A new waste characterization method for the anaerobic digestion based on ADM1

In studies of waste treatment, waste characterization can be regarded as one of the most important tasks because the waste composition and concentrations greatly affect the process behaviors. This paper proposes a waste characterization method for anaerobic digestion based on ADM1. The relationships between the steady state of the process and the concentrations of the influent components are investigated and determined based on the use of information regarding the process output to estimate the waste characteristics. In addition, a new procedure of parameter division and optimization for characterizing the influent waste is proposed. Here, the parameters to be estimated are divided based on the bi-linear nature of the problem, identifiability and information content of the parameters, under the given measurements. Parameter division can greatly reduce the search space for optimization problem and can ensure that the estimate is minimally sensitive to the selection of initial parameter values. The proposed method is tested through a case study of the pilot-scale anaerobic digester and through a numerical simulation. Simulation results show that the waste characteristics estimated using the proposed method best fit the critical states of the process although some parameters are difficult to identify. In addition, it is proved that the parameter division can find the maximal number of parameters which are identifiable from the given measurements and can improve the estimation accuracy.     

用图解法进行系统辨识

目前参数估计的方法很多,本文介绍用图解法进行参数估计,此法算式简单,能得到较好的参数估计,不存在收敛问题。     

Optimal sensor placement for agro-hydrological systems

The estimation of soil moisture is essential for developing advanced closed-loop irrigation schemes. One associated problem is how to place the sensors appropriately in the soil to provide good measurements for state estimation. In this work, we address the problem of optimal sensor placement for state estimation of agro-hydrological systems. A systematic approach is proposed to find the minimum number of sensors that ensures the observability of the entire system and then to find the best locations of the sensors in terms of degree of observability. The Richards equation that is used to describe the dynamics of the agro-hydrological system is discretized into a large-scale nonlinear state-space model. In the proposed procedure, the key steps include order reduction of the large-scale system model, exploration of the minimum number of sensors needed for state estimation and optimal placement of the sensors in the soil. Three different scenarios are considered and optimal sensor placement is addressed for all the scenarios using the proposed procedure. Simulation results show the effectiveness of the proposed procedure and methods.     

非线性分布参数系统状态估计的最佳测量位置

研究了分布参数系统状态估计中特有的最佳测量位置问题．建立了基于后集中方法的分布参数系统的非线性状态估计器,包括状态估计偏微分方程和微分灵敏度矩阵偏微分方程,并用适当的数值计算方法实现状态估计器的求解;以一个最小化的空间域上积分函数表达最佳测量位置的目标函数,并相应地用非线性约束优化方法求解系统具有一个或多个测量时的最佳测量位置．还以壁冷式单管固定床反应器为例,讨论了各种因素对最佳测量位置的影响及其灵敏度,并得出了一些有普遍意义的结论．     

On the feasibility and reliability of nonlinear kinetic parameter estimation for a multi-component photocatalytic process

Nonlinear kinetic parameter estimation plays an essential role in kinetic study in reaction engineering. In the present study, the feasibility and reliability of the simultaneous parameter estimation problem is investigated for a multi-component photocatalytic process. The kinetic model is given by the L-H equation, and the estimation problem is solved by a hybrid genetic-simplex optimization method. Here, the genetic algorithm is applied to find out, roughly, the location of the global optimal point, and the simplex algorithm is subsequently adopted for accurate convergence. In applying this technique to a real system and analyzing its reliability, it is shown that this approach results in a reliable estimation for a rather wide range of parameter value, and that all parameters can be estimated simultaneously. Using this approach, one can estimate kinetic parameters for all components from data measured in only one time experiment.     

Recursive state estimation techniques for nonlinear differential algebraic systems

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. While state and parameter estimation of ODE systems has been studied extensively, differential algebraic equation (DAE) systems have received much less attention. However, most realistic chemical engineering processes are modelled as DAE systems and hence state and parameter estimation of DAE systems is a significant problem. Becerra et al. (2001) proposed an extension of the extended kalman filter (EKF) for estimating the states of a system described by nonlinear differential-algebraic equations (DAE). One limitation of this approach is that it only utilizes measurements of the differential states, and is therefore not applicable to processes in which algebraic states are measured. In this paper, we address the state estimation of constrained nonlinear DAE systems. The novel aspects of this work are: (i) development of a modified EKF approach that can utilize measurements of both algebraic and differential states, (ii) development of a recursive approach for the inclusion of constraints, and (iii) development of approaches that utilize unscented sampling in state and parameter estimation of nonlinear DAE systems; this has not been attempted before. The utility of these estimators is demonstrated using electrochemical and reactive distillation processes.     

Effective parameter estimation within a multi-dimensional population balance model framework

This study considers optimization problems with multi-dimensional population balance models embedded. The objective function is formulated as a least-squares problem, minimizing the difference between target data and simulated model output and the goal is to find model parameter values that best fit the data. Results show that derivative-free methods, such as the Nelder–Mead simplex method, fail to converge to an optimal solution. A similar result was obtained with gradient-based methods such as BFGS, quasi-Newton, Newton, Gauss–Newton, Levenberg–Marquardt and SQP, and with a stochastic genetic algorithm. It was hypothesized that three main issues could contribute to these convergence failures: (1) gradients were calculated based on finite differences, and as a result of improper step size determination, the numerical error could be prohibitive resulting in inaccurate derivative information, (2) the parameters may not be identifiable and (3) numerical instability could occur during the course of optimization. To circumvent these issues, this work addresses the calculation of derivative information based on automatic differentiation and sensitivity analysis to ensure increased accuracy. Issues such as parameter identifiability are also dealt with by analyzing an accurate Fisher information matrix. Given the computational burden in calculating accurate Jacobians and Hessians, compounded by the potential nonsmoothness introduced into the objective function as a result of granule nucleation, other optimization strategies may be warranted and this work addresses those accordingly. Overall, by systematically assessing the problem formulation and mechanisms, the results show that substantial improvements in convergence can be achieved by utilizing appropriate optimization techniques, thus leading to more successful and optimal parameter estimation.     

Kinetic parameter estimation of HDPE slurry process from molecular weight distribution: Estimability analysis and multistep methodology

This study addresses kinetic parameter estimation for a high‐density polyethylene (HDPE) slurry process based on fitting molecular weight distributions (MWDs). From the process model, we conduct an estimability analysis by assessing the relative sensitivity between output variables and kinetic parameters as well as confidence intervals. This determines which parameters can be estimated. Conversely, a major challenge remains with the solution of an ill‐conditioned parameter estimation problem with MWD as the output variable. To overcome the convergence difficulties with the associated problem, we develop a novel multistep methodology where we first obtain MWD parameters by matching to data and then estimate kinetic parameters by matching to the regressed MWD parameters. Computational results and eigenvalue analysis show this multistep methodology separates an ill‐conditioned problem into two well‐conditioned subproblems. Moreover, we consider simulation‐based and industrial HDPE case studies. These results demonstrate the applicability, potential, and efficiency of this solution procedure. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3442–3459, 2014     

On sequentially adaptive asymptotically efficient rank statistics

For the simple regression model ( containing the two—sample location model as a special case ), adaptive ( linear ) rank statistics arising in the context of ( asymtotically) efficient testing and estimation procedures are considered. An orthonormal system based on the classical Legendre polynomial system is incorporated in the adaptive determination of the score generating function, and the proposed sequential procedure is based on a suitably posed stopping rule. Various properties of this sequentailly adaptive procedure and the allied stopping rule are studied. Asymptotic linearity results ( in a shift or regression parameter ) of linear rank statistics are studied with special reference to the Legendre polynomial system and some improved rates of convergence are estabilished in this context.     

Nonlinear dynamic data reconciliation and parameter estimation through particle swarm optimization: Application for an industrial polypropylene reactor

This work presents a procedure to solve nonlinear dynamic data reconciliation (NDDR) problems with simultaneous parameter estimation based on particle swarm optimization (PSO). The performance of the proposed procedure is compared to the performance of a standard Gauss-Newton (GN) scheme in a real industrial problem, as presented previously by Prata et al. [2006. Simultaneous data reconciliation and parameter estimation in bulk polypropylene polymerizations in real time. Macromolecular Symposia 243, 91-103; 2008. In-line monitoring of bulk polypropylene reactors based on data reconciliation procedures. Macromolecular Symposia 271, 26-37]. Both methods are used to solve the NDDR problem in an industrial bulk propylene polymerization process, using real data in real time for the simultaneous estimation of model parameters and process states. A phenomenological model of the real process, based on the detailed mass and energy balances and constituted by a set of algebraic-differential equations, was implemented and used for interpretation of the actual plant behavior in real time. The resulting nonlinear dynamic optimization problem was solved iteratively on a moving time window, in order to capture the current process behavior and allow for dynamic adaptation of model parameters. Obtained results indicate that the proposed PSO procedure can be implemented in real time, allowing for estimation of more reliable process states and model parameters and leading to much more robust and reproducible numerical performance.     

Parameter identification for state estimation—application to bioprocess software sensors

Together with some on-line measurements, a reliable process model is the key ingredient of a successful state observer design. In common practice, the model parameters are inferred from experimental data so as to minimize a model prediction error, e.g. so as to minimize an output least-squares criterion. In this procedure, no care is actually exercised to ensure that the unmeasured model states are sensitive to the measured states. In turn, if sensitivity is too low, the resulting state observer will probably generate poor estimates of the unmeasured states. To alleviate these problems, a new parameter identification procedure is proposed in this study, which is based on a cost function combining a conventional prediction error criterion with a state estimation sensitivity measure. Minimization of this combined cost function produces a model dedicated to state estimation purposes. A thorough analysis of the procedure is presented in the context of bioreactor modeling, including parameter identification, model validation and design of extended Kalman filters and full horizon observers.     

A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through integrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.     

An inverse problem for estimating the time-dependent reaction coefficient in an autocatalytic reaction pathway

An inverse algorithm based on the Iterative Regularization Method (IRM) is applied in this study in determining the unknown time-dependent reaction coefficient for an autocatalytic reaction pathway by using measurements of concentration components. Since no prior information is available on the functional form of the unknown reaction coefficient, thus it can be classified as function estimation for the inverse calculations. The accuracy of this inverse problem is examined by using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation of the time-dependent reaction coefficient can be obtained within a very short CPU time on a Pentium IV 1.4 GHz personal computer.     

Estimation of a state-dependent model parameter

A numerical algorithm was developed which estimates a state-dependent model parameter on the basis of transient state observation data. The algorithm was presented for the problem of estimating the temperature dependence of thermal diffusivity in a one-dimensional heat equation. The estimation problem was converted into a finite dimensional optimization problem by the least-squares formulation and B-splines representation of the parameter. Numerical experiments were performed using simulated observation data as well as the actual observation data obtained in a heat conduction experiment on rubber compound layers. The performance of the algorithm was discussed in relation to the effect of the parameter representation scheme, the quality and quantity of the data.     

Predicting conversion using temperature as the measured variable in the RIM process. Part I: Simulation and measurement structure

In general the monitoring and control of many industrial processes is so complicated by problems associated with the on-line measurement of the desired objectives that they must be inferred from available measurements. This leads to a state estimation problem in which the selection and adaptation of the structure of the measurements plays an important role. In particular, in the reaction injection molding (RIM) process, an accurate on-line estimate of the conversion field is highly desirable. Since conversions cannot be determined readily by direct measurements, and a thermocouple can provide reliable dynamic temperature data, we can predict the conversion field from the solution of a state estimation problem using temperature as the measured variable. In this article, we describe an algorithm for designing the optimal arrangement of measuring sensors and analyze the RIM process dynamics which influence the structure depending on the operating conditions. The search for the optimal measurement structure for the purpose of state estimation makes up the bulk of the results. No particular estimation-control strategy is investigated in this paper. Work is underway to develop the on-line corrective system, which will use the temperature measurements to correct model predictions. The results of that work will appear in part II of this series.     

Tracking of moving interfaces in sedimentation processes using electrical impedance tomography

Sedimentation monitoring is widely used to control and optimize industrial processes. In this paper we propose a novel computational method for sedimentation monitoring using electrical impedance tomography (EIT). EIT measurements consist of electric current and voltage measurements that are made on the surface of the sedimentation tank and therefore they do not interfere with the sedimentation process. The proposed computational method is based on shape estimation and state estimation formulation of the EIT problem. The sedimentation is parameterized by the locations of the phase interfaces and conductivities of the phase layers. Three different evolution models for the state parameters are considered and the state estimates are computed using the extended Kalman filter algorithm. The performance of the method and the models are evaluated using simulated data from a six electrode EIT measurement configuration. From the results a promising performance of the method can be seen.     

含时滞测量值下间歇过程的双维状态估计

基于粒子滤波研究了间歇过程的状态估计问题。根据间歇过程双维动态特性,针对关键参数在线检测精度低、离线分析时滞大等问题,分别建立一种双维状态转移模型和时滞测量模型,并利用贝叶斯方法及前/后向平滑,提出一种含时滞测量值下的双维状态估计算法。该算法通过融合先前批次和时滞测量值的信息提高估计精度,并且克服了离线采样周期和时滞时间不确定的问题。在数字仿真和啤酒发酵过程中的仿真应用验证了该算法的有效性。     

On-line identification of interacting two-tank system

In order to demonstrate the effectiveness of the process identification algorithm, on-line parameter estimator is evaluated experimentally by using two-tank system with interaction. On-line parameter estimator used in this paper is based on a recursive parameter estimation algorithm. MIMO linear, bilinear and quadratic models based on ARMA model are used to identify two-tank system. A quadratic model for two-tank system with interaction is developed to confirm the propriety of MIMO quadratic model used in identification of two-tank system. The results of on-line identification experiments on the two-tank system show that the estimated parameters of each model converge and the output tracking errors are bounded by disturbance bound. But, the quadratic model showed the best convergence.