CN111754088A - Food digestion rule modeling method based on filtering - Google Patents

Food digestion rule modeling method based on filtering Download PDF

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CN111754088A
CN111754088A CN202010504494.2A CN202010504494A CN111754088A CN 111754088 A CN111754088 A CN 111754088A CN 202010504494 A CN202010504494 A CN 202010504494A CN 111754088 A CN111754088 A CN 111754088A
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王子赟
肖奕霖
徐子恒
黄俊翰
祝家勋
黄鑫
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Jiangnan University
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Abstract

The invention discloses a food digestion rule modeling method based on filtering. Belongs to the field of food science. The method comprises the steps of establishing an exponential model with errors according to the change data of gastric contents along with the digestion duration, obtaining a polynomial after Taylor expansion and standardizing the polynomial into an identification model, and iterating through a least square method to obtain a final fitting curve. The invention is beneficial to the grammer to master the digestion habit of the cultured organisms, so that a proper amount of feed can be fed in a proper time, the feeding efficiency is improved, and unnecessary waste is saved.

Description

Food digestion rule modeling method based on filtering
Technical Field
The embodiment of the invention relates to the field of food science, in particular to a food digestion rule modeling method based on filtering.
Background
As the meal ages, the dry weight, wet weight, etc. of the food as it is digested in the stomach changes. The emptying of gastric contents can be modeled using a variety of mathematical models, including linear, square root, logarithmic, exponential, and the like.
In the modern breeding industry, objective and accurate evaluation of the nutrient biological value of feed raw materials is a main decision basis for determining the animal nutrition requirement and optimizing the feed formula.
In practical application, the speed of gastric emptying affects the food intake, food digestibility and physiological metabolic level of fishes, and is often used for researching the problems of the food intake, ecological conversion efficiency and predation relationship of the fishes in natural living environment, the nutritional grade relationship of the fishes in a food chain and the like; gastric emptying can be used as an important indicator for assessing fish digestive function and feed digestibility; in addition, it can be used as a simple method to evaluate the feeding frequency of fish. Researches show that the appetite recovery condition of the fishes can be known through the relationship between digestion and gastric emptying of the fishes, the food intake rate of the fishes can be maximized and the feed benefits can be increased by feeding the fishes when the appetite of the fishes is recovered, the optimal feeding frequency can be estimated by knowing the relationship between the gastric emptying of the fishes and the appetite recovery, and the cultured fishes can formulate a feeding scheme through a gastric emptying experiment to improve the production benefits.
At present, most of gastric contents are approximately attenuated in an exponential mode along with the change of time, so that the application of an exponential fitting model is wide. However, when the gastric emptying curve fitting model is established, if the exponential model is directly adopted for fitting, the error is large. In addition, direct fitting may not meet the accuracy requirement, and the fitting degree is not good.
In addition, most of the existing food digestion law index fitting methods are direct fitting, are suitable for rough estimation and are not suitable for accurate judgment.
Disclosure of Invention
In order to solve the problems of the prior art, the invention provides a food digestion law modeling method based on filtering, wherein the filtering represents the suppression of noise signals and reduces the influence and interference of noise on a system, and the method comprises the following steps:
step 101, establishing an index model with errors according to the change data of the gastric contents along with the digestion duration, wherein the model is as follows:
F(i)＝F0e-i+B(z)(i) (1)
wherein F (i) represents the stomach content input data obtained by the ith sampling,
Figure BDA0002526025620000021
F0the weight of food ingested by the animal at the beginning, the wet weight of the intragastric residue after each meal that has not yet begun to be digested; b (z) is a polynomial coefficient, and B (z) is 1+ b1z-1+b2z-2，b1、b2Is an unknown constant to be solved, z is a backward step operator, z is an undetermined coefficient-j× (i) is (i-j), i-j is a positive integer, (i) represents a calculation error;
step 102, e-iAfter Taylor expansion, F (i) is converted to a polynomial and normalized to an identification model.
E is to be-iExpand with taylor's formula and take the first eight terms at i ═ 0:
Figure BDA0002526025620000022
order to
Figure BDA0002526025620000023
Then:
Figure BDA0002526025620000024
wherein the information vector
Figure BDA0002526025620000025
The information vector represents sampled or estimated information originating from the system;
Figure BDA0002526025620000026
parameter vector
Figure BDA0002526025620000027
The parameter vector represents a model parameter which is unknown to the system but needs to be solved;
λs＝[a0,a1,a2,a3,a4,a5,a6,a7]T，λn＝[b1,b2]T；
step 103, constructing parameter estimation values
Figure BDA0002526025620000028
The method is characterized in that the coefficient is a key intermediate variable when a rule function is analyzed, the parameter estimation precision η is given, and k is 1, and the method is specifically constructed as follows:
sampling and acquiring gastric content input data { i, F (i) } corresponding to time, wherein i is sampling frequency, i is 1,2
F＝[F(L),F(L-1),...,F(1)]T(4)
The construction containing the amount of sampling time and the amount of noise
Figure BDA0002526025620000029
And
Figure BDA00025260256200000210
Figure BDA0002526025620000031
Figure BDA0002526025620000032
obtaining the k-th parameter estimation value
Figure BDA0002526025620000033
Comprises the following steps:
Figure BDA0002526025620000034
constructing an error value for the kth gastric content wet mass calculation:
Figure BDA0002526025620000035
104, calculating whether the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is less than or equal to the given parameter estimation precision;
if the difference between the kth parameter estimation value and the kth-1 th parameter estimation value is less than or equal to the given parameter estimation precision, taking the kth parameter estimation value as an actual parameter value of the exponential model with the error;
if the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is greater than the given parameter estimation precision, enabling k to be k +1 and continuously comparing the difference between the k-th parameter estimation value and the k-1-th parameter estimation value;
that is to say if
Figure BDA0002526025620000036
Then get it at that time
Figure BDA0002526025620000037
Is the required actual parameter value; otherwise, let k equal to k +1 and construct a new one
Figure BDA0002526025620000038
And
Figure BDA0002526025620000039
to obtain new
Figure BDA00025260256200000310
A value;
step 105: the gastric content emptying curve can be finally fit to:
Figure BDA00025260256200000311
in one embodiment of the present invention, e is-iThe number of terms to be expanded can be arbitrarily chosen according to requirements, and the increase of the number of terms can make the result more accurate, but also can cause the increase of the calculation amount and overfitting.
The method of the invention is applied to the scientific culture of organisms.
Has the advantages that:
establishing an index model with errors according to the change data of the gastric contents along with the digestion duration, obtaining a polynomial after Taylor expansion and normalizing the polynomial into an identification model, constructing parameter estimation values, giving parameter estimation precision, and making k equal to 1, if the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is less than or equal to the given parameter estimation precision, taking the k-th parameter estimation value as the actual parameter value of the index model with errors, and if the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is greater than the given parameter estimation precision, making k equal to k +1 and continuously comparing the difference between the k-th parameter estimation value and the k-1-th parameter estimation value; the calculation accuracy is improved by the form of a polynomial expanded by Taylor, and the more the number of acquired terms is, the more accurate the calculation is; iteration is carried out through a least square method, and the given precision is met; the problem that the fitting degree of the existing food digestion rule model is not enough is solved; the effect of improving the food digestion rule modeling analysis precision is achieved.
According to the method, the cuttlefish is taken as a research object, the experimental result is fitted with the mathematical model to obtain the optimal model of the cuttlefish for gastric emptying, and the gastric emptying and appetite recovery time is obtained so as to guide the feeding of the feed in the culture production, reduce the feed waste and improve the culture benefit.
Drawings
Fig. 1 is a flow chart of a method of filter-based modeling analysis of food digestion laws.
FIG. 2 is a comparison of fitted curves.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Example 1
Referring to fig. 1, a method for modeling and analyzing food digestion rules based on filtering is shown, which is described by taking a process of sepiella maindroni for food digestion modeling as an example, sepiella maindroni (abbreviated as sepiella maindroni) is an important economic category of marine fishery in China and is widely distributed in coastal waters of fujian and zhejiang.
The method comprises the following steps:
step 101, establishing an index model with errors according to the change data of the content of the stomach of the cuttlefish along with the digestion duration, wherein the model is as follows:
F(i)＝F0e-i+B(z)(i) (1)
wherein, F (i) represents the cuttlefish stomach content input data obtained by the ith sampling;
the sampling method comprises the following steps: preparing a plurality of cases of cuttlefish with similar weight, wherein each case has the same amount, such as 10 cuttlefish; stopping feeding and ensuring that the gastric contents of the cuttlefishes are completely emptied in the first 24 hours, feeding the cuttlefishes with the iced fresh bait of the lobster gigantes at one time, removing residual bait after 30 minutes, and designing 10 cuttlefishes in each culture barrel as samples of one sampling point in order to reduce the stress response to the cuttlefishes at the residual time point in the sampling process;
at each sampling point, 10 cuttlefishes are taken out of the breeding barrel at the same time, then are killed quickly and are placed on an ice tray, are cut open along the midline of the abdomen by scissors, the visceral mass of the cuttlefishes is exposed, the cardia part and the pylorus part of the stomach are clamped by hemostatic forceps respectively, are cut off by scissors from the front end and the rear end, are placed in a culture dish, are cut open to enable the contents of the cuttlefishes to flow out completely, the wet weight of each residue in the stomach is weighed, and the average value is taken;
Figure BDA0002526025620000041
F0the weight of food ingested by the cuttlefish at the beginning; b (z) is a polynomial coefficient, and B (z) is 1+ b1z-1+b2z-2，b1、b2Is an unknown constant to be solved, z is a backward step operator, z is an undetermined coefficient-j× (i) is (i-j), i-j is a positive integer, and (i) represents a calculation error.
Step 102, e-iAfter Taylor expansion, F (i) is converted to a polynomial and normalized to an identification model.
E is to be-iExpand with taylor's formula and take the first eight terms at i ═ 0:
Figure BDA0002526025620000051
note that in other embodiments, e-iThe number of terms to be expanded can be arbitrarily selected according to requirements, the result is more accurate due to the increase of the number of terms, but the calculation amount is increased and the possibility of overfitting is caused, and the first eight terms are taken in the embodiment.
Order to
Figure BDA0002526025620000052
Then:
Figure BDA0002526025620000053
wherein the information vector
Figure BDA0002526025620000054
Figure BDA0002526025620000055
Parameter vector
Figure BDA0002526025620000056
λs＝[a0,a1,a2,a3,a4,a5,a6,a7]T，λn＝[b1,b2]T。
Step 103, constructing parameter estimation values
Figure BDA0002526025620000057
Given the parameter estimation accuracy η, and let k equal to 1, the specific construction is as follows:
sampling once every two hours, and acquiring corresponding stomach content input data { i, F (i) }, wherein i is sampling frequency, i is 1,2, L, L is maximum sampling frequency, and F (i) represents the cuttlefish stomach content input data acquired by the ith sampling and is constructed
F＝[F(L),F(L-1),...,F(1)]T(4)
The construction containing the amount of sampling time and the amount of noise
Figure BDA0002526025620000058
And
Figure BDA0002526025620000059
Figure BDA00025260256200000510
Figure BDA00025260256200000511
obtaining the k-th parameter estimation value
Figure BDA00025260256200000512
Comprises the following steps:
Figure BDA00025260256200000513
constructing an error value of the wet mass calculation of the content of the cuttlefish stomach at the kth time:
Figure BDA0002526025620000061
104, calculating whether the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is less than or equal to the given parameter estimation precision;
if the difference between the kth parameter estimation value and the kth-1 th parameter estimation value is less than or equal to the given parameter estimation precision, taking the kth parameter estimation value as an actual parameter value of the exponential model with the error;
if the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is greater than the given parameter estimation precision, enabling k to be k +1 and continuously comparing the difference between the k-th parameter estimation value and the k-1-th parameter estimation value;
that is to say if
Figure BDA0002526025620000062
Then get it at that time
Figure BDA0002526025620000063
Is the required actual parameter value; otherwise, let k equal to k +1 and construct a new one
Figure BDA0002526025620000064
And
Figure BDA0002526025620000065
to obtain new
Figure BDA0002526025620000066
The value is obtained.
Step 105: the gastric content emptying curve of the cuttlefish can be finally fit as follows:
Figure BDA0002526025620000067
as shown in fig. 2.
Example 2
This example illustrates the accuracy of the present invention by comparing it with a least squares linear fit, exponential model directly fit curve.
Data on the change in the wet weight of the gastric content when the cuttlefish digests food was collected as in example 1, and the data was sampled every two hours, where i is the true value when i is 0, which is the wet weight percentage of the gastric content when the cuttlefish had not digested.
As shown in fig. 2, the asterisks indicate the true values, the dotted lines are fitting curves fitted by the least square method, the dotted lines are curves directly fitted by the exponential model, and the solid lines are fitting curves fitted by the method of the present invention. The fit values obtained by the three methods are statistically shown in table 1 below. The error value, i.e., the difference between the fit value and the true value, is shown in table 2 below.
TABLE 1 statistical table of fitting values
Number of samplings 0 1 2 3 4 5 6 7
True value (%) 3.59 2.32 1.71 1.37 1.21 0.74 0.61 0.50
Linear fitting value (%) 2.8917 2.4958 2.1000 1.7042 1.3083 0.9125 0.5167 0.1208
Direct exponential fit value (%) 3.4200 2.5324 1.8715 1.3831 1.0222 0.7555 0.5583 0.4118
Inventive method fitting value (%) 3.6843 2.2358 1.7423 1.3570 1.2150 0.7978 0.6490 0.5086
TABLE 2 statistical table of error values
Figure BDA0002526025620000068
Figure BDA0002526025620000071
Therefore, the fitting error value of the method is less than the exponential direct fitting error value and less than the linear fitting error value, and the food digestion law model improves the fitting precision. For cuttlefish breeding, the accurate fitting of the food digestion rule curve is beneficial to the grammer to master the digestion habit of cuttlefish, the accurate prediction is facilitated to be achieved in advance, then a proper amount of feed can be fed in a proper time, the feeding efficiency is improved, and unnecessary waste is saved. For example, as can be seen from the fitted curve, after the third sampling, i.e., six hours, the rate of digestion of food by the cuttlefish tends to be flat, so that the cuttlefish can be fed every 6 hours.
In addition, the fourth true value is slightly higher, the result can be reflected by the fitting curve of the method, and the traditional exponential model is excessively dependent on the model, so that the fitting curve is necessarily decreased progressively and cannot be reflected. It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, where the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The scope of the present invention is not limited to the above embodiments, and any modifications, equivalent substitutions, improvements, etc. that can be made by those skilled in the art within the spirit and principle of the inventive concept should be included in the scope of the present invention.

Claims (4)

1. A food digestion law modeling method based on filtering is characterized by comprising the following steps:
step 101, establishing an index model with errors according to the change data of the gastric contents along with the digestion duration, wherein the model is as follows:
F(i)＝F0e-i+B(z)(i) (1)
wherein F (i) represents the stomach content input data obtained by the ith sampling,
Figure FDA0002526025610000011
F0the weight of food ingested by the animal at the beginning, the wet weight of the intragastric residue after each meal that has not yet begun to be digested; b (z) is a polynomial coefficient, and B (z) is 1+ b1z-1+b2z-2，b1、b2To be determined, the coefficients are those to be solvedKnowing the constant, z is the step-back operator, z-j× (i) is (i-j), i-j is a positive integer, (i) represents a calculation error;
step 102, e-iAfter Taylor expansion, converting F (i) into a polynomial and standardizing the polynomial into an identification model;
e is to be-iExpand with taylor's formula and take the first eight terms at i ═ 0:
Figure FDA0002526025610000012
order to
Figure FDA0002526025610000013
Then:
Figure FDA0002526025610000014
wherein the information vector
Figure FDA0002526025610000015
Figure FDA0002526025610000016
T is a transposed symbol of the matrix;
parameter vector
Figure FDA0002526025610000017
λs＝[a0,a1,a2,a3,a4,a5,a6,a7]T，λn＝[b1,b2]T；
Step 103, constructing parameter estimation values
Figure FDA0002526025610000021
Figure FDA0002526025610000022
The method is characterized in that the coefficient is a key intermediate variable when a rule function is analyzed, the parameter estimation precision η is given, and k is 1, and the method is specifically constructed as follows:
sampling and acquiring gastric content input data { i, F (i) } corresponding to time, wherein i is sampling frequency, i is 1,2
F＝[F(L),F(L-1),...,F(1)]T(4)
The construction containing the amount of sampling time and the amount of noise
Figure FDA0002526025610000023
And
Figure FDA0002526025610000024
Figure FDA0002526025610000025
Figure FDA0002526025610000026
obtaining the k-th parameter estimation value
Figure FDA0002526025610000027
Comprises the following steps:
Figure FDA0002526025610000028
constructing an error value for the kth gastric content wet mass calculation:
Figure FDA0002526025610000029
104, when the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is less than or equal to the given parameter estimation precision η, taking the current value
Figure FDA00025260256100000210
Is the required actual parameter value;
step 105: the gastric content emptying curve can be finally fit to:
Figure FDA00025260256100000211
2. the filtering-based food digestion law modeling method according to claim 1, wherein said step 104 is:
if the difference between the kth parameter estimation value and the kth-1 th parameter estimation value is less than or equal to the given parameter estimation precision, taking the kth parameter estimation value as an actual parameter value of the exponential model with the error;
if the difference between the k-th parameter estimation value and the k-1-th parameter estimation value is greater than the given parameter estimation precision, enabling k to be k +1 and continuously comparing the difference between the k-th parameter estimation value and the k-1-th parameter estimation value;
that is to say if
Figure FDA00025260256100000212
Then get it at that time
Figure FDA00025260256100000213
Is the required actual parameter value; otherwise, let k equal to k +1 and construct a new one
Figure FDA00025260256100000214
And
Figure FDA00025260256100000215
to obtain new
Figure FDA00025260256100000216
The value is obtained.
3. The filter-based food digestion law modeling method according to claim 1, wherein said e-iThe number of items expanded canOptionally, an increase in the number of terms will make the result more accurate, but will also result in an increase in the amount of computation and overfitting.
4. A method for modeling food digestion law according to any of the claims 1 to 3, characterized in that said method is applied to the scientific cultivation of living beings.
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