AU2020102572A4 - Method for predicting food microorganism and shelf life by dimensional analysis and pi theorem - Google Patents

Abstract

The invention provides a method for predicting food microorganisms and shelf life by utilizing dimensional analysis and pi theorem, the method comprises the following steps of: preparing a detection sample, and sealing and storing; Establishing a model for predicting microorganism growth through a dimensional analysis method and pi theorem; Detecting the detection sample through setting detection parameters to obtain sample detection data; Inputting the sample detection data into the model of predicting microorganism growth to obtain the microorganism growth condition of food in the shelf life, and verifying the model of predicting microorganism growth. According to the invention, the dimensional analysis method and the pi theorem principle are combined, and the growth or inhibition of all microorganisms is modelled from a new point of view, so that the defects caused by modelling depending on experimental data in the prior art are avoided, a unified microorganism prediction model is obtained, the universal value is achieved, and the microorganism growth model is improved to a new level because of this invention. -1/6 Preparing a detection sample, sealing and storing Establishment of a Model for Predicting Microorganism Growth by Dimensional Analysis and Pi Theorem Detecting the detection sample by setting detection parameters to obtain sample detection data Inputting the sample detection data into the model for predicting microorganism growth and shelf life, verifying the model for predicting microorganism growth Figure 1

Description

-1/6

Preparing a detection sample, sealing and storing

Establishment of a Model for Predicting Microorganism Growth by Dimensional Analysis and Pi Theorem

Detecting the detection sample by setting detection parameters to obtain sample detection data

Inputting the sample detection data into the model for predicting microorganism growth and shelf life, verifying the model for predicting microorganism growth

Figure 1

AUSTRALIA

PATENTS ACT 1990

PATENT SPECIFICATION FOR THE INVENTIONENTITLED: METHOD FOR PREDICTING FOOD MICROORGANISM AND SHELF LIFE BY DIMENSIONAL ANALYSIS AND PI THEOREM

The invention is described in the following statement:-

Method for predicting food microorganism and shelf life by dimensional analysis and pi theorem

TECHNICAL FIELD

The invention relates to the technical field of microbial thermodynamics, in particular to a method for predicting food microorganisms and shelf life by utilizing dimensional analysis and pi theorem.

BACKGROUND

Microbial prediction has important significance in food industry, and the prediction of food microorganisms has important value in the prediction of food shelf life. However, the existing prediction methods have some disadvantages, basically, they are mostly based on statistical analysis of regression fitting analysis of actual data, and then lack of general models based on biophysical and mathematical principles. Moreover, the existing models basically need to know the number of initial microorganisms to be predicted, but since the number of initial microorganisms is usually small, particularly pathogenic microorganisms, it is difficult to detect or accurately detect the initial microorganisms.

Therefore, the current method for predicting food microorganisms is basically based on data simulation, so that a plurality of models are created, and the popularization and the application of these models are not facilitated. At the same time, there are many challenges in establishing the prediction model of microorganisms: the corresponding physiological response of microorganisms to the change of environmental conditions is complex, which is known very little by people; the biological variability of the growth itself of microorganisms is very high; When the growth conditions are limited, the activity of microorganisms is greatly changed. Therefore, it is necessary to develop a new unified form of microorganism growth prediction model for solving the problems existed in the existing models so as to conveniently and accurately predict microorganisms in food and improve the prediction efficiency.

It is therefore entirely necessary to provide a theoretical-based microbial growth prediction model representing the growth, death and survival of all microbial forms, or integrating growth and death functions together.

SUMMARY

According to the method, the growth or inhibition processes of all microorganisms are modeled from a new point of view by combining dimensional analysis and pi theorem principles. The method avoids the defects caused by the fact that the prior art relies on experimental data modeling, further obtains a uniform microorganism prediction model, has universal value and improves the microorganism growth model to a new level.

In order to achieve the above object, the present invention provides a method for predicting food microorganisms and shelf life using dimensional analysis and pi-theorem, characterized by comprising the steps of:

Preparing a detection sample, sealing and storing;

Establishing a prediction microorganism growth model through dimensional analysis method and pi theorem;

Detecting the detection sample by setting detection parameters to obtain sample detection data;

And inputting the sample detection data into the prediction microorganism growth model to obtain the microorganism growth condition of the food in the shelf life, and verifying the prediction microorganism growth model.

Preferably, the method for establishing the prediction microorganism growth model comprises the following steps of: carrying out dimensional analysis on factors influencing the microbial quantity NT in unit food quality at time T to obtain dimensionless numbers and dimensionless quasi numbers; And establishing an equation relationship between the dimensionless numbers and the dimensionless quasi numbers according to pi theorem to obtain the prediction microorganism growth model.

Preferably, the factors affecting the microbial quantity per unit food quality NT include the temperature 0, the specific heat Cp, the time T, the microbial quantity per unit food quality NT at the time of T, the surface area ST, the microbial quantity per surface area and unit food quality NT/ST at the time of T, the pH value of food pHT at time of T, the water activity of food a.T at time of T, and the percentage content of oxygen 02T in the gas space in which the food is stored at time of T.

Preferably, the detection parameters include the temperature 0, the specific heat Cp, the time T, the microbial quantity per unit food quality NT

at the time of T,

the surface area ST, the microbial quantity per surface area and unit food quality NT/ST at the time of T, the pH value of food pHT at time of T, the water activity of food a.1 at time of T, and the percentage content of oxygen 02Tin the gas space in which the food is stored at time of T.

Preferably, the model verification comprises an internal evaluation and an external evaluation.

Preferably, the model verification is performed according to an evaluation index, wherein the evaluation index comprises a determination coefficient R 2, an adjusted determination coefficient R 2aaj, a relative error RE of model prediction, a median relative error MRE, an mean absolute relative error MARE, a mean square error MSE, a root mean square error RMSE, a prediction standard error % SEP, an accuracy factor Af and a deviation factor Bf.

The invention discloses the following technical effects:

(1) The method of the invention establishes a unified microorganism prediction model which has universal value, and the invention simulates and establishes the model based on principle rather than experimental data for the first time to improve the microorganism growth prediction model to a new level;

(2) The model established by the method of the invention can be used for predicting the shelf life of microorganisms in solid food (such as dried beef or ham) and liquid food (such as yogurt), can also be used for predicting the growth state and growth inhibition state of microorganisms, and can be used for predicting microorganisms such as pseudomonas, lactobacillus and the like and biological prediction of bacteria, such as prediction of the total number of bacteria, and has wide versatility;

(3) The model established by the method of the present invention does not need to know the number of initial microorganisms, only needs to know the number of microorganisms stored to a certain day, helps to exert the versatility of the model of the present invention, and helps to reveal the properties of biophysical mathematical principles behind the growth or inhibition of food microorganisms.

BRIEF DESCRIPTION OF THE FIGURES

In order to provide a clearer picture of the embodiment of the present invention or the technical scheme in the prior art, a brief introduction of the appended drawings to be used in the embodiment is given below. Obviously, the appended drawings described below are only some embodiments of the present invention. For the ordinary technical personnel in this field, other appended drawings may be obtained on the basis of the appended drawings without the cost of creative labour.

Figure 1 is a flow chart of the method according to the invention;

Figure 2 is a schematic diagram showing changes in measurement parameters of dried beef at 10 °Cand 15 °C in an embodiment of the present invention, while Figure 2(a) is a change at 10 °C, and Figure 2(b) is a change at 15 °C;

Figure 3 is a schematic diagram showing changes in measurement parameters of ham at 4 °C, 10 °C, and 15 °C in an embodiment of the present invention, and Figure 3(a) is a change in temperature at 4 °C, Figure 3(b) is a change in temperature at 10 °C, and Figure 3(c) is a change in temperature at 15 °C;

Figure 4 is a schematic diagram showing changes in measurement parameters of yogurt at 5 °C, 10 °C, and 15 °C in an embodiment of the present invention, and Figure 4(a) is a change in temperature at 5 °C, Figure 4(b) is a change in temperature at 10 °C, and Figure 4(c) is a change in temperature at 15 °C;

Figure 5 is a schematic comparison diagram of measured values of internal data with predicted logNTobserved values or DAM-based observed values of different foods in an embodiment of the present invention, and Figures 5(a) and 5(b) are schematic comparison of measured values and observed values of dried beef, Figures 5(c) and 5(d) are schematic comparison of measured values and observed values of ham, and Figures (e) and 5(f) are schematic comparison of measured values and observed values of yogurt;

Figure 6 is a schematic diagram showing a comparison between an observed value of external data and a predicted observed value of logNT or an observed value of storage time of different foods based on DAM in an embodiment of the present invention, Figures 6(a) and 6(b) are schematic diagram showing a comparison between an measured value of beef and an observed value, Figures 6(c) and 6(d) are schematic diagram showing a comparison between an measured value of ham and an observed value, and Figures 6(e) and 6(f) are schematic diagram showing a comparison between an measured value of yogurt and an observed value.

DESCRIPTION OF THE INVENTION

Following is a clear and complete description of the technical scheme in the embodiment of the invention in conjunction with the appended drawing in the embodiment of the invention. Obviously, the embodiment described is only part of the embodiments of the invention, not the whole embodiments. Based on the embodiment of the invention, all other embodiments obtained by ordinary technicians in the field without making creative labour are within the scope of protection of the invention.

In order to make the above-mentioned purposes, characteristics and advantages of the present invention more clearly understood, a step-by-step detailed description of the present invention is given in combination with the appended drawing and the concrete implementation method.

Referring to figure 1, an embodiment of the present invention provides a method for predicting food microorganisms and shelf life with dimensional analysis and pi theorem, comprising the steps of:

S1. Preparing a detection sample, and sealing and storing the detection sample.

In the embodiment, dried beef, ham and yogurt are selected as detection samples, dried beef and yogurt are prepared, and ham is purchased from supermarkets.

S11. Obtaining raw material for preparing sample

Fresh beef, salt, garlic, ginger, fresh red pepper, sesame, tea polyphenol, glucose, pepper, monosodium glutamate (MSG), white liquor and other materials, all of which are purchased in local supermarkets and all of which are food-grade.

Lactobacillusplantarum SQ-4 (1x10' CFU/mL), Flavor yeast (5x10' CFU/mL), Staphylococcus aureus ATCC 2997 (8x 108 CFU/mL), Streptococcus

thermophilus (1.25 x 108 CFU/mL), Lactobacilluspentosaceus MT-4

(1.25x108 CFU/mL), Bifidobacterium animalis subsp. Lactis BZ11 (1.25x108CFU/mL) and Bifidobacterium longum BLI (1.25x108CFU/mL), all of which were prepared in lab; The fermentation agents of

Staphylococcus xylosus, yeast and Lactobacillusplantarum were mixed in a

ratio of 1%: 2%: 2% as fermentation additives for preparing dried beef

(NGB). Yogurt starter mixed with Streptococcus thermophilus,

Lactobacilluspentosaceus MT-4, Bifidobacterium animalisBZ11 and

Bifidobacterium longum BL1in a ratio of 1: 1: 1: 1 (V/V) was used as

additive for preparing yogurt.

Pseudomonas agar medium: 16.0 g of protein, 10.0 g of hydrolyzed

casein, 10.0 g of anhydrous potassium sulfate, 1.4 g of magnesium chloride,

10.0 ml of glycerol, 5 vials of Pseudomonas medium selector CFC (OXOID,

UK), 20 g of agar and 1000 ml of distilled water; The pH value of the medium was adjusted to 7.0 0.2.

Plate counting agar medium (PCA): pancreatic protein 5.0 g, yeast

powder 2.5 g, glucose 1.0 g, agar 15.0 g, distilled water 1000 mL, the pH value of medium 7.0 0.2.

MRS agar medium was prepared by adding 20 g agar per liter of MRS

medium.

Fresh milk and ham come from a local supermarket in Huaxi District,

Guiyang City, China.

All chemicals used in the embodiments of the present invention are

analytically pure and are commercially available.

S12. Preparation of dried beef

Cutting raw meat along muscle line, removing fascia and fat, and cleaning blood water. The meat strips were cut to a size of 3 cmx 2 cmx2 cm, neat and uniform in thickness, and stored at 4 °C for no more than 3 hours.

Soaking cleaned and chopped beef hind leg meat in Chinese liquor for about 20 minutes, inoculating 0.8% MT-4 (0.6x 108 CFU/g), 0.8% yeast (0.7x108 CFU/g) and 1% Staphylococcus aureus (0.7x108 CFU/g) as additives, adding adjuvants and mixing them evenly. The adjuvants (g/ 100g) including glucose 1.5, salt 1.5, Perilla seed 2, tea polyphenol 0.01, ginger 6, red pepper 0.6, garlic 6, orange peel 1, and pepper 1.

The pickling of the mixture was repeated until the surface of the meat became wet and softened, then the mixture was fermented in a closed vessel at 20 °C for 36 hours, then the fermented dried beef was taken out and dried in an oven at 70 °C until the moisture content was about 30%, and finally it was cooled and packaged under vacuum.

S13. Preparation of Yoghurt

The yogurt was prepared by fermenting fresh milk with 4% yogurt starter at 37 °C until its pH value reached 4.4.

S14. Sealing and packaging the prepared ham, dried beef and yogurt, and storing the ham, dried beef and yogurt in thermostats with different temperatures for several days to obtain final detection samples.

S2. Establishing a prediction microorganism growth model through dimensional analysis method and pi theorem.

The food contains abundant nutrition and is suitable for growth of microorganisms, and the nutritional ingredients of the food are sufficient for the growth of the microorganisms before the food is deteriorated. Generally speaking, the main factors affecting the growth of food microbe are temperature 0, specific heat Cp, time T, the surface areaST, the microbial quantity per surface area and unit food quality NT/STat the time of T, the pH value of food pHTat time of T, the water activity of food awTat time of T, and the percentage content of oxygen02Tin the gas space in which the food is stored at time of T.

It is thus possible to:

NT=f(NT/ST,0,Cp,T,pH,awT,02T) (1)

Wherein: NT is the microbial quantity per unit quality of food (CFU/ g) at time of T, and since the amount of microorganisms can also be expressed as the mass, NT itself is dimensionless (representing the amount of microorganisms per unit food quality, since the mass of individual microorganisms is certain, e. g., the mass of a Pseudomonas cell is about 2x10-12 g, so that CFU/ g can be considered dimensionless); ST is the surface area of the food at time of T.

According to the dimensionless pi term or group obtained by dimensionless analysis, a quasi-number He=CpOT 2N/STcan be obtained. In

addition, pHT, awTand02Tare also dimensionless numbers.

According to the pi theorem, the following equation can be obtained:

NT=K[(NT/ST) C,O T2 ]" pHTr2a,302T (2)

Wherein T is time d, K, ni, n2, n3and n4are undetermined constants, Cp is specific heat capacity, the specific heat Cp of dried beef and ham is about

1.1 kJ/( kg °C), the specific heat capacity Cp of yogurt is 2.5 kJ/(kg °C), and the Cp is basically unchanged during storage.

Considering the sealed packaging of dried beef, ham and yogurt, it is basically considered that the change of 02 and a, is not significant, that is, the effect on the index is basically unchanged in the shelf life. Therefore, in order to simplify the calculation process, the present embodiment no longer takes into account the influence of 02 and a, on the prediction of microorganisms in subsequent experiments, and thus the expression of Equation (2) becomes:

NT=K[(NT/ST) C9 T 2 ]" pHr"2 (3)

Equation (3) is called the dimensional analysis model (DAM), let y=NT,x1=CPOT 2(NT/ST), x2=pH, and logarithm the two sides of Equation

(3) to a linear function (called the dimensional model DM) to obtain:

Logy=LogK+n1Logx1+n2Logx2 (4)

In formula (3): He=N, COT2 <when the microorganism is in the CT 2

growth state, i.e., n=1, He=NT , dimension is ST

[Kg CO] [unit of heat energy] .

[Kg 2 22 [Kineat energy [energyunit], i.e., dimensionless, indicating

[Kg /2S ] [Kinetic energy unit]

that the growth of the microorganism is positively correlated with the heat energy provided by the environment, and the heat energy satisfies the kinetic energy required by the growth of the microorganism; When the

microorganism is in the growth inhibition state, i.e., n=- 1, He= NT( CPOT 2 1 ST Y,

[Kg m 2 / S] [Kinetic energy unit] dimension is-- =[energy unit, i.e.,

[Kg CO] [unit of heat energy]

dimensionless, indicating that the growth inhibition of the microorganism is negatively correlated with the heat energy provided, but positively correlated with the "kinetic energy".

It can thus be seen that the dimensional analysis model established in this embodiment conforms to the biological principle of microbial growth or inhibition, and that the number of He is easily understood from the other side: the growth or inhibition of microorganisms is closely related to the number of microorganisms surface area of per unit food (microbial contamination or growth usually starts from the surface) or the number of microorganisms per unit food quality, the calories of the food, and the storage time of the food. Therefore, the above parameters are also in accordance with biological principles, so that it is also possible to combine these parameters into a dimensionless standard He.

S3. Detecting the detection sample by setting detection parameters to obtain sample detection data.

The detection parameters in this example specifically include the temperature 0, specific heat Cp, time T, the microbial amount NTper unit food quality at the time of T, surface areaSTat the time of T, the microbial quantity per surface area and unit food quality NT/STat the time of T, the pH value of food pHTat time of T, the water activity of food a.Tat time of T, and the percentage content of oxygen02Tin the gas space in which the food is stored at time of T.

The ham, dried beef and yogurt were hermetically packaged and stored in thermostats at various temperatures for several days, and the samples were taken out for analysis.

Measuring the surface area of the detection sample : completely wrapping the dried beef with a paper towel and measuring the surface area of the paper towel, wherein the surface area (m 2 or cm 2) of the dried beef is obtained; And the ham and the bottled yogurt have regular shapes, and the surface area of the ham and the bottled yogurt is easy to determine.

And measuring pH: pH value can be measured by a pH meter.

Pseudomonas bovis colony determination: 25 g bovine dried beef sample was taken at the same time interval in a sterile operating environment and placed in an Erlenmeyer flask, 225 mL of sterile saline was added and sealed, and shaken in a shaker for about 1 hour; Then, the number of Pseudomonas bovis was determined through a Pseudomonas agar medium plate and incubated at 30 °C for 48 hours.

Ham bacterial colony determination: 25 g of ham samples was collected at the same time interval in a sterile operating environment and placed in a conical flask, 225 mL of sterile saline was added and sealed, and shaken in a shaker for 1 hour. The number of bacteria was then determined by spreading the PCA plates and incubating at 30°C for 48 hours.

Yogurt Lactic Acid Bacteria Colony determination: the number of lactic acid bacteria in yoghurt during storage can be determined by spreading MRS plates and incubating at 37 °C in an incubator in 20% (v/v)C0 2 -80%

(v/v) atmosphere for 48 hours. The mass of yogurt was equal to the volume of yogurt multiplied by the density of yogurt (1.15 kg/m3 ).

S4. Inputting the sample detection data into a prediction microorganism growth model, predicting the microorganism growth condition of the food in the shelf life and the food storage period, and verifying the prediction microorganism growth model.

Model validation is an essential method to evaluate the ability of new development models to interpolate and is a key step in model development. The first stage of model validation is internal evaluation, using model building data for model validation. Model verification with model-building data can ensure that the model can accurately describe the data generated by the model, and can ensure that the model can reflect any biological trend of the data. The second stage of model validation is an external assessment by using new data from stored dried beef, ham and yogurt, which are randomly selected within the experimental design of this embodiment.

The evaluation index adopted by the evaluation method of the embodiment comprises a determination coefficient R2, an adjusted determination coefficient R'adj, a model prediction relative error (RE), a median relative error (MRE), an mean absolute relative error (MARE), a mean square error (MSE), a root mean square error (RMSE), a prediction standard error (% SEP), an accuracy factor (Af) and a deviation factor (B).

2 (os - predi)2 R 2=1- 1(5) 2 1 (obs,-obs)

R2 aj -(1-R 2 )(n-1) (6) (n-N-1)

RE= pred - obs (7) obs

RiM4SE I E(obs, -pred,)2 (8) n

1 0 0 Z( obs,- pred,)2 %SEP=- (9) 9 obs n

log(pred;lobs) ( =(10)

B,=1 log(oshpred/) Bf~IO n

Wherein: obsi or obs is the observed value; predi or pred is the predicted value of the prediction model; obs is the average of the observed values; n is the number of observed values; N represents the number of variable parameters in the prediction model.

All experiments in this embodiment were repeated 3 times with data expressed as mean SD, and correlation analysis, regression analysis and mapping were performed using statistical software SPSS 19.0 and origin 2018.

S31. Establishing a dimensional model of the growth of the pseudomonas in the dried beef, and predicting the microbial growth of the dried beef in the shelf life and the storage period of the dried beef.

Figure 2 shows the variation of the measured parameters at 10 °C and °C for stored dried beef. From Figure 2, it can be seen that the number of Pseudomonas increases with increasing storage time, and the pH also increases, which is consistent with the general changes in microorganisms and pH values in dried beef foods.

According to the dimensional analysis model of the formula (4) and the data in Figure 1, the following linear regression equation is obtained:

Logy= -2.896+0.357 Logxl+2.077 Logx2(R2 =0.994, adjustment R2 =0.985)(12)

Therefore, the dimensional analysis model of the dried beef is established as follows:

35 7

[N )C 0 T20 N2.896 pH 2 .0 7 7 (T>10d) (13)

Therefore, it is possible to:

102.896N.643 S (14) T° 2 zo 2.077( )°O (100C<O<150C) (14) pH Cpo

From the above, the linear regression equation (12) has higher R2 =0.994 and adjusted R2 =0.985. The preliminary results show that the

model based on dimensional analysis and pi theorem can predict pseudomonas and storage time of dried beef with high accuracy.

S32. Establishing a dimensional model of bacterial growth in the ham, and predicting the microbial growth condition of the ham in the shelf life and the storage period of the ham.

Figure 3 shows changes in the measured parameters of stored ham at 4 °C, 10 °C, 15 0C. As can be seen from Figure 3, the number of bacteria also increases with prolonging of storage time, while the pH value fluctuates within a small range. According to equations (4) and Figure 2, the following linear regression equation can be obtained when the pH value (p> 0.05) which is not important is ignored:

Logy=-0.41+0.566 Logx1(R2 =0.987, adjusted R2 =0.987) (15)

Therefore, the dimensional analysis model of the ham is established as follows:

NT = i o41rT-7 CpOT 2| (16)

Therefore, it is possible to:

4 34 T1.132 =N 0° 1O.410°4 O(17)

From the above, the linear regression equation (15) has higher R2 =0.987 and adjusted R2 =0.987. It is shown that the model based on dimensional analysis and pi theorem can predict the total number of bacteria and storage time in ham with high accuracy.

S33. Establishing a dimensional model for the growth of the lactic acid bacteria in the yoghourt, and predicting the growth condition of the lactic acid bacteria in the shelf life of the yoghourt and the storage period of the yoghourt.

Figure 4 shows changes in measured parameters of stored yoghurt at 5 °C, 10 °C, 15 °C. Generally, at the first three days or four days after storage, the microorganisms are still in the growth state, and the period is called the early storage period; And the yoghurt deterioration mainly occurs in the later storage period, when the number of the microorganisms decreases along with the prolonging of the storage time. It can be seen from Figure 4 that the number of lactic acid bacteria in the yogurt after storage for three to four days (the criterion selected is that the number of microorganisms reaches the highest point and then decreases) decreases with prolonging of storage time.

Therefore, the result shows that the growth environment of the microorganism inhibits the growth of the microorganism, and the pH value gradually decreases with the increase of the storage time. Meanwhile, based on the dimensional analysis and the pi theorem, the microbial dimensional analysis model is adjusted to as follows: -~ al

NT=K! N7S, pH 2 (18) C,OT2

Wherein al and a2 are undetermined parameters.

Let y=NT,ui=NTST/(CPOT 2 ), u2=pHT toobtain:

Logy=LogK+a1Logui +a 2 Logu 2 (19)

When the storage cycle data in the range of 5-25 °C were modeled, it was found that the storage time error (7.7%-177.8%, average error 63.25%) was too large due to the large temperature span, which was mainly due to the different growth characteristics of microorganisms in different temperature ranges. Therefore, the present embodiment divides the temperature into two parts based on dimensional analysis and pi theorem, and constructs the dimensional analysis models of lactic acid bacteria growth in yogurt.

When the temperature is 5°C<O<15°C, obtaining:

Logy=9.733+0.623 Logui-5.529 Logu 2(R 2 =0.962, adjustment R2 =0.957)(20)

The dimensional analysis model of the obtained yogurt is as follows: - 0.623

NT =io 9 73 3 N7ST 2 pH-529(50 C<<15 0 C) (21) eCo ,T2

Therefore, it is possible to:

T246 =109733NT-0. 377pH-5.529 S 3 (22)

When the temperature is 15°C<O<25°C, obtaining:

Logy=9.733+0.623 Logui-5.529 Logu2(R 2 =0.962, adjustment R2 =0.957)(23)

Therefore, the dimensional analysis model of the yogurt is established as follows: r N0.726

N7 =C109.1 N7ST 2 pH 6 1 0 1 (15 0C<O<25 0C) (24)

[C,0T 2

Therefore, it is possible to: 0 726 T1452 =1io9818gNT- 0 274 H6101 ST (25

From the above, the linear regression equations (20) and (23) have higher R 2 =0.962 and adjusted R2 =0.957. It is shown that the analysis model based on dimension analysis and pi theorem can predict the number of lactic acid bacteria and storage time in yogurt with high accuracy.

S34. Validation of three dimensional models of dried beef, ham and yogurt.

Figure 5 is a comparison of the observed values of the internal data with the observed values of the predicted logNT or the observed values of the storage time of different foods based on DAM, where al, a2 are dried beef; bI, b2 are ham; cI, c2 are yogurt. Figure 6 is a comparison of the observed values of the external data with the predicted logNT or the observed values of the storage time of different foods based on DAM, where al, a2 are dried beef; bI, b2 are ham; cI, c2 are yogurt.

From the predicted values and the observed values in Figures 4 and 5, MRE, RMSE, % SEP, Af, and Bf can be easily calculated, and the calculation results are shown in Table 1.

Table 1 M sam R

% Equation (Eq) data RE Af Bf pie MSE SEP /00

- 0. 2.3 1.02 1.000 Inter 0.33 0329 696 03 1 Eq 12 (predicted logNT) 1 0. 3.0 1.03 0.999 Exter NG .81 0426 858 06 6

B 2 2. 9.0 1.08 1.005 Inter Eq 14(predicted stroed Time .55 1988 746 36 4

4 2. 8.7 1.08 1.007 Exter .55 1285 844 65 5

4 0. 2.4 1.02 1.000 Inter .31 076 62 23 2 Eq 16(predicted logNT) - 0. 2.5 1.02 Exter 0.994 Ha 0.41 078 266 38

m 4 4. 16. 1.13 1.001 Inter Eq 17(predicted stroed Time .1 0072 3783 91 1

0 1. 6.4 1.06 1.011 Exter .99 5891 951 25 8

Inter 0 0. 1.1 1.00 0.999 Eq 21 (5°C<<15°C) .15 0936 44 88 6 Yog or Eq 24 (15' <250 C) - 0. 1.3 1.00 0.998 urt (predicted logNT) Exter 0.26 1086 24 68 7

Eq 22 (5°C<O<15°C) or Eq Inter 2 1. 13. 1.13 0.994

25(15°C<0<25°C) .165 7082 7932 29 5 (predicted stroed Time) 0 0. 4.6 1.04 0.971 Exter .82 5747 405 28 9

MRE represents the middle position of the error between the predicted value and the observed value, and the variation range of MRE is between 0.26% and 4.55%, so that the error is small; RMSE can be used as a digital index for measuring the prediction accuracy, so that the dispersion degree of the predicted value of the model can be explained. As can be seen from Table 1, the RMSE variation of all prediction models of the present embodiment ranges from 0.0329 to 4.0072, which indicates that the degree of dispersion is small. SEP% refers to the standard deviation of the difference between the predicted and observed values of the prediction model, which can measure and verify the accuracy of the prediction model, which is similar to the relative standard deviation, the smaller the SEP%, the prediction model can better describe the experimental data, and the % SEP of all the prediction models of this embodiment ranges from 1.144 to 16.3783, most of which is less than 10, which indicates that the prediction model of this embodiment can well describe the observed microbial biomass or storage time.

For accuracy factors, the ideal prediction model should have Af=1.00, which indicates that the ideal prediction model is fitted when the predicted and actual response values are equal, and it is considered acceptable when the Af value is 1.10-1.15. For Bf, the value of Bf is considered good in the range 0.9-1.05; Be considered acceptable in the range 0.7-0.9 or 1.06-1.15; Be considered unacceptable when Br<0.7 or Bf>1.15.

As can be seen from Table 1, all prediction models of this embodiment Af values are between 1.0068 and 1.1391, most of which are between 1.0 and 1.09, all Bf values are between 0.9719 and 1.0118, and most of which are between 0.99 and 1.01, very close to 1, indicating that the prediction models established by this embodiment have higher accuracy and little deviation, and the models are acceptable.

Therefore, whether internal verification or external verification, whether it is one or more microorganisms, whether the environment promotes growth or inhibits growth of the microorganisms, and whether it is prediction of the microorganisms or prediction of the storage time (in fact, the models of prediction of the microorganisms and prediction of the storage time are essentially the same models, because the equations change of the two is the same), all of these evaluation indicators together indicate that the dimensional model established by the present embodiment is accurate and reliable.

The above-described embodiments are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements thereof made by those of ordinary skill in the art without departing from the spirit of the design of the present invention are intended to fall within the scope of protection defined by the claims.

Claims (6)

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A method for predicting food microorganisms and shelf life using dimensional analysis and pi-theorem, comprising the steps of:

Preparing a detection sample, sealing and storing;

Establishing a model for predicting microorganism growth through dimensional analysis method and pi theorem;

Detecting the detection sample by setting detection parameters to obtain sample detection data;

And inputting the sample detection data into the model for predicting microorganism growth to obtain the microorganism growth condition of the food in the shelf life, and verifying the model for predicting microorganism growth.

2. The method for predicting food microorganisms and shelf life by using dimensional analysis and pi theorem according to claim 1, wherein the method for establishing the model for predicting microorganism growth comprises the following steps of: performing dimensional analysis on factors which influence the microbial quantity NT in per unit food quality at time of T to obtain dimensionless numbers and dimensionless quasi-numbers; And establishing an equality relationship between the dimensionless numbers and the dimensionless quasi-numbers according to the pi-theorem to obtain the model for predicting microorganism growth.

3. The method for predicting food microorganisms and shelf life using dimensional analysis and pi theorem according to claim 2, wherein the factors affecting the microbial amount per unit food quality NT include the temperature 0, specific heat Cp, time T, the microbial amount per unit food quality NT at the time of of T, surface area ST at the time of T, the microbial quantity per surface area and unit food quality NT/ST at the time of T, the pH value of food pHT at time of T, the water activity of food a.1 at time of T, and the percentage content of oxygen 02T in the gas space in which the food is stored at time of T.

4. The method for predicting food microorganisms and shelf life using dimensional analysis and pi theorem according to claim 1, wherein the detection parameters include the temperature 0, specific heat Cp, time T, the microbial amount per unit food quality NT at the time of T, surface area ST at the time of T, the surface area ST, the microbial quantity per surface area and unit food quality NT/ST at the time of T, the pH value of food pHT at time of T, the water activity of food awT at time of T, and the percentage content of oxygen 02Tin the gas space in which the food is stored at time of T.

5. The method for predicting food microorganisms and shelf life using dimensional analysis and pi theorem according to claim 1, wherein the model verification comprises an internal evaluation and an external evaluation.

6. The method for predicting food microorganisms and shelf life by dimensional analysis and pi theorem according to claim 1, wherein the model verification is performed according to an evaluation index, and the evaluation index comprises a determination coefficient R2, an adjusted determination coefficient R2adj, a model prediction relative error RE, a median relative error MRE, an average absolute relative error MARE, a mean square error MSE, a root mean square error RMSE, a prediction standard error % SEP, an accuracy factor Af and a deviation factor Bf.

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Preparing a detection sample, sealing and storing 2020102572

Establishment of a Model for Predicting Microorganism Growth by Dimensional Analysis and Pi Theorem

Detecting the detection sample by setting detection parameters to obtain sample detection data

Inputting the sample detection data into the model for predicting microorganism growth and shelf life, verifying the model for predicting microorganism growth

Figure 1

-2/6- 02 Oct 2020

logNT (logCFU/g) ST (1×10-4m2) pH

Observed Pseudomonas number logNT (logCFU/g) ST 4 pH 6.0 (a) 40 5.8 2020102572

5.6 3 36 5.4

5.2 32 2 5.0

4.8 28 4.6 1 24 4.4

4.2

0 20 4.0 10 15 20 25 30 35 40 Strored time (d)

Figure 2 a

NT (logCFU/g) ST pH Observed Pseudomonas number NT (logCFU/g)

4.0 7.0 (b) -4 2 ST (1×10 m ) 48 6.8 3.5 pH 6.6 44 6.4 3.0 6.2 40 6.0 2.5 5.8 36 5.6 2.0 5.4 32 5.2 1.5 5.0 1.0 28 4.8 4.6 0.5 24 4.4 4.2 0.0 20 4.0 10 15 20 25 30 35 40 Strored time (d)

Figure 2 b

-3/6- 02 Oct 2020

logNT (logCFU/g) St pH 4.0 St (cm2) 80 6.

6 O b serv ed b acterial n u m b er lo g N T (lo g C F U /g )

(a) 2020102572

logNT (logCFU/g) St pH pH 76 4.5 80 7.2

Observed bacterial number logN T (logCFU/g) 6.4 (b) St (cm2) 3.5 72 76 6.9 pH 6.2 4.0 72 6.6 68 6.0 6.3 3.0 64 3.5 68 6.0 64 60 5.8 5.7 3.0 60 2.5 56 5.4 5.6 2.5 56 52 5.1 5.4 52 4.8 2.0 48 2.0 48 4.5 5.2 44 1.5 44 4.2 1.5 40 5.0 40 3.9 5 10 15 20 25 30 35 40 45 50 0 10 20 30 40 50 Strored time (d) Strored time (d)

Figure 3a Figure 3 b

logNT (logCFU/g) St pH 4.5 80 7.2 Observed bacterial number logNT (logCFU/g)

(c) St (cm2) 76 6.9 pH 4.0 6.6 72 6.3 68 3.5 6.0 64 5.7 3.0 60 5.4 56 5.1 2.5 52 4.8 48 4.5 2.0 44 4.2 1.5 40 3.9 0 5 10 15 20 25 30 35 40 Strored time (d)

Figure 3 C

-4/6- 02 Oct 2020

Observed lactic acid bacteria number logNT (logCFU/g) Observed number of lactic acid bacteria (a) pH 9.0 4.5

4.4 8.5

4.3

pH 8.0 4.2 2020102572

7.5 4.1

7.0 4.0

0 5 10 15 20 25 30 Strored time (d)

Figure 4(a) Observed lactic acid bacteria number logNT (logCFU/g)

9.5 (b) Observed number of lactic acid bacteria 4.3 pH 9.0 4.2

8.5 4.1

pH 8.0 4.0

3.9 7.5

3.8 7.0

3.7 6.5 2 4 6 8 10 12 14 16 18 20 22 Strored time (d)

Figure 4(b) Observed lactic acid bacteria number logNT (logCFU/g)

9.6 (c) Observed number of lactic acid bacteria 4.10 pH 9.4 4.05 9.2 4.00 9.0 3.95 8.8 pH

3.90 8.6 3.85 8.4 3.80 8.2

8.0 3.75

7.8 3.70

4 5 6 7 8 9 10 Strored time (d)

Figure 4(c)

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Predicted Pseudomonas number logNT (logCFU/g) (a1) 45 (a2) R2=0.9589 2.0 R2=0.9873 R2adj=0.9552 R2adj=0.9861 40 1.8

Predicted stored time (d) 35 1.6 30

1.4 25

1.2 20 2020102572

15 1.0

10 0.8 1.0 1.2 1.4 1.6 1.8 2.0 10 15 20 25 30 35 40 Observed Pseudomonas number logNT (logCFU/g) Stored time (d)

Figure 5(a) Figure 5(b)

4.5 60 Predicted bacterial number logNT (logCFU/g)

(b1) (b2) R2=0.9264 4.0 R2=0.9871 R2adj=0.9238 50 R2adj=0.9867 Predicted stored time (d)

3.5 40

3.0 30

2.5 20

2.0 10

0 1.5 0 10 20 30 40 50 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Observed bacterial number logNT (logCFU/g) Stored time (d)

Figure 5(c) Figure 5(d)

35 Predicted lactic acid bacterial number logNT (logCFU/g)

(c2) R2 = 0.9466 (c1) 9.5 2 30 R2adj = 0.9441 R = 0.9817 R2adj = 0.9810 Predicted stored time (d)

9.0 25

8.5 20

8.0 15

7.5 10

7.0 5

6.5 6.5 7.0 7.5 8.0 8.5 9.0 9.5 0 Observed lactic acid bacterial number logNT (logCFU/g) 0 5 10 15 20 25 30 Stored time (d)

Figure 5(e) Figure 5(f)

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Predicted Pseudomonas number logNT (logCFU/g) (a1) 45 (a2) R2=0.9589 2.0 R2 = 0.9782 R2adj=0.9552 R2adj = 0.9762 40 1.8

Predicted stored time (d) 35 1.6 30

1.4 25

1.2 20 2020102572

1.0 15

10 0.8 1.0 1.2 1.4 1.6 1.8 2.0 10 15 20 25 30 35 40 Observed Pseudomonas number logNT (logCFU/g) Stored time (d)

Figure 6(a) Figure 6(b)

4.5 (b1) R2 = 0.9888 (b2) Predicted bacterial number logNT (logCFU/g)

50 R2=0.9913 R2adj = 0.9884 4.0 R2adj=0.9909 Predicted stored time (d)

40 3.5

3.0 30

2.5 20

2.0 10

1.5 0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 10 20 30 40 50

Observed bacterial number logNT (logCFU/g) Stored time (d)

Figure 6(c) Figure 6(d) Predicted lactic acid bacterial number logNT (logCFU/g)

10.0 35 (c1) (c2) R2=0.9970 R2 = 0.9792 R2adj = 0.9783 30 R2adj=0.9969 9.5 Predicted stored time (d)

25 9.0

20 8.5

15 8.0

10 7.5

5 7.0

0 7.0 7.5 8.0 8.5 9.0 9.5 0 5 10 15 20 25 30 Observed lactic acid bacterial number logNT (logCFU/g) Stored time (d)

Figure 6(e) Figure 6