WO2023077683A1 - Cell culture state on-line estimation and replenishment optimization regulation and control method - Google Patents

Cell culture state on-line estimation and replenishment optimization regulation and control method Download PDF

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WO2023077683A1
WO2023077683A1 PCT/CN2022/073489 CN2022073489W WO2023077683A1 WO 2023077683 A1 WO2023077683 A1 WO 2023077683A1 CN 2022073489 W CN2022073489 W CN 2022073489W WO 2023077683 A1 WO2023077683 A1 WO 2023077683A1
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cell
state
cell culture
estimation
optimal
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刘飞
吴杰
栾小丽
赵顺毅
陈珺
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江南大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/25—Design optimisation, verification or simulation using particle-based methods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
    • G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
    • G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
    • G01N21/359—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using near infrared light
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/62—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light
    • G01N21/63—Systems in which the material investigated is excited whereby it emits light or causes a change in wavelength of the incident light optically excited
    • G01N21/65—Raman scattering
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
    • G16B5/00—ICT specially adapted for modelling or simulations in systems biology, e.g. gene-regulatory networks, protein interaction networks or metabolic networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]

Definitions

  • the invention relates to the technical field of biomanufacturing control, in particular to a method for online estimation of cell culture status and optimization of feeding regulation.
  • the formation of products is closely related to the growth and metabolism of bacterial cells, and the supply of nutrient substrates directly affects cell growth and metabolism.
  • the feeding of substrates can avoid substrate inhibition, cell starvation and metabolism. Repression, which optimizes the feed rate of substrates according to the different conditions of bacterial cell growth and product synthesis, provides an optimal growth environment for microorganisms, and is an effective means of regulation to improve the efficiency of biomanufacturing processes.
  • the feeding method of the cell culture process initially relied on manual experience, and gradually studied according to the mathematical model of cell culture and production goals to solve the optimal feeding trajectory in advance, and then use the feeding trajectory as the process control curve in the actual production process.
  • actual cell growth involves complex physical, chemical and biological reactions, and its metabolic flow and kinetic evolution are complex.
  • the optimal process curve obtained based on mathematical models may not be able to achieve optimal results. Even seriously affect cell metabolism and product synthesis.
  • the optimization control method of cell culture and product production process based on mathematical model is essentially an open-loop control, which fails to feed back the optimization effect and adjust the future feeding strategy.
  • the purpose of the present invention is to provide a method for online estimation of cell culture status and optimization of feeding regulation, which integrates estimation of cell growth status, optimization of production benefits, online process control and real-time feedback of results, and can sense the growth status of bacterial cells in a timely manner.
  • Rolling optimized feeding at different stages provides an optimal culture environment and maximizes economic benefits.
  • the present invention provides a method for online estimation of cell culture status and optimization of feed regulation, comprising the following steps:
  • establishing a cell culture state model specifically includes the following steps:
  • x(k), u(k) are the cell state and feeding rate at time k, respectively, and f[x(k), u(k)] is the linear or nonlinear relationship between x(k), u(k) function, considering the disturbance noise of the cultivation process as w(k+1).
  • step S2 specifically includes the following steps:
  • x(T f ), u(T f ) are the cell state and feeding rate at the final moment, respectively, and m[x(T f ),u(T f )] is about x(T f ), u(T f ) is a linear or nonlinear function corresponding to the volume of the culture solution, n[x(k), u(k)] is a linear or nonlinear function about x(k), x(k) corresponding to the substrate concentration, u max and u min denote the upper and lower limits of the cell feeding rate u(k) at time k, respectively.
  • the economic benefit optimization target includes:
  • the optimization objective J is defined as the maximum output P(T f ) at the end point.
  • the cell culture state x(k) in is related to the feeding rate u(k), that is, the benefit optimization objective is expressed as follows:
  • L[x(k),u(k)] is the functional relationship between the terminal output, cell culture state and feeding rate
  • the cost factor is introduced, and the economic benefit optimization goal selects the ratio of the net profit of a batch production to the production time, that is, the process benefit.
  • the specific benefit optimization goal is expressed as follows:
  • r is the sales price of the unit product
  • c is the cost price of the unit feed
  • T p is the time interval between two adjacent production batches of the same bioreactor
  • the conversion rate from substrate to product is pursued, and the economic benefit optimization goal selects the ratio of the product amount of a batch to the total amount of feed, that is, the product yield.
  • the specific benefit optimization goal is expressed as follows :
  • an indirect measurement method is used to estimate the cell state, or a direct measurement method is used to obtain an estimated value of the cell state at the current moment.
  • the indirect measurement method when the indirect measurement method is selected to estimate the cell state, it includes the following steps: based on biochemical mechanism or experiment, analyze and synthesize the relationship between the basic variable y(k) in the bacterial cell and the cell state x(k), Construct the measurement equation:
  • g[x(k)] is the constructed measurement function, assuming that v(k) is the measurement noise, first measure y(k) by glucosamine method, ergosterol method or nucleic acid method, and then obtain indirectly by estimation method Estimated cell state at the current moment
  • the estimation method selects Kalman filter method, extended Karl One of the methods of Mann filter, rolling time domain estimation, unscented Kalman filter, Bayesian estimation, particle filter or finite impulse response filter is used to estimate the cell state. Predict the cell state, update and correct the prediction to obtain the estimated value of the cell state at the current moment according to the current measured value of the basic variable y(k)
  • the extended Kalman filter algorithm is used to estimate the cell culture state, including the following steps:
  • P(k) is the estimated value of covariance at time k
  • Q is the covariance matrix of process noise
  • F(k) is the state transition matrix, if the cell culture model is nonlinear, then
  • solving the optimal feed rate trajectory satisfying the constraint conditions under the optimized economic benefits specifically includes the following steps:
  • the nonlinear programming optimization algorithm is used to solve the economic benefit J optimization problem satisfying the constraints, that is, to solve Get the optimal feeding trajectory U k , where the optimization algorithm includes interior point method, exterior point method, sequential quadratic programming method, genetic algorithm and particle swarm algorithm;
  • the present invention takes the economic benefit of the biomanufacturing process as the optimization target, and is different from the commonly used optimal feeding method, and directly integrates production optimization, online control and feedback mechanism into one framework for implementation, at each sampling time , estimate the state of cell culture through the current production basic variables, use the mathematical model to predict the future state and economic benefits, use the feeding rate in the future production time domain as the decision variable to optimize the benefits, and implement the optimization results in time.
  • the present invention is based on the measurable state of cell culture. Since most states of the cell growth process (such as intracellular metabolites, cell concentration, substrate concentration, etc.) The measurement of variables, and then use the state estimation method to estimate the cell state that is difficult to obtain online. On the other hand, advanced measuring instruments such as Raman spectroscopy, near-infrared spectroscopy, and emission spectroscopy can be used to directly measure the state of some cell cultures. , these estimation and measurement tools provide the support for rolling optimized feeding.
  • Fig. 1 is a schematic diagram of the implementation process of the present invention
  • Fig. 2 is to utilize fructose to produce polyhydroxybutyric acid process to optimize feeding rate locus figure;
  • Fig. 3 is to utilize urea to produce polyhydroxybutyric acid process to optimize feeding rate locus figure
  • Fig. 4 is the graph of the change of bacterial cell specific growth rate
  • Fig. 5 is the state change diagram of substrate concentration in the production process of polyhydroxybutyric acid
  • Fig. 6 is a diagram showing the state change of fructose concentration during the production of polyhydroxybutyric acid
  • Fig. 7 is a diagram of the state change of urea concentration in the production process of polyhydroxybutyric acid
  • Fig. 8 is a graph showing the state change of fermentation broth volume during the production of polyhydroxybutyric acid.
  • the present invention provides a method for online estimation of cell culture status and optimization of feed regulation, comprising the following steps:
  • the present invention establishes the cell culture state model (1), analyzes the production process requirements, and determines the constraint conditions (2)-(4) that the cell culture manufacturing process needs to meet; selects the economic benefit optimization target , if the feeding cost is low, use the maximum yield (5) as the economic benefit index; if the pursuit of high yield and take into account the substrate cost, use the maximum process benefit (6) as the index; if the conversion rate from substrate to product is emphasized, then Select the maximum product yield (7) as the benefit index. Benefit optimization depends on the state of cell culture.
  • the first measurement method is to construct the measurement equation (8), by measuring the basic variable y(k) related to the cell state, and indirectly obtain the estimated value of the cell state by the estimation method
  • the second measurement method is to use advanced spectral technology to directly measure the estimated value of the state
  • the extended Kalman filter and other estimation methods are used to predict the current state from the previous cell state according to (9) (10), and then according to (11)-(13) from the current measurement of the basic variables value, update the revised predicted value to obtain the estimated value Estimated by cell state and the proposed feeding rate U k as input, use the computer numerical solution method to solve the cell state model, and obtain the cell state vector in the future; then use the nonlinear programming optimization method to solve A new optimal feeding trajectory U k is obtained.
  • Implement u(k) at the current moment in the feeding trajectory U k in the cell culture production process, and repeat the above process until the production process ends.
  • the whole process involves the feed regulation technology of the nutrient substrate in the biomanufacturing process.
  • Optimizing the feed rate of the substrate according to the different conditions of bacterial cell growth and product synthesis is an effective regulation method to improve the efficiency of the biomanufacturing process.
  • the present invention takes the economic benefits of the biomanufacturing process as the optimization goal, integrates the cell culture process requirements, growth state estimation, online rolling optimization, real-time implementation and other links in a framework, and at each sampling time , estimate the state of cell culture through the current production variables, use the mathematical model to predict the future state and economic benefits, use the feeding rate in the future production time domain as the decision variable to optimize the benefits, and implement the optimization results in time, so rolling operation, this method is suitable for Cell culture models and processes require known biomanufacturing processes.
  • Step 1 Establish a mathematical model of the cell culture state:
  • x(k) and u(k) are the cell state and feeding rate at time k, respectively, f[ ] is a linear or nonlinear function, and w(k+1) is considered to be the disturbance noise in the culture process.
  • the Euler method is used to discretize it with T f sampling intervals.
  • Step 2 Determine the constraints of the cultivation process:
  • m[ ] and n[ ] are linear or nonlinear functions, u max and u min represent the upper limit and lower limit of the feeding rate respectively;
  • formula (2) represents the terminal constraints of the culture process, such as the volume of culture medium in production Do not overflow the bioreactor at the end;
  • formula (3) represents the restrictive conditions that need to be met throughout the manufacturing process, such as in order to avoid the metabolic inhibition of bacterial cells caused by excessive substrate concentration, the substrate concentration in the production process must be is lower than a certain upper limit;
  • formula (4) is the feed rate constraint imposed by considering the operating capacity of the actual equipment and the impact on the growth of bacterial cells;
  • Step 3 Select the economic benefit optimization target:
  • the economic benefit objectives of the biomanufacturing process are diverse and should be set according to the actual needs of production. If the substrate cost is low, the economic benefit optimization objective is to maximize the amount of optional products, and the optimization objective J is defined as the maximum output P(T f ) at the end point, and the end point output is generally the product of the product concentration at the end time and the volume of the fermentation broth, and is related to The cell culture state x(k) in the production process is related to the feeding rate u(k), that is, the benefit index is expressed as follows:
  • L[ ⁇ ] is to describe the functional relationship between the end point production, cell culture state and feed rate.
  • the cost factor is introduced, and the economic benefit optimization goal selects the ratio of the net profit of a batch production to the production time, that is, the process benefit.
  • the specific benefit indicators are expressed as follows:
  • r is the sales price of the unit product
  • c is the cost price of the unit feed
  • Tp is the time interval between two adjacent production batches of the same bioreactor, that is, the time required for tank release, cleaning, sterilization, inoculation, etc. operating time.
  • the conversion rate of substrate to product is pursued, and the economic benefit optimization goal is to choose the ratio of the product amount of a batch to the total amount of fed materials, that is, the product yield.
  • the specific benefit indicators are expressed as follows:
  • Cost-effective optimization goals also include best cell growth, lowest by-products, and lowest energy consumption.
  • Step 4 Select the cell culture state measurement method:
  • the end-point yield P(T f ), process efficiency, conversion rate and other indicators of manufacturing directly depend on the state of cell culture, and the detection of cell culture state is difficult.
  • g[ ⁇ ] is the constructed measurement function, assuming that v(k) is the measurement noise.
  • Step 1 Spectral preprocessing, the methods include smoothing, wavelet transform, multivariate scattering correction (MSC), standard normal variable transformation (SNV), orthogonal signal correction (OSC) , derivative algorithm (Der), etc.; step 2: selection of characteristic bands, the methods include continuous projection method (SPA), partial least squares method (PLS), uninformative variable elimination method (UVE), etc.; step 3: spectral data and
  • the establishment of the cell culture state mapping model includes principal component regression (PCR), partial least squares regression (PLSR), support vector machine regression (SVMR), deep learning methods, etc.
  • Step 5 Estimation of cell state based on state model and measurement equation:
  • the cell state can be obtained indirectly by using the measurable basic variables and selecting estimation or filtering methods.
  • estimation or filtering methods According to different situations such as the form of the state model, the process and the statistical distribution of the measurement noise, Kalman filter, extended Kalman filter, rolling time domain estimation, unscented Kalman filter, Bayesian estimation, particle filter, finite impulse response can be used State estimation methods such as filtering and corresponding extended forms.
  • f[ ] and g[ ] are nonlinear in the biological manufacturing process.
  • the extended Kalman filter algorithm is used to estimate the cell culture state as follows:
  • Step 1 Prediction of cell state and its covariance:
  • P(k) is the estimated value of covariance at time k
  • Q is the covariance matrix of process noise
  • F(k) is the state transition matrix, if the cell culture model f[ ⁇ ] is nonlinear, then
  • Step 2 Update of cell state and its covariance:
  • Step 6 Online solution and rolling implementation of optimal feeding rate trajectory:
  • the benefit index J is related to the future state and the feeding rate trajectory, based on the estimated value of the state at the current moment and the required rate trajectory U k , use the production process state model to iteratively calculate the cell state in the future time domain, and then calculate the benefit index.
  • Step 3 According to the future X k+1 , use nonlinear programming optimization method to solve Get the new feeding trajectory U k , the optimization algorithm includes interior point method, exterior point method, sequential quadratic programming method, genetic algorithm, particle swarm algorithm, etc.;
  • Step 4 Implement u(k) at the current moment in the feeding trajectory U k in the cell culture production process
  • Step 6 If you use the fourth step scheme 2 to directly measure and obtain the cell state value Then go to step 9 of the sixth step; otherwise, apply the solution 1 of the fourth step and go to the following step 7;
  • Step 7 From step 1 of the fifth step, predict the state of the current moment from the state of the cell at the previous moment;
  • Step 8 Use step 2 of the fifth step to update and correct the predicted value from the newly collected measured value y(k) to obtain the estimated value of the cell state
  • Step 9 If the production process is not over, go to Step 2 of Step 6.
  • the online estimation and optimization control method of cell culture state in biomanufacturing proposed by the present invention is applied to the process of producing polyhydroxybutyric acid (PHB) by fed-batch fermentation with fructose and urea, and its continuous kinetic state model is:
  • x 1 is the concentration of non-PHB substances in the cell
  • x 2 is the concentration of product PHB
  • x 3 is the concentration of fructose
  • x 4 is the concentration of urea
  • x 5 is the volume of fermentation broth
  • u 1 is the feed rate of fructose
  • u 2 is the feed rate of urea.
  • the input constraints are:
  • the covariance matrix is set to
  • the method of the present invention is used to realize the optimization and regulation of cell culture in the PHB manufacturing process, and its optimal feeding trajectory, specific growth rate and state changes are shown in Figure 2- Figure 8 respectively. It can be seen from Figures 2-8 that the entire manufacturing process can be roughly divided into two stages: cell growth and product synthesis.
  • the first stage is the cell growth stage (0-25h).
  • fructose and urea are supplemented at the same time as a carbon source and a nitrogen source, respectively, to maintain the growth of the cell at the maximum specific growth rate, wherein between 0-10h, Since the initial substrate concentration in the culture medium was sufficient for the growth of the bacteria, the feeding amount of fructose and urea was very small, and then the feeding was gradually increased with the consumption of nutrients.
  • the second stage is the product synthesis stage (25-49h). Due to the reduction of the nitrogen source utilization capacity of the bacteria, the number of bacteria could not be obtained in the early stage.
  • the online rolling optimization feeding method proposed by the present invention can timely regulate the flow acceleration rate of the nutrient substrate according to the actual situation of bacterial cell culture, thereby effectively improving the yield of biomanufacturing and increasing economic benefits.

Abstract

Disclosed is a cell culture state on-line estimation and replenishment optimization regulation and control method. The method comprises the following steps: establishing a cell culture state model; determining a constraint condition that must be met during cell culturing; selecting an economic benefit optimization target; performing cell state estimation, and obtaining a cell state estimation value at a current moment; solving the cell culture state model, and obtaining a cell state vector at a future moment; by using nonlinear programming, obtaining an optimal replenishment rate trajectory meeting the constraint condition; and during cell culture production, implementing the replenishment rate at the current moment in the replenishment rate trajectory, and repeatedly optimizing and solving the replenishment rate trajectory until production is finished. In the present invention, cell growth state estimation, production benefit optimization, process on-line control, and real-time result feedback are integrated into a whole. Bacterial cell growth conditions can be sensed promptly, rolling replenishment optimization is performed for different stages, and the optimal culture environment is provided, thus maximizing the economic benefits.

Description

一种细胞培养状态在线估计及优化补料调控方法A method for online estimation of cell culture status and optimal feed regulation 技术领域technical field
本发明涉及生物制造控制技术领域，具体涉及一种细胞培养状态在线估计及优化补料调控方法。The invention relates to the technical field of biomanufacturing control, in particular to a method for online estimation of cell culture status and optimization of feeding regulation.
背景技术Background technique
在生物制造过程中，产物的形成与菌体细胞的生长和代谢密切相关，而营养底物的供给直接影响细胞生长和代谢，底物的流加补料可以避免底物抑制、细胞饥饿及代谢阻遏，根据菌体细胞生长及产物合成的不同情况对底物的补料速率进行优化，为微生物提供最优的生长环境，是提高生物制造过程效益的有效调控手段。In the biomanufacturing process, the formation of products is closely related to the growth and metabolism of bacterial cells, and the supply of nutrient substrates directly affects cell growth and metabolism. The feeding of substrates can avoid substrate inhibition, cell starvation and metabolism. Repression, which optimizes the feed rate of substrates according to the different conditions of bacterial cell growth and product synthesis, provides an optimal growth environment for microorganisms, and is an effective means of regulation to improve the efficiency of biomanufacturing processes.
细胞培养过程补料方式最初依赖人工经验，逐步研究根据细胞培养的数学模型及生产目标，事先求解出最优的补料轨迹，然后实际生产过程中以该补料轨迹为工艺调控曲线。然而实际细胞生长涉及复杂的物理化学及生物反应，其代谢流及动力学演化复杂，数学模型难以准确描述细胞实际生长过程，由此基于数学模型获得的最优工艺曲线未必能达到最优效果，甚至严重影响细胞代谢和产物合成。事实上，基于数学模型的细胞培养及产物生产过程的优化控制方法本质上为开环控制，未能将优化效果进行反馈并调整未来的补料策略。The feeding method of the cell culture process initially relied on manual experience, and gradually studied according to the mathematical model of cell culture and production goals to solve the optimal feeding trajectory in advance, and then use the feeding trajectory as the process control curve in the actual production process. However, actual cell growth involves complex physical, chemical and biological reactions, and its metabolic flow and kinetic evolution are complex. It is difficult for mathematical models to accurately describe the actual growth process of cells. Therefore, the optimal process curve obtained based on mathematical models may not be able to achieve optimal results. Even seriously affect cell metabolism and product synthesis. In fact, the optimization control method of cell culture and product production process based on mathematical model is essentially an open-loop control, which fails to feed back the optimization effect and adjust the future feeding strategy.
发明内容Contents of the invention
本发明的目的是提供一种细胞培养状态在线估计及优化补料调控方法，集细胞生长状态估计、生产效益优化、过程在线控制及结果实时反馈于一体，可及时感知菌体细胞生长状况，针对不同阶段进行滚动优化补料，提供最优的培 养环境，实现经济效益最大化。The purpose of the present invention is to provide a method for online estimation of cell culture status and optimization of feeding regulation, which integrates estimation of cell growth status, optimization of production benefits, online process control and real-time feedback of results, and can sense the growth status of bacterial cells in a timely manner. Rolling optimized feeding at different stages provides an optimal culture environment and maximizes economic benefits.
为了解决上述技术问题，本发明提供了一种细胞培养状态在线估计及优化补料调控方法，包括以下步骤：In order to solve the above-mentioned technical problems, the present invention provides a method for online estimation of cell culture status and optimization of feed regulation, comprising the following steps:
S1：建立细胞培养状态模型；S1: Establish a cell culture state model;
S2：确定细胞培养过程中需要满足的约束条件；S2: Determine the constraints that need to be met during the cell culture process;
S3：选定经济效益优化目标；S3: Select the economic benefit optimization target;
S4：进行细胞状态估计，获得当前时刻的细胞状态估计值；S4: Estimate the cell state and obtain the estimated value of the cell state at the current moment;
S5：根据当前时刻的细胞状态估计值和拟定的补料速率轨迹，基于细胞培养状态模型，求解得到未来时刻细胞状态向量；S5: According to the estimated value of the cell state at the current moment and the proposed feeding rate trajectory, based on the cell culture state model, the cell state vector at the future time is obtained by solving;
S6：根据得到未来时刻细胞状态向量和经济效益优化目标，采用非线性规划方法，求解最优化经济效益下，满足约束条件的最优补料速率轨迹；S6: According to the obtained cell state vector and economic benefit optimization goal in the future, use the nonlinear programming method to solve the optimal feeding rate trajectory satisfying the constraint conditions under the optimal economic benefit;
S7：将最优补料速率轨迹中当前时刻的补料速率实施于细胞培养生产过程，重复步骤S4-S7，直至生产过程结束。S7: Apply the current feeding rate in the optimal feeding rate track to the cell culture production process, and repeat steps S4-S7 until the production process ends.
作为本发明的进一步改进，建立细胞培养状态模型，具体包括以下步骤：As a further improvement of the present invention, establishing a cell culture state model specifically includes the following steps:
采用欧拉法将细胞培养生产周期划分为T f个采样间隔，根据细胞菌体培养及产物生成动力学，建立关于采样时刻k＝1，…，T f的细胞培养状态模型： The cell culture production cycle is divided into T f sampling intervals by the Euler method, and a cell culture state model is established at the sampling time k=1,..., T f according to the cell culture and product generation kinetics:
x(k+1)＝f[x(k)，u(k)]+w(k+1)            (1)x(k+1)=f[x(k), u(k)]+w(k+1) (1)
其中，x(k)、u(k)分别为k时刻细胞状态和补料速率，f[x(k)，u(k)]为关于x(k)、u(k)的线性或非线性函数，考虑培养过程干扰噪声为w(k+1)。Among them, x(k), u(k) are the cell state and feeding rate at time k, respectively, and f[x(k), u(k)] is the linear or nonlinear relationship between x(k), u(k) function, considering the disturbance noise of the cultivation process as w(k+1).
作为本发明的进一步改进，所述步骤S2具体包括以下步骤：As a further improvement of the present invention, the step S2 specifically includes the following steps:
将细胞培养过程中对底物浓度、培养液体积、以及补料速率的物理限制，表述为以下约束条件：The physical limitations on substrate concentration, medium volume, and feed rate during cell culture are expressed as the following constraints:
m[x(T f),u(T f)]≤0   (2) m[x(T f ),u(T f )]≤0 (2)
n[x(k),u(k)]≤0   (3)n[x(k),u(k)]≤0 (3)
u min≤u(k)≤u max   (4) u min ≤ u(k) ≤ u max (4)
其中，x(T f)、u(T f)分别为最终时刻细胞状态和补料速率，m[x(T f),u(T f)]为关 于x(T f)、u(T f)对应培养液体积的线性或非线性函数，n[x(k),u(k)]为关于x(k)、x(k)对应底物浓度的线性或非线性函数，u max和u min分别表示k时刻细胞补料速率u(k)的上限和下限。 Among them, x(T f ), u(T f ) are the cell state and feeding rate at the final moment, respectively, and m[x(T f ),u(T f )] is about x(T f ), u(T f ) is a linear or nonlinear function corresponding to the volume of the culture solution, n[x(k), u(k)] is a linear or nonlinear function about x(k), x(k) corresponding to the substrate concentration, u max and u min denote the upper and lower limits of the cell feeding rate u(k) at time k, respectively.
作为本发明的进一步改进，经济效益优化目标包括：As a further improvement of the present invention, the economic benefit optimization target includes:
当底物成本较低，经济效益优化目标选产物量最大，优化目标J定义为终点产量P(T f)最大化，而终点产量为终端时刻产物浓度和发酵液体积的乘积，并与生产过程中的细胞培养状态x(k)及补料速率u(k)有关，即效益优化目标表示如下： When the substrate cost is low and the economic benefit optimization target selects the largest product, the optimization objective J is defined as the maximum output P(T f ) at the end point. The cell culture state x(k) in is related to the feeding rate u(k), that is, the benefit optimization objective is expressed as follows:
J 1＝P(T f)＝L[x(k),u(k)]   (5) J 1 =P(T f )=L[x(k),u(k)] (5)
其中，L[x(k),u(k)]是描述终点产量与细胞培养状态及补料速率间函数关系；Among them, L[x(k),u(k)] is the functional relationship between the terminal output, cell culture state and feeding rate;
当追求高产量的同时兼顾底物成本，则引入成本因子，经济效益优化目标选择一个批次生产的净利润与生产时间的比值，即过程效益，具体效益优化目标表示如下：When pursuing high yield while taking into account the substrate cost, the cost factor is introduced, and the economic benefit optimization goal selects the ratio of the net profit of a batch production to the production time, that is, the process benefit. The specific benefit optimization goal is expressed as follows:
Figure PCTCN2022073489-appb-000001
Figure PCTCN2022073489-appb-000001
其中，r为单位产物的销售价格，c为单位补料的成本价格，
Figure PCTCN2022073489-appb-000002
为从当前时刻至生产结束时的补料投入总量，T p为同一个生物反应罐相邻两个生产批次之间的时间间隔； Among them, r is the sales price of the unit product, c is the cost price of the unit feed,
Figure PCTCN2022073489-appb-000002
is the total amount of feed input from the current moment to the end of production, T p is the time interval between two adjacent production batches of the same bioreactor;
当对于底物成本较高的生产过程，追求底物到产物的转化率，经济效益优化目标选择一个批次的产物量与补料总量的比值，即产物得率，具体效益优化目标表示如下：For the production process with high substrate cost, the conversion rate from substrate to product is pursued, and the economic benefit optimization goal selects the ratio of the product amount of a batch to the total amount of feed, that is, the product yield. The specific benefit optimization goal is expressed as follows :
Figure PCTCN2022073489-appb-000003
Figure PCTCN2022073489-appb-000003
作为本发明的进一步改进，采用间接测量方法进行细胞状态估计，或直接测量方法获得当前时刻的细胞状态估计值。As a further improvement of the present invention, an indirect measurement method is used to estimate the cell state, or a direct measurement method is used to obtain an estimated value of the cell state at the current moment.
作为本发明的进一步改进，当采用直接测量方法进行细胞状态估计，包括以下步骤：As a further improvement of the present invention, when the direct measurement method is used to estimate the cell state, the following steps are included:
利用光谱测量细胞，对光谱进行预处理和特征波段选择，通过建立光谱数据与细胞培养状态映射模型，直接得到细胞状态估计值
Figure PCTCN2022073489-appb-000004
Use the spectrum to measure the cells, preprocess the spectrum and select the characteristic band, and directly obtain the estimated value of the cell state by establishing a mapping model between the spectral data and the cell culture state
Figure PCTCN2022073489-appb-000004
作为本发明的进一步改进，当选择间接测量方法进行细胞状态估计，包括以下步骤：基于生化机理或实验，分析综合出菌体细胞内基础变量y(k)与细胞状态x(k)的关系，构造测量方程：As a further improvement of the present invention, when the indirect measurement method is selected to estimate the cell state, it includes the following steps: based on biochemical mechanism or experiment, analyze and synthesize the relationship between the basic variable y(k) in the bacterial cell and the cell state x(k), Construct the measurement equation:
y(k)＝g[x(k)]+v(k)      (8)y(k)=g[x(k)]+v(k) (8)
其中，g[x(k)]是构建的测量函数，假设v(k)为测量噪声，先通过氨基葡萄糖法、麦角固醇法或核酸法测量出y(k)，再通过估计方法间接获得当前时刻的细胞状态估计值
Figure PCTCN2022073489-appb-000005
Among them, g[x(k)] is the constructed measurement function, assuming that v(k) is the measurement noise, first measure y(k) by glucosamine method, ergosterol method or nucleic acid method, and then obtain indirectly by estimation method Estimated cell state at the current moment
Figure PCTCN2022073489-appb-000005
作为本发明的进一步改进，当选择间接测量方法进行细胞状态估计时，所述估计方法根据可测基础变量和细胞状态模型的形式、过程和测量噪声的统计分布，选择卡尔曼滤波法、扩展卡尔曼滤波法、滚动时域估计法、无迹卡尔曼滤波法、贝叶斯估计法、粒子滤波法或有限脉冲响应滤波法中的一种进行细胞状态估计，由前一时刻细胞状态对当前时刻细胞状态进行预测，根据基础变量y(k)的当前测量值，更新修正预测获得当前时刻的细胞状态估计值
Figure PCTCN2022073489-appb-000006
As a further improvement of the present invention, when the indirect measurement method is selected for cell state estimation, the estimation method selects Kalman filter method, extended Karl One of the methods of Mann filter, rolling time domain estimation, unscented Kalman filter, Bayesian estimation, particle filter or finite impulse response filter is used to estimate the cell state. Predict the cell state, update and correct the prediction to obtain the estimated value of the cell state at the current moment according to the current measured value of the basic variable y(k)
Figure PCTCN2022073489-appb-000006
作为本发明的进一步改进，当细胞状态模型和测量方程为非线性函数，且有高斯白噪声的情形下，采用扩展卡尔曼滤波算法，进行细胞培养状态估计，包括以下步骤：As a further improvement of the present invention, when the cell state model and the measurement equation are nonlinear functions and there is Gaussian white noise, the extended Kalman filter algorithm is used to estimate the cell culture state, including the following steps:
a.细胞状态及其协方差的预测：由k时刻的估计值
Figure PCTCN2022073489-appb-000007
和补料速率u(k)对k+1时刻的细胞状态进行预测： a. Prediction of cell state and its covariance: from the estimated value at time k
Figure PCTCN2022073489-appb-000007
and the feeding rate u(k) to predict the cell state at time k+1:
Figure PCTCN2022073489-appb-000008
Figure PCTCN2022073489-appb-000008
Figure PCTCN2022073489-appb-000009
Figure PCTCN2022073489-appb-000009
其中，
Figure PCTCN2022073489-appb-000010
和
Figure PCTCN2022073489-appb-000011
分别为k+1时刻细胞状态及协方差的预测值，P(k)为k时刻的协方差估计值，Q为过程噪声的协方差矩阵；F(k)为状态转移矩阵，若细胞培养模型
Figure PCTCN2022073489-appb-000012
为非线性，则
Figure PCTCN2022073489-appb-000013
in,
Figure PCTCN2022073489-appb-000010
and
Figure PCTCN2022073489-appb-000011
are the predicted values of the cell state and covariance at time k+1, respectively, P(k) is the estimated value of covariance at time k, Q is the covariance matrix of process noise; F(k) is the state transition matrix, if the cell culture model
Figure PCTCN2022073489-appb-000012
is nonlinear, then
Figure PCTCN2022073489-appb-000013
b.细胞状态及其协方差的更新：在k+1时刻，利用获得的测量值y(k+1)对k时刻的预测进行更新修正：b. Update of the cell state and its covariance: At time k+1, use the obtained measured value y(k+1) to update and correct the prediction at time k:
Figure PCTCN2022073489-appb-000014
Figure PCTCN2022073489-appb-000014
Figure PCTCN2022073489-appb-000015
Figure PCTCN2022073489-appb-000015
Figure PCTCN2022073489-appb-000016
Figure PCTCN2022073489-appb-000016
其中，
Figure PCTCN2022073489-appb-000017
为k+1时刻细胞状态估计值，K(k+1)为卡尔曼增益，R为测量噪声的协方差矩阵；H(k)为测量矩阵，若测量方程g[x(k)]为非线性，则
Figure PCTCN2022073489-appb-000018
in,
Figure PCTCN2022073489-appb-000017
is the estimated value of the cell state at time k+1, K(k+1) is the Kalman gain, R is the covariance matrix of the measurement noise; H(k) is the measurement matrix, if the measurement equation g[x(k)] is not linear, then
Figure PCTCN2022073489-appb-000018
作为本发明的进一步改进，求解最优化经济效益下，满足约束条件的最优补料速率轨迹，具体包括以下步骤：As a further improvement of the present invention, solving the optimal feed rate trajectory satisfying the constraint conditions under the optimized economic benefits specifically includes the following steps:
以当前时刻的细胞培养状态估计值
Figure PCTCN2022073489-appb-000019
以及拟定的补料速率轨迹U k＝[u(k)，…，u(T f-1)] T为输入，用计算机数值解法求解细胞状态模型，得到未来时刻细胞状态向量X k+1＝[x(k+1)，…，x(T f)] T，其中，计算机数值解法包括离散状态模型迭代计算、连续状态模型龙格库塔法及欧拉法； Estimated value of the cell culture state at the current moment
Figure PCTCN2022073489-appb-000019
And the proposed feeding rate trajectory U k =[u(k),...,u(T f -1)] T is input, and the cell state model is solved by computer numerical solution, and the cell state vector X k+1 = [x(k+1),...,x(T f )] T , where the computer numerical solutions include discrete state model iterative calculation, continuous state model Runge-Kutta method and Euler method;
根据未来时刻细胞状态向量X k+1，采用非线性规划寻优算法，求解满足约束条件的经济效益J最优化问题，即求解
Figure PCTCN2022073489-appb-000020
得到最优补料轨迹U k，其中，寻优算法包括内点法、外点法、序贯二次规划法、遗传算法和粒子群算法； According to the cell state vector X k+1 at the future time, the nonlinear programming optimization algorithm is used to solve the economic benefit J optimization problem satisfying the constraints, that is, to solve
Figure PCTCN2022073489-appb-000020
Get the optimal feeding trajectory U k , where the optimization algorithm includes interior point method, exterior point method, sequential quadratic programming method, genetic algorithm and particle swarm algorithm;
将补料轨迹U k中当前时刻的补料速率u(k)实施于细胞培养生产过程； Apply the feeding rate u(k) at the current moment in the feeding trajectory U k to the cell culture production process;
令k＝k+1，重复求解最优补料轨迹U k并实施当前时刻的补料速率u(k)过程，直至生产过程结束。 Let k=k+1, repeatedly solve the optimal feeding trajectory U k and implement the feeding rate u(k) process at the current moment until the end of the production process.
本发明的有益效果：本发明以生物制造过程经济效益作为优化目标，区别于常用最优补料方法，直接将生产优化、在线控制以及反馈机制集成在一个框架内进行实施，在每个采样时刻，通过当前生产基础变量估计细胞培养状态，利用数学模型预测未来状态及经济效益，以未来生产时域内补料速率为决策变量进行效益优化，并将优化结果及时实施，如此滚动运行，提供最优的培养环境，实现经济效益最大化；Beneficial effects of the present invention: the present invention takes the economic benefit of the biomanufacturing process as the optimization target, and is different from the commonly used optimal feeding method, and directly integrates production optimization, online control and feedback mechanism into one framework for implementation, at each sampling time , estimate the state of cell culture through the current production basic variables, use the mathematical model to predict the future state and economic benefits, use the feeding rate in the future production time domain as the decision variable to optimize the benefits, and implement the optimization results in time. The cultivation environment to maximize economic benefits;
本发明建立在细胞培养状态可测量基础上，由于细胞生长过程多数状态(如胞内代谢物质、菌体浓度、底物浓度等)不能在线测量，一方面借助细胞培养过 程中组分含量等基础变量的测量，再利用状态估计方法，对难以获取的细胞状态进行在线估计，另一方面可利用拉曼光谱、近红外光谱、发射光谱等的先进测量仪器，实现对一些细胞培养状态的直接测量，这些估计和测量手段为滚动优化补料提供了支撑。The present invention is based on the measurable state of cell culture. Since most states of the cell growth process (such as intracellular metabolites, cell concentration, substrate concentration, etc.) The measurement of variables, and then use the state estimation method to estimate the cell state that is difficult to obtain online. On the other hand, advanced measuring instruments such as Raman spectroscopy, near-infrared spectroscopy, and emission spectroscopy can be used to directly measure the state of some cell cultures. , these estimation and measurement tools provide the support for rolling optimized feeding.
附图说明Description of drawings
图1是本发明实施流程示意图；Fig. 1 is a schematic diagram of the implementation process of the present invention;
图2是利用果糖生产聚羟基丁酸过程优化补料速率轨迹图；Fig. 2 is to utilize fructose to produce polyhydroxybutyric acid process to optimize feeding rate locus figure;
图3是利用尿素生产聚羟基丁酸过程优化补料速率轨迹图；Fig. 3 is to utilize urea to produce polyhydroxybutyric acid process to optimize feeding rate locus figure;
图4是菌体比生长率变化图；Fig. 4 is the graph of the change of bacterial cell specific growth rate;
图5是聚羟基丁酸生产过程中底物浓度状态变化图；Fig. 5 is the state change diagram of substrate concentration in the production process of polyhydroxybutyric acid;
图6是聚羟基丁酸生产过程中果糖浓度状态变化图；Fig. 6 is a diagram showing the state change of fructose concentration during the production of polyhydroxybutyric acid;
图7是聚羟基丁酸生产过程中尿素浓度状态变化图；Fig. 7 is a diagram of the state change of urea concentration in the production process of polyhydroxybutyric acid;
图8是聚羟基丁酸生产过程中发酵液体积状态变化图。Fig. 8 is a graph showing the state change of fermentation broth volume during the production of polyhydroxybutyric acid.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.
参考图1，本发明提供了一种细胞培养状态在线估计及优化补料调控方法，包括以下步骤：Referring to Fig. 1, the present invention provides a method for online estimation of cell culture status and optimization of feed regulation, comprising the following steps:
S1：建立细胞培养状态模型；S1: Establish a cell culture state model;
S2：确定细胞培养过程中需要满足的约束条件；S2: Determine the constraints that need to be met during the cell culture process;
S3：选定经济效益优化目标；S3: Select the economic benefit optimization target;
S4：进行细胞状态估计，获得当前时刻的细胞状态估计值；S4: Estimate the cell state and obtain the estimated value of the cell state at the current moment;
S5：根据当前时刻的细胞状态估计值和拟定的补料速率轨迹，基于细胞培 养状态模型，求解得到未来时刻细胞状态向量；S5: According to the estimated value of the cell state at the current moment and the proposed feeding rate trajectory, based on the cell culture state model, the cell state vector at the future time is obtained by solving;
S6：根据得到未来时刻细胞状态向量和经济效益优化目标，采用非线性规划方法，求解最优化经济效益下，满足约束条件的最优补料速率轨迹；S6: According to the obtained cell state vector and economic benefit optimization goal in the future, use the nonlinear programming method to solve the optimal feeding rate trajectory satisfying the constraint conditions under the optimal economic benefit;
S7：将最优补料速率轨迹中当前时刻的补料速率实施于细胞培养生产过程，重复步骤S4-S7，直至生产过程结束。S7: Apply the current feeding rate in the optimal feeding rate track to the cell culture production process, and repeat steps S4-S7 until the production process ends.
本发明根据菌体培养及产物生成动力学，建立细胞培养状态模型(1)，分析生产工艺要求，确定细胞培养制造过程需要满足的约束条件(2)-(4)；选定经济效益优化目标，若补料成本较低，采用产量最大(5)作为经济效益指标；若追求高产量并兼顾底物成本，采用过程效益最大(6)作为指标；若强调底物到产物的转化率，则选择产物得率最大(7)为效益指标。效益优化取决于细胞培养状态，其测量方式一是构建测量方程(8)，通过测量与细胞状态相关的基础变量y(k)，由估计方法间接获得细胞状态估计值
Figure PCTCN2022073489-appb-000021
测量方式二是利用先进的光谱技术直接测量状态估计值
Figure PCTCN2022073489-appb-000022
在测量方式一中，采用扩展卡尔曼滤波等估计方法，根据(9)(10)由前一时刻细胞状态对当前时刻状态进行预测，再根据(11)-(13)由基础变量的当前测量值，更新修正预测值获得估计值
Figure PCTCN2022073489-appb-000023
以细胞状态估计值
Figure PCTCN2022073489-appb-000024
以及拟定的补料速率U k为输入，用计算机数值解法求解细胞状态模型，得到未来时刻细胞状态向量；再采用非线性规划寻优方法求解
Figure PCTCN2022073489-appb-000025
得到新的最优补料轨迹U k。将补料轨迹U k中当前时刻的u(k)实施于细胞培养生产过程，重复以上过程，直至生产过程结束。 According to the cell culture and product generation kinetics, the present invention establishes the cell culture state model (1), analyzes the production process requirements, and determines the constraint conditions (2)-(4) that the cell culture manufacturing process needs to meet; selects the economic benefit optimization target , if the feeding cost is low, use the maximum yield (5) as the economic benefit index; if the pursuit of high yield and take into account the substrate cost, use the maximum process benefit (6) as the index; if the conversion rate from substrate to product is emphasized, then Select the maximum product yield (7) as the benefit index. Benefit optimization depends on the state of cell culture. The first measurement method is to construct the measurement equation (8), by measuring the basic variable y(k) related to the cell state, and indirectly obtain the estimated value of the cell state by the estimation method
Figure PCTCN2022073489-appb-000021
The second measurement method is to use advanced spectral technology to directly measure the estimated value of the state
Figure PCTCN2022073489-appb-000022
In the first measurement method, the extended Kalman filter and other estimation methods are used to predict the current state from the previous cell state according to (9) (10), and then according to (11)-(13) from the current measurement of the basic variables value, update the revised predicted value to obtain the estimated value
Figure PCTCN2022073489-appb-000023
Estimated by cell state
Figure PCTCN2022073489-appb-000024
and the proposed feeding rate U k as input, use the computer numerical solution method to solve the cell state model, and obtain the cell state vector in the future; then use the nonlinear programming optimization method to solve
Figure PCTCN2022073489-appb-000025
A new optimal feeding trajectory U k is obtained. Implement u(k) at the current moment in the feeding trajectory U k in the cell culture production process, and repeat the above process until the production process ends.
整个过程涉及生物制造过程中营养底物的补料调控技术，根据菌体细胞生长及产物合成的不同情况对底物的补料速率进行优化，是提高生物制造过程效益的有效调控手段。区别于常用最优补料方法，本发明以生物制造过程经济效益作为优化目标，将细胞培养工艺要求、生长状态估计、在线滚动优化、实时实施等环节集成在一个框架内，在每个采样时刻，通过当前生产变量估计细胞培养状态，利用数学模型预测未来状态及经济效益，以未来生产时域内补料速率为决策变量进行效益优化，并将优化结果及时实施，如此滚动运行，该方法 适用于细胞培养模型和工艺要求已知的生物制造过程。The whole process involves the feed regulation technology of the nutrient substrate in the biomanufacturing process. Optimizing the feed rate of the substrate according to the different conditions of bacterial cell growth and product synthesis is an effective regulation method to improve the efficiency of the biomanufacturing process. Different from the commonly used optimal feeding method, the present invention takes the economic benefits of the biomanufacturing process as the optimization goal, integrates the cell culture process requirements, growth state estimation, online rolling optimization, real-time implementation and other links in a framework, and at each sampling time , estimate the state of cell culture through the current production variables, use the mathematical model to predict the future state and economic benefits, use the feeding rate in the future production time domain as the decision variable to optimize the benefits, and implement the optimization results in time, so rolling operation, this method is suitable for Cell culture models and processes require known biomanufacturing processes.
具体在实施过程中：Specifically in the implementation process:
第一步：建立细胞培养状态数学模型：Step 1: Establish a mathematical model of the cell culture state:
将细胞培养生产周期划分为T f个采样间隔，根据菌体培养及产物合成动力学，建立关于采样时刻k＝1，…，T f的细胞培养状态模型： Divide the cell culture production cycle into T f sampling intervals, and establish a cell culture state model at the sampling time k=1,..., T f according to the bacterial cell culture and product synthesis kinetics:
x(k+1)＝f[x(k)，u(k)]+w(k+1)               (1)x(k+1)=f[x(k), u(k)]+w(k+1) (1)
其中x(k)、u(k)分别为k时刻细胞状态和补料速率，f[·]为线性或非线性函数，考虑培养过程干扰噪声为w(k+1)。Among them, x(k) and u(k) are the cell state and feeding rate at time k, respectively, f[ ] is a linear or nonlinear function, and w(k+1) is considered to be the disturbance noise in the culture process.
对于已有细胞培养的连续状态模型，采用欧拉法以T f个采样间隔将其离散化。 For the continuous state model of the existing cell culture, the Euler method is used to discretize it with T f sampling intervals.
第二步：确定培养过程约束条件：Step 2: Determine the constraints of the cultivation process:
将生产工艺对底物浓度、培养液体积、以及补料速率等物理限制，表述为以下约束条件：The physical limitations of the production process on substrate concentration, culture solution volume, and feeding rate are expressed as the following constraints:
m[x(T f),u(T f)]≤0   (2) m[x(T f ),u(T f )]≤0 (2)
n[x(k),u(k)]≤0   (3)n[x(k),u(k)]≤0 (3)
u min≤u(k)≤u max  (4) u min ≤ u(k) ≤ u max (4)
其中，m[·]、n[·]为线性或非线性函数，u max和u min分别表示补料速率的上限和下限；式(2)表示培养过程终端约束条件，如培养液体积在生产结束时不可溢出生物反应器；式(3)表示在整个制造过程中都需要满足的限制条件，如为了避免过高的底物浓度造成菌体细胞的代谢抑制，生产过程中的底物浓度须低于一定上限；式(4)为考虑实际设备的操作能力及对菌体细胞生长的冲击影响所施加的补料速率约束； Among them, m[ ] and n[ ] are linear or nonlinear functions, u max and u min represent the upper limit and lower limit of the feeding rate respectively; formula (2) represents the terminal constraints of the culture process, such as the volume of culture medium in production Do not overflow the bioreactor at the end; formula (3) represents the restrictive conditions that need to be met throughout the manufacturing process, such as in order to avoid the metabolic inhibition of bacterial cells caused by excessive substrate concentration, the substrate concentration in the production process must be is lower than a certain upper limit; formula (4) is the feed rate constraint imposed by considering the operating capacity of the actual equipment and the impact on the growth of bacterial cells;
第三步：选定经济效益优化目标：Step 3: Select the economic benefit optimization target:
生物制造过程经济效益目标多样，根据生产实际需要进行设置。若底物成 本较低，经济效益优化目标可选产物量最大，优化目标J定义为终点产量P(T f)最大化，而终点产量一般为终端时刻产物浓度和发酵液体积的乘积，并与生产过程中的细胞培养状态x(k)及补料速率u(k)有关，即效益指标表示如下： The economic benefit objectives of the biomanufacturing process are diverse and should be set according to the actual needs of production. If the substrate cost is low, the economic benefit optimization objective is to maximize the amount of optional products, and the optimization objective J is defined as the maximum output P(T f ) at the end point, and the end point output is generally the product of the product concentration at the end time and the volume of the fermentation broth, and is related to The cell culture state x(k) in the production process is related to the feeding rate u(k), that is, the benefit index is expressed as follows:
J 1＝P(T f)＝L[x(k),u(k)]  (5) J 1 =P(T f )=L[x(k),u(k)] (5)
其中，L[·]是描述终点产量与细胞培养状态及补料速率间函数关系。Among them, L[·] is to describe the functional relationship between the end point production, cell culture state and feed rate.
若追求高产量的同时兼顾底物成本，则引入成本因子，经济效益优化目标选择一个批次生产的净利润与生产时间的比值，即过程效益，具体效益指标表示如下：If the cost of the substrate is taken into consideration while pursuing high yield, the cost factor is introduced, and the economic benefit optimization goal selects the ratio of the net profit of a batch production to the production time, that is, the process benefit. The specific benefit indicators are expressed as follows:
Figure PCTCN2022073489-appb-000026
Figure PCTCN2022073489-appb-000026
其中，r为单位产物的销售价格，c为单位补料的成本价格，
Figure PCTCN2022073489-appb-000027
为从当前时刻至生产结束时的补料投入总量，T p为同一个生物反应罐相邻两个生产批次之间的时间间隔，即放罐、清洗、灭菌、接种等所需的操作时间。 Among them, r is the sales price of the unit product, c is the cost price of the unit feed,
Figure PCTCN2022073489-appb-000027
is the total amount of feed input from the current moment to the end of production, Tp is the time interval between two adjacent production batches of the same bioreactor, that is, the time required for tank release, cleaning, sterilization, inoculation, etc. operating time.
对于底物成本较高的生产过程，追求底物到产物的转化率，经济效益优化目标选择一个批次的产物量与补料总量的比值，即产物得率，具体效益指标表示如下：For the production process with high substrate cost, the conversion rate of substrate to product is pursued, and the economic benefit optimization goal is to choose the ratio of the product amount of a batch to the total amount of fed materials, that is, the product yield. The specific benefit indicators are expressed as follows:
Figure PCTCN2022073489-appb-000028
Figure PCTCN2022073489-appb-000028
经济效益优化目标还包括细胞生长最好、副产物最低、能量消耗最少。Cost-effective optimization goals also include best cell growth, lowest by-products, and lowest energy consumption.
第四步：选择细胞培养状态测量方式：Step 4: Select the cell culture state measurement method:
生产制造的终点产量P(T f)、过程效益、转化率等指标直接取决于细胞培养状态，而细胞培养状态的检测是难点。 The end-point yield P(T f ), process efficiency, conversion rate and other indicators of manufacturing directly depend on the state of cell culture, and the detection of cell culture state is difficult.
方案1：间接测量方式：基于生化机理或实验，分析综合出菌体细胞内一些基础变量y(k)(如组分含量等)与细胞状态x(k)的关系，构造测量方程：Scheme 1: Indirect measurement method: Based on biochemical mechanism or experiment, analyze and synthesize the relationship between some basic variables y(k) (such as component content, etc.) in the bacterial cell and the cell state x(k), and construct the measurement equation:
y(k)＝g[x(k)]+v(k)    (8)y(k)=g[x(k)]+v(k) (8)
式中g[·]是构建的测量函数，假设v(k)为测量噪声。先通过氨基葡萄糖法、麦角固醇法、核酸法等方法测量出y(k)，再由估计方法间接获得细胞状态估计值
Figure PCTCN2022073489-appb-000029
where g[·] is the constructed measurement function, assuming that v(k) is the measurement noise. First measure y(k) by glucosamine method, ergosterol method, nucleic acid method and other methods, and then indirectly obtain the estimated value of the cell state by the estimation method
Figure PCTCN2022073489-appb-000029
方案2：直接测量方式：利用拉曼光谱、近红外光谱、发射光谱等实现底物浓度等细胞培养状态估计值
Figure PCTCN2022073489-appb-000030
的直接测量。利用光谱技术直接测量的具体实施步骤为：步骤1：光谱预处理，其方法包括平滑处理、小波变换、多元散射校正(MSC)、标准正态变量变换(SNV)、正交信号校正(OSC)、导数算法(Der)等；步骤2：特征波段的选择，其方法包括连续投影法(SPA)、偏最小二乘法(PLS)、无信息变量消除法(UVE)等；步骤3：光谱数据与细胞培养状态影射模型的建立，其方法包括主成分回归(PCR)、偏最小二乘回归(PLSR)、支持向量机回归(SVMR)、深度学习方法等。 Scheme 2: Direct measurement method: use Raman spectroscopy, near-infrared spectroscopy, emission spectroscopy, etc. to realize the estimated value of cell culture status such as substrate concentration
Figure PCTCN2022073489-appb-000030
direct measurement. The specific implementation steps of direct measurement using spectral technology are: Step 1: Spectral preprocessing, the methods include smoothing, wavelet transform, multivariate scattering correction (MSC), standard normal variable transformation (SNV), orthogonal signal correction (OSC) , derivative algorithm (Der), etc.; step 2: selection of characteristic bands, the methods include continuous projection method (SPA), partial least squares method (PLS), uninformative variable elimination method (UVE), etc.; step 3: spectral data and The establishment of the cell culture state mapping model includes principal component regression (PCR), partial least squares regression (PLSR), support vector machine regression (SVMR), deep learning methods, etc.
第五步：基于状态模型和测量方程的细胞状态估计：Step 5: Estimation of cell state based on state model and measurement equation:
生产实际中的细胞培养状态难以获取，基于测量方程和细胞状态模型，利用可测基础变量，选用估计或滤波方法间接获取细胞状态。根据状态模型的形式、过程和测量噪声的统计分布等不同情形，可选用卡尔曼滤波、扩展卡尔曼滤波、滚动时域估计、无迹卡尔曼滤波、贝叶斯估计、粒子滤波、有限脉冲响应滤波及相应的扩展形式等状态估计方法。It is difficult to obtain the state of cell culture in actual production. Based on the measurement equation and cell state model, the cell state can be obtained indirectly by using the measurable basic variables and selecting estimation or filtering methods. According to different situations such as the form of the state model, the process and the statistical distribution of the measurement noise, Kalman filter, extended Kalman filter, rolling time domain estimation, unscented Kalman filter, Bayesian estimation, particle filter, finite impulse response can be used State estimation methods such as filtering and corresponding extended forms.
一般生物制造过程f[·]和g[·]为非线性，当系统和测量有高斯白噪声的情形下，采用扩展卡尔曼滤波算法，细胞培养状态的估计步骤如下：Generally, f[ ] and g[ ] are nonlinear in the biological manufacturing process. When the system and measurement have Gaussian white noise, the extended Kalman filter algorithm is used to estimate the cell culture state as follows:
步骤1：细胞状态及其协方差的预测：Step 1: Prediction of cell state and its covariance:
由k时刻的估计值
Figure PCTCN2022073489-appb-000031
和补料速率u(k)对k+1时刻的细胞状态进行预测： From the estimated value at time k
Figure PCTCN2022073489-appb-000031
and the feeding rate u(k) to predict the cell state at time k+1:
Figure PCTCN2022073489-appb-000032
Figure PCTCN2022073489-appb-000032
Figure PCTCN2022073489-appb-000033
Figure PCTCN2022073489-appb-000033
其中，
Figure PCTCN2022073489-appb-000034
和
Figure PCTCN2022073489-appb-000035
分别为k+1时刻细胞状态及协方差的预测值，P(k) 为k时刻的协方差估计值，Q为过程噪声的协方差矩阵；F(k)为状态转移矩阵，若细胞培养模型f[·]为非线性，则
Figure PCTCN2022073489-appb-000036
in,
Figure PCTCN2022073489-appb-000034
and
Figure PCTCN2022073489-appb-000035
are the predicted values of cell state and covariance at time k+1 respectively, P(k) is the estimated value of covariance at time k, Q is the covariance matrix of process noise; F(k) is the state transition matrix, if the cell culture model f[·] is nonlinear, then
Figure PCTCN2022073489-appb-000036
步骤2：细胞状态及其协方差的更新：Step 2: Update of cell state and its covariance:
在k+1时刻，利用获得的测量值y(k+1)对k时刻的预测进行更新修正：At time k+1, use the obtained measurement value y(k+1) to update and correct the prediction at time k:
Figure PCTCN2022073489-appb-000037
Figure PCTCN2022073489-appb-000037
Figure PCTCN2022073489-appb-000038
Figure PCTCN2022073489-appb-000038
Figure PCTCN2022073489-appb-000039
Figure PCTCN2022073489-appb-000039
其中，
Figure PCTCN2022073489-appb-000040
为k+1时刻细胞状态估计值，K(k+1)为卡尔曼增益，R为测量噪声的协方差矩阵；H(k)为测量矩阵，若测量方程g[·]为非线性，则
Figure PCTCN2022073489-appb-000041
in,
Figure PCTCN2022073489-appb-000040
is the estimated value of the cell state at time k+1, K(k+1) is the Kalman gain, R is the covariance matrix of the measurement noise; H(k) is the measurement matrix, if the measurement equation g[·] is nonlinear, then
Figure PCTCN2022073489-appb-000041
第六步：最优补料速率轨迹在线求解与滚动实施：Step 6: Online solution and rolling implementation of optimal feeding rate trajectory:
在当前时刻k，寻找满足约束条件(2)(3)(4)的最优补料速率轨迹U k＝[u(k)，…，u(T f-1)] T，使得经济效益J最优化，即
Figure PCTCN2022073489-appb-000042
At the current moment k, find the optimal feed rate trajectory U k =[u(k),...,u(T f -1)] T that satisfies the constraints (2)(3)(4), so that the economic benefit J optimization, that is
Figure PCTCN2022073489-appb-000042
效益指标J与未来状态及补料速率轨迹有关，基于当前时刻状态估计值
Figure PCTCN2022073489-appb-000043
和待求速率轨迹U k,利用生产过程状态模型迭代计算未来时域的细胞状态，进而计算效益指标。 The benefit index J is related to the future state and the feeding rate trajectory, based on the estimated value of the state at the current moment
Figure PCTCN2022073489-appb-000043
and the required rate trajectory U k , use the production process state model to iteratively calculate the cell state in the future time domain, and then calculate the benefit index.
效益指标最优的补料速率轨迹求解步骤如下：The steps to solve the feeding rate trajectory with the optimal benefit index are as follows:
步骤1：令时刻k＝0时，设置初始细胞培养状态
Figure PCTCN2022073489-appb-000044
初始补料速率轨迹U k； Step 1: When time k=0, set the initial cell culture state
Figure PCTCN2022073489-appb-000044
Initial feed rate trajectory U k ;
步骤2：以状态
Figure PCTCN2022073489-appb-000045
和补料速率U k为输入，用计算机数值解法求解细胞状态模型，得到未来时刻细胞状态向量X k+1＝[x(k+1)，…，x(T f)] T；计算机数值解法包括离散状态模型迭代计算、连续状态模型龙格库塔法及欧拉法。 Step 2: Take the status
Figure PCTCN2022073489-appb-000045
and the feeding rate U k as input, solve the cell state model with the computer numerical solution method, and obtain the cell state vector X k+1 =[x(k+1),...,x(T f )] T in the future; the computer numerical solution method Including discrete state model iterative calculation, continuous state model Runge-Kutta method and Euler method.
步骤3：根据未来的X k+1，采用非线性规划寻优方法求解
Figure PCTCN2022073489-appb-000046
得到新的补料轨迹U k，寻优算法包括内点法、外点法、序贯二次规划法、遗传算法、粒 子群算法等； Step 3: According to the future X k+1 , use nonlinear programming optimization method to solve
Figure PCTCN2022073489-appb-000046
Get the new feeding trajectory U k , the optimization algorithm includes interior point method, exterior point method, sequential quadratic programming method, genetic algorithm, particle swarm algorithm, etc.;
步骤4：将补料轨迹U k中当前时刻的u(k)实施于细胞培养生产过程； Step 4: Implement u(k) at the current moment in the feeding trajectory U k in the cell culture production process;
步骤5：令k＝k+1；Step 5: let k=k+1;
步骤6：若采用第四步方案2直接测量获得细胞状态值
Figure PCTCN2022073489-appb-000047
则转第六步的步骤9；否则应用第四步方案1，转以下步骤7； Step 6: If you use the fourth step scheme 2 to directly measure and obtain the cell state value
Figure PCTCN2022073489-appb-000047
Then go to step 9 of the sixth step; otherwise, apply the solution 1 of the fourth step and go to the following step 7;
步骤7：由第五步的步骤1由前一时刻细胞状态对当前时刻状态进行预测；Step 7: From step 1 of the fifth step, predict the state of the current moment from the state of the cell at the previous moment;
步骤8：利用第五步的步骤2，由新采集测量值y(k)对预测值进行更新修正，获得细胞状态估计值
Figure PCTCN2022073489-appb-000048
Step 8: Use step 2 of the fifth step to update and correct the predicted value from the newly collected measured value y(k) to obtain the estimated value of the cell state
Figure PCTCN2022073489-appb-000048
步骤9：若生产过程未结束，则转到第六步的步骤2。Step 9: If the production process is not over, go to Step 2 of Step 6.
实施例Example
采用本发明提出的生物制造中细胞培养状态在线估计及优化调控方法，应用于利用果糖和尿素流加发酵生产聚羟基丁酸(PHB)的过程，其连续动力学状态模型为：The online estimation and optimization control method of cell culture state in biomanufacturing proposed by the present invention is applied to the process of producing polyhydroxybutyric acid (PHB) by fed-batch fermentation with fructose and urea, and its continuous kinetic state model is:
Figure PCTCN2022073489-appb-000049
Figure PCTCN2022073489-appb-000049
Figure PCTCN2022073489-appb-000050
Figure PCTCN2022073489-appb-000050
Figure PCTCN2022073489-appb-000051
Figure PCTCN2022073489-appb-000051
Figure PCTCN2022073489-appb-000052
Figure PCTCN2022073489-appb-000052
Figure PCTCN2022073489-appb-000053
Figure PCTCN2022073489-appb-000053
Figure PCTCN2022073489-appb-000054
Figure PCTCN2022073489-appb-000054
其中，x 1为胞内非PHB物质浓度，x 2为产物PHB浓度，x 3为果糖浓度，x 4为尿素浓度，x 5为发酵液体积，μ菌体比生长速率。u 1为果糖的流加率，u 2为尿素的流加率。定义细胞培养状态x＝[x 1,x 2,x 3,x 4,x 5] T，流加速率u＝[u 1，u 2] T。生产过程持续时间设置为49h，采用欧拉法以采样间隔Δ＝4.9h将上述过程状态模型 离散化。 Among them, x 1 is the concentration of non-PHB substances in the cell, x 2 is the concentration of product PHB, x 3 is the concentration of fructose, x 4 is the concentration of urea, x 5 is the volume of fermentation broth, and the specific growth rate of μ cells. u 1 is the feed rate of fructose, and u 2 is the feed rate of urea. Define cell culture state x=[x 1 ,x 2 ,x 3 ,x 4 ,x 5 ] T , flow acceleration rate u=[u 1 ,u 2 ] T . The duration of the production process is set to 49h, and the Euler method is used to discretize the above-mentioned process state model with a sampling interval Δ=4.9h.
考虑实际生产工艺，细胞培养过程状态约束为：Considering the actual production process, the state constraints of the cell culture process are:
0≤x 1(k)+x 2(k)≤280， 0≤x1 (k)+ x2 (k)≤280,
0≤x 3(k)≤90.11， 0≤x3 (k)≤90.11,
0≤x 4(k)≤10.11， 0≤x4 (k)≤10.11,
0≤x 5(T f)≤10； 0≤x 5 (T f )≤10;
输入约束为：The input constraints are:
0≤u 1(k)≤2， 0≤u1 (k)≤2,
0≤u 2(k)≤2； 0≤u2 (k)≤2;
采用终点产物最大化作为优化的目标函数，即优化效益指标为J＝P(T f)＝x 2(T f)*x 5(T f)；设置初始时刻细胞培养状态为
Figure PCTCN2022073489-appb-000055
The maximization of the terminal product is used as the objective function of optimization, that is, the optimization benefit index is J=P(T f )=x 2 (T f )*x 5 (T f ); the cell culture state at the initial moment is set as
Figure PCTCN2022073489-appb-000055
假设实际细胞培养过程在10h时菌体的氮源利用能力降低，并且考虑干扰和测量噪声均为相互独立的高斯白噪声，其协方差矩阵分别设置为Assuming that the nitrogen source utilization capacity of the bacteria decreases at 10 h in the actual cell culture process, and considering that the interference and measurement noise are Gaussian white noises that are independent of each other, the covariance matrix is set to
Q＝diag(10 -2,10 -2,10 -2,10 -4,10 -3)，R＝diag(10 -4,10 -4,10 -4)； Q=diag(10 −2 , 10 −2 , 10 −2 , 10 −4 , 10 −3 ), R=diag(10 −4 , 10 −4 , 10 −4 );
采用扩展卡尔曼滤波估计细胞状态x 1和x 2，利用直接测量法采用先进测量手段测量x 3、x 4以及x 5并构造线性测量方程，其测量矩阵H(k)为常值矩阵 Estimate cell states x 1 and x 2 by using extended Kalman filter, measure x 3 , x 4 and x 5 with advanced measurement means by direct measurement method and construct a linear measurement equation, and its measurement matrix H(k) is a constant matrix
Figure PCTCN2022073489-appb-000056
Figure PCTCN2022073489-appb-000056
根据以上过程，采用本发明的方法实现对PHB制造过程中细胞培养进行优化调控，其最优补料轨迹、比生长率以及状态变化分别如图2-图8。从图2-图8中可以看出，整个制造过程大致可以分为菌体生长和产物合成两个阶段。第一阶段为菌体生长阶段(0-25h)，该阶段果糖和尿素同时补充投料，分别作为碳 源和氮源，以维持菌体以最大比生长率生长，其中在0-10h之间，由于培养基中初始底物浓度足够菌体生长所需，因此果糖和尿素的补料量极少，之后随着营养物质的消耗逐渐增加补料。第二阶段为产物合成阶段(25-49h)，由于菌体氮源利用能力降低，前期未能获得足够的菌体数量，因此25-30h仍然少量投喂尿素，延迟生长期，从而获得足够的数量的菌体细胞；30h后停止尿素投喂，诱导菌体进入产物合成阶段，仅提供产物合成所需的果糖，此时胞内PHB大量合成。49h后PHB产量为1352.2g，与已有文献中的离线优化方法相比，其产量提高近12.6％。由此本发明提出的在线滚动优化补料方法能够根据菌体细胞培养的实际情况及时调控营养底物的流加速率，从而有效提高生物制造产量，增加经济收益。According to the above process, the method of the present invention is used to realize the optimization and regulation of cell culture in the PHB manufacturing process, and its optimal feeding trajectory, specific growth rate and state changes are shown in Figure 2-Figure 8 respectively. It can be seen from Figures 2-8 that the entire manufacturing process can be roughly divided into two stages: cell growth and product synthesis. The first stage is the cell growth stage (0-25h). At this stage, fructose and urea are supplemented at the same time as a carbon source and a nitrogen source, respectively, to maintain the growth of the cell at the maximum specific growth rate, wherein between 0-10h, Since the initial substrate concentration in the culture medium was sufficient for the growth of the bacteria, the feeding amount of fructose and urea was very small, and then the feeding was gradually increased with the consumption of nutrients. The second stage is the product synthesis stage (25-49h). Due to the reduction of the nitrogen source utilization capacity of the bacteria, the number of bacteria could not be obtained in the early stage. After 30 hours, stop urea feeding, induce the bacteria to enter the product synthesis stage, and only provide the fructose needed for product synthesis, and a large amount of PHB is synthesized in the cells at this time. After 49h, the yield of PHB was 1352.2g, which was nearly 12.6% higher than the offline optimization method in the existing literature. Therefore, the online rolling optimization feeding method proposed by the present invention can timely regulate the flow acceleration rate of the nutrient substrate according to the actual situation of bacterial cell culture, thereby effectively improving the yield of biomanufacturing and increasing economic benefits.
以上所述实施例仅是为充分说明本发明而所举的较佳的实施例，本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换，均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。The above-mentioned embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be determined by the claims.

Claims (10)

  1. 一种细胞培养状态在线估计及优化补料调控方法，其特征在于：括以下步骤：A method for online estimation of cell culture status and optimal feed regulation, characterized in that it comprises the following steps:
    S1：建立细胞培养状态模型；S1: Establish a cell culture state model;
    S2：确定细胞培养过程中需要满足的约束条件；S2: Determine the constraints that need to be met during the cell culture process;
    S3：选定经济效益优化目标；S3: Select the economic benefit optimization target;
    S4：进行细胞状态估计，获得当前时刻的细胞状态估计值；S4: Estimate the cell state and obtain the estimated value of the cell state at the current moment;
    S5：根据当前时刻的细胞状态估计值和拟定的补料速率轨迹，基于细胞培养状态模型，求解得到未来时刻细胞状态向量；S5: According to the estimated value of the cell state at the current moment and the proposed feeding rate trajectory, based on the cell culture state model, the cell state vector at the future time is obtained by solving;
    S6：根据得到未来时刻细胞状态向量和经济效益优化目标，采用非线性规划方法，求解最优化经济效益下，满足约束条件的最优补料速率轨迹；S6: According to the obtained cell state vector and economic benefit optimization goal in the future, use the nonlinear programming method to solve the optimal feeding rate trajectory satisfying the constraint conditions under the optimal economic benefit;
    S7：将最优补料速率轨迹中当前时刻的补料速率实施于细胞培养生产过程，重复步骤S4-S7，直至生产过程结束。S7: Apply the current feeding rate in the optimal feeding rate track to the cell culture production process, and repeat steps S4-S7 until the production process ends.
  2. 如权利要求1所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：建立细胞培养状态模型，具体包括以下步骤：A method for online estimation of cell culture status and optimal feed regulation as claimed in claim 1, characterized in that: establishing a cell culture status model specifically comprises the following steps:
    采用欧拉法将细胞培养生产周期划分为T f个采样间隔，根据细胞菌体培养及产物生成动力学，建立关于采样时刻k＝1，…，T f的细胞培养状态模型： The cell culture production cycle is divided into T f sampling intervals by the Euler method, and a cell culture state model is established at the sampling time k=1,..., T f according to the cell culture and product generation kinetics:
    x(k11)＝f[x(k)，u(k)]+w(k+1)    (1)x(k11)=f[x(k),u(k)]+w(k+1) (1)
    其中，x(k)、u(k)分别为k时刻细胞状态和补料速率，f[x(k)，u(k)]为关于x(k)、u(k)的线性或非线性函数，考虑培养过程干扰噪声为w(k+1)。Among them, x(k), u(k) are the cell state and feeding rate at time k, respectively, and f[x(k), u(k)] is the linear or nonlinear relationship between x(k), u(k) function, considering the disturbance noise of the cultivation process as w(k+1).
  3. 如权利要求1所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：所述步骤S2具体包括以下步骤：A method for online estimation of cell culture status and optimal feeding control method according to claim 1, characterized in that: said step S2 specifically comprises the following steps:
    将细胞培养过程中对底物浓度、培养液体积、以及补料速率的物理限制， 表述为以下约束条件：The physical limitations on substrate concentration, medium volume, and feeding rate during cell culture are expressed as the following constraints:
    m[x(T f),u(T f)]≤0  (2) m[x(T f ),u(T f )]≤0 (2)
    n[x(k),u(k)]≤0  (3)n[x(k),u(k)]≤0 (3)
    u min≤u(k)≤u max  (4) u min ≤ u(k) ≤ u max (4)
    其中，x(T f)、u(T f)分别为最终时刻细胞状态和补料速率，m[x(T f),u(T f)]为关于x(T f)、u(T f)对应培养液体积的线性或非线性函数，n[x(k),u(k)]为关于细胞状态x(k)和补料速率u(k)对应底物浓度的线性或非线性函数，u max和u min分别表示k时刻细胞补料速率u(k)的上限和下限。 Among them, x(T f ), u(T f ) are the cell state and feeding rate at the final moment, respectively, and m[x(T f ),u(T f )] is about x(T f ), u(T f ) is a linear or nonlinear function corresponding to the volume of the culture medium, n[x(k),u(k)] is a linear or nonlinear function of the cell state x(k) and feeding rate u(k) corresponding to the substrate concentration , u max and u min represent the upper and lower limits of the cell feeding rate u(k) at time k, respectively.
  4. 如权利要求1所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：经济效益优化目标包括：A method for online estimation of cell culture status and optimal feed regulation as claimed in claim 1, characterized in that: the economic benefit optimization target includes:
    当底物成本较低，经济效益优化目标选产物量最大，优化目标J定义为终点产量P(T f)最大化，而终点产量为终端时刻产物浓度和发酵液体积的乘积，并与生产过程中的细胞培养状态x(k)及补料速率u(k)有关，即效益优化目标表示如下： When the substrate cost is low and the economic benefit optimization target selects the largest product, the optimization objective J is defined as the maximum output P(T f ) at the end point. The cell culture state x(k) in is related to the feeding rate u(k), that is, the benefit optimization objective is expressed as follows:
    J 1＝P(T f)＝L[x(k),u(k)]  (5) J 1 =P(T f )=L[x(k),u(k)] (5)
    其中，L[x(k),u(k)]是描述终点产量与细胞培养状态及补料速率间函数关系；Among them, L[x(k),u(k)] is the functional relationship between the terminal output, cell culture state and feeding rate;
    当追求高产量的同时兼顾底物成本，则引入成本因子，经济效益优化目标选择一个批次生产的净利润与生产时间的比值，即过程效益，具体效益优化目标表示如下：When pursuing high yield while taking into account the substrate cost, the cost factor is introduced, and the economic benefit optimization goal selects the ratio of the net profit of a batch production to the production time, that is, the process benefit. The specific benefit optimization goal is expressed as follows:
    Figure PCTCN2022073489-appb-100001
    Figure PCTCN2022073489-appb-100001
    其中，r为单位产物的销售价格，c为单位补料的成本价格，
    Figure PCTCN2022073489-appb-100002
    为从 当前时刻至生产结束时的补料投入总量，T p为同一个生物反应罐相邻两个生产批次之间的时间间隔；     Among them, r is the sales price of the unit product, c is the cost price of the unit feed,
    Figure PCTCN2022073489-appb-100002
    is the total amount of feed input from the current moment to the end of production, T p is the time interval between two adjacent production batches of the same bioreactor;
    当对于底物成本较高的生产过程，追求底物到产物的转化率，经济效益优化目标选择一个批次的产物量与补料总量的比值，即产物得率，具体效益优化目标表示如下：For the production process with high substrate cost, the conversion rate from substrate to product is pursued, and the economic benefit optimization goal selects the ratio of the product amount of a batch to the total amount of feed, that is, the product yield. The specific benefit optimization goal is expressed as follows :
    Figure PCTCN2022073489-appb-100003
    Figure PCTCN2022073489-appb-100003
  5. 如权利要求1所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：采用间接测量方法进行细胞状态估计，或直接测量方法获得当前时刻的细胞状态估计值。The method for on-line estimation of cell culture state and optimal feeding control method according to claim 1, characterized in that: the cell state estimation is performed by an indirect measurement method, or the cell state estimation value at the current moment is obtained by a direct measurement method.
  6. 如权利要求5所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：当采用直接测量方法进行细胞状态估计，包括以下步骤：A method for online estimation of cell culture status and optimal feed regulation as claimed in claim 5, characterized in that: when the direct measurement method is used to estimate the cell status, the method comprises the following steps:
    利用光谱测量细胞，对光谱进行预处理和特征波段选择，通过建立光谱数据与细胞培养状态映射模型，直接得到细胞状态估计值
    Figure PCTCN2022073489-appb-100004
    Use the spectrum to measure the cells, preprocess the spectrum and select the characteristic band, and directly obtain the estimated value of the cell state by establishing a mapping model between the spectral data and the cell culture state
    Figure PCTCN2022073489-appb-100004
  7. 如权利要求5所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：当采用间接测量方法进行细胞状态估计，包括以下步骤：基于生化机理或实验，分析综合出菌体细胞内基础变量y(k)与细胞状态x(k)的关系，构造测量方程：A method for on-line estimation of cell culture status and optimal feed regulation as claimed in claim 5, characterized in that: when the indirect measurement method is used to estimate the cell status, it includes the following steps: based on biochemical mechanisms or experiments, analyzing and synthesizing the bacterial cells The relationship between the basic variable y(k) in the cell and the cell state x(k), construct the measurement equation:
    y(k)＝g[x(k)]+v(k)  (8)y(k)=g[x(k)]+v(k) (8)
    其中，g[x(k)]是构建的测量函数，假设v(k)为测量噪声，先通过氨基葡萄糖法、麦角固醇法或核酸法测量出y(k)，再通过估计方法间接获得当前时刻的细胞状态估计值
    Figure PCTCN2022073489-appb-100005
    Among them, g[x(k)] is the constructed measurement function, assuming that v(k) is the measurement noise, first measure y(k) by glucosamine method, ergosterol method or nucleic acid method, and then obtain indirectly by estimation method Estimated cell state at the current moment
    Figure PCTCN2022073489-appb-100005
  8. 如权利要求7所述的一种细胞培养状态在线估计及优化补料调控方法， 其特征在于：当选择间接测量方法进行细胞状态测量时，所述估计方法根据可测基础变量和细胞状态模型的形式、过程和测量噪声的统计分布，选择卡尔曼滤波法、扩展卡尔曼滤波法、滚动时域估计法、无迹卡尔曼滤波法、贝叶斯估计法、粒子滤波法或有限脉冲响应滤波法中的一种进行细胞状态估计，由前一时刻细胞状态对当前时刻细胞状态进行预测，根据基础变量y(k)的当前测量值，更新修正预测获得当前时刻的细胞状态估计值
    Figure PCTCN2022073489-appb-100006
    A method for online estimation of cell culture status and optimal feed regulation as claimed in claim 7, characterized in that: when the indirect measurement method is selected for cell state measurement, the estimation method is based on the measurable basic variables and the cell state model Statistical distribution of form, process, and measurement noise, with a choice of Kalman filtering, extended Kalman filtering, rolling time domain estimation, unscented Kalman filtering, Bayesian estimation, particle filtering, or finite impulse response filtering One of them estimates the cell state, predicts the cell state at the current moment from the cell state at the previous moment, and updates and corrects the prediction according to the current measured value of the basic variable y(k) to obtain the estimated value of the cell state at the current moment
    Figure PCTCN2022073489-appb-100006
  9. 如权利要求8所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：细胞状态模型和测量方程为非线性函数，且有高斯白噪声的情形下，采用扩展卡尔曼滤波算法，进行细胞培养状态估计，包括以下步骤：A method for online estimation of cell culture state and optimal feeding control method as claimed in claim 8, characterized in that: the cell state model and the measurement equation are nonlinear functions, and in the case of Gaussian white noise, the extended Kalman filter is used Algorithm for cell culture state estimation, comprising the following steps:
    a.细胞状态及其协方差的预测：由k时刻的估计值
    Figure PCTCN2022073489-appb-100007
    和补料速率u(k)对k+1时刻的细胞状态进行预测：     a. Prediction of cell state and its covariance: from the estimated value at time k
    Figure PCTCN2022073489-appb-100007
    and the feeding rate u(k) to predict the cell state at time k+1:
    Figure PCTCN2022073489-appb-100008
    Figure PCTCN2022073489-appb-100008
    Figure PCTCN2022073489-appb-100009
    Figure PCTCN2022073489-appb-100009
    其中，
    Figure PCTCN2022073489-appb-100010
    和
    Figure PCTCN2022073489-appb-100011
    分别为k+1时刻细胞状态及协方差的预测值，P(k)为k时刻的协方差估计值，Q为过程噪声的协方差矩阵；F(k)为状态转移矩阵，若细胞培养模型
    Figure PCTCN2022073489-appb-100012
    为非线性，则
    Figure PCTCN2022073489-appb-100013
    in,
    Figure PCTCN2022073489-appb-100010
    and
    Figure PCTCN2022073489-appb-100011
    are the predicted values of the cell state and covariance at time k+1, respectively, P(k) is the estimated value of covariance at time k, Q is the covariance matrix of process noise; F(k) is the state transition matrix, if the cell culture model
    Figure PCTCN2022073489-appb-100012
    is nonlinear, then
    Figure PCTCN2022073489-appb-100013
    b.细胞状态及其协方差的更新：在k+1时刻，利用获得的测量值y(k+1)对k时刻的预测进行更新修正：b. Update of the cell state and its covariance: At time k+1, use the obtained measured value y(k+1) to update and correct the prediction at time k:
    Figure PCTCN2022073489-appb-100014
    Figure PCTCN2022073489-appb-100014
    Figure PCTCN2022073489-appb-100015
    Figure PCTCN2022073489-appb-100015
    Figure PCTCN2022073489-appb-100016
    Figure PCTCN2022073489-appb-100016
    其中，
    Figure PCTCN2022073489-appb-100017
    为k+1时刻细胞状态估计值，K(k+1)为卡尔曼增益，R为测量噪声的协方差矩阵；H(k)为测量矩阵，若测量方程g[x(k)]为非线性，则
    Figure PCTCN2022073489-appb-100018
    in,
    Figure PCTCN2022073489-appb-100017
    is the estimated value of the cell state at time k+1, K(k+1) is the Kalman gain, R is the covariance matrix of the measurement noise; H(k) is the measurement matrix, if the measurement equation g[x(k)] is not linear, then
    Figure PCTCN2022073489-appb-100018
  10. 如权利要求1-9中任一项所述的一种细胞培养状态在线估计及优化补料调控方法，其特征在于：求解最优化经济效益下，满足约束条件的最优补料速率轨迹，具体包括以下步骤：A method for on-line estimation of cell culture status and optimal feeding control method according to any one of claims 1-9, characterized in that: solving the optimal feeding rate trajectory that satisfies the constraint conditions under the optimized economic benefits, specifically Include the following steps:
    以当前时刻的细胞培养状态估计值
    Figure PCTCN2022073489-appb-100019
    以及拟定的补料速率轨迹U k＝[u(k)，…，u(T f-1)] T为输入，用计算机数值解法求解细胞状态模型，得到未来时刻细胞状态向量X k+1＝[x(k+1)，…，x(T f)] T，其中，计算机数值解法包括离散状态模型迭代计算、连续状态模型龙格库塔法及欧拉法；     Estimated value of the cell culture state at the current moment
    Figure PCTCN2022073489-appb-100019
    And the proposed feeding rate trajectory U k =[u(k),...,u(T f -1)] T is input, and the cell state model is solved by computer numerical solution, and the cell state vector X k+1 = [x(k+1),...,x(T f )] T , where the computer numerical solutions include discrete state model iterative calculation, continuous state model Runge-Kutta method and Euler method;
    根据未来时刻细胞状态向量X k+1，采用非线性规划寻优算法，求解满足约束条件的经济效益J最优化问题，即求解
    Figure PCTCN2022073489-appb-100020
    得到最优补料轨迹U k，其中，寻优算法包括内点法、外点法、序贯二次规划法、遗传算法和粒子群算法；     According to the cell state vector X k+1 at the future time, the nonlinear programming optimization algorithm is used to solve the economic benefit J optimization problem satisfying the constraints, that is, to solve
    Figure PCTCN2022073489-appb-100020
    Get the optimal feeding trajectory U k , where the optimization algorithm includes interior point method, exterior point method, sequential quadratic programming method, genetic algorithm and particle swarm algorithm;
    将补料轨迹U k中当前时刻的补料速率u(k)实施于细胞培养生产过程； Apply the feeding rate u(k) at the current moment in the feeding trajectory U k to the cell culture production process;
    令k＝k+1，重复求解最优补料轨迹U k并实施当前时刻的补料速率u(k)过程，直至生产过程结束。 Let k=k+1, repeatedly solve the optimal feeding trajectory U k and implement the feeding rate u(k) process at the current moment until the end of the production process.
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