Robust modeling of a microalgal heterotrophic fed-batch bioreactor

Microalgal feedstocks have shown potential for the production of biofuels and fine chemicals. Recently, an optimal experimental input profile for the identification of parameters of a microalgal bioreactor, containing 6 states and 12 unknown parameters has been proposed. In this work, the proposed design is implemented and parameters are estimated. It was found that the parameter estimation procedure can be made more computational efficient by the use of a novel iterative non-linear model reparameterization algorithm. By applying the proposed algorithm to experimental data, a good degree of output prediction was achieved along with bounds on the parameter values. The final, validated, model can be used for optimal control and process simulation.     

Optimization of the Wear Properties of Polyoxymethylene Components Under Injection Process Conditions

This study investigates the influences of two processing conditions on wear properties of Polyoxymethylene (POM) polymer, and further determines the optimal parameter setting for the injection molding process to achieve optimal wear quality. This study uses two experimental designs, including the conventional single factor design and Taguchi L₉ orthogonal design. Moreover, morphology of worn surfaces was analyzed by scanning electron microscopy (SEM). Analytic results confirm that combining the Taguchi experimental design with the analysis of variance (ANOVA) can link controlled parameters and targeted output, and rapidly predict the optimal parameter settings for various injection-molding conditions.     

OPTIMAL DESIGN OF A CLOSED LOOP CONTROLLER FOR ESTIMATION OF PARAMETER COUPLES OF MICROBIAL GROWTH KINETICS

This paper deals with the design of a feedback controller for the decorrelated estimation of a parameter couple appearing in an unstructured model for growth of one biomass on one limiting substrate in a fed-batch bioreactor. By optimal experimental design, feed rate strategies for decorrelated parameter estimation have been constructed (as reported elsewhere). These profiles have in common a feeding phase in which the substrate concentration is kept constant at a setpoint value by a feedforward controller. On simulation level this controller can be applied as an open loop controller. However, in practice these feed rate strategies are to be implemented in closed loop. Since during experimental design on simulation level a nominal parameter set is required, an iterative approach is needed to end up with a truly optimal experiment for estimation of the unknown parameters. Such an iterative scheme is proposed and its convergence properties are discussed     

Sequential experimental design based on multiobjective optimization procedures

Model-based sequential experimental designs are frequently applied for discrimination of rival models and/or estimation of precise model parameters. Although the development and use of a single design criterion to perform the simultaneous model discrimination and precise parameter estimation seem appealing, published material indicates that previous attempts to develop such a single design criterion have not been successful. Despite that, this problem has rarely been analyzed with the help of multiobjective optimization procedures. In this work, a multiobjective optimization method based on the particle swarm optimization procedure is used to build the Pareto fronts in experimental design problems where distinct design criteria used for discrimination of rival models and/or estimation of precise model parameters are considered simultaneously. It is shown through the rigorous analysis of the Pareto sets that both design objectives are frequently conflicting, which means that optimum discrimination of rival models and estimation of precise model parameters cannot be performed simultaneously in many cases. However, it is also shown that the use of the posterior covariance matrix of estimated model parameters for model discrimination makes the design of experiments for the simultaneous optimum model discrimination and estimation of model parameters possible in many experimental design problems.     

A real-time estimation approach to time-varying time delay and parameters of NARX processes

This paper presents a solution to the joint time-varying time delay and parameter estimation of NARX (nonlinear autoregressive with exogenous inputs) processes, where only pure time delay in input signal is considered. A modified strong tracking filter (MSTF) is proposed, and is adopted as an adaptive estimation algorithm. Three kinds of specific NARX processes are considered. The first is also the simplest, the output signal is the input with time delay plus disturbance; The second one is a simple NARX process plus disturbance; The third NARX process even has unknown time-varying parameters. For each of the NARX processes, we set up a specific estimation model, with these models the proposed MSTF algorithm can be applied to the real-time time delay and parameter estimation of the above three NARX processes. Computer simulation results demonstrate the effectiveness of the proposed approach. Moreover the robustness of the proposed algorithm against some model/process parameter mismatches is also tested via computer simulations.     

Sequential experimental design for model discrimination: Taking into account the posterior covariance matrix of differences between model predictions

Techniques for experimental design of experiments for model discrimination constitute important tools for scientists and engineers, as analyzed phenomena can very often be described fairly well by different mathematical models. As interpretation and use of available experimental data depend on the model structure, techniques for design of experiments for selection of the best model are of fundamental importance. Besides, experiments must often be designed for estimation of model parameters and reduction of variances of model predictions (or parameter estimates). These two classes of experimental design techniques generally lead to different experimental designs, although model discrimination and reduction of variances of parameter estimates are closely related to each other. In this work the posterior covariance matrix of difference between model predictions is taken into account during the design for model discrimination for the first time. The obtained results show that the model discrimination power becomes much higher when the posterior covariance matrix of difference between model predictions are considered during the experimental design, increasing the capability of model discrimination and simultaneously leading to improved parameter estimates.     

On the costs of parameter uncertainties. Part 2: Impact of EVOP procedures on the optimization and design of experiments

Pinto (1998) showed that an economical value might be assigned to model parameter uncertainties, which could be used for process optimization and for taking decisions during sequential experimental designs. The procedure is extended to take into account the fact that plant operation conditions change with time, leading to improvements of the plant operation and allowing the partial recovering of losses introduced by uncertain parameters during plant design. It is shown that the use of EVOP (Evolutionary Operation Procedures) during plant operation may reduce the cost of parameter uncertainties, exerting a major impact on process optimization and optimal design of experiments.     

Optimal allocation for estimating the mean of a bivariate polynomial

Suppose we wish to estimate the mean of some polynomial function of random variables from two independent Bernoulli populations, the parameters of which. rhemselves, are modeled as independent beta random variables. It. is assumed that the t.otal sample size for the experiment is fixed, but that the number of experimental units observed from each population may be random. This problem arises, ior example, when estimating the fault tolerance of a system by testing its compomentc individually. Using a decision theorebic approach, we seek to minimize the Bayes risk that arises from using a squared error loss function The Bayes estimator can lw detrmined in a straightforwardmanner, so the problem of optimal estimation rcduces. therefore, to a problem of optimallocatton of the samples between the two populatiorls. This can be solved via dynamic programming. Similar programming techniques are utilized to evaluate properties of a number of ad hoc allocation strategies that might also be collsidered for use in this problem.Two sample polynomials are analyzed along with a number of examples indicating the effects of different prior parameter settings. The effects of differences between prior pararueters used in the design and analysis stages of the experiment are also examined. For the polynomials considered, the adaptive strategies are found to be especially robust. We discuss computational techniques that facilitate such analyses by permitting rapid re-evaluation of strategies. Capabilities of this sort enrouragepeople to explorr designs more fully and to consider them from a number of different viewpuillts.     

Adaptive two-stage optimal designs for phase II clinical studies that allow early futility stopping

Abstract

Adaptive designs play an important role in contemporary clinical trials to make designs flexible and efficient. In cancer clinical trials, given a relatively small sample size, it is important to obtain as much information as possible during this phase. We propose a new adaptive optimal design that stops for futility only in the first stage as Simon’s two-stage design. The existing adaptive two-stage designs are often allowed to be stopped for futility or efficacy due to computational advantage. It is difficult to search for an optimal design with futility stopping only in the first stage by using efficient search algorithms; for example, the branch-and-bound algorithm. We have to use multiple computational techniques to search for the optimal design. The proposed adaptive design meets the important property of the monotonic property that the second stage sample size is a nonincreasing function of the number of responses from the first stage. In this article, we show that the proposed adaptive design always has a smaller expected sample size than Simon’s optimal design. We recommend it for use in practice as an alternative to the commonly used Simon’s design.     

Feedback linearizing control of a fluidized bed reactor

The design of an adaptive nonlinear controller for the control of a fluidized bed reactor is derived by using exact linearization techniques. Reset action and parameter adaptation are used to make more robust the precise compensation of nonlinear terms, which is called for in the linearization technique. A nonlinear antiwindup mechanism is introduced to handle reset windup problem and to provide fast response without large overshoot. Simulation results show that the proposed adaptive controller guarantees good setpoint tracking. The developed estimation algorithm allows accurate estimation of the parameters for which the regressor component is not zero.     

New results on VRFT design of PID controller

Virtual reference feedback tuning (VRFT) design method can be applied to determine the parameters of a PID controller from the available process input and output data without resorting to the identification of a process model. Although it is an attractive alternative to the popular model-based controller design methods, the existing results are restricted to the linear systems. In this paper, an adaptive VRFT design method with application to the adaptive PID controller design is proposed. In addition, the relationship between the VRFT and IMC designs is analyzed as well. Simulation results are presented to illustrate the advantage of the adaptive VRFT design over the conventional VRFT design.     

Latent variable projections of sensitivity data for experimental screening and kinetic modeling

In microkinetic modeling the number of kinetic parameters is large and the precision of the “known” parameters is often very low. The standard approach is then to fit only the most uncertain parameters while regarding the fixed parameter as “true”. This assumption will have consequences also on the fitted parameters since the correlation structure often is quite significant. In this study we have taken the approach to fit many parameters and then try to use more efficient experimental designs to break the correlation structure and thus obtain more precise parameter estimation despite the large number of fitted parameters. After performing sensitivity analysis of many candidate experiments, a latent variable model (PCA) is made from the resulting sensitivity matrix and the score matrix is used as a candidate set prior to experiment selection. Due to the correlation structure in the sensitivity matrix, the number of components from the PCA model is fewer than the number of parameters. The columns in the score matrix are furthermore orthogonal whereas the columns in the original sensitivity matrix are not. Different designs were generated using the original sensitivity matrix, the score matrix as well as using a space-filling design and performing a sequential approach. Both steady state and transient experiments were evaluated. These different designs were used to fit kinetic parameters to a simulated dataset made using published parameter values. The results show no significant difference when using the original sensitivity matrix or the score matrix. However, since the score matrix has fewer columns than the full sensitivity matrix, the use of designs based on the score matrix enables more efficient designs when few experiments are required. The number of components in the PCA model also gives the rank of the parameter space induced by the candidate experiments. This is useful information when fitting many parameters in a microkinetic model and provides an assessment of the value of every candidate experiment before it is even performed.     

Precise parameter estimation for chemical batch reactions in heterogeneous medium

A sequential experimental strategy for precise parameter estimation has been used in the case of liquid-liquid dispersions in batch-stirred tank reactors where slow chemical reactions take place. The mathematical model for a batch reaction in a stirred tank reactor is formulated as a system of non-linear differential equations standing for the mass balance of each component. Physical kinetic parameters and chemical kinetic parameters which arise from this model are estimated simultaneously. The estimation problem is posed as a weighted least squares problem and solved by using a standard Levenberg-Marquardt algorithm. In this work, we intend to show how it is possible to develop efficient experimental design strategies that lead to an accurate estimation of the parameters involved in phenomenological models and most particularly in kinetic models. Three design criteria for designing the experiments have been employed in order to increase the precision on the parameter estimates of the model. A standard non-linear sequential quadratic programming method ensures the determination of the operating conditions which define the experimental design. The well-known alkaline hydrolysis of esters in aqueous phase has been treated as a numerical application example.     

Adaptive Designs to Maximize Power in Clinical Trials with Multiple Treatments

Abstract

We consider a clinical trial with three competing treatments and study designs that allocate subjects sequentially in order to maximize the power of relevant tests. Two different criteria are considered: the first is to find the best treatment and the second is to order all three. The power converges to one in an exponential rate and we find the optimal allocation that maximizes this rate by large deviation theory. For the first criterion the optimal allocation has the plausible property that it assigns a small fraction of subjects to the inferior treatment. The optimal allocation depends heavily on the unknown parameters and, therefore, in order to implement it, a sequential adaptive scheme is considered. At each stage of the trial the parameters are estimated and the next subject is allocated according to the estimated optimal allocation. We study the asymptotic properties of this design by large deviations theory and the small sample behavior by simulations. Our results demonstrate that, unlike the two-treatments case, adaptive design can provide significant improvement in power.     

ADAPTIVE MULTIVARIABLE PID CONTROLOF A DISTILLATION COLUMN WITH UNKNOWN AND VARYING DEAD TIME

A new, reliable, and easy-to-use adaptive control strategy has been developed to overcome the long-existing difficulties in adaptive control practice caused by unknown and varying process dead time. A self-tuning PID control algorithm is adopted to control a distillation column possessing second-order-plus-dead-time dynamics. The self-tuning strategy is based on recursive least-squares estimation of process parameters. U-D factorization is applied to stabilize the parameter estimation calculations. A variable forgetting factor is used to alleviate wind-up in the estimator. A simulation study and an experimental evaluation demonstrate the capability of the adaptive algorithm.     

Optimal experiment design for nonlinear dynamic (bio)chemical systems using sequential semidefinite programming

Optimal experiment design (OED) for parameter estimation in nonlinear dynamic (bio)chemical processes is studied in this work. To reduce the uncertainty in an experiment, a suitable measure of the Fisher information matrix or variance–covariance matrix has to be optimized. In this work, novel optimization algorithms based on sequential semidefinite programming (SDP) are proposed. The sequential SDP approach has specific advantages over sequential quadratic programming in the context of OED. First of all, it guarantees on a matrix level a decrease of the uncertainty in the parameter estimation procedure by introducing a linear matrix inequality. Second, it allows an easy formulation of E‐optimal designs in a direct optimal control optimization scheme. Finally, a third advantage of SDP is that problems involving the inverse of a matrix can be easily reformulated. The proposed techniques are illustrated in the design of experiments for a fed‐batch bioreactor and a microbial kinetics case study. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1728–1739, 2014     

Nonlinear parameter estimation through particle swarm optimization

Parameter estimation procedures are very important in the chemical engineering field for development of mathematical models, since design, optimization and advanced control of chemical processes depend on model parameter values obtained from experimental data. Model nonlinearity makes the estimation of parameter and the statistical analysis of parameter estimates more difficult and more challenging. In this work, it is shown that many of these difficulties can be overcome with the use of heuristic optimization methods, such as the particle swarm optimization (PSO) method. Parameter estimation problems are solved here with PSO and it is shown that the PSO method is efficient for both minimization and construction of the confidence region of parameter estimates. Moreover, it is shown that the elliptical approximation of confidence regions of nonlinear model parameters can be very poor sometimes and that more accurate likelihood confidence regions can be constructed with PSO, allowing for more reliable statistical analysis of the significance of parameter estimates.     

基于适应策略差分进化算法的化工反应动力学参数估值

为了更准确地通过煤烟气成分推测汞元素氧化程度,建立精确的汞氧化过程动力学模型至关重要。目前已有的汞氧化过程动力学模型中存在一些难以确定的未知参数,为了确定模型中这些参数的最优值,本文提出一种改进的适应策略差分进化算法（ASDE）。该算法引入变异策略、缩放因子（F）和交叉参数（CR）候选集合,同时为集合中每个候选参数赋予一定的选择概率。在进化搜索过程中,以历史成功搜索信息为基础,实时更新每个候选集合中各参数对应的选择概率,并根据选择概率自适应为下一时刻进化群体中每个个体分配变异策略和对应控制参数。将改进算法用于汞氧化过程动力学参数估值问题,实验结果显示,相对其他6种算法,改进算法ASDE求解得到模型更加接近实际,是一种求解化工反应动力学参数估值问题的有效方法。     

藉助自适应支持向量机为延迟焦化反应过程建模

The performance of support vector regression estimation was studied. It is found that the insensitive factor ε, penalty factor, and the kernel function along with its parameter are the main factors affecting the performance of support vector regression estimation. It remains a critical unsolved problem to determine the parmaeters of SVM. Cross-validation methods are commonly used in practice to decide the parameters of SVM, but they are usually expensive in computing time. A novel adaptive support vector machine (A-SVM) was proposed to determine the optimal parameters adaptively. The algorithms for adaptively tuning parameters of SVM were worked out. A-SVM was successfully applied in modeling delayed coking process. Compared with RBFN-PLSR methods, A-SVM was superior in both fitting accuracy and prediction performance. The proposed algorithms in general may be used in modeling complex chemical processes.     

Analysis of process dynamics in bioreactors

The dynamic behaviour of bioreactors was analysed by means of experimental process identification using correlation analysis with pseudo-random binary input signals (PRBS) for excitation of the process. Agitation speed and airflow were used as input signals. The correlation with oxygen partial pressure in the liquid and oxygen and carbon dioxide concentrations in the exhaust gas were calculated. Results of the computation are: degree of a linear differential equation and coefficients of the equation, which can then be used to design adaptive controllers. The dead time of the system can be found by comparing the least squares of different models. The variation of the parameters during process time are shown for a low order adaptive controller.