Parameter estimation for nonlinear systems with multirate measurements and random delays

We present an approach for parameter estimation with multirate measurements, with the slow measurements having variable time delays due to laboratory analysis, and also being functions of all the states during the sample collection. We formulate a particle filter-based approach under the framework of the expectation maximization algorithm to develop the estimates. The effectiveness and applicability of the proposed method are demonstrated though a simulation example, a hybrid tank experiment and an industrial case study; in each case, the slow and fast measurements are for the same variable. We show that this approach results in improved parameter estimation when the information from the delayed measurements is fused with the fast measurement information.     

利用状态空间模型和不敏卡尔曼滤波的分批补料发酵过程在线估计(英文)

On-line estimation of unmeasurable biological variables is important in fermentation processes, directly influencing the optimal control performance of the fermentation system as well as the quality and yield of the targeted product. In this study, a novel strategy for state estimation of fed-batch fermentation process is proposed. By combining a simple and reliable mechanistic dynamic model with the sample-based regressive measurement model, a state space model is developed. An improved algorithm, swarm energy conservation particle swarm optimization (SECPSO), is presented for the parameter identification in the mechanistic model, and the support vector machines (SVM) method is adopted to establish the nonlinear measurement model. The unscented Kalman filter (UKF) is designed for the state space model to reduce the disturbances of the noises in the fermentation process. The proposed on-line estimation method is demonstrated by the simulation experiments of a penicillin fed-batch fermentation process.     

FIR model identification of multirate processes with random delays using EM algorithm

The motivation for this article comes from our development of soft sensors for chemical processes where several challenges are encountered. For example, quality variables in chemical processes are often measured off‐line through laboratory analysis. Collection of samples and subsequent analyses inevitably introduce uncertain time delays associated with the irregularly sampled quality variables, which add significant difficulty in identification of process with multirate (MR) data. Considering the MR system with random sampling delays described by a finite impulse response (FIR) model, an Expectation–Maximization (EM)‐based algorithm to estimate its parameters along with the time delays is developed. Based on the identified FIR model, two algorithms are proposed to recover the approximate output error (OE) or transfer function model. Two simulation examples as well as a pilot‐scale experiment are provided to illustrate the effectiveness of the proposed methods. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4124–4132, 2013     

Distributed state estimation from infrequent and delayed measurements in large-scale processes

Effective control and monitoring of a process usually require frequent and delay-free measurements of important process output variables. However, these measurements are often either not available or available infrequently with significant time delays. This article presents a method that allows for improving the performance of distributed state estimators implemented on large-scale manufacturing processes. The method uses a sample state augmentation approach that permits using delayed measurements in distributed state estimation. The method can be used with any state estimator, including unscented Kalman filters, extended Kalman filters, and moving horizon state estimators. The method optimally handles the tradeoff between computational time and estimation accuracy in distributed state estimation implemented using a computer with parallel processors. Its implementation and performance are shown using a few simulated examples.     

Parameter estimation in models with hidden variables : An application to a biotech process

Biological processes are often characterised by significant nonlinearities, noisy measurements and hidden process variables. The dynamic behaviour of such processes can be represented by stochastic differential equations obtained from physical laws. We propose a Bayesian algorithm for parameter estimation in stochastic nonlinear biological processes with unmeasured (or hidden) variables. The proposed algorithm, involves drawing random samples iteratively from a posterior density functions of the parameters and the hidden variables. A Bayesian sampling techniques is used to approximate these posterior density functions. Both Metropolis–Hastings algorithm and Gibbs sampling are used for sample generation. The algorithm is extended to handle multiple data sets and missing observations. The algorithm is applied to an experimental data set collected from an algal bioreactor system. © 2011 Canadian Society for Chemical Engineering     

Scale-Up studies of non-aerated fed-batch fermentation of dextransucrase and the industrial synthesis of dextran using the enzymatic route

High activities of the enzyme dextransucrase were repeatedly produced using slowly agitated non-aerated fed-batch fermentations of Leuconostoc mesenteroides B-512(F). Activities in excess of 24.0 U cm^?3 were obtained consistently in a 16 dm³ laboratory fermenter using a 6 dm³ initial work volume. Yeast extract type was identified to be one of the important factors influencing the enzyme yield. Studies on aerating the medium with different gases indicated that the presence of carbon dioxide in the medium favoured high enzyme production. Agitation rates did not appear to have significant effects on either cell growth or enzyme production. One type of antifoam (silicone antifoam) was observed to affect enzyme production but not the cell growth. Scale-up of the non-aerated process was carried out up to a 1000 dm³ scale with enzyme broths containing up to 21.0 U cm^?3 being produced. Two batches of the enzyme that were produced at the large scale were used for the first time to synthesize dextran at a 50000 dm³ industrial scale. The dextran yields were up to 95.5% of the conventional industrial yields and were achieved in much shorter reaction time intervals.     

Adaptive linear quadratic gaussian (LQG) control of a bioreactor

The paper deals with the modelling and adaptive control of a continuous-flow fermentation process for the production of alcohol. The fermenter model has been developed from mass balance and leads to nonlinear differential equations. In practice, control strategies are difficult to derive using this non-linear model. The dilution rate and the substrate concentration have been considered as control and controlled variables, respectively. The adaptive control algorithm implemented is based on the linear quadratic control approach, where the associated Riccati equation is iterated until the system closed-loop poles belong to a restricted stability domain which is included in the unit circle. A single input/output model is used for control purposes. The model parameters are estimated on-line using a robust identification algorithm which includes: data normalization, time-varying forgetting factor, covariance matrix factorization, etc. Experimental results show the performance of this adaptive scheme and its ability to control biotechnological processes.     

Consensus-based approach for parameter and state estimation of agro-hydrological systems

The development of advanced closed-loop irrigation systems requires accurate soil moisture information. In this work, we address the problem of soil moisture estimation for the agro-hydrological systems in a robust and reliable manner. A nonlinear state-space model is established based on the discretization of the Richards equation to describe the dynamics of the agro-hydrological systems. We consider that model parameters are unknown and need to be estimated together with the states simultaneously. We propose a consensus-based estimation mechanism, which comprises two main parts: (a) a distributed extended Kalman filtering algorithm used to estimate several model parameters; and (b) a distributed moving horizon estimation algorithm used to estimate the state variables and one remaining model parameter. Extensive simulations are conducted, and comparisons with existing methods are made to demonstrate the effectiveness and superiority of the proposed approach. In particular, the proposed approach can provide accurate soil moisture estimate even when poor initial guesses of the parameters and the states are used, which can be challenging to be handled using existing algorithms.     

Recursive least squares scheme for operating a class of continuous fermentation processes at optimal steady state productivity

This paper has developed a recursive least squares scheme for operating a class of continuous fermentation processes at the optimal steady state productivity. More precisely, the class of continuous fermentation processes under investigation is described by a widely accepted non-segregated fermentation process model. Based on a recursive least squares algorithm, an on-line estimation scheme for estimating the optimal set points for feed substrate concentration and dilution rate is developed. Finally, via simulation, it is shown that this on-line estimation scheme is robust against measurement time (sampling time). © 1998 Society of Chemical Industry     

Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

The cobalt removal process with arsenic salt of zinc hydrometallurgy has serious non-linearity, uncertainty, and mutual coupling. Its accurate dynamic modelling has always been a challenging problem. On the basis of in-depth analysis of cobalt removal process and reaction mechanism, considering the cascade relationship between the reactors, a dynamic synergistic continuously stirred tank reactor (SCSTR) mechanism model of the cobalt removal process was constructed. Aiming at the unknown parameters in the SCSTR model, the idea of the Kalman filter was introduced, and the unknown parameters were characterized as unknown states; a method of estimating the unknown model parameters was developed using the augmented state equation and the unscented Kalman filter (UKF) algorithm. Simulation results with industrial data of a zinc smeltery showed that the parameter estimation model has high accuracy, and the estimated parameters can be used in the SCSTR model. An intensive simulation analysis of the dynamic characteristics of the complete SCSTR model was carried out to verify the influence of different input disturbances on the output ion concentration of each reactor, which demonstrated the excellent dynamic performance and potential of the model. Ultimately, according to the industrial calculation analysis, the SCSTR model has a guiding effect on the addition of zinc powder in the reactors, overcomes the blindness in the production process, and provides a momentous basis for the optimization control of the cobalt removal process.     

Long range predictive control of a polymerization reactor

This paper examines the application of generalized predictive control (GPC), one in the class of long-range predictive algorithms, to the control of conversion of methyl methacrylate (MMA) monomer in a simulated CSTR, and to the control of temperature in a pilot plant batch polymer reactor. The control objective is regulation in the presence of (i) stochastic disturbances due to impurities (in the case of the CSTR), and (ii) pulse disturbances from the addition of cold solvent and initiator (in the case of the batch reactor). The role of the observer polynomial as a detuning parameter for trading off performance against variability in the control action is emphasized. Also, the role of data prefiltering, prior to model parameter estimation, is examined. A frequency domain interpretation of the least squares estimation algorithm is used to clarify the role of the filter.     

On-line estimation of VFA concentration in anaerobic digestion via methane outflow rate measurements

This paper deals with the design of a robust nonlinear observer as a software sensor to achieve the on-line estimation of the concentration of Volatile Fatty Acids (VFA) in a class of continuous anaerobic digesters (AD). Taking into account the limited availability of on-line sensors for AD process, in this contribution is assumed that only the methane outflow rate is available for on-line measurement. The estimation method is based on a modified version for a two-dimensional mathematical model of AD process. From the differential algebraic observability approach it is shown that the VFA concentration is detectable from the methane outflow rate measurements. The observer convergence is analyzed by using Lyapunov stability techniques. Numerical simulations illustrate the effectiveness of the proposed estimation method for a four-dimensional AD model with uncertainties associated with unmodeled dynamics and disturbances in the inflow composition.     

自适应混合粒子群约束优化算法及其在软测量模型参数估计中的应用

对于软测量模型参数估计问题, 针对传统梯度法求解非线性最小二乘模型时依赖初值、需要追加趋势分析进行验证和无法直接求解复杂问题的缺陷, 提出将参数估计化为约束优化问题, 使用混合优化算法求解的新思路。为此提出一种自适应混合粒子群约束优化算法(AHPSO-C)。在AHPSO-C算法中, 为平衡全局搜索(混沌粒子群)和局部搜索(内点法), 引入自适应内点法最大函数评价次数更新策略。对12个经典测试函数的仿真结果表明, AHPSO-C是求解约束优化问题的一种有效算法。将算法用于淤浆法高密度聚乙烯(HDPE)串级反应过程中熔融指数软测量模型参数估计, 验证了方法的可行性与优越性。     

Primary beer fermentation by immobilised yeast—a review on flavour formation and control strategies

Immobilised cells are increasingly being used in bio‐industries and may also have benefits for the brewing industry. The major challenge to applying this technology successfully in breweries is focused on the main fermentation in combination with the secondary fermentation. In particular, the control and fine‐tuning of the flavour profile during the main fermentation require further investigation. In this review, the influence of immobilised cell technology on the production of the flavour‐active compounds (i.e. higher alcohols, esters and vicinal diketones) is discussed. Control strategies that are based on the manipulation of parameters during fermentation such as temperature, feed volume, wort gravity, wort composition and aeration are explained. Finally, bioreactor configurations that may facilitate immobilised cells in performing the primary fermentation are evaluated. Copyright © 2006 Society of Chemical Industry     

氧化还原电位调控混合糖为底物的丁醇发酵

控制丁醇发酵过程中的氧化还原电位（oxidoreduction potential, ORP）能够大幅提高丁醇产量和果糖利用率,并降低终点有机酸浓度。实验考察了以葡萄糖和果糖混合糖为底物,通过泵入无菌空气控制ORP分别不低于-490、-460、-430及-400 mV丁醇发酵情况。其中,控制ORP不低于-460 mV时,丁醇和总溶剂产量分别达到13.19 g·L^-1及19.71 g·L^-1,相对于不控制ORP的丁醇自然发酵分别提高了139.38%及117.07%,残糖浓度降低至3.20 g·L^-1,糖利用率高达94.18%。该调控策略有效地解决了以葡萄糖和果糖混合糖为底物的丁醇发酵过程中存在的残糖浓度高、丁醇产量低的问题。     

Comparison of parameter estimation methods in stochastic chemical kinetic models: Examples in systems biology

Stochastic chemical kinetics has become a staple for mechanistically modeling various phenomena in systems biology. These models, even more so than their deterministic counterparts, pose a challenging problem in the estimation of kinetic parameters from experimental data. As a result of the inherent randomness involved in stochastic chemical kinetic models, the estimation methods tend to be statistical in nature. Three classes of estimation methods are implemented and compared in this paper. The first is the exact method, which uses the continuous‐time Markov chain representation of stochastic chemical kinetics and is tractable only for a very restricted class of problems. The next class of methods is based on Markov chain Monte Carlo (MCMC) techniques. The third method, termed conditional density importance sampling (CDIS), is a new method introduced in this paper. The use of these methods is demonstrated on two examples taken from systems biology, one of which is a new model of single‐cell viral infection. The applicability, strengths and weaknesses of the three classes of estimation methods are discussed. Using simulated data for the two examples, some guidelines are provided on experimental design to obtain more information from a limited number of measurements. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1253–1268, 2014