Maotai-flavor liquor saccharification pile geometric parameter calculation method based on mathematical model

Abstract

The invention provides a method for calculating geometric parameters of a Maotai-flavor liquor saccharification pile based on a mathematical model, and relates to the technical field of stacking fermentation, a catenary equation is utilized to fit the stacking contour of the Maotai-flavor liquor saccharification pile, and the boundary condition of the stacking contour of the Maotai-flavor liquor saccharification pile is substituted into the catenary equation to calculate the geometric parameters of the Maotai-flavor liquor saccharification pile. Obtaining a bending coefficient equation of the catenary equation, solving the bending coefficient equation through a Newton iteration method, obtaining a stacking contour expression of the Maotai-flavor white spirit saccharification pile, and obtaining a geometric parameter solving formula of the Maotai-flavor white spirit saccharification pile based on an inverse function of the stacking contour expression of the Maotai-flavor white spirit saccharification pile. Therefore, the geometric attributes of the saccharification heap can be obtained only by knowing the boundary conditions of the Maotai-flavor liquor saccharification heap, the problem that the geometric parameters of the Maotai-flavor liquor saccharification heap cannot be calculated before the Maotai-flavor liquor saccharification heap enters the cellar is solved, and the method is suitable for calculating the geometric parameters of the Maotai-flavor liquor saccharification heap.

Description

Technical Field

[0001] The invention relates to the technical field of stack fermentation, and in particular to a method for calculating geometric parameters of a Maotai-flavor liquor saccharification stack based on a mathematical model. Background Art

[0002] The stacking fermentation stage of Maotai-flavor liquor is an open fermentation process, namely the saccharification pile, which mainly saccharifies the gelatinized starch through the enrichment of environmental microorganisms, and synthesizes the precursor substances and flavor components of the Maotai style under the catalytic action of numerous enzymes, providing the necessary microbial and enzyme basis for subsequent fermentation in the cellar.

[0003] The saccharification pile has a decisive influence on the quality of Maotai-flavor liquor, and the calculation of the geometric parameters of the saccharification pile is crucial. The calculation of the geometric parameters of the existing saccharification pile is not convenient. For example, the volume calculation usually measures the change in the volume of the cellar before and after the saccharification pile is put into the cellar to obtain the actual volume of the saccharification pile, and the volume of the saccharification pile cannot be calculated before entering the cellar. Summary of the invention

[0004] Technical problem solved by the present invention: The present invention provides a method for calculating the geometric parameters of a saccharification pile of a sauce-flavor liquor based on a mathematical model, thereby solving the problem that the geometric parameters of the existing sauce-flavor liquor saccharification pile are inconvenient to calculate.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a method for calculating the geometric parameters of the Maotai-flavor liquor saccharification pile based on a mathematical model, comprising the following steps:

[0006] S1. Use the catenary equation to fit the accumulation profile of the saccharification pile of Maotai-flavor liquor;

[0007] S2. Substituting the stacking contour boundary conditions of the Maotai-flavor liquor saccharification pile into the catenary equation to obtain the bending coefficient equation of the catenary equation, solving the bending coefficient equation by Newton's iteration method to obtain the stacking contour expression of the Maotai-flavor liquor saccharification pile;

[0008] S3. Based on the inverse function of the stacking profile expression of the Maotai-flavor liquor saccharification pile, a formula for solving the geometric parameters of the Maotai-flavor liquor saccharification pile is obtained, and the geometric parameters are obtained by solving the formula.

[0009] Furthermore, the catenary equation is: Where k is the bending coefficient, (x, y) represents the coordinates of the point on the catenary, and cosh() represents the hyperbolic cosine function.

[0010] Furthermore, the bending coefficient equation of the catenary is: or Where h represents the height of the saccharification pile of the Maotai-flavor liquor, and r represents the bottom radius of the saccharification pile.

[0011] Furthermore, the inverse function of the stacking profile expression of the Maotai-flavor liquor saccharification pile is: Among them, arccosh() represents the inverse function of the hyperbolic cosine function, and the value range of y is [k, k+h].

[0012] Furthermore, if the geometric parameter of the saccharification pile is volume, the solution formula for the volume is: Where π is the ratio of a circle to its circumference.

[0013] Furthermore, if the geometric parameter of the saccharification pile is the surface area, the solution formula for the surface area is: in, express The derivative of .

[0014] Furthermore, S2 also includes obtaining a three-dimensional visualization model of the Maotai-flavor liquor saccharification pile by flipping and rotating according to the stacking contour expression of the Maotai-flavor liquor saccharification pile.

[0015] Furthermore, the method also includes calculating the layered volume of the Maotai-flavor liquor saccharification pile based on the three-dimensional visualization model of the Maotai-flavor liquor saccharification pile.

[0016] The beneficial effects of the present invention are as follows: the present invention provides a method for calculating the geometric parameters of a saccharification pile of a sauce-flavor liquor based on a mathematical model, the catenary equation is used to fit the stacking contour of the sauce-flavor liquor saccharification pile, the boundary conditions of the stacking contour of the sauce-flavor liquor saccharification pile are substituted into the catenary equation to obtain the bending coefficient equation of the catenary equation, the bending coefficient equation is solved by the Newton iteration method to obtain the stacking contour expression of the sauce-flavor liquor saccharification pile, the geometric parameter solution formula of the sauce-flavor liquor saccharification pile is obtained based on the inverse function of the stacking contour expression of the sauce-flavor liquor saccharification pile, and the geometric parameters are solved to obtain the formula, thereby, the geometric properties of the saccharification pile can be obtained by only knowing the boundary conditions of the sauce-flavor liquor saccharification pile, thereby solving the problem that the geometric parameters of the sauce-flavor liquor saccharification pile cannot be calculated before entering the cellar. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a method for calculating geometric parameters of a Maotai-flavor liquor saccharification pile based on a mathematical model provided by the present invention;

[0018] Figure 2 It is a three-dimensional visualization diagram of a saccharification pile in a method for calculating geometric parameters of a sauce-flavor liquor saccharification pile based on a mathematical model provided by the present invention. DETAILED DESCRIPTION

[0019] Aiming at the problem that it is inconvenient to calculate the geometric parameters of a saccharification pile of a sauce-flavor liquor, the present invention provides a method for calculating the geometric parameters of a saccharification pile of a sauce-flavor liquor based on a mathematical model, uses a catenary equation to fit the stacking profile of the sauce-flavor liquor saccharification pile, substitutes the stacking profile boundary conditions of the sauce-flavor liquor saccharification pile into the catenary equation, obtains a bending coefficient equation of the catenary equation, solves the bending coefficient equation by Newton's iteration method, obtains the stacking profile expression of the sauce-flavor liquor saccharification pile, obtains a geometric parameter solution formula of the sauce-flavor liquor saccharification pile based on an inverse function of the stacking profile expression of the sauce-flavor liquor saccharification pile, and obtains the geometric parameters by solving the solutions, thereby, the geometric properties of the saccharification pile can be obtained by only knowing the boundary conditions of the sauce-flavor liquor saccharification pile, and solves the problem that the geometric parameters of the sauce-flavor liquor saccharification pile cannot be calculated before entering the cellar.

[0020] The present invention provides a method for calculating the geometric parameters of the Maotai-flavor liquor saccharification pile based on a mathematical model. Figure 1 As shown, the following steps are included:

[0021] S1. Use the catenary equation to fit the accumulation profile of the saccharification pile of Maotai-flavor liquor;

[0022] Specifically, assuming that the mash particles are small enough to be analogized as particles, and the interaction between the mash particles during the stacking process can be ignored, an inverted catenary can be used to approximate the stacking profile of the saccharification pile. The catenary equation is: Where k is the bending coefficient, (x, y) represents the coordinates of the point on the catenary, and cosh() represents the hyperbolic cosine function.

[0023] S2. Substituting the stacking contour boundary conditions of the Maotai-flavor liquor saccharification pile into the catenary equation to obtain the bending coefficient equation of the catenary equation, solving the bending coefficient equation by Newton's iteration method to obtain the stacking contour expression of the Maotai-flavor liquor saccharification pile;

[0024] Specifically, the stacking contour boundary condition of the Maotai-flavor liquor saccharification pile is: when x=r or x=-r, y=h, which is substituted into the catenary equation to obtain the bending coefficient equation of the catenary equation: Since the catenary equation is symmetric about the Y axis, the bending coefficient equation of the catenary equation can be simplified to or That is, they can all be converted to: Where e is a natural constant, h represents the height of the saccharification pile of the Maotai-flavor liquor, and r represents the bottom radius of the saccharification pile. Then the Newton iteration method is used to solve it. The Newton iteration method can be implemented with the help of MATLAB to obtain the value of the bending coefficient k, and then the stacking profile expression of the Maotai-flavor liquor saccharification pile can be obtained: Among them, the value range of x is [-r, r], and the value range of y is [k, k+h]. In order to visualize the saccharification pile of Maotai-flavor liquor, the stacking contour expression of the Maotai-flavor liquor saccharification pile is flipped along the X-axis and rotated with the Y-axis as the rotation center to obtain a three-dimensional visualization model of the Maotai-flavor liquor saccharification pile, as shown in Figure 2 shown.

[0025] S3. Based on the inverse function of the stacking profile expression of the Maotai-flavor liquor saccharification pile, a formula for solving the geometric parameters of the Maotai-flavor liquor saccharification pile is obtained, and the geometric parameters are obtained by solving the formula.

[0026] Specifically, the accumulation profile of the saccharification pile of the Maotai-flavor liquor is flipped along the y=x axis to obtain the inverse function of the accumulation profile expression of the Maotai-flavor liquor saccharification pile. The inverse function of the accumulation profile expression of the Maotai-flavor liquor saccharification pile is: Among them, arccosh() represents the inverse function of the hyperbolic cosine function, and the value range of y is [k, k+h];

[0027] If the geometric parameter of the saccharification pile is volume, that is, the volume of the shape enclosed by rotating the inverse function along the X-axis in three-dimensional space is solved. The volume can be obtained by integrating the area, and the volume formula is: After substituting the inverse function, the volume formula is: Therefore, we only need to know the radius r and height h of the saccharification pile, and use the Newton iteration method to solve the value of the bending coefficient k, and the volume of the sauce-flavor liquor saccharification pile can be obtained through the volume formula;

[0028] If the geometric parameter of the saccharification pile is the surface area, that is, the surface area of ​​the shape enclosed by the inverse function rotated along the X-axis in three-dimensional space is solved. The surface area can be obtained by integrating the perimeter, and the surface area formula is: After substituting the inverse function, the surface area formula is: Among them, π is the ratio of the circumference of a circle, express Therefore, we only need to know the radius r and height h of the saccharification pile, and use Newton's iteration method to solve the value of the bending coefficient k. The surface area of ​​the sauce-flavor liquor saccharification pile can be obtained through the surface area formula.

[0029] By using the method for calculating the geometric parameters of the saccharification pile of Maotai-flavor liquor based on a mathematical model provided by the present invention, it is only necessary to measure the radius and height of the saccharification pile of Maotai-flavor liquor to calculate the geometric parameters of the Maotai-flavor liquor, which is convenient and quick.

[0030] In particular, based on the three-dimensional visualization model of the sauce-flavor liquor saccharification pile, the stratified volume of the sauce-flavor liquor saccharification pile can also be calculated according to the three-dimensional visualization model of the sauce-flavor liquor saccharification pile, and the stratification includes stratification according to the height of the sauce-flavor liquor saccharification pile, or stratification according to the contour of the sauce-flavor liquor saccharification pile. The saccharification efficiency and fermentation speed of the saccharification pile can also be analyzed based on the three-dimensional visualization model of the sauce-flavor liquor saccharification pile.

[0031] The accuracy of volume calculation for the saccharification pile of Maotai-flavor liquor is verified, as shown in Table 1, where the actual volume is obtained by the change in cellar volume before and after entering the cellar.

[0032] Table 1 Accuracy of volume calculation of Maotai-flavor liquor saccharification pile

[0033] Serial number Radius of saccharification pile Saccharification pile height Actual volume Calculating volume Accuracy 1 2.56 1.46 13.42 13.32 99.25％ 2 2.45 1.56 13.83 14.47 95.37％ 3 2.51 1.50 14.14 13.75 97.24％ 4 2.45 1.55 13.94 14.26 97.70％ 5 2.60 1.50 14.35 14.28 99.51％

[0034] The accuracy of the surface area calculation of the Maotai-flavor liquor saccharification pile is verified, as shown in Table 2.

[0035] Table 2 Accuracy of surface area calculation of Maotai-flavor liquor saccharification pile

[0036] Serial number Actual surface area Calculating surface area Accuracy 1 23.92 23.52 98.34％ 2 24.12 24.47 98.55％ 3 24.36 23.86 97.97％ 4 24.34 23.86 98.02％ 5 24.13 24.59 98.11％ 6 23.48 24.29 96.56％ 7 24.12 24.64 97.85％ 8 24.32 23.86 98.10％ 9 23.56 23.91 98.53％

Claims

1. A method for calculating geometric parameters of a Maotai-flavor liquor saccharification pile based on a mathematical model, characterized in that: The following steps are involved: S1. Use the catenary equation to fit the accumulation profile of the saccharification pile of Maotai-flavor liquor; S2. Substituting the stacking contour boundary conditions of the Maotai-flavor liquor saccharification pile into the catenary equation to obtain the bending coefficient equation of the catenary equation, solving the bending coefficient equation by Newton's iteration method to obtain the stacking contour expression of the Maotai-flavor liquor saccharification pile; S3. Based on the inverse function of the stacking profile expression of the Maotai-flavor liquor saccharification pile, a formula for solving the geometric parameters of the Maotai-flavor liquor saccharification pile is obtained, and the geometric parameters are obtained by solving the formula.

2. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on mathematical model according to claim 1, characterized in that: The catenary equation is: Where k is the bending coefficient, x and y represent the coordinates of the point on the catenary, and cosh() represents the hyperbolic cosine function.

3. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on mathematical model according to claim 2, characterized in that: The bending coefficient equation of the catenary is: or Where h represents the height of the saccharification pile of the Maotai-flavor liquor, and r represents the bottom radius of the saccharification pile.

4. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on mathematical model according to claim 3, characterized in that: The inverse function of the stacking profile expression of the Maotai-flavor liquor saccharification pile is: Among them, arccosh() represents the inverse function of the hyperbolic cosine function, and the value range of y is [k, k+h].

5. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on mathematical model according to claim 4, characterized in that: If the geometric parameter of the saccharification pile is volume, the solution formula for the volume is: Among them, π is the ratio of a circle to its circumference.

6. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on mathematical model according to claim 4, characterized in that: If the geometric parameter of the saccharification pile is the surface area, the solution formula for the surface area is: Among them, π is the ratio of the circumference of a circle, express The derivative of .

7. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on a mathematical model according to any one of claims 1 to 6, characterized in that: S2 also includes a three-dimensional visualization model of the Maotai-flavor liquor saccharification pile obtained by flipping and rotating according to the stacking contour expression of the Maotai-flavor liquor saccharification pile.

8. The method for calculating geometric parameters of Maotai-flavor liquor saccharification pile based on mathematical model according to claim 7, characterized in that: The method also includes calculating the layered volume of the Maotai-flavor liquor saccharification pile based on the three-dimensional visualization model of the Maotai-flavor liquor saccharification pile.

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