Method and system for calculating saturation concentration of sucrose conversion

Abstract

The application discloses a method and system for calculating saturation concentration of sucrose conversion, which comprises the following steps: establishing a total sugar concentration target equation, and combining solubility data to express coordinate points to obtain a conversion sugar concentration-total sugar concentration point distribution; performing least square method curve fitting according to the conversion sugar concentration-total sugar concentration point distribution to obtain a quadratic equation of total sugar concentration-conversion sugar concentration; expressing coefficients of the quadratic equation of total sugar concentration-conversion sugar concentration in coordinate points to obtain a temperature-coefficient point distribution; performing least square method curve fitting according to the temperature-coefficient point distribution to obtain a quadratic equation of the coefficients; and solving the sucrose saturation concentration under the target temperature and the conversion sugar concentration according to the quadratic equation of total sugar concentration-conversion sugar concentration and the quadratic equation of the coefficients. By using the application, the total sugar concentration of sucrose at the saturation concentration can be solved under the conditions of known temperature and conversion sugar concentration, which provides convenience for obtaining sucrose solubility in industrial production.

Description

Technical Field

[0001] This invention relates to the field of industrial sugar production, and in particular to a method and system for calculating the saturation concentration of sucrose conversion. Background Technology

[0002] Invert sugar syrup is a mixture of sucrose, glucose, and fructose obtained by reacting sucrose in an aqueous solution with dilute acid or enzymes. The sucrose content varies depending on the degree of inversion. Due to the presence of invert sugar, the solubility of sucrose in water decreases at the same temperature. During the production process, heating is generally required to dissolve sucrose in water, which increases sucrose solubility. To ensure that the produced invert sugar syrup does not crystallize after cooling or during storage, it is necessary to know the solubility of sucrose in water at different temperatures in the presence of invert sugar. However, there is currently no simple method to calculate the solubility of sucrose at any temperature and with any concentration of invert sugar. Summary of the Invention

[0003] To address the aforementioned technical problems, the present invention aims to provide a method and system for calculating the saturation concentration of sucrose conversion, which can quickly determine the sucrose solubility at any temperature and invert sugar concentration while ensuring experimental accuracy.

[0004] The first technical solution adopted in this invention is: a method for calculating the saturation concentration of sucrose conversion, comprising the following steps:

[0005] A target equation for total sugar concentration was established, and coordinate points were used to represent the total sugar concentration using solubility data, resulting in a point distribution of invert sugar concentration versus total sugar concentration.

[0006] Based on the point distribution of invert sugar concentration versus total sugar concentration, least squares curve fitting was performed to obtain a quadratic equation for total sugar concentration versus invert sugar concentration;

[0007] Representing the coefficients of the quadratic equation of total sugar concentration versus invert sugar concentration using coordinate points yields the temperature-coefficient point distribution.

[0008] Based on the temperature-coefficient point distribution, least squares curve fitting is performed to obtain the quadratic equation of the coefficient;

[0009] The sucrose saturation concentration at the target temperature and invert sugar concentration is determined based on the quadratic equation of total sugar concentration minus invert sugar concentration and the quadratic equation of coefficients.

[0010] In this embodiment, given the temperature and the solubility of invert sugar, the solubility of sucrose at that temperature and the solubility of invert sugar can be calculated. The calculation is convenient and simple, and the calculation result has a small error compared with the experimental result, making it suitable for practical production applications.

[0011] Furthermore, the step of establishing the target equation for total sugar concentration and combining solubility data to represent it as coordinate points to obtain the point distribution of invert sugar concentration versus total sugar concentration specifically includes:

[0012] Based on the sucrose conversion conditions, establish a target equation for total sugar concentration;

[0013] The solubility data is input into the total sugar concentration target equation to obtain the total sugar concentration matrix;

[0014] Each row of the total sugar concentration matrix is ​​converted into a coordinate point representation of invert sugar concentration - total sugar concentration, resulting in a point distribution of invert sugar concentration - total sugar concentration with invert sugar concentration as the x-axis and total sugar concentration as the y-axis.

[0015] In this embodiment, the solubility data can be represented in matrix form based on the total sugar solubility target equation, and then represented in point coordinate form, making the relationship between total sugar solubility and temperature and invert sugar solubility clearer.

[0016] Furthermore, the target equation for total sugar concentration is expressed as:

[0017] Y = f(T, R)

[0018] Where Y represents the total sugar concentration when the syrup is saturated with sucrose, T represents the temperature of the syrup, and R represents the concentration of invert sugar in the syrup.

[0019] Furthermore, the total sugar concentration matrix is ​​represented as follows:

[0020]

[0021] Among them, Y 40 …Y 65 Represents the total sugar concentration vector at the corresponding temperature, R1, R2…R n These represent the concentrations of invert sugar at the corresponding temperatures in the solubility data.

[0022] Furthermore, the quadratic equation for the total sugar concentration minus the invert sugar concentration is expressed as:

[0023] Y(T)=C(T)*R 2 +B(T)*R+A(T)

[0024] Where Y(T) represents the total sugar concentration at the corresponding temperature T, R represents the invert sugar concentration at the corresponding temperature T, and C(T), B(T), and A(T) represent the quadratic coefficient, linear coefficient, and constant term of the quadratic equation of total sugar concentration minus invert sugar concentration, respectively.

[0025] Furthermore, the step of representing the coefficients of the quadratic equation of total sugar concentration - invert sugar concentration with point coordinates to obtain the temperature-coefficient point distribution specifically includes:

[0026] The coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration at each temperature are extracted and integrated to establish a coefficient matrix;

[0027] Based on the relationship between coefficients and temperature in the coefficient matrix, point coordinates are used to obtain a temperature-coefficient point distribution with temperature as the horizontal axis and coefficients as the vertical axis.

[0028] In this implementation, the coefficient matrix is ​​obtained by summarizing and integrating the coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration at each temperature, and then converted into point coordinate representation to highlight the relationship between the coefficients and temperature.

[0029] Furthermore, the coefficient matrix is ​​represented as follows:

[0030]

[0031] Where A(T), B(T), and C(T) represent the coefficients in the quadratic equation of total sugar concentration minus invert sugar concentration at the corresponding temperature T.

[0032] Furthermore, the quadratic equation for the coefficients is expressed as:

[0033] A(T)=M(a)*T 2 +N(a)*T+P(a)

[0034] B(T)=M(b)*T 2 +N(b)*T+P(b)

[0035] C(T) = M(c)*Tw + N(c)*T + P(c)

[0036] Among them, M(a), N(a), P(a), M(b), N(b), P(b), M(c), N(c), and P(c) are all constants.

[0037] The second technical solution adopted in this invention is: a system for calculating the saturation concentration of sucrose conversion, comprising:

[0038] A model module was established, a target equation for total sugar concentration was created, and coordinate points were used to represent the total sugar concentration using solubility data, resulting in the point distribution of invert sugar concentration versus total sugar concentration.

[0039] The total sugar fitting module performs least squares curve fitting based on the distribution of invert sugar concentration versus total sugar concentration points to obtain a quadratic equation for total sugar concentration versus invert sugar concentration.

[0040] The coefficient solving module represents the coefficients of the quadratic equation of total sugar concentration - invert sugar concentration as point coordinates, and obtains the temperature-coefficient point distribution;

[0041] The coefficient fitting module performs least squares curve fitting based on the temperature-coefficient point distribution to obtain the quadratic equation of the coefficient.

[0042] The model solution module calculates the sucrose saturation concentration at the target temperature and invert sugar concentration based on the quadratic equation of total sugar concentration minus invert sugar concentration and the quadratic equation of coefficients.

[0043] The beneficial effects of the method and system of this invention are as follows: Based on solubility data and the solubility target equation, this invention obtains the quadratic equation for total sugar solubility and the quadratic equation for the coefficients through two least squares curve fitting operations. This allows the sucrose solubility at any temperature and invert sugar solubility to be solved based on the two data points of temperature and invert sugar solubility. Furthermore, the error between the solved data and the experimental data is small, which provides convenience for obtaining sucrose solubility in industrial production. Attached Figure Description

[0044] Figure 1 This is a flowchart of the steps in the method for calculating the saturation concentration of sucrose conversion according to the present invention;

[0045] Figure 2 This is a structural block diagram of a sucrose conversion saturation concentration estimation system according to the present invention;

[0046] Figure 3 This is a curve obtained by least-squares fitting of the point distribution of total sugar concentration versus invert sugar concentration according to the present invention. Detailed Implementation

[0047] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

[0048] like Figure 1 As shown, this invention provides a method for estimating the saturation concentration of sucrose conversion, which includes the following steps:

[0049] 101. Establish the target equation for total sugar concentration, and combine it with solubility data to represent it with coordinate points, thereby obtaining the point distribution of invert sugar concentration versus total sugar concentration.

[0050] In this step, the target equation for total sugar concentration is first established based on the sucrose conversion conditions;

[0051] Since the total sugar concentration is related to both temperature and invert sugar concentration, the target equation for total sugar is expressed as follows:

[0052] Y = f(T, R)

[0053] Where Y represents the total sugar concentration when the syrup is saturated with sucrose, T represents the temperature of the syrup, and R represents the concentration of invert sugar in the syrup.

[0054] Next, the solubility data is input into the total sugar concentration target equation to obtain the total sugar concentration matrix;

[0055] The solubility data can be a commonly used sucrose solubility table in the sugarcane sugar refining industry, or other sucrose conversion solubility data. This solubility data needs to include temperature and the corresponding invert sugar concentration. This scheme uses known solubility data, inputting it into the total sugar concentration target equation to obtain the total sugar concentration matrix, represented as:

[0056]

[0057] Among them, Y 40 …Y 65 Represents the total sugar concentration vector at the corresponding temperature, R1, R2…R n These represent the concentrations of invert sugar at the corresponding temperatures in the solubility data.

[0058] Finally, each row of the total sugar concentration matrix is ​​converted into a coordinate point representation of invert sugar concentration - total sugar concentration, resulting in a distribution of invert sugar concentration - total sugar concentration points with invert sugar concentration as the x-axis and total sugar concentration as the y-axis.

[0059] Based on the total sugar concentration matrix, the data in the first column of the total sugar concentration matrix is ​​first extracted, and then divided into R1…R n Let f(40, R1)...f(40, R) be the x-coordinate. n Using R1…R2 as the ordinate, establish the coordinate distribution of total sugar concentration and invert sugar concentration under 40-degree conditions. Then, extract the data from the second column of the total sugar concentration matrix and assign it to R1…R2. n Let f(41, R1)...f(41, R) be the x-coordinate. n Using y as the vertical axis, establish the coordinate point distribution of total sugar concentration and invert sugar concentration under 41°C conditions. Then, similarly, establish the coordinate point distribution of total sugar concentration and invert sugar concentration under 40°C-65°C conditions.

[0060] 102. Based on the point distribution of invert sugar concentration versus total sugar concentration, least squares curve fitting was performed to obtain a quadratic equation for total sugar concentration versus invert sugar concentration.

[0061] By sequentially performing least squares curve fitting on the coordinate point distributions of total sugar solubility and invert sugar solubility within the temperature range of 40℃-65℃, the quadratic equation of total sugar concentration minus invert sugar concentration for the corresponding curves was obtained. Summarizing this quadratic equation for total sugar concentration minus invert sugar concentration within the 40℃-65℃ temperature range, a unified model for the quadratic equation of total sugar concentration minus invert sugar concentration is obtained as follows:

[0062] Y(T)=C(T)*R 2 +B(T)*R+A(T)

[0063] Where Y(T) represents the total sugar concentration at the corresponding temperature T, R represents the invert sugar concentration at the corresponding temperature T, and C(T), B(T), and A(T) represent the quadratic coefficient, linear coefficient, and constant term of the quadratic equation of total sugar concentration minus invert sugar concentration, respectively.

[0064] 103. Represent the coefficients of the quadratic equation of total sugar concentration - invert sugar concentration using coordinate points to obtain the temperature-coefficient point distribution.

[0065] In this step, the coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration at each temperature are first extracted and integrated to establish a coefficient matrix;

[0066] Specifically, the coefficients of the quadratic equation for total sugar concentration minus invert sugar concentration at the corresponding temperatures within the 40℃-65℃ temperature range are extracted. Using the coefficients of each term in the quadratic equation for total sugar concentration minus invert sugar concentration at each temperature as column vectors, these coefficients are integrated to obtain the aforementioned coefficient matrix, represented as follows:

[0067]

[0068] Where A(T), B(T), and C(T) represent the coefficients in the quadratic equation of total sugar concentration minus invert sugar concentration at the corresponding temperature T.

[0069] Next, point coordinates are represented based on the relationship between coefficients and temperature in the coefficient matrix, resulting in a temperature-coefficient point distribution with temperature as the horizontal axis and coefficients as the vertical axis.

[0070] Based on the above coefficient matrix, the row vector data corresponding to coefficient A(T) is extracted. Using temperatures of 40, 41, ... 65 as the abscissa and the coefficient values ​​A(40), A(41), ... A(65) at the corresponding temperatures as the ordinate, the coordinate point distribution of coefficient A(T) and temperature is established. Similarly, the row vector data corresponding to coefficient B(T) is extracted. Using temperatures of 40, 41, ... 65 as the abscissa and the coefficient values ​​B(40), B(41), ... B(65) at the corresponding temperatures as the ordinate, the coordinate point distribution of coefficient B(T) and temperature is established. The row vector data corresponding to coefficient C(T) is extracted. Using temperatures of 40, 41, ... 65 as the abscissa and the coefficient values ​​C(40), C(41), ... C(65) at the corresponding temperatures as the ordinate, the coordinate point distribution of coefficient C(T) and temperature is established.

[0071] 104. Based on the temperature-coefficient point distribution, perform least squares curve fitting to obtain the quadratic equation of the coefficient.

[0072] Based on the coordinate point distributions of coefficients A(T) and temperature, B(T) and temperature, and C(T) and temperature, respectively, least squares curve fitting is performed to obtain the quadratic equations of the coefficients, expressed as:

[0073] A(T)=M(a)*T 2 +N(a)*T+P(a)

[0074] B(T)=M(b)*T 2 +N(b)*T+P(b)

[0075] C(T)=M(c)*T 2 +N(c)*T+P(c)

[0076] Where M(a), N(a), P(a), M(b), N(b), P(b), M(c), N(c), and P(c) are all constants. Preferably, the known solubility values ​​are calculated as follows: M(a) = 10 -5 , N(a)=0.001, P(a)=0.643, M(b)=-9*10 -6 , N(b)=-0.006, P(b)=0.2191, M(c)=10 -5 , N(c)=0.0014, P(c)=0.0697.

[0077] 105. Solve for the sucrose saturation concentration at the target temperature and invert sugar concentration based on the quadratic equation of total sugar concentration minus invert sugar concentration and the quadratic equation of coefficients.

[0078] Based on the quadratic equations for total sugar concentration and invert sugar concentration, and the quadratic equations for the coefficients, the total sugar concentration at any temperature and invert sugar concentration can be calculated, and thus the sucrose concentration under the corresponding conditions can be determined. (Refer to...) Figure 3 Based on the quadratic equation of total sugar concentration - invert sugar concentration and the quadratic equation of coefficient, a fitting curve of total sugar concentration - invert sugar concentration is obtained for temperatures ranging from 0℃ to 90℃ and invert sugar concentration ranging from 0% to 100%. This can be further extended to obtain the total sugar concentration at any temperature and with any invert sugar concentration.

[0079] Specifically, when the temperature is T0 and the invert sugar concentration is R0, the calculation process for the total sugar concentration of sucrose at saturation is as follows:

[0080] For any temperature T0, the quadratic equation for its coefficients is:

[0081] A(T0)=M(a)*T0 2 +N(a)*T0+P(a)

[0082] B(T0)=M(b)*T0 2 +N(b)*T0+P(b)

[0083] C(Y0) = M(c) * T0 2 +N(c)*T0+P(c)

[0084] At any invert sugar concentration R0, the total sugar concentration of sucrose at saturation is:

[0085] Y(T0)=C(T0)*R0 2 +B(T0)*R0+A(T0)

[0086] This completes the calculation of the sucrose concentration under the corresponding conditions.

[0087] In a specific embodiment, when the temperature is 17°C and the invert sugar concentration is 53%, the total sugar concentration of sucrose at saturation is calculated. First, the coefficient values ​​at 17°C are calculated based on the coefficient matrix:

[0088] A(17)=10 -5 *17 2 +0.001*17+0.643=0.663

[0089] B(17)=-9*10 -6 *17 2 +0.006*17 + 0.2191 = 0.199

[0090] C(17)=10 -5 *17 2 +0.0014*17+0.0697=0.0964

[0091] Substituting the above coefficient values ​​into the quadratic equation of total sugar concentration - invert sugar concentration, we get:

[0092] Y(17)=0.0964*0.53 2 +0.199*0.53+0.663=0.796=79.6%

[0093] Thus, the total sugar concentration under the condition of 17℃ and 53% invert sugar concentration is obtained. Under this condition, the sucrose concentration is 26.6%, which means that crystallization will occur when the sucrose concentration reaches 26.6% under this condition.

[0094] like Figure 2 As shown, a system for calculating the saturation concentration of sucrose conversion includes:

[0095] A model module was established, a target equation for total sugar concentration was created, and coordinate points were used to represent the total sugar concentration using solubility data, resulting in the point distribution of invert sugar concentration versus total sugar concentration.

[0096] The total sugar fitting module performs least squares curve fitting based on the distribution of invert sugar concentration versus total sugar concentration points to obtain a quadratic equation for total sugar concentration versus invert sugar concentration.

[0097] The coefficient solving module represents the coefficients of the quadratic equation of total sugar concentration - invert sugar concentration as point coordinates, and obtains the temperature-coefficient point distribution;

[0098] The coefficient fitting module performs least squares curve fitting based on the temperature-coefficient point distribution to obtain the quadratic equation of the coefficient.

[0099] The model solution module calculates the sucrose saturation concentration at the target temperature and invert sugar concentration based on the quadratic equation of total sugar concentration minus invert sugar concentration and the quadratic equation of coefficients.

[0100] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0101] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for calculating the saturation concentration of sucrose conversion, characterized in that, Includes the following steps: A target equation for total sugar concentration was established, and coordinate points were used to represent the total sugar concentration using solubility data to obtain the point distribution of invert sugar concentration versus total sugar concentration. Specifically, this involved: establishing a target equation for total sugar concentration based on sucrose conversion conditions; inputting solubility data into the target equation to obtain a total sugar concentration matrix; and converting each row of the total sugar concentration matrix into a coordinate point representation of invert sugar concentration versus total sugar concentration to obtain the point distribution of invert sugar concentration versus total sugar concentration with invert sugar concentration as the x-axis and total sugar concentration as the y-axis. The target equation for total sugar concentration is expressed as follows: Where Y represents the total sugar concentration when the syrup is saturated with sucrose, T represents the temperature of the syrup, and R represents the concentration of invert sugar in the syrup; The total sugar concentration matrix is ​​represented as follows: in, … This represents the vector of total sugar concentration at the corresponding temperature. , ... These represent the concentrations of invert sugar at the corresponding temperatures in the solubility data; Based on the point distribution of invert sugar concentration versus total sugar concentration, least squares curve fitting was performed to obtain a quadratic equation for the total sugar concentration versus invert sugar concentration. This quadratic equation is expressed as: in, This indicates the total sugar concentration at the corresponding temperature T. , , These represent the quadratic coefficient, linear coefficient, and constant term of the quadratic equation for the total sugar concentration minus the invert sugar concentration at the corresponding temperature T; The coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration are represented by coordinate points to obtain the temperature-coefficient point distribution. Specifically, this includes: extracting and integrating the coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration at each temperature to establish a coefficient matrix; and representing the coefficients in the coefficient matrix with temperature as the abscissa and coefficients as the ordinate to obtain the temperature-coefficient point distribution. The coefficient matrix is ​​represented as follows: Based on the temperature-coefficient point distribution, least squares curve fitting is performed to obtain the quadratic equation of the coefficient; the quadratic equation of the coefficient is expressed as: in, , , , , , , , , All are constants; The total sugar concentration at the target temperature and target invert sugar concentration is calculated by solving the quadratic equation of total sugar concentration minus invert sugar concentration and the quadratic equation of the coefficient. The sucrose saturation concentration is obtained by subtracting the target invert sugar concentration from the obtained total sugar concentration.

2. A system for calculating the saturation concentration of sucrose conversion, characterized in that, include: A model module is established to create a target equation for total sugar concentration and, in conjunction with solubility data, represent it as coordinate points to obtain the point distribution of invert sugar concentration versus total sugar concentration. Specifically, this includes: establishing a target equation for total sugar concentration based on sucrose conversion conditions; inputting solubility data into the target equation to obtain a total sugar concentration matrix; and converting each row of the total sugar concentration matrix into a coordinate point representation of invert sugar concentration versus total sugar concentration, resulting in a point distribution of invert sugar concentration versus total sugar concentration with invert sugar concentration as the x-axis and total sugar concentration as the y-axis. The target equation for total sugar concentration is expressed as follows: Where Y represents the total sugar concentration when the syrup is saturated with sucrose, T represents the temperature of the syrup, and R represents the concentration of invert sugar in the syrup; The total sugar concentration matrix is ​​represented as follows: in, … This represents the vector of total sugar concentration at the corresponding temperature. , … These represent the concentrations of invert sugar at the corresponding temperatures in the solubility data; The total sugar fitting module is used to perform least squares curve fitting based on the distribution of invert sugar concentration versus total sugar concentration, obtaining a quadratic equation for the total sugar concentration versus invert sugar concentration. This quadratic equation is expressed as: in, This indicates the total sugar concentration at the corresponding temperature T. , , These represent the quadratic coefficient, linear coefficient, and constant term of the quadratic equation for the total sugar concentration minus the invert sugar concentration at the corresponding temperature T; The coefficient solving module is used to represent the coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration with coordinate points to obtain the temperature-coefficient point distribution. Specifically, it includes: extracting and integrating the coefficients of the quadratic equation of total sugar concentration minus invert sugar concentration at each temperature to establish a coefficient matrix; and representing the coefficients with coordinate points according to the relationship between the coefficients and temperature in the coefficient matrix to obtain the temperature-coefficient point distribution with temperature as the abscissa and coefficients as the ordinate. The coefficient matrix is ​​represented as follows: The coefficient fitting module is used to perform least squares curve fitting based on the temperature-coefficient point distribution to obtain the quadratic equation of the coefficients; the quadratic equation of the coefficients is expressed as: in, , , , , , , , , All are constants; The model solution module is used to solve for the total sugar concentration at the target temperature and the target invert sugar concentration based on the quadratic equation of the total sugar concentration minus the invert sugar concentration and the quadratic equation of the coefficients. The total sugar concentration is then subtracted from the target invert sugar concentration to obtain the sucrose saturation concentration.

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