMC method). be able to.

The Young's modulus and density can be estimated without measuring the density by simply obtaining the stress wave propagation velocity of the wood to be measured by the above method. Even if the wood is incorporated in the structure, it will be shipped from now on. Even for wood that can be used, Young's modulus can be easily obtained.

A stress wave propagation velocity measuring device used in the present invention. Young's modulus-Probability distribution curve on the density coordinate. The figure which reflected the Young's modulus line in the probability distribution curve. Probability distribution curve parallel to Young's modulus axis. The figure which shows the error of the estimation and true value by this invention. The figure which shows the relationship between the estimated Young's modulus and water content by this invention.

The relationship between the Young's modulus E (GPa) of a material and the density ρ (kg/m ³ ) is shown by the following equation (1), where the stress wave velocity of the material is v (m/s). This principle basically applies to the relationship between the rate E and the density ρ.

<Formula 1>

Therefore, in order to obtain the Young's modulus E of the wood, it is naturally necessary to obtain the density ρ and the stress wave propagation velocity v of the wood to be measured. However, in the present invention, as described below, the stress wave propagation By obtaining the velocity, the density and Young's modulus can be estimated simultaneously. That is, the Young's modulus can be estimated by obtaining the stress wave propagation velocity without measuring the density.

FIG. 2 is a probability distribution obtained by assuming that the probability distribution of Young's modulus and density is a bivariate normal distribution based on a clear database of Young's modulus and density of wood (Table 1). That is, the probability density p is taken perpendicularly to the Young's modulus and density coordinate planes and expressed as a three-dimensional probability distribution curved surface M. A curved surface with a density of 500 kg/m ³ and a probability peak near Young's modulus of 15 GPa is obtained. Here, Table 1 shows a part of the database, and the number of samples in the database is not limited, but it goes without saying that the larger the number, the higher the accuracy.

The bivariate normal distribution is expressed as in equation (2), where μ is the average, σ is the standard deviation, and R is the correlation coefficient. Each subscript E and ρ indicates its attribute (that is, E is Young's modulus and ρ is density).

The five parameters μ _E , μ _ρ , σ _E , σ _ρ , and R of the equation (2) can be obtained by the Bayesian statistics, for example, the Hamiltonian Monte Carlo method (HMC method), and the results are shown in Table 2.

<Formula 2>

Table 2 Values of E and ρ bivariate normal distribution parameters obtained by the HMC method.

Since wood has annual rings and nodes and the density is not uniform, even if the formula (1) is basically followed as described above, there are some variations in Young's modulus depending on the individual. Consider the density of individuals to be uniform.

With the probability distribution curved surface obtained, the stress wave propagation velocity of the wood to be measured is measured by the device described below.

As a result, the slope v ^{2 of the} equation (1) is obtained, and the straight line Sl corresponding to the equation (1) can be drawn on the Young's modulus-density coordinate system as shown in FIG. However, in FIG. 3, the straight line is extended in the direction of the probability density axis to form the surface Su.

A probability curve L (hereinafter referred to as an intersection curve) of Young's modulus E and density ρ when the stress wave propagation velocity is v is obtained at a position intersecting the probability distribution curved surface M. The peak p of this intersection curve is the estimation point of Young's modulus and density of the wood to be measured.

FIG. 1 shows an example of a Young's modulus estimation device according to the present invention. The stress wave propagation velocities measured by the two probes 11 and the sound velocity measuring means 12 are input to the intersection curve calculating means 30.

That is, a pair of needle-shaped probes 11 and 11 are derived from a Young's modulus estimating device, and the two probes 11 and 11 are driven while maintaining a predetermined distance on the measurement target wood, and one probe 11 is hammered (not shown). When hit with an impact sound, the sound velocity measuring means 12 measures the time from when the impact sound is detected by the one probe 11 to when the impact sound is detected by the other probe 11. As a result, the velocity of the stress wave propagating through the wood is obtained by the sound velocity measuring means 12.

The above configuration for obtaining the velocity of the stress wave is an example, and the present invention is not limited to the above configuration, and it is sufficient if the stress wave velocity v is obtained as a result (see Patent Document 1).

The stress wave sonic velocity thus obtained is sent to the straight line calculating means 30 where the straight line corresponding to the equation (1) is obtained.

On the other hand, the above-mentioned probability curved surface is stored in the storage means 20 in advance as the equation (2) and five parameters.

In this state, when the straight line corresponding to the equation (1) is obtained as described above, the straight line is sent to the estimated value calculation means 40. The estimated value calculation means 40 reads out the equation (2) representing the probability curved surface from the storage means 20, obtains an intersection curve appearing at the intersection position with the surface corresponding to the equation (1), and determines the peak of the intersection curve as the target wood. The Young's modulus and density are estimated. This estimated point can be analytically obtained from the equation (1) corresponding to the five parameters of the equation (2) and the sound velocity.

Specifically, it is expressed by the following equation (3).

<Formula 3>

The Young's modulus and the density of the estimated points thus obtained are displayed as numerical values on the display unit 50 or together with the probability curved surface corresponding to the equation (2) and the surface Su corresponding to the equation (1). It will be.

The Young's modulus obtained as described above is evaluated.

FIG. 4 is a view of FIG. 3 as viewed from the Young's modulus axis side, and the intersecting curve L shows the shape of a normal distribution. From this, the variance σ ² can be calculated, and the accuracy of the estimation, for example, the 95% credit interval (that is, the range of ±2σ) can be shown.

FIG. 5 is a plot of the Young's modulus estimated by the above analysis with respect to the true value of the Young's modulus. As shown here, it shows a very good correlation. Further, FIG. 6 is an overwriting of the values obtained by the Monte Carlo simulation method disclosed in Japanese Patent Laid-Open No. 2007-232698 in FIG. It is shown that the estimation methods are almost equivalent.

Although any formula may be used as the above probability distribution formula, the bivariate normal distribution formula is also used in the present invention because a general probability distribution is generally a normal distribution. Thereby, the peak position of the intersection curve can be used as the Young's modulus and density estimation point.

Moreover, although the Hamiltonian Monte Carlo method is adopted as a method for determining the parameters, it does not deny that other methods are adopted.

As described above, the present application makes it possible to easily estimate the Young's modulus and the density of the wood even if the wood is incorporated in the structure because the Young's modulus and the density of the wood can be estimated simply by obtaining the stress wave propagation velocity. You can ask. Moreover, since the structure of the device is simple, it is possible to easily carry out the evaluation of the wood by bringing it into a lumbering site or the like.

11-Probe 12-Sonic velocity measuring means 20-Storage means 30-Straight line calculating means 40-Estimated value calculating means 50-Display means M-Probability surface L-Probability curve p-Peak (estimated value )

Claims (4)

From the database of Young's modulus and density of wood, the step of obtaining the formula expressing the probability distribution curved surface with its probability density as the vertical axis on the Young's modulus-density coordinate plane along with its parameters,
In the above state, the stress wave propagation velocity v of the measurement target wood is obtained in advance, and the step of obtaining a straight line of E=ρv ² on the Young's modulus E-density ρ coordinate plane from the stress wave propagation velocity v A Young's modulus estimation method comprising a step of obtaining Young's modulus and density estimation points from a peak obtained from an intersection curve of a plane perpendicular to the coordinate plane corresponding to and the probability distribution curved surface. The Young's modulus estimation method according to claim 1, wherein the equation representing the probability distribution surface is an equation representing a bivariate normal distribution, and each parameter in the equation is obtained by the Hamiltonian Monte Carlo method. From a database of Young's modulus and density of wood, Young's modulus-on the density coordinate plane, a storage means for obtaining and storing a probability distribution curved surface having the probability density as the vertical axis,
Sound velocity measuring means for determining the stress wave propagation velocity of the measurement target wood;
Straight line calculating means for obtaining a straight line of E=ρv ² on the Young's modulus E-density ρ coordinate plane from the stress wave propagation velocity v,
Young's body of wood, comprising: a plane perpendicular to the coordinate plane corresponding to the straight line; and an estimation calculation means for obtaining an estimation point of Young's modulus and density from a peak obtained from an intersection curve of the probability distribution curved surface. Rate estimator. The Young's modulus estimator according to claim 3, wherein the equation representing the probability distribution curved surface is an equation representing a bivariate normal distribution, and each parameter in the equation is obtained by the Hamiltonian Monte Carlo method.

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