# US 12,002,549 B2 · Knowledge reuse-based method and system for predicting cell concentration in fermentation process

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- Number: US 12,002,549 B2
- Document ID: US12002549B2
- Status: Granted
- Kind: B2
- Application number: 18/220,633
- Filed: 2023-07-11
- Published: 2024-02-01
- Granted: 2024-06-04
- Earliest claimed: 2022-07-26
- Assignees: Jiangnan University
- Applicants: Jiangnan University
- Inventors: Xiaoli Luan; Xiaojing Ping; Haiying Wan; Fei Liu
- Web page: https://patentgrep.com/patent/US12002549B2

## CPC

- G16B 5/30: Dynamic-time models
- C12M 41/48: {Automatic or computerized control (automatic analysis G01N35/00)}
- G16B 40/20: Supervised data analysis
- Y02P 90/30: Computing systems specially adapted for manufacturing
- G16B: BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
- C12M: APPARATUS FOR ENZYMOLOGY OR MICROBIOLOGY; {APPARATUS FOR CULTURING MICROORGANISMS FOR PRODUCING BIOMASS, FOR GROWING CELLS OR FOR OBTAINING FERMENTATION OR METABOLIC PRODUCTS, i.e. BIOREACTORS OR FERMENTERS}
- Y02P: CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS

## Abstract

The present invention provides a knowledge reuse-based method and system for predicting a cell concentration in a fermentation process. The method includes: constructing a cell concentration soft sensor universal model in a fermentation process; acquiring and preprocessing process data of a fermentation stage A; determining a cell concentration soft sensor model of the fermentation stage A; designing a cell concentration online soft sensor of a fermentation stage B; and predicting a cell concentration of the fermentation stage B according to the cell concentration online soft sensor of the fermentation stage B. The present invention resolves the problems of weak generalization of a cell concentration soft sensor model and high costs of establishing models for fermentation stages separately, thereby improving the prediction accuracy of a cell concentration soft sensor.

## Claims

### Claim 1

A knowledge reuse-based method for predicting a cell concentration in a fermentation process, comprising:
S1: constructing a cell concentration soft sensor universal model in a fermentation process, wherein the fermentation process is divided into four stages in time order: a lag phase, an exponential growth phase, a stationary phase, and a decline phase, and for two stages that occur successively, it is defined that a former stage is a fermentation stage A and a latter stage is a fermentation stage B;
S2: acquiring and preprocessing process data of the fermentation stage A;
S3: determining a cell concentration soft sensor model of the fermentation stage A based on the cell concentration soft sensor universal model in combination with a process data result of the fermentation stage A after the preprocessing;
S4: acquiring process data of the fermentation stage B, and after preprocessing, designing a cell concentration online soft sensor of the fermentation stage B with the cell concentration soft sensor model of the fermentation stage A; and
S5: predicting a cell concentration of the fermentation stage B according to the cell concentration online soft sensor of the fermentation stage B,
wherein a method for designing a cell concentration online soft sensor of the fermentation stage B in step S4 is:
S41: setting a parameter estimation of the cell concentration soft sensor model of the fermentation stage B to:
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wherein at a moment k+τ+1, for the cell concentration soft sensor model of the fermentation stage B, a delay is τB=τA, orders are pB=pA and qB=qA, the parameter estimation is {circumflex over (θ)}k+τ+1=[â, ⋅ ⋅ ⋅ , âpB, {circumflex over (b)}1, ⋅ ⋅ ⋅ , {circumflex over (b)}qB]T, â1, ⋅ ⋅ ⋅ , âpB, {circumflex over (b)}1, ⋅ ⋅ ⋅ , {circumflex over (b)}qB is an estimate of each parameter in the parameter vector of the fermentation stage B at the moment k+τ+1, where a is a parameter of a autoregressive model and b is a parameter of a moving model, {circumflex over (θ)}A is a parameter estimation of the fermentation stage A, Ĥk+τ+1 is a gain matrix of the cell concentration soft sensor model of the fermentation stage B at the moment k+τ+1, Ek+τ+1 is an innovation vector at the moment k+τ+1, Yk+τ+1 is a cell concentration matrix of the fermentation stage B at the moment k+τ+1, and Xk+τ+1 is an input matrix of the fermentation stage B at the moment k+τ+1;
S42: calculating the gain matrix Ĥk+τ+1 of the cell concentration soft sensor model of the fermentation stage B in step S41;
S43: designing the cell concentration online soft sensor of the fermentation stage B based on a parameter estimation vector {circumflex over (θ)}k+τ+1 and the gain matrix Ĥk+τ+1 of the cell concentration soft sensor model of the fermentation stage B.

### Claim 2 (depends on 1)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 1, wherein a method for constructing a cell concentration soft sensor universal model in a fermentation process in step S1 comprises:
S11: selecting a dilution ratio as an auxiliary variable based on dynamic characteristics of the fermentation process, and setting the cell concentration soft sensor model to:
yk+τ+a1yk+τ−1+ ⋅ ⋅ ⋅ +apyk+τ−p=b0uk+b1uk−1+ ⋅ ⋅ ⋅ +bquk−q+vk+τ,
wherein k is a moment, τ is the delay of the soft sensor model, p and q are the orders of the soft sensor model, a and b are coefficients, yk+τ is a cell concentration at a moment k+τ, uk is an auxiliary variable at the moment k, vk+τ is a cell concentration measurement noise at the moment k+τ, and a type of the noise is selected from white noises satisfying Gaussian distribution, t distribution, and Poisson distribution; and
S12: performing vector transformation on the cell concentration soft sensor model, to obtain the cell concentration soft sensor universal model:
yk+τ=xk+τTθ+vk+τ,
wherein an input vector is xk+τ=[yk+τ−1 yk+τ−2 ⋅ ⋅ ⋅ yk+τ−p uk ⋅ ⋅ ⋅ uk−q]T, and a parameter is θ=[a1, ⋅ ⋅ ⋅ , ap, b0, ⋅ ⋅ ⋅ , bq]T.

### Claim 3 (depends on 1)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 1, wherein a method for preprocessing process data of the fermentation stage A in step S2 is:
eliminating a nonnumerical sample point in the process data of the fermentation stage A, and eliminating abnormal working condition data according to a working condition record; eliminating an outlier in the process data of the fermentation stage A; filling a missing value in the process data of the fermentation stage A; and removing a dimensional difference between an auxiliary variable and a quality variable in the fermentation stage A.

### Claim 4 (depends on 1)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 1, wherein a method for calculating the gain matrix Ĥk+τ+1 of the cell concentration soft sensor model of the fermentation stage B in step S42 comprises:
step 1: defining a loss function of a knowledge reuse-based soft sensor model:
J=trace{E[(θB−{circumflex over (θ)}k+τ+1)(θB−{circumflex over (θ)}k+τ+1)T]},
wherein θB is an actual parameter value of the fermentation stage B, {circumflex over (θ)}k+τ+1 is the parameter estimation of the fermentation stage B at the moment k+τ+1, E[⋅] is an averaging operation, trace {⋅} is a trace operation of a matrix, J is a loss function with respect to Ĥk+τ+1; and
step 2: calculating the gain matrix Ĥk+τ+1 based on a method of minimizing the loss function:
Ĥk+τ+1=(Fk+τ+1+{circumflex over (D)}k+τ+1−1)−1Xk+1TΣk+1−1,
wherein Fk+τ+1=Xk+1TΣk+τ+1−1Xk+1, {circumflex over (D)}k+τ+1−1={circumflex over (d)}k+τ+1{circumflex over (d)}k+τ+1T,
Xk+1T{circumflex over (d)}k+τ+1=Ek+τ+1,
Fk+τ+1 is a Fisher information matrix of the soft sensor model of the fermentation stage B at the moment k+τ+1, Σk+1−1 is an inverse of a measurement noise covariance matrix of the fermentation stage B at a moment k+1, {circumflex over (D)}k+τ+1− is a difference covariance matrix between the fermentation stage A and the fermentation stage B at the moment k+τ+1, and {circumflex over (d)}k+τ+1 is a parameter difference between the fermentation stage A and the fermentation stage B at the moment k+τ+1.

### Claim 5 (depends on 1)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 1, wherein a method for designing the cell concentration online soft sensor of the fermentation stage B based on a parameter estimation vector {circumflex over (θ)}k+τ+1 and the gain matrix Ĥk+τ+1 of the cell concentration soft sensor model of the fermentation stage B in step S43 comprises:
step 1: initializing {circumflex over (d)}0, G0, and Q0 at an initial moment of the fermentation stage B;
wherein {circumflex over (d)} is a model parameter difference between the fermentation stage A and the fermentation stage B, {circumflex over (d)}0 and G0 are (pB+qB)-dimensional zero vectors, and Q0 is a (pB+qB)×(pB+qB)-dimensional zero matrix;
step 2: solving the cell concentration online soft sensor of the fermentation stage B, specifically denoted as follows:
{circumflex over (θ)}k+τ+1={circumflex over (θ)}A+Pk+τ+1Gk+τ+1,
where
Fk+τ+1=Fk+τ+σk+1−2xk+τ+1xk+τ+1T=Qk+τ+fk+τ+1,
Gk+τ+1=Gk+τ+σk+τ+1−2xk+τ+1(yk+τ+1−xk+τ+1T{circumflex over (θ)}A)=Gk+τ+gk+τ+1,
Pk+τ+1≤(Fk+τ+1+{circumflex over (D)}k+τ+1−1)−1,
{circumflex over (θ)}A is the parameter estimation of the fermentation stage A, {circumflex over (θ)}k+τ+1 is the parameter estimation of the fermentation stage B at the moment k+τ+1, σk+τ+1−2 is a measurement noise variance of a cell concentration of the fermentation stage B at the moment k+τ+1, xk+τ+1 is an input vector of the fermentation stage B at the moment k+τ+1, yk+τ+1 is a cell concentration of the fermentation stage B at the moment k+τ+1, and when new measurement data is acquired, Fk+τ+1 has updated data quality of the fermentation stage B, and Gk+τ+1 and Pk+τ+1 have updated a difference between the fermentation stages A and B; and
step 3: before the fermentation stage B ends, when new measurement data is acquired, sequentially calculating Fk+τ+1, Gk+τ+1, and Pk+τ+1, and updating a parameter {circumflex over (θ)}k+τ+1 of the soft sensor model.

### Claim 6 (depends on 2)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 2, wherein a method for predicting a cell concentration of the fermentation stage B according to the cell concentration online soft sensor of the fermentation stage B in step S5 comprises:
introducing the parameter estimation {circumflex over (θ)}k+τ+1 of the soft sensor into the soft sensor universal model yk+τ=xk+τTθ+vk+τ, to obtain a predicted cell concentration value ŷk+τ+1 of the fermentation stage B:
ŷk+τ1=xk+τ+1T{circumflex over (θ)}k+τ+1,
wherein θ is a parameter of the universal model, {circumflex over (θ)}k+τ+1 is the parameter estimation of the fermentation stage B at the moment k+τ+1, xk+τ is the input vector at the moment k+τ, vk+τ is the cell concentration measurement noise at the moment k+τ, ŷk+τ+1 is the predicted cell concentration value of the fermentation stage B at the moment k+τ+1.

### Claim 7 (depends on 4)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 4, wherein the method of minimizing the loss function is selected from a feasible direction method, a quadratic programming method, a particle swarm algorithm, Bayesian optimization, and a random search and gradient descent method.

### Claim 8 (depends on 4)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 4, wherein a method for calculating the inverse of the noise covariance matrix is selected from a Kalman filter and an extended form thereof, statistical hypothesis testing, and regression analysis.

### Claim 9 (depends on 4)

The knowledge reuse-based method for predicting a cell concentration in a fermentation process according to claim 4, wherein a method for calculating the model parameter difference {circumflex over (d)} between the fermentation stage A and the fermentation stage B is selected from a recursive least squares method, a recursive extended least squares method, a recursive maximum likelihood method, a random Newton method, Kalman estimation, a prediction error method, and a long short-term memory network.