CN110428121B - Hidden Markov model food quality assessment method based on gray correlation analysis - Google Patents
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Abstract
The invention discloses a hidden Markov model food quality assessment method based on grey correlation analysis, which comprises the following steps: and obtaining index weights corresponding to the influence factors according to a gray correlation analysis algorithm and each influence factor, obtaining risk indexes corresponding to the indexes according to each index and each index weight, training the hidden Markov model by taking the risk indexes as input data of the hidden Markov model, and evaluating and predicting the food quality by using the trained hidden Markov model. The technical scheme provided by the invention realizes the risk assessment of the food quality more accurately, thereby being beneficial to improving the accuracy and efficiency of the food quality assessment. Therefore, the technical scheme provided by the invention realizes the evaluation and prediction of the food quality, can analyze the cause and severity of the generated problems, and makes or adjusts risk control measures in advance so as to propose suggestions for food production, inspection and management departments.
Description
Technical Field
The invention relates to the technical field of food safety, in particular to a hidden Markov model food quality assessment method based on gray correlation analysis.
Background
The risk assessment and early warning system of food quality safety needs to be perfected.
Disclosure of Invention
In order to solve the limitations and defects existing in the prior art, the invention provides a hidden Markov model food quality assessment method based on gray correlation analysis, which comprises the following steps:
obtaining a reference vector and a comparison vector, the reference vector x 0 And the comparison vector x i The method comprises the following steps of:
x 0 ＝{x 0 (1)，x 0 (2)，...，x 0 (n)}；
x i ＝{x i (1)，x i (2)，...，x i (n)}；
wherein n is the number of samples, i=0, 1,2,..m-1, m is the number of all indexes;
and carrying out normalization processing on each index, wherein the normalization processing formula is as follows:
obtaining y i (k) And y 0 (k) Gray correlation coefficient at k time, wherein the gray correlation coefficient is:
wherein ρ ε (0, 1);
obtaining a sequence y according to the grey correlation coefficient 0 And sequence y i The correlation coefficient between the two is as follows:
obtaining a correlation coefficient matrix of all indexes according to the correlation coefficient, wherein the correlation coefficient matrix is as follows:
obtaining index weights corresponding to the indexes according to the correlation coefficient matrix;
obtaining a risk index corresponding to each index according to each index and the index weight;
training the hidden Markov model by taking the risk index as input data of the hidden Markov model;
the food quality is evaluated and predicted using a hidden markov model after training.
Optionally, the step of obtaining the risk index corresponding to the index according to each index and the index weight includes:
the local state is initialized according to the Viterbi algorithm as follows:
δ l (i)＝π i b i (o l )，i＝1，2，...，N
the local state at the time T of the dynamic programming recurrence time t=2, 3, … is:
the maximum value is obtained at the moment T, and the hidden state is as follows:
and obtaining a corresponding risk index according to the hidden state and the index weight.
Optionally, before the step of obtaining the corresponding risk index according to the hidden state and the index weight, the method includes:
δ T (i) The maximum value is obtained at the moment T, and the probability of occurrence of the hidden state sequence is as follows:
optionally, the method further comprises:
using local statesBacktracking is performed, and for t=t-1, T-2, …,1, the corresponding hidden state sequence is:
obtaining an optimal path according to the hidden state sequence, wherein the optimal path is as follows:
I*＝{i 1 *，i 2 *，...，i T *}。
optionally, the step of obtaining the index weight corresponding to each index according to the correlation coefficient matrix includes:
obtaining an average value of each index according to each index in the correlation coefficient moment;
and taking the average value of each index as the index weight corresponding to each index.
The invention has the following beneficial effects:
the hidden Markov model food quality assessment method based on gray correlation analysis provided by the invention comprises the following steps: and obtaining index weights corresponding to the influence factors according to a gray correlation analysis algorithm and each influence factor, obtaining risk indexes corresponding to the indexes according to each index and each index weight, training the hidden Markov model by taking the risk indexes as input data of the hidden Markov model, and evaluating and predicting the food quality by using the trained hidden Markov model. The technical scheme provided by the invention realizes the risk assessment of the food quality more accurately, thereby being beneficial to improving the accuracy and efficiency of the food quality assessment. Therefore, the technical scheme provided by the invention realizes the evaluation and prediction of the food quality, can analyze the cause and severity of the generated problems, and makes or adjusts risk control measures in advance so as to propose suggestions for food production, inspection and management departments.
Drawings
Fig. 1 is a schematic diagram of a hidden markov model based on gray correlation analysis according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of risk classification criteria according to an embodiment of the invention.
Fig. 3 is a schematic diagram of a sterilized milk risk assessment hidden markov model according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of accuracy of a model in a training set according to a first embodiment of the present invention.
Fig. 5 is a schematic diagram of accuracy of a model provided in a training set and a testing set according to a first embodiment of the present invention.
FIG. 6 is a schematic diagram showing the accuracy of the model provided in the first embodiment of the present invention in various training sets and test sets.
Fig. 7 is a schematic diagram of a viterbi algorithm visualization process according to a first embodiment of the invention.
Fig. 8 is a schematic diagram showing a law of a change of the quality of sterilized milk with time according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of a hidden markov model risk assessment result according to an embodiment of the present invention.
Detailed Description
In order to enable those skilled in the art to better understand the technical scheme of the invention, the hidden Markov model food quality assessment method based on gray correlation analysis provided by the invention is described in detail below with reference to the accompanying drawings.
Example 1
In this embodiment, a hidden markov model is used for risk assessment, and training the model first obtains each evaluation index weight, and in the prior art, an expert system and a hierarchical analysis method are used for obtaining the index weight. However, the expert system method has the disadvantages of greater subjectivity and inconsistency, low sensitivity and great subjective influence. Although the analytic hierarchy process uses a qualitative and quantitative combination method, the analytic hierarchy process is complex in hierarchy construction and depends on subjective judgment of an expert. Because the factors influencing the food safety are complex, the influencing factors and the detection data of the food safety have strong nonlinearity, so that the nonlinear correlation analysis is more suitable for solving the food data.
Gray correlation analysis (Grey Relational Analysis, GRA) is an important branch of gray system theory, the basic idea is to judge whether the connection between different sequences is tight or not according to the sequence curve geometry, and the method is suitable for analyzing and processing nonlinear data. Aiming at the nonlinear characteristics of food detection data, a gray correlation analysis algorithm can be used for constructing a correlation coefficient matrix among various indexes in food safety, so that various index weights are obtained.
Hidden Markov models (Hidden Markov Model, HMM) are models developed based on Markov chains that perceive the presence of states and their course through a stochastic process. The hidden Markov model is applied to risk assessment, and can be combined with the time characteristics of data, so that the assessment result has better instantaneity and pertinence, and the dynamic assessment of the risk is realized. The hidden Markov model is a statistical analysis model, and is represented by five elements, and comprises 2 state sets and 3 probability matrices, namely an hidden state Q, an observable state O, an initial state probability matrix pi, an hidden state transition probability matrix A and an observable state transition probability matrix B. Firstly initializing II, A and B, training a hidden Markov model by using a Baum-Welch algorithm and combining input data to obtain a trained hidden Markov model, and performing risk assessment and prediction by using a Viterbi algorithm and combining an observable state. The hidden Markov model is used for dynamically evaluating the quality safety of food, and risk control measures are adjusted in advance, so that the loss caused by quality safety problems is reduced.
Fig. 1 is a schematic diagram of a hidden markov model based on gray correlation analysis according to an embodiment of the present invention. As shown in fig. 1, the weight of each index is calculated by gray correlation analysis, the risk index of each index is obtained by integrating each influencing factor, and then the risk index is used as input data of a hidden markov model to train the hidden markov model, so as to obtain trained model dynamic evaluation and forecast food quality safety. The technical scheme provided by the invention realizes the risk assessment of the food quality more accurately, thereby being beneficial to improving the accuracy and efficiency of the food quality assessment.
Aiming at the multiple and nonlinearity of food safety data, the traditional hidden Markov model cannot effectively analyze the nonlinearity data, the embodiment utilizes a gray correlation analysis algorithm to improve the hidden Markov model, solves the weight of each index, and then uses a Baum-Welch algorithm and a Viterbi algorithm to realize model training and risk assessment, thereby realizing dynamic risk assessment. The gray correlation analysis method aims at the nonlinearity of the data, obtains the weight of each index, and more accurately analyzes the food safety data. Thus, the hidden Markov model may combine the temporal characteristics of the food data to perform dynamic risk assessment for quality safety.
In the embodiment, each index weight is solved through grey correlation analysis, and then the weights are combinedAnd calculating a risk index. Each index serves as a reference sequence and the remaining indexes serve as comparison sequences. Setting the reference vector as x 0 ＝{x 0 (1)，x 0 (2)，…，x 0 (n) }, n is the number of samples, and the comparison vector is x i ＝{x i (1)，x i (2)，…，x i (n) }, i=0, 1,2, …, m-1, m is the number of all indexes, and then a correlation coefficient matrix is established according to gray correlation analysis.
In this embodiment, the m groups of indexes are normalized to eliminate the influence of dimension, and the processing formula is as follows:
the present embodiment calculates the gray correlation coefficient, y at time k i (k) And y 0 (k) The gray correlation coefficient of (2) is as follows:
wherein, xi i (k) For gray correlation coefficients, ρ e (0, 1), adjusting the parameter ρ may enhance the variability of the individual coefficients. Sequence y 0 And sequence y i The correlation coefficient between can be expressed as:
each index serves as a reference sequence, and the correlation coefficient matrix of all indexes can be obtained by the formula (3):
in this embodiment, the average value of each index in the correlation coefficient is taken, that is, the weight corresponding to each index. In addition, the mathematical representation of the five elements of the hidden Markov model is as follows:
Q＝{q 1 ，q 2 ，…，q N } (5)
O＝{o 1 ，o 2 ，…，o M } (6)
Π＝{[π(i)] N ，π(i)＝P(q i )} (7)
A＝{[a ij ] N×N ，a ij ＝P(q j |q i )} (8)
B＝{[b j (k)] N×M ，b j (k)＝P(o k |q j )} (9)
in the embodiment, the Baum-Welch algorithm is used for solving the model parameter lambda of the hidden Markov model, and all pi is randomly initialized i ，a ij ，b j (k) A. The invention relates to a method for producing a fibre-reinforced plastic composite The model parameter formula provided in this embodiment is as follows:
π i ＝γ 1 (i) (10)
if pi i ，a ij ，b j (k) If the value of (2) is converged, a final result is obtained, otherwise, iteration is continued.
The present embodiment uses the Viterbi algorithm to solve the corresponding hidden state sequence that is most likely to occur given the observed sequence. First, the present embodiment initializes a local state, and the formula is as follows:
δ l (i)＝π i b i (o l )，i＝1，2，...，N (13)
in this embodiment, the local states of the dynamic programming recursion time t=2, 3, …, T are expressed as follows:
delta at time tmax T (i) For the probability of occurrence of the most probable hidden state sequence, time tmaxFor the most probable hidden state at time T, the calculation formula is as follows:
the present embodiment uses local statesStarting backtracking, for the hidden state sequence corresponding to the time t=t-1, T-2, …,1, the formula is as follows:
the optimal path finally obtained in this embodiment is:
I*＝{i 1 *，i 2 *，...，i T *} (20)
the optimal path is the most probable hidden state sequence.
In order to verify the effectiveness and accuracy of food quality safety risk assessment based on a hidden Markov model of gray correlation analysis, the embodiment takes sterilized milk data as a research object based on certain provincial food safety data, and uses the hidden Markov model of gray correlation analysis to carry out risk assessment on sterilized milk detection data, dynamically assess and predict the change rule of risks along with time.
The sterilized milk test dataset contained 970 test data from 8.2013 to 2.2016, with the present example model training using 375 pieces of data from 8.2013 to 10.2015, with the remaining data used for model prediction and assessment. All the processing technology of the batch of sterilized milk is ultra-high temperature sterilized milk. According to national standards, the technical standards of sterilized milk include raw material requirements, sensory requirements, physicochemical indexes, pollutant limits, mycotoxin limits and microbial requirements. The detection indexes used in this embodiment include: protein, fat, non-fat milk solids, acidity, mercury, lead, arsenic, chromium, and aflatoxin M1. The partial detection data of 2016, 6 and 2014, 10 are shown in Table 1, and the national standard is shown in Table 2.
Table 1 partial test data
TABLE 2 national Standard
In this example, the data was normalized using equation (1), and the partial results obtained are shown in table 3.
Table 3 partial test data after normalization
In this embodiment, the gray correlation coefficient is calculated on the normalized data by using the formula (2) and the formula (3), and each index serves as a reference sequence, so that a correlation coefficient matrix is obtained as shown in table 4.
TABLE 4 correlation coefficient matrix
In this embodiment, the average value of each index weight is obtained, and the weight corresponding to each index is shown in table 5.
TABLE 5 index weights
In this embodiment, the quality safety risk of the sample is evaluated by using the sample detection data and the difference between the national standards, and the national standards indicate that the contents of fat, protein and non-fat milk solids in the qualified sample are required to satisfy the national standards, and are defined as forward indexes. The acidity is defined as neutral index in the interval meeting the national standard requirement. Lead, mercury, arsenic, chromium and aflatoxin meet the national standard or less, and are defined as negative indexes. The formula of the difference between the detection data and the national standard is shown in Table 6 in combination with the classification of the index.
Table 6 formula for difference
Taking the data in table 1 as an example, the result obtained by taking the difference between the detection data and the national standard is calculated as follows, and five risk levels can be obtained by dividing the quality data according to the numerical values. The calculation results and the classification results are shown in table 7. Fig. 2 is a schematic diagram of risk classification criteria according to an embodiment of the invention. As shown in fig. 2, the risk level is classified according to a 5-scale method in combination with quality data.
TABLE 7 differential calculation results
Fig. 3 is a schematic diagram of a sterilized milk risk assessment hidden markov model according to an embodiment of the present invention. As shown in FIG. 3, the present embodiment uses Baum-Welch algorithm for model training, and defines that the hidden Markov model has five hidden states, states 1-5 represent the quality security risk of the sample, and the larger the number, the higher the quality security risk. And taking the risk index as input data of the model, namely the observable state. The initialization probability matrix is as follows:
π i ＝[0.2 0.2 0.2 0.2 0.2] T (32)
this example uses 375 pieces of data from 8 months in 2013 to 10 months in 2015 as an example for model training. The hidden Markov model results obtained from the above initialization results were trained using the Baum-Welch algorithm as follows.
π i ＝[0 1 0 0 0] T (35)
In this embodiment, reliability of the model is determined using the confusion matrix, TP represents a positive sample that is predicted to be positive by the model, TN represents a true negative, a negative sample that is predicted to be negative by the model, FP represents a false positive, a negative sample that is predicted to be positive by the model, FN represents a false negative, and a positive sample that is predicted to be negative by the model. The experiment provided in this embodiment is a multi-classification problem, where each class is considered "positive" alone and all other types are considered "negative" when using the confusion matrix to determine accuracy. Setting the risk threshold to 0 starts with an increase of 0.2 per round until 1 is reached. Fig. 4 is a schematic diagram of accuracy of a model in a training set according to a first embodiment of the present invention. As shown in fig. 4, 1,2 and 3 represent TPR and TNR at training set sizes of 350, 250 and 450, respectively. As can be seen from fig. 4, the decreasing rates of TPR and TNR increase sharply with increasing threshold, and TPR and TNR are maximized when the threshold is selected to be 0.6 while ensuring the accuracy of the evaluation.
Fig. 5 is a schematic diagram of accuracy of a model provided in a training set and a testing set according to a first embodiment of the present invention. As shown in fig. 5, taking the training set size of 350 as an example, the test is performed using the same size test set data. The accuracy on the training set is slightly higher than the accuracy on the test set. Taking a risk threshold of 0.6 as an example, the risk assessment system measures 83.14% and 80.48% of TPR and 95.79% and 95.12% of TNR on the training set and the test set, respectively, and the accuracy on the training set is higher than the accuracy on the test set.
With a risk threshold of 0.6, another experiment was performed in this example to investigate the effect of training set size on TPR and TNR. In the embodiment, training sets with different sizes are used as model training data, the rest data sets are used as test sets, and the accuracy of the model on the training sets and the test sets is tested respectively. FIG. 6 is a schematic diagram showing the accuracy of the model provided in the first embodiment of the present invention in various training sets and test sets. As shown in fig. 6, the training set size starts at 250 and increases by 25 per round. When the training set reaches 375 bars, the accuracy of the model does not get better by adding training data sets, i.e., 375 bars of data are sufficient for model training.
Fig. 7 is a schematic diagram of a viterbi algorithm visualization process according to a first embodiment of the invention. As shown in fig. 7, in this embodiment, the Viterbi algorithm is used to perform risk prediction and evaluation in combination with a trained model, and the optimal path (2, 4, …,1, 5) corresponding to a given observation state is obtained by using a backtracking method assuming that the state corresponding to the maximum probability is state 5, where the path shown by the solid line is the optimal path from the start state to the final state.
Fig. 8 is a schematic diagram showing a law of a change of the quality of sterilized milk with time according to an embodiment of the present invention. As shown in fig. 8, the hidden markov model is a dynamic evaluation algorithm, and can evaluate the data set by combining the time characteristics of the data, analyze the time characteristics of the sterilized milk data, and make the proportion of high-quality batch products change with seasons. The data from the fourth quarter in 2013 to the fourth quarter in 2015 are combined to show that the proportion of the second quarter in 2015, the third quarter in 2015 and the second quarter in 2014 is obviously lower than that of other quarters, and the phenomenon is probably caused by high temperature in summer, which is unfavorable for storage of sterilized milk products and is easy to cause deterioration of raw milk. The above shows that the quality of the sterilized milk product has obvious difference with time, and the quality of the sterilized milk can be well estimated and predicted by combining the time characteristic by using the dynamic estimation algorithm of the hidden Markov model.
In the embodiment, the trained hidden Markov model is applied to all the sterilized milk detection data to evaluate the quality safety of the sterilized milk, and the time characteristics of the sterilized milk are combined to obtain the time-dependent change rule of the quality safety risk evaluation result of the sterilized milk. Fig. 9 is a schematic diagram of a hidden markov model risk assessment result according to an embodiment of the present invention. As shown in fig. 9, the bar graph is the result of applying the hidden markov model to risk assessment of sterilized milk detection data, the line graph is the input data of the model, namely the result of changing the quality of sterilized milk with time, and compared with two groups of results, the obtained risk trend is basically consistent, and the quality safety risk is the largest in the second quarter in 2014, the second quarter in 2015 and the third quarter in 2015.
By risk assessment of the quality safety of the sterilized milk, a method for improving the quality of the sterilized milk can be obtained by combining the time characteristics of the quality of the sterilized milk. Firstly, the quality safety of the sterilized milk product in the production link is strictly controlled, and microorganisms are easy to nourish in summer due to higher temperature, so that the quality safety of the product is threatened. Therefore, the production enterprises need to strictly keep in charge from the inspection and acceptance of the raw milk, the whole process quality control from the raw material entering the factory to the finished product leaving the factory is ensured, and the quality safety of the product is ensured. Secondly, the method is popularized in the transportation and sales links, the harm of microorganisms can be reduced through control measures such as temperature, time and operation standards of each link, a critical limiting index is determined for each critical control point to serve as a control standard, and each critical control point is ensured to be limited in a safety range.
According to the experiment, nonlinear data can be effectively processed through gray correlation analysis to obtain each index weight, and then model training, risk dynamic assessment and prediction are carried out by using a hidden Markov model, so that the reasons for quality problems are analyzed, and the direction for improving the food quality is obtained.
The hidden Markov model food quality assessment method based on gray correlation analysis provided by the embodiment comprises the following steps: and obtaining index weights corresponding to the influence factors according to a gray correlation analysis algorithm and each influence factor, obtaining risk indexes corresponding to the indexes according to each index and each index weight, training the hidden Markov model by taking the risk indexes as input data of the hidden Markov model, and evaluating and predicting the food quality by using the trained hidden Markov model. The technical scheme provided by the embodiment realizes the risk assessment of the food quality more accurately, thereby being beneficial to improving the accuracy and efficiency of the food quality assessment. The technical scheme provided by the embodiment realizes the evaluation and prediction of the food quality, can analyze the cause and severity of the generated problems, and makes or adjusts risk control measures in advance so as to propose suggestions for food production, inspection and management departments.
It is to be understood that the above embodiments are merely illustrative of the application of the principles of the present invention, but not in limitation thereof. Various modifications and improvements may be made by those skilled in the art without departing from the spirit and substance of the invention, and are also considered to be within the scope of the invention.
Claims (1)
1. A hidden markov model food quality assessment method based on gray correlation analysis, comprising:
obtaining a reference vector and a comparison vector, the reference vector x 0 And the comparison vector x i The method comprises the following steps of:
；
；
wherein n is the number of samples,i=1, 2,3, …, m-1, m is the number of all indices;
and carrying out normalization processing on each index, wherein the normalization processing formula is as follows:
；
obtainingAnd->At->Gray correlation coefficient of time, wherein the gray correlation coefficient is as follows:
；
wherein,；
obtaining a sequence from the grey correlation coefficientAnd sequence->The correlation coefficient between the two is as follows:
；
obtaining a correlation coefficient matrix of all indexes according to the correlation coefficient, wherein the correlation coefficient matrix is as follows:
；
obtaining index weights corresponding to the indexes according to the correlation coefficient matrix;
obtaining a difference value between the detection data and the national standard according to the following difference value formula, and then calculating the difference value and the index weight to obtain risk indexes corresponding to the indexes;
；
training the hidden Markov model by taking the risk index as input data of the hidden Markov model;
evaluating and predicting food quality using the trained hidden Markov model;
the step of obtaining the index weight corresponding to each index according to the correlation coefficient matrix comprises the following steps:
obtaining an average value of each index according to each index in the correlation coefficient matrix;
and taking the average value of each index as the index weight corresponding to each index.
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| CN111626749A (en) * | 2020-05-15 | 2020-09-04 | 贵州理工学院 | Food quality safety tracing and safety level evaluation system |
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