CN110956365B - Colony total number dynamic risk assessment method of wheat flour supply chain based on hybrid Bayesian network - Google Patents

Colony total number dynamic risk assessment method of wheat flour supply chain based on hybrid Bayesian network Download PDF

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CN110956365B
CN110956365B CN201911095119.0A CN201911095119A CN110956365B CN 110956365 B CN110956365 B CN 110956365B CN 201911095119 A CN201911095119 A CN 201911095119A CN 110956365 B CN110956365 B CN 110956365B
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赵峙尧
王小艺
陈谦
熊科
张新
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Abstract

The invention provides a dynamic risk assessment method for the total number of colonies of a wheat flour supply chain based on a hybrid Bayesian network, and belongs to the technical field of food safety risk assessment. The invention comprises the following steps: selecting key monitoring nodes in a wheat flour supply chain, establishing a Bayesian network model of the wheat flour supply chain, taking the key nodes as discrete modes, switching among the modes representing probabilistic migration of the total number of colonies on the supply chain, describing continuous dynamic behavior of the total number of the colonies through a dynamic growth model of the colonies under each mode, and establishing a hybrid Bayesian network model; establishing a discrete time reasoning evolution mechanism of the hybrid Bayesian network, predicting the total colony number distribution of the wheat flour supply chain based on Monte Carlo simulation, and measuring the total colony number hazard degree according to hazard indexes. The method is suitable for detection and evaluation of food safety in complex environment, improves detection efficiency and risk evaluation accuracy, and solves the problem that process risk is difficult to accurately and quantitatively measure.

Description

Colony total number dynamic risk assessment method of wheat flour supply chain based on hybrid Bayesian network
Technical Field
The invention belongs to the technical field of food safety risk assessment, and particularly relates to a dynamic risk assessment method for the total number of colonies in a wheat flour supply chain based on a hybrid Bayesian network.
Background
Wheat is the second major food crop in the world, and is also the third major crop in china following corn and rice. Since the beginning of the 80's of the 20 th century, the worldwide wheat production has increased significantly, the annual wheat production in China exceeds 1.2 hundred million tons, China has become the world's largest wheat producing country, and wheat is one of the most important staple foods in China. However, in recent years, wheat flour food safety problems have emerged endlessly and have attracted wide attention in various social circles. To ensure the quality of wheat and its by-products, food safety regulations need to cover the whole supply chain, and perform the whole process inspection and supervision of wheat flour quality from raw materials to finished products, rather than just end product detection in the traditional sense. In recent years, the international food safety organization is strongly pushing the application of risk assessment techniques to assess food safety issues.
However, the existing safety risk assessment methods aiming at food hazards mostly study the hazards in the raw materials or products of the supply chain through chemical test methods, do not consider the migration characteristics of the hazards on the complete supply chain from 'raw materials to finished products', mostly only consider the management factors such as manpower, logistics, funds and the like, and do not consider the risks brought by the hazards.
Disclosure of Invention
The invention aims to make up the deficiency of research on risk problems of supply chain hazards, provides a dynamic risk assessment method for the total number of colonies of a wheat flour supply chain based on a hybrid Bayesian network by taking 'risk' as a guide, and provides a new solution and a feasible solution for solving the safety problem of biological hazards of a food supply chain.
The invention provides a dynamic risk assessment method for the total number of colonies of a wheat flour supply chain based on a hybrid Bayesian network, which comprises the following specific steps:
the method comprises the following steps: establishing a hybrid Bayesian network model of colony total number distribution characteristics of a wheat flour supply chain;
and establishing a bacterial colony dynamic growth model which comprises a bacterial colony growth dynamic model, a dynamic parameter model and an environment model. The input of the colony growth kinetic model is time, the output is colony total number, and important parameters in the model are determined by the kinetic parameter model. The input of the dynamic parameter model is temperature and humidity, and the output is lag phase and specific growth rate. The environment model is divided into a temperature model and a humidity model, the input is time, and the output is temperature and humidity respectively.
According to expert experience, selecting key nodes for monitoring total number of colonies in each link of a wheat flour supply chain, and establishing a Bayesian network model of the wheat flour supply chain.
Nodes of the Bayesian network are defined as discrete modes, and switching between the modes is modeled by Bayesian conditional probability so as to describe probabilistic migration of colony counts on a supply chain. And describing the continuous dynamic behavior of the colony count growth in each mode through a colony dynamic growth model to obtain a hybrid Bayesian network model of the colony count distribution characteristics of the wheat flour supply chain.
Step two: predicting the colony total number distribution characteristics of the wheat flour supply chain;
establishing a discrete time reasoning evolution mechanism of the hybrid Bayesian network, and dividing the discrete time reasoning evolution mechanism into a continuous process variable evolution part and a discrete switching evolution part; in discrete switch evolution, a discrete set of conditional probability events across key segments of the wheat flour supply chain
Figure GDA0002480776620000021
Middle extraction mode switching probability matrix pi ═ piij]M×MM denotes the total number of discrete modes, πijTo representMode qiSwitching to mode qjThe modal probability of the next moment is calculated by combining the modal switching probability and the modal probability of the current moment; the colony count distribution of the wheat flour supply chain is then predicted based on the Monte Carlo simulation.
Step three: and calculating the colony total hazard degree according to the predicted colony total distribution of the wheat flour supply chain.
Compared with the prior art, the invention has the following advantages:
(1) the invention effectively combines qualitative and quantitative risk assessment methods, and carries out quantitative risk assessment aiming at key nodes in the wheat flour supply chain, thereby not only reducing the detection and assessment range and improving the detection efficiency and the assessment efficiency, but also ensuring the accuracy of the detection result and the risk assessment.
(2) According to the invention, the distribution characteristics of the total number of the bacterial colonies in the food supply chain are modeled into the hybrid Bayesian network, a dynamic growth model of the bacterial colonies is introduced, the uncertainty of continuous dynamic growth and discrete transfer of the bacterial colonies is considered, the Bayesian network model and the hybrid system are effectively combined, the food safety detection and evaluation under the complex environment are adapted, and the applicability and the accuracy of the detection and the risk evaluation are improved.
(3) The invention provides a hazard index for measuring the total number of bacterial colonies in a food supply chain, solves the problem that the process risk is difficult to accurately and quantitatively measure, and improves the risk evaluation precision compared with the process variable as a measurement index.
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FIG. 1 is a flow chart of a risk assessment method of the present invention based on the total number of colonies on the hybrid Bayesian network food supply chain;
FIG. 2 is a simplified flow diagram of the wheat flour supply chain according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a Bayesian network structure of a wheat flour supply chain established in an embodiment of the present invention;
FIG. 4 is a diagram showing an example of a hybrid Bayesian network structure for the colony count distribution characteristic of the wheat flour supply chain according to the present invention;
FIG. 5 is a schematic view of a general hazard space;
FIG. 6 is a graph of unit colony growth in a particular mode of an embodiment of the invention;
FIG. 7 is a graph of colony population distribution characteristics predicted based on a hybrid Bayesian network in accordance with an embodiment of the present invention;
FIG. 8 is a graph showing the calculation results of the colony count hazard in the wheat flour supply chain according to the example of the present invention.
Detailed Description
The present invention will be described in further detail and with reference to the accompanying drawings so that those skilled in the art can understand and practice the invention.
As shown in fig. 1, the present invention provides a dynamic risk assessment method for colony count of wheat flour supply chain based on hybrid bayesian network, which includes firstly, establishing a hybrid bayesian network model of colony count distribution characteristics on the wheat flour supply chain, wherein the discrete mode of the model qualitatively considers colony count distribution state under key link in the supply chain; continuous dynamic behaviors of each mode are described by a dynamic growth model of the bacterial colony, and the growth environments of the bacterial colonies in different modes are different; the migration characteristics of the total number of colonies between different modalities satisfy a conditional probability distribution, which is determined by the production process and obeys certain distribution characteristics. Then, probability distribution characteristic prediction of the total number of wheat flour colonies is realized by using a Monte Carlo method. Finally, a risk index is provided for carrying out quantitative risk assessment on the total number of colonies in the wheat flour supply chain. The following is described in detail in three steps.
The method comprises the following steps: and establishing a colony total number distribution characteristic model of the wheat flour supply chain to describe the colony growth condition under the environment to be tested. The method integrates the existing classical colony growth dynamics model, the dynamics parameter model and the parameters, adds the environment model to establish a new complete colony dynamic growth model, fuses the Bayesian network and the hybrid system based on the characteristics of an evaluation object, and provides a new technology for evaluating the colony risk of the wheat flour supply chain by using the hybrid Bayesian network.
Step 101, firstly, a bacterial colony dynamic growth model is established, wherein the bacterial colony dynamic growth model comprises a bacterial colony growth dynamic model, a dynamic parameter model and an environment model. The input of the colony growth kinetic model is time, the output is colony total number, and important parameters in the model are determined by the kinetic parameter model. The input of the dynamic parameter model is temperature and humidity, and the output is lag phase and specific growth rate. The environment model is divided into a temperature model and a humidity model, the input is time, and the output is temperature and humidity respectively.
The established colony dynamic growth model is as follows:
Figure GDA0002480776620000031
ln(1/λ)＝C0+C1·bw+C2·bw 2+C3·T+C4·T2+C5·T·bw(2)
μ(T,aw)＝μopt·τ(T)·ρ(aw) (3)
Figure GDA0002480776620000032
Figure GDA0002480776620000033
T(t)＝fT(T(t-1))+ωT(6)
Figure GDA0002480776620000034
formula (1) represents a colony growth kinetic model for describing the growth condition of colonies under a specific environment, wherein N (t) represents the total number of colonies at the time t, and N0The initial value of the total number of colonies is shown, A is the maximum value of the total number of colonies, mu is the ratio of the total number of colonies to the growth rate, lambda is the growth lag phase of the total number of colonies, and t is the time. Equation (2) represents a kinetic parametric model of the parameter λ, consisting of temperature T and humidity awDeciding, for better hyperbolic fitting effect, that
Figure GDA0002480776620000035
bwAs an intermediate parameter, C0-C5Are fitting parameters. Equation (3) represents a kinetic parametric model of the parameter μ, also represented by temperature T and humidity awDetermination of μoptExpressing the colony population ratio to the growth rate optimum value, and τ (T) representing the temperature factor model, as shown in equation (4), ρ (a)w) The humidity factor model is expressed as shown in equation (5). T ismin、TmaxRespectively representing the minimum and maximum values of the temperature growth interval, ToptRepresents the temperature optimum for microbial growth. a isw,minMinimum boundary value of humidity growth interval, aw,optRepresents the humidity optimum for microbial growth. Equations (6) and (7) represent the temperature and humidity environment models, respectively, fTRepresenting the temperature dynamic variation function, omegaTIs the system noise of the temperature environment model,
Figure GDA0002480776620000041
a function representing the dynamic variation of the humidity,
Figure GDA0002480776620000042
is the system noise of the humidity environment model.
Expressing the colony total ratio growth rate and the growth lag phase at the time t as mu (t) and lambda (t), respectively, establishing a process variable vector x and a parameter vector theta of a colony dynamic growth model, as follows:
x＝(N(t),μ(t),λ(t))T
θ＝(C1,C2,C3,C4,C5,Tmin,Tmax,Topt,aw,min,aw,opt)T
assuming that the above model parameter vector θ is constant, the dynamic growth model of the colony for a specific environment is represented by equation (8):
Figure GDA0002480776620000043
wherein f (x, theta) is a dynamic colony growth model consisting of the formulas (1) to (7). The above models in combination can describe the growth of colonies under a specific dynamic environment.
Step 102, secondly, establishing a Bayesian network model of the wheat flour supply chain. And qualitatively selecting key nodes for monitoring the total number of colonies from each link of the wheat flour supply chain according to an expert experience method, and constructing a Bayesian network model based on the key nodes to describe the migration rule of the total number of the colonies in each link. The bayesian network model will serve as the basic framework for carrying out a risk assessment of the total number of colonies on the wheat flour supply chain.
According to expert experience, M key links of colony total number distribution characteristics in the wheat flour supply chain are selected in a setting mode to form a simplified wheat flour supply chain Bayesian network model, as shown in figure 2, for example, the key links in the whole wheat flour supply chain are as follows: the method comprises a raw wheat storage and cleaning link 1, a wheat wetting and cleaning link 2, a grinding and screening link, a packaging link, a finished product storage link and the like, wherein the wheat wetting link relates to a water consumption link, and the packaging link relates to a packaging material link. Expressing the selected key links as node sets
Figure GDA0002480776620000044
Therein node EjRepresents j is 1,2, …, M, and the relation between each key ring is defined by discrete conditional probability event pijRepresenting, and composing event sets
Figure GDA0002480776620000045
Collection
Figure GDA0002480776620000046
And
Figure GDA0002480776620000047
combined establishing Bayesian network model
Figure GDA0002480776620000048
Event pijRepresenting events, sets of events, from the ith link to the jth link
Figure GDA0002480776620000049
An event in (1) generally occurs in an adjacent link. Numbering the links shown in FIG. 2, a Bayesian network structure of the wheat flour supply chain can be established as shown in FIG. 3, where a node represents a key link in the wheat flour supply chain, e.g., E1Representing a coarse wheat storage link, E4Represents the wheat wetting link.
And 103, establishing a colony total number distribution characteristic hybrid Bayesian network model of the wheat flour supply chain.
Nodes of the Bayesian network are defined as discrete modes, and switching between the modes is modeled by Bayesian conditional probability so as to describe probabilistic migration of colony counts on a supply chain. And describing the continuous dynamic behavior of the colony count growth in each mode through a colony dynamic growth model to obtain a hybrid Bayesian network model of the colony count distribution characteristics of the wheat flour supply chain.
The invention takes a Bayesian network model of a wheat flour supply chain as a framework, introduces a microorganism dynamic growth model, considers the continuous dynamic growth of microorganisms in each node and the discrete transfer of microorganisms caused by discrete conditional probability events, and establishes a hybrid Bayesian network model aiming at the total number distribution characteristics of colonies
Figure GDA0002480776620000051
Hybrid Bayesian network model with established colony total number distribution characteristics
Figure GDA0002480776620000052
The following were used:
Figure GDA0002480776620000053
wherein the content of the first and second substances,
Figure GDA0002480776620000054
middle element qjIs node EjM represents the total number of discrete modes, one mode for each node.
For the
Figure GDA0002480776620000055
Dynamic growth mode capable of being divided into bacterial colonies
Figure GDA0002480776620000056
And static growth mode of colony
Figure GDA0002480776620000057
Figure GDA0002480776620000058
Dynamic growth mode in colony
Figure GDA0002480776620000059
Then, the bacterial colony grows by itself according to the growth rule shown in the formulas (1) to (7); in the static growth mode of colony
Figure GDA00024807766200000510
Then, colonies hardly grew by themselves. The switching between modalities is modeled by a bayesian network as follows:
Figure GDA00024807766200000511
wherein t is sampling time;
Figure GDA00024807766200000512
represents node EjMode q at time tjBy modal probability hjRepresents, satisfies
Figure GDA00024807766200000513
Figure GDA00024807766200000514
Represents node EiModality q at time t-1i(t-1) conversion to node EjMode q at time tj(t) probability of switching from mode to mode piijRepresents, satisfies
Figure GDA00024807766200000515
For the
Figure GDA00024807766200000516
There is a discrete-time continuous (variable) dynamic behavior:
Figure GDA00024807766200000517
wherein x (t) and y (t) represent the process equation and the measurement equation, respectively, of a process variable vector x, FjIs a system equation for
Figure GDA00024807766200000518
Fj(x (t-1)) can be obtained by discretizing equations (1) - (7) in time; for the
Figure GDA00024807766200000519
Then there is Fj(x(t-1))＝x(t-1)。
Figure GDA00024807766200000520
Is of mode qjThe process noise of (a) is generated,
Figure GDA00024807766200000521
Figure GDA00024807766200000522
in the form of a normal distribution of the signals,
Figure GDA00024807766200000523
is of mode qjThe noise covariance matrix of the process equation,
Figure GDA00024807766200000524
is of mode qjThe noise-driven term of the process equation.
Figure GDA00024807766200000525
Is of mode qjIs subject to a normal distribution
Figure GDA00024807766200000526
Figure GDA00024807766200000527
Is of mode qjA noise covariance matrix of the measurement equation,
Figure GDA00024807766200000528
is of mode qjThe noise-driven term of the measurement equation. CjIs a matrix of measurement equation coefficients.
Thus, a colony total number distribution characteristic hybrid Bayesian network model of the wheat flour supply chain is established. In the example of the present invention, M is 9, and the total number of colonies of the established wheat flour supply chain is mixed with the structure of the bayesian network model, as shown in fig. 4.
Step two: the colony count distribution characteristics of the wheat flour supply chain are predicted.
Since the wheat flour supply chain is a spatio-temporal sequence chain, the distribution characteristics and the risk degree of aspergillus flavus vary with time and space on the chain. Therefore, the established hybrid Bayesian network model has deductive characteristics in both time and space dimensions, and is mainly reflected in discrete modal evolution and microorganism continuous process variable evolution based on Bayesian theory. The hybrid Bayesian network inference evolution has randomness, and is mainly reflected in dynamic random change of a storage environment and migration probability change caused by uncertain fluctuation of performance of each production link. In order to solve the problems, the invention utilizes a Monte Carlo method and combines a probability statistical rule to obtain the probability distribution characteristics of the total number of each colony on different time-space points.
Step 201, establishing a discrete time inference evolution mechanism of the hybrid Bayesian network. The Bayesian evidence theory and the hybrid system evolution are combined and applied to a discrete time reasoning evolution mechanism of the hybrid Bayesian network, and the distribution characteristics of the later time sequence evaluation object can be predicted through the known detection data at the specific time point.
Given a process variable evolution time horizon [0, K ]]K is a positive integer and represents the total number of sampling time; initial miscellaneous state s of process variable vector0＝(q0,x0)，q0Denotes the initial modality, x0Representing the initial process variable vector, one takes on three dimensions
Figure GDA0002480776620000061
Space(s)
Figure GDA0002480776620000062
Random process of (a), (b), (c), (d]Is the execution of the hybrid bayesian network model,
Figure GDA0002480776620000063
representing a set of accepted real numbers. The execution of the hybrid Bayesian network model of the colony count of the wheat flour supply chain is mainly divided into two parts of continuous process variable evolution and discrete switching evolution.
(1) Continuous process variable evolution of colony counts of wheat flour supply chain is determined by corresponding continuous variation model for each mode for which
Figure GDA0002480776620000064
The medium continuous process variable evolution is determined by equation (11).
In addition, for
Figure GDA0002480776620000065
The continuous process variable evolution of (2) needs modeling of the modal environment, and the modeling is as follows:
Figure GDA0002480776620000066
Figure GDA0002480776620000067
wherein the content of the first and second substances,
Figure GDA0002480776620000068
representation mode qjTime tThe temperature of (a) is set to be,
Figure GDA0002480776620000069
is of mode qjThe set temperature of (a) is set,
Figure GDA00024807766200000610
representation mode qjSystem noise of temperature model, normal distribution
Figure GDA00024807766200000611
Figure GDA00024807766200000612
A noise covariance matrix that is a modal-specific temperature model;
Figure GDA00024807766200000613
representation mode qjThe humidity at the time of the next t,
Figure GDA00024807766200000614
is of mode qjThe set humidity of (a) is set,
Figure GDA00024807766200000615
representation mode qjSystematic noise of humidity model, compliance
Figure GDA00024807766200000616
Figure GDA00024807766200000617
A noise covariance matrix that is a particular modal process equation.
And the total number variable of the colonies in the dynamic growth modes under different environments continuously evolves according to a specific colony dynamic growth model.
(2) Discrete switch evolution of colony counts for wheat flour supply chains, satisfying Bayesian networks, from discrete conditional probability event sets
Figure GDA00024807766200000618
Mid-extraction mode switching probability matrix
Figure GDA00024807766200000619
At time t-1, the modal probabilities are as shown in equation (14):
Figure GDA00024807766200000620
wherein the content of the first and second substances,
Figure GDA00024807766200000621
representing the j-th node as the mode q at the moment t-1jBy modal probability hj(t-1).
At time t, mode qjThe probability of (c) is:
Figure GDA0002480776620000071
wherein h isi(t-1) represents the mode q at the time t-1iThe probability of (c).
(3) The hybrid Bayesian network evolution discrete time execution algorithm comprises the following steps;
step a, setting t to 0 and q (0) to q0,x(0)＝x0；
Step b, if t is less than K, obtaining the expression according to the formulas (14) to (15)
Figure GDA0002480776620000072
Representing the mode at the moment t + 1;
and c, if q (t +1) ═ q (t), acquiring according to the formula (11)
Figure GDA0002480776620000073
Otherwise, according to the switching probability matrix
Figure GDA0002480776620000074
Obtaining
Figure GDA0002480776620000075
As the initial value of the next mode;
step d, t is increased by 1;
and e, if t is equal to K, ending the algorithm.
Step 202, colony count distribution prediction for wheat flour supply chain based on Monte Carlo simulation.
In the step, the hybrid Bayesian network evolution process is simulated for a plurality of times through Monte Carlo simulation, the noise influence can be weakened by combining with the probability statistical rule, more accurate probability distribution of the total number of the bacterial colonies on different time points is obtained, and the uncertainty problem of continuous dynamic growth and discrete transfer of the bacterial colonies is solved. The specific flow steps of colony total number distribution prediction of the wheat flour supply chain based on Monte Carlo simulation in the step are as follows:
2021. setting initial values of model parameters to theta0The number of Monte Carlo simulation particles is I; each particle represents a set of colony counts and model parameters;
2022. at a given time range [0, K]Based on the total number of colonies and the initial value (x) of the model parameter0,θ0) The d-th particle is assigned with an initial value (x)0 (d),θ0 (d)) The following are:
x0 (d)＝x0,θ0 (d)＝θ0(16)
2023. and for the moment t, based on the colony count and the model parameter value at the moment t-1, performing single-step prediction by using an evolution discrete time execution algorithm of the colony count distribution characteristic hybrid Bayesian network of the wheat flour supply chain to obtain a colony count predicted value at the moment t.
2024. If t is less than K, t is increased by 1, the step 2023 is performed, otherwise, the step 2025 is performed.
2025. If d is less than I, d is increased by 1, the step 2022 is performed, otherwise, the step 2026 is performed.
2026. To pair
Figure GDA0002480776620000076
Calculating the probability density function P (x) of the total number of coloniest|(x0,θ0))；
Figure GDA0002480776620000077
Wherein, P (x)t|(x0,θ0) Is based on (x)0,θ0) The probability density function of the total number of colonies of (2) represents a dirac function.
Step three: and calculating the colony total harmfulness of the wheat flour supply chain.
Generally, a food safety risk quantitative evaluation method directly utilizes process variables (such as heavy metal content, pesticide residue content and the like) as quantitative indexes to evaluate the dynamic risk degree of food, and the result is easily influenced by external noise, so that the evaluation is not accurate. Therefore, the invention provides a hazard index for quantitative risk assessment of food supply chain hazards, which can consider uncertainty in the risk assessment and improve the assessment accuracy.
For a dynamic system, assume an n-dimensional space in which its state variables lie
Figure GDA0002480776620000081
Divisible into a secure space
Figure GDA0002480776620000082
And hazardous spaces
Figure GDA0002480776620000083
Figure GDA0002480776620000084
For a certain time t, the system's hazard r (t) is:
Figure GDA0002480776620000085
wherein R (t) is that the dynamic system stays in the hazard space at the time of t
Figure GDA0002480776620000086
The probability of the inner.
And for a promiscuous Bayesian network model, promiscuous states
Figure GDA0002480776620000087
Figure GDA0002480776620000088
Representing a process variable miscellaneous state space. For discrete modes
Figure GDA0002480776620000089
In that
Figure GDA00024807766200000810
Spatially, can be divided into safety spaces
Figure GDA00024807766200000811
And a hazardous space
Figure GDA00024807766200000812
Figure GDA00024807766200000813
At qjIn the state, for a given time t, the degree of harmfulness of the system
Figure GDA00024807766200000814
Can be expressed as:
Figure GDA00024807766200000815
for the total number of colonies in the wheat flour supply chain, the degree of harmfulness refers to the possibility that the content exceeds the standard at a specific moment in different links, as shown in fig. 5, wherein Ω: risk set represents the modal hazard space settings.
In the embodiment of the invention, the mode q is selected9Next, a predicted time length N is setTSetting the standard exceeding threshold of the total number of bacterial colonies
Figure GDA00024807766200000816
And carrying out N on the harmfulness of the total number of the bacterial coloniessSubsampling estimates to predict changes in the risk level of colony population.
Example (b):
the method of the present invention was used to perform a dynamic risk assessment of the total number of colonies in the wheat flour supply chain as shown in FIG. 2.
The method comprises the following steps: and establishing a colony total number hybrid Bayesian network model of the wheat flour supply chain.
Considering the distribution characteristics of the colony counts of the wheat flour supply chain in each link, defining each mode of the colony count hybrid Bayesian network model
Figure GDA00024807766200000817
The distribution characteristic state of the colony count under each key link in the supply chain is respectively shown. According to the qualitative division of the supply chain environment,
Figure GDA00024807766200000818
and other modalities belong to
Figure GDA00024807766200000819
The dynamic model of colony count in each mode has a process equation and a measurement equation. For each modal process equation, it can be obtained from equation (11).
For process noise and noise-driven arrays in the process equation, there is the following equation (20):
Figure GDA00024807766200000820
total number of colonies each modality corresponds to the same measurement equation. The process variables can all be measured directly, i.e. C is taken asjI, then the measurement equation is y (t) ═ x (t) +vv (t), for the process noise and noise driving matrix in the measurement equation, there is equation (21) as follows:
Figure GDA00024807766200000821
wherein I represents a measurement coefficient identity matrix.w、Qw、v、QvAre all set known matrices.
Based on this, the modal switching probability distribution characteristics are set as follows:
Figure GDA0002480776620000091
wherein, trunc (0, Uniform (a)1,b1) Represents a modal switching probability pi11Is characterized by taking a constant interval [ a ]1,b1]The medium random value is used as a switching probability value; trunc (0, Uniform (a)2,b2) Represents a modal switching probability pi33Is characterized by taking a constant interval [ a ]2,b2]The medium random value is used as a switching probability value; trunc (0, Uniform (a)3,b3) Represents a modal switching probability pi44Is characterized by taking a constant interval [ a ]3,b3]The medium random value is used as a switching probability value; trunc (0, Uniform (a)4,b4) Represents a modal switching probability pi55Is characterized by taking a constant interval [ a ]4,b4]The medium random value is used as a switching probability value; trunc (0, Uniform (a)5,b5) Represents a modal switching probability pi77Is characterized by taking a constant interval [ a ]5,b5]The medium random value is used as a switching probability value.
The colony count hybrid bayesian network model parameters in this example are shown in table 1:
TABLE 1 colony count hybrid Bayesian network model parameters
Figure GDA0002480776620000092
Step two: predicting colony total number distribution characteristics of a wheat flour supply chain;
the colony count distribution characteristics were predicted according to formulas (12) to (17). Wherein the evolution diagram and distribution characteristics of the total number of colonies per unit time interval are shown in FIGS. 6 and 7.
Step three: calculating the total colony number harmfulness of the wheat flour supply chain;
calculating q according to equation (19)9Specific time of modalityAnd (4) marking the total colony damage degree, wherein the result is shown in FIG. 8, which shows that the damage degree can effectively reflect the total colony damage evolution of the wheat flour supply chain. The harm degree is increased along with the increase of time, and the change trend of the harm degree can obviously reflect the harm evolution of the total number of bacterial colonies of the wheat flour supply chain.
Through the embodiment, the method can be applied to food safety management of the total number of the bacterial colonies in a wheat flour supply chain, the harm degree of the total number of the bacterial colonies in a later time sequence can be deduced through detected prior data, and the prior data are visually fed back to an operator for corresponding problem handling, so that quality monitoring is carried out on the wheat flour in each link from production to sale.

Claims (3)

1. A dynamic risk assessment method for colony count of a wheat flour supply chain based on a hybrid Bayesian network is characterized by comprising the following steps:
the method comprises the following steps: establishing a hybrid Bayesian network model of colony total number distribution characteristics of a wheat flour supply chain;
a dynamic colony growth model is established by combining the colony growth dynamic model, the dynamic parameter model and the environment model,
the established colony dynamic growth model is as follows:
Figure FDA0002496435390000011
ln(1/λ)＝C0+C1·bw+C2·bw 2+C3·T+C4·T2+C5·T·bw(2)
μ(T,aw)＝μopt·τ(T)·ρ(aw) (3)
Figure FDA0002496435390000012
Figure FDA0002496435390000013
T(t)＝fT(T(t-1))+ωT(6)
Figure FDA0002496435390000014
formula (1) represents a colony growth kinetic model for describing the growth condition of colonies under a specific environment, wherein N (t) represents the total number of colonies at the time t, and N0Expressing the initial value of the total number of colonies, A expressing the maximum value of the total number of colonies, mu expressing the growth rate of the total number of colonies, lambda expressing the growth lag phase of the total number of colonies, and t expressing the time; equation (2) represents a kinetic parametric model of the parameter λ, consisting of temperature T and humidity awDetermination of wherein
Figure FDA0002496435390000015
bwAs an intermediate parameter, C0-C5Is a fitting parameter; equation (3) represents a kinetic parametric model of the parameter μ, also represented by temperature T and humidity awDetermination of μoptExpressing the colony total number to growth rate optimum value; τ (T) represents a temperature factor model; ρ (a)w) Representing a humidity factor model; t ismin、TmaxRespectively representing the minimum and maximum values of the temperature growth interval, ToptA temperature optimum value representing the growth of the microorganism; a isw,minMinimum boundary value of humidity growth interval, aw,optA moisture optimum representing microbial growth; equations (6) and (7) represent the temperature and humidity environment models, respectively, fTRepresenting the temperature dynamic variation function, omegaTIs the system noise of the temperature environment model,
Figure FDA0002496435390000016
a function representing the dynamic variation of the humidity,
Figure FDA0002496435390000017
system noise that is a model of the humidity environment;
expressing the colony total ratio growth rate and the growth lag phase at the time t as mu (t) and lambda (t), respectively, establishing a process variable vector x and a parameter vector theta of a colony dynamic growth model, as follows:
x＝(N(t),μ(t),λ(t))T
θ＝(C1,C2,C3,C4,C5,Tmin,Tmax,Topt,aw,min,aw,opt)T；
the colony dynamic growth model is expressed as f (x, theta), the f (x, theta) is the colony dynamic growth model composed of formulas (1) - (7), x is a process variable vector and is composed of the total number of colonies, the specific growth rate of the total number of colonies and a growth lag phase, and theta is a parameter vector; selecting key nodes for monitoring the total number of colonies from all links of a wheat flour supply chain according to expert experience, and constructing a Bayesian network of the wheat flour supply chain; the bayesian network for constructing the wheat flour supply chain is: the selected key links are represented as node sets
Figure FDA0002496435390000021
Therein node EjRepresents j-th key link, j is 1,2, …, M, and the association between each key link is composed of discrete conditional probability event pijRepresenting, and composing event sets
Figure FDA0002496435390000022
Collection
Figure FDA0002496435390000023
And
Figure FDA0002496435390000024
combined establishing Bayesian network model
Figure FDA0002496435390000025
Event pijRepresenting events from the ith link to the jth link, wherein each node in the Bayesian network is a discrete mode, each node corresponds to one mode, the switching between the modes is modeled by Bayesian conditional probability, and the total number of colonies under each discrete mode grows continuous dynamic behavior through the colony movementDescribing by an ecological growth model, obtaining a hybrid Bayesian network model of the colony total number distribution characteristics of the wheat flour supply chain, and expressing as
Figure FDA0002496435390000026
Representative node EjM represents the total number of discrete modes of the population count distribution characteristic of (a); the promiscuous state of the promiscuous bayesian network model is denoted as s ═ q, x,
Figure FDA0002496435390000027
step two: predicting colony total number distribution characteristics of a wheat flour supply chain;
firstly, establishing a discrete time reasoning evolution mechanism of a hybrid Bayesian network model of the total number of colonies in a wheat flour supply chain, wherein the discrete time reasoning evolution mechanism is divided into a continuous process variable evolution part and a discrete switching evolution part; in discrete switch evolution, a discrete set of conditional probability events across key segments of the wheat flour supply chain
Figure FDA0002496435390000028
Middle extraction mode switching probability matrix pi ═ piij]M×M，πijRepresentation mode qiSwitching to mode qjThe modal probability of the next moment is calculated by combining the modal switching probability and the modal probability of the current moment; then, predicting the colony count distribution of the wheat flour supply chain based on Monte Carlo simulation;
step three: evaluating the total colony damage degree according to the predicted total colony distribution of the wheat flour supply chain;
in the step one, each mode qjUnder a dynamic growth mode of the bacterial colony, self-growing according to the dynamic growth model of the bacterial colony;
the switching between the setup modalities is as follows:
Figure FDA0002496435390000029
Figure FDA00024964353900000210
wherein, t is the sampling time,
Figure FDA00024964353900000211
represents node EjMode q at time tjBy modal probability hjRepresents and satisfies
Figure FDA00024964353900000212
Figure FDA00024964353900000213
Represents node EiModality q at time t-1i(t-1) conversion to node EjMode q at time tj(t) probability of switching from mode to mode piijRepresents, satisfies
Figure FDA00024964353900000214
For the
Figure FDA00024964353900000215
All have discrete-time continuous dynamic behavior, expressed as follows:
Figure FDA00024964353900000216
Figure FDA00024964353900000217
where x (t) and y (t) represent the process and measurement equations, respectively, for a process variable vector x, where x is expressed as (n (t), μ (t), λ (t))TN (t) represents the total number of colonies at time t, μ (t) represents the ratio of the total number of colonies at time t to the growth rate, and λ (t) represents the growth lag phase of the total number of colonies at time t; fjIndicating colony dynamicsSystem equation of growth model, Fj(x (t-1)) is obtained by discretizing the system equation in time, Fj(x(t-1))＝x(t-1)；
Figure FDA00024964353900000218
Is of mode qjThe process noise of (a) is generated,
Figure FDA00024964353900000219
is of mode qjA noise-driven term of the process equation;
Figure FDA00024964353900000220
is of mode qjThe noise of the measurement of (2) is,
Figure FDA00024964353900000221
is of mode qjMeasuring a noise-driven term of an equation; cjIs a coefficient matrix of the measurement equation;
in the second step, the continuous process variable evolution of the hybrid Bayesian network model of the colony total number of the wheat flour supply chain is determined by the continuous change model corresponding to each discrete mode, and the mode q is matchedjIn the continuous process variable evolution, the model environment needs to be modeled as follows:
Figure FDA0002496435390000031
Figure FDA0002496435390000032
wherein the content of the first and second substances,
Figure FDA0002496435390000033
representation mode qjThe temperature at the time of the next t,
Figure FDA0002496435390000034
is of mode qjThe set temperature of (a) is set,
Figure FDA0002496435390000035
representation mode qjSystem noise of the temperature model;
Figure FDA0002496435390000036
representation mode qjThe humidity at the time of the next t,
Figure FDA0002496435390000037
is of mode qjThe set humidity of (a) is set,
Figure FDA0002496435390000038
representation mode qjSystem noise of the humidity model;
in the second step, the discrete switching evolution of the hybrid Bayesian network model of the colony count of the wheat flour supply chain is set as the mode q at the time t-1iHas a probability of hi(t-1), then at time t, the mode qjProbability h ofj(t) is:
Figure FDA0002496435390000039
wherein the content of the first and second substances,
Figure FDA00024964353900000310
a hybrid bayesian network model characterizing the colony count distribution in the wheat flour supply chain.
2. The method as claimed in claim 1, wherein the step two, the colony count distribution prediction of the wheat flour supply chain based on Monte Carlo simulation comprises the following steps:
step 2021, setting initial values θ of model parameters0The number of Monte Carlo simulated particles I; each particle represents a set of colony counts and model parameters;
step 2022, at a given time range [0, K ]]Based on the total number of colonies and the initial value (x) of the model parameter0,θ0) The d-th particle is assigned with an initial value (x)0 (d),θ0 (d)) The following are:
x0 (d)＝x0,θ0 (d)＝θ0
step 2023, for the time t, based on the total number of colonies and the model parameter at the time t-1, performing single-step prediction by using the discrete switching evolution of the hybrid bayesian network of the total number of colonies of the wheat flour supply chain to obtain a predicted value of the total number of colonies at the time t;
step 2024, if t is less than K, t is increased by 1, the step 2023 is returned, otherwise, the step 2025 is performed;
step 2025, if d is less than I, increasing d by 1, returning to step 2022, otherwise, performing step 2026;
step 2026, for
Figure FDA00024964353900000311
Calculating the probability density function P (x) of the total number of coloniest|(x0,θ0))；
Figure FDA00024964353900000312
Wherein the dirac function is represented.
3. The method of claim 1, wherein the step three comprises the steps of:
for discrete modes
Figure FDA00024964353900000313
In n-dimensional space
Figure FDA00024964353900000314
Upper, is divided into a safe space
Figure FDA00024964353900000315
And a hazardous space
Figure FDA00024964353900000316
In mode qjThe degree of harm of the total number of colonies at time t is expressed as
Figure FDA00024964353900000317
Wherein x (t) represents the process variable vector at time t;
setting the over-standard threshold of the total number of the bacterial colonies for the selected modes
Figure FDA0002496435390000041
And setting the prediction duration, and predicting the probability that the content exceeds the standard at a specific moment in a corresponding link in the wheat flour supply chain by sampling and estimating the harm degree of the total number of the colonies for multiple times.
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