Guaranteed non-linear estimation using constraint propagation on sets

Bounded-error estimation is the estimation of the parameter or state vector of a model from experimental data, under the assumption that some suitably defined errors should belong to some prior feasible sets. When the model outputs are linear in the vector to be estimated, a number of methods are available to contain all estimates that are consistent with the data within simple sets such as ellipsoids, orthotopes or parallelotopes, thereby providing guaranteed set estimates. In the non-linear case, the situation is much less developed and there are very few methods that produce such guaranteed estimates. In this paper, the problem of characterizing the set of all state vectors that are consistent with all data in the case of non-linear discrete-time systems is cast into the more general framework of constraint satisfaction problems. The state vector at time k should be estimated either on-line from past measurement only or off-line from a series of measurements that may include measurements posterior to k . Even in the causal case, prior information on the future value of the state and output vectors, due for instance to physical constraints, is readily taken into account. Algorithms taken from the literature of interval constraint propagation are extended by replacing intervals by more general subsets of real vector spaces. This makes it possible to propose a new algorithm that contracts the feasible domain for each uncertain variable optimally (i.e. no smaller domain could be obtained) and efficiently.     

A kinetic model for beer production under industrial operational conditions

A kinetic model for beer production is proposed. The model takes into account five responses: biomass, sugar, ethanol, diacetyl and ethyl acetate. In contrast with previously published models, this model segregates biomass into three components: lag, active and dead cells and considers the active cells as the only fermentation agent. Experiments were first performed at laboratory scale and isothermal runs were carried out at five temperatures (8°C, 12°C, 16°C, 20°C and 24°C). Fitting of experimental data was made by non-linear regression. Parameter values calculated were similar to those given in the literature. The kinetic model was able to fit experimental data with a very good agreement. Afterwards, experiments were conducted at pilot plant scale and runs were now carried out changing temperature with time, in the industrial way. The kinetic model, with the parameter values calculated as a function of temperature, was able to predict with a very high accuracy the non-isothermal experimental data achieved. This model can be used for simulation of the industrial process under different operational conditions and for faults detection. It can also be utilized for the optimization and even for the supervised control of the process and its automatization.     

Rotary drying process modeling and online compensation

Rotary drying process modeling is a complex procedure due to the difficulties in measurement and estimation of kinetic model parameters. To solve the problem, a hybrid modeling method with online compensation is proposed in the present study. A mathematical model is built to describe the axial characteristics of rotary drying process. The drying rate which is the key parameter in the model is estimated by using a SVR-based fuzzy modeling approach, which can automatically extract fuzzy IF-THEN rules from support vectors. Laboratory experiments are conducted to obtain the drying rate sample data for the modeling purpose. In order to reduce the modeling errors for an industrial rotary dryer and improve the hybrid model prediction accuracy, an online matching coefficient is introduced, and a method based on improved online SVR is then applied for modeling error compensation. The experiment dada based modeling results have verified the effectiveness and demonstrated the accuracy and adaptability of the proposed hybrid modeling method.     

Getting the most out of it: Optimal experiments for parameter estimation of microalgae growth models

Mathematical models are expected to play a pivotal role for driving microalgal production towards a profitable process of renewable energy generation. To render models of microalgae growth useful tools for prediction and process optimization, reliable parameters need to be provided. This reliability implies a careful design of experiments that can be exploited for parameter estimation. In this paper, we provide guidelines for the design of experiments with high informative content based on optimal experiment techniques to attain an accurate parameter estimation. We study a real experimental device devoted to evaluate the effect of temperature and light on microalgae growth. On the basis of a mathematical model of the experimental system, the optimal experiment design problem was formulated and solved with both static (constant light and temperature) and dynamic (time varying light and temperature) approaches. Simulation results indicated that the optimal experiment design allows for a more accurate parameter estimation than that provided by the existing experimental protocol. For its efficacy in terms of the maximum likelihood properties and its practical aspects of implementation, the dynamic approach is recommended over the static approach.     

Enhancing fermentation development procedures via artificial neural networks

This paper describes how artificial neural networks can aid in recombinant fermentation process development. Two specific areas are addressed. Firstly, neural networks are used to increase the quality of information available during the course of a run. Available on-line measurements, together with a network model, are used to estimate key bioprocess parameters. Secondly, neural networks are used to formulate process models to aid in the specification of fermentation operational procedures. The ability to capture non-linear bioprocess characteristics is particularly significant and is an enhancement to existing experimental design procedures. Both the off-line experimental design and online parameter estimation techniques can aid in the progression from shake flask scale to large pilot scale operation.     

基于递推最小二乘估计的动力学模型参数识别

动力学建模过程中,模型参数的不确定性和参数的未知变化使得建模精度大为降低。通过对非线性最小二乘估计理论的研究,提出动力学模型参数的最小二乘估计,并设计出相应的估计器,基于现场数据给予模型较为准确的定论。应用于曲柄滑块机构中滑块与滑动面间的摩擦系数的估计,经过较少的迭代次数获得满意的估计效果。为动力学模型参数识别,建立更精确模型提供一个有效的途径。     

序贯实验设计法在吸附平衡实验中的应用

采用序贯实验设计法对正葵烷在5A分子筛上的吸附等温线实验进行了实验设计。根据Box和Lucas所提出的使待估参数联合置信域的容积趋于最小的参数估算的序贯实验设计准则，推导得出了正葵烷吸附等温线实验观测点的安排原则，发现对于一元线性模型，实验观测点应安排在可操作区的两端。对序贯设计实验和未经设计实验做了比较，经过序贯设计的实验所得到的模型参数的联合置信域比未经设计实验的小得多，表明序贯实验设计可提高模型参数估算的精度，减少实验工作量。     

Robust and efficient map-to-image registration with line segments

This work investigates map-to-image registration for planar scenes in the context of robust parameter estimation. Registration is posed as the problem of estimating a projective transformation which optimally aligns transformed model line segments from a map with data line segments extracted from an image. Matching and parameter estimation is solved simultaneously by optimizing an objective function which is based on M-estimators, and depends on overlap and the weighted orthogonal distance between transformed model segments and data segments. An extensive series of registration experiments was conducted to test the performance of the proposed parameter estimation algorithm. More than 200 000 registration experiments were run with different objective functions for 12 aerial images and randomly corrupted maps distorted by randomly selected projective transformations. Received: 10 August 2000 / Accepted: 29 January 2001     

An inquiry into the applicability of Kantorovich’s idea to the thermodynamic optimization

A feasible region is employed to describe unknown parameters in thermodynamic models. The method is based on interval estimation of experimental observations, and it is applied to thermodynamic optimization of liquid phase in Ag–Mg system. A final feasible region is an overlapping area among all feasible regions calculated from different groups of data. A discussion of computational advantages on this method suggests that it is a promising method for parameter estimation, but its limitations require more studies on problems such as non-linear inequalities, multi-dimensional visualization and uncertainties in experimental conditions.     

Comments on `Identification of non-linear parametrically varying models using separable least squares’ by F. Previdi and M. Lovera: black-box or open box?

This note compares and contrasts the non-linear parameter varying (NLPV) and state-dependent parameter (SDP) model classes. It shows that, while they have similarities, the two-stage SDP modelling procedure, involving non-parametric identification, followed by parametric estimation, is quite different from the single stage NLPV procedure. In particular, the SDP procedure allows for the identification of the model structure and the nature of the non-linearities, prior to the estimation of the parameters that characterize this identified model structure. In contrast to NLPV modelling, therefore, SDP estimation opens up the ‘black box’ and reveals the inner nature of the non-linear system.     

Identification of non-linear parametrically varying models using separable least squares

In this paper a novel identification algorithm for a class of non-linear, possibly parameter varying models is proposed. The algorithm is based on separable least squares ideas. These models are given in the form of a linear fractional transformation (LFT) where the ‘forward’ part is represented by a conventional linear regression and the ‘feedback’ part is given by a non-linear map which can take into account scheduling variables available for measurement. The non-linear part of the model can be parameterized according to various paradigms, like, e.g. neural network (NN) or general nonlinear autoregressive exogenous (NARX) models. The estimation algorithm exploits the separability of the criterion used to estimate the parameters. When using a NN, it is possible the explicit computation of the Frechet derivative needed to implement a separable least square algorithm.     

基于小波逼近变换的非线性分布参数系统辨识

利用Haar小波正交规范基的微分运算矩阵及其运算性质,将描述一类非线性分布参数系统的偏微分方程转化为代数矩阵方程,结合最小二乘法,确定出待辨识的系统参数,避免了对偏微分方程进行多重积分运算的繁琐;并且,可以不考虑初始条件和边界条件,较其他采用积分运算矩阵的辨识方法要简单得多,简化了分布参数系统辨识的求解过程。该方法简单,计算量小,辨识精度高。仿真结果表明了该算法应用在非线性分布参数系统辨识中的有效性。     

基于遗传算法的锂离子电池等效电路参数识别

结合锂离子电池双极性等效电路模型提出了一种基于遗传算法的参数识别方法,该方法通过指数函数对电路模型中的电阻、电容、恒压源等元件进行有理逼近,根据电池在不同充放电速率下的输出电压特性数据,通过实数编码遗传算法得到最优的函数参数,从而得到最优的电阻、电容,开路电压等电路参数值,针对电池在不同的工作状态,不同的工作参数下的运行数据,系列仿真和实验结果表明该算法原理简明,收敛较快,辨识得到的最优模型其电压输出特性与电池的实际电压输出特性基本吻合,能较精确的反映电池的实际特性,具有较高的辨识精度。     

Contrasting ideal and realistic conditions as a means to improve judgment-based software development effort estimation

Context

The effort estimates of software development work are on average too low. A possible reason for this tendency is that software developers, perhaps unconsciously, assume ideal conditions when they estimate the most likely use of effort. In this article, we propose and evaluate a two-step estimation process that may induce more awareness of the difference between idealistic and realistic conditions and as a consequence more realistic effort estimates. The proposed process differs from traditional judgment-based estimation processes in that it starts with an effort estimation that assumes ideal conditions before the most likely use of effort is estimated.

Objective

The objective of the paper is to examine the potential of the proposed method to induce more realism in the judgment-based estimates of work effort.

Method

Three experiments with software professionals as participants were completed. In all three experiments there was one group of participants which followed the proposed and another group which followed the traditional estimation process. In one of the experiments there was an additional group which started with a probabilistically defined estimate of minimum effort before estimating the most likely effort.

Results

We found, in all three experiments, that estimation of most likely effort seems to assume rather idealistic assumptions and that the use of the proposed process seems to yield more realistic effort estimates. In contrast, starting with an estimate of the minimum effort, rather than an estimate based on ideal conditions, did not have the same positive effect on the subsequent estimate of the most likely effort.

Conclusion

The empirical results from our studies together with similar results from other domains suggest that the proposed estimation process is promising for the improvement of the realism of software development effort estimates.     

Designing priors for robust Bayesian optimal experimental design

Building mathematical models is a common task in process systems engineering, which requires estimation of model parameters as the final step of modeling exercise. Model based experimental design has evolved as a potential statistical tool for reducing uncertainties in parameter estimates. Often a huge volume of process information is generated as an end result of an experimental design. Designing optimal experiments based on current or prior process knowledge is still an open research problem. This paper deals with how information, available a priori, can be organized and systematically used for designing robust Bayesian dynamic experiments, in the presence of process constraints. The designed experiments are ‘robust’ to a poor choice of nominal parameter values. Several novel techniques for organizing a priori process knowledge are explored from a theoretical view point. The influence of proposed prior designs on parameter estimates is demonstrated on a semi-continuous baker's yeast fermenter problem.     

Set-membership estimation from poor quality data sets: Modelling ammonia volatilisation in flooded rice systems

A set-membership (bounded-error) estimation approach can handle small and poor quality data sets as it does not require testing of statistical assumptions which is possible only with large informative data sets. Thus, set-membership estimation can be a good tool in the modelling of agri-environmental systems, which typically suffers from limited and poor quality observational data sets. The objectives of the paper are (i) to demonstrate how six parameters in an agri-environmental model, developed to estimate NH₃ volatilisation in flooded rice systems, were estimated based on two data sets using a set-membership approach, and (ii) to compare the set-membership approach with conventional non-linear least-squares methods. Results showed that the set-membership approach is efficient in retrieving feasible parameter-vectors compared with non-linear least-squares methods. The set of feasible parameter-vectors allows the formation of a dispersion matrix of which the eigenvalue decomposition reflects the parameter sensitivity in a region.     

An Artificial Neural Network-Based Model for Effective Software Development Effort Estimation

In project management, effective cost estimation is one of the most crucial activities to efficiently manage resources by predicting the required cost to fulfill a given task. However, finding the best estimation results in software development is challenging. Thus, accurate estimation of software development efforts is always a concern for many companies. In this paper, we proposed a novel software development effort estimation model based both on constructive cost model II (COCOMO II) and the artificial neural network (ANN). An artificial neural network enhances the COCOMO model, and the value of the baseline effort constant A is calibrated to use it in the proposed model equation. Three state-of-the-art publicly available datasets are used for experiments. The backpropagation feedforward procedure used a training set by iteratively processing and training a neural network. The proposed model is tested on the test set. The estimated effort is compared with the actual effort value. Experimental results show that the effort estimated by the proposed model is very close to the real effort, thus enhanced the reliability and improving the software effort estimation accuracy.     

On the Robust Nonlinear Motion Position and Force Control of Flexible Joints Robot Manipulators

The design of a robust nonlinear position and force controller for a flexible joints robot manipulator interacting with a rigid environment is presented. The controller is designed using the concept of feedback linearization, sliding mode techniques, and LQE estimation methodologies. It is shown that the nonlinear robot manipulator model is feedback linearizable. A robust performance of the proposed control approach is achieved by accounting for the system parameters uncertainties in the derivation of the nonlinear control law. An upper bound of the error introduced by parametric uncertainties in the system is computed. Then, the feedback linearizing control law is modified by adding a switching action to compensate the errors and to guarantee the achievement of the desired tracking performance. The relationship between the minimum achievable boundary layer thickness and the parametric uncertainties is derived. The proposed controller is tested using an experimental flexible joints robot manipulator, and the results demonstrate its potential benefits in reducing the number of sensors required and the complexity of the design. This is achieved by eliminating the need for nonlinear observers. A robust performance is obtained with minimum control effort by taking into account the effect of system parameter uncertainties and measurement noise.     

Experimental comparison and application of various parameter-adaptive control algorithms

Various recursive parameter estimation algorithms and controller design procedures can be combined to build up parameter-adaptive control algorithms. Two parameter estimation methods and six control algorithms have been selected, taking into account good convergence properties and small computational expense and regarding the conditions for closed-loop identification. The resulting 12 parameter-adaptive control algorithms are compared and tested with a process computer in on-line operation with analog simulated stable and unstable processes for stochastic disturbances and step changes of the reference signal. The results are very promising. In many cases a good control performance is achieved. As a priori knowledge only the sampling time, the process model order and time delay and in some cases a weighting factor for the process input signal are required. Some parameter-adaptive control algorithms with good properties are applied to digital adaptive control of an air heater. Conclusions are given for the selection of parameter-adaptive control algorithms, depending on the type of process and its disturbances.The adaptive control algorithms may be applied for adaptive control of constant and time variant, linear and weakly non-linear stable and unstable processes with process computers or micro computers or for self-tuning of control algorithms or tuning of conventional analog PID controllers, if external disturbances act on the loop.