On the modelling of heat exchangers and heat exchanger network dynamics using bond graphs

ABSTRACT

Heat exchanger networks are important systems in most thermal engineering systems and are found in applications ranging from power plants and the process industry to domestic heating. Achieving cost-effective design of heat exchanger networks relies heavily on mathematical modelling and simulation-based design. Today, stationary design calculations are carried out for all new designs, but for some special applications, the transient response of complete networks has been researched. However, simulating large heat exchanger networks poses challenges due to computational speed and stiff initial value problems when flow equations are cast in differential algebraic form. In this article, a systems approach to heat exchanger and heat exchanger network modelling is suggested. The modelling approach aims at reducing the cost of system model development by producing modular and interchangeable models. The approach also aims at improving the capability for large and complex network simulation by suggesting an explicit formulation of the network flow problem.     

An MINLP retrofit approach for improving the flexibility of heat exchanger networks

A mixed integer nonlinear programming (MINLP) model for the retrofit of heat exchanger networks (HENs) in order to improve their flexibility is presented in this paper. As stream flowrates and inlet temperatures and/or heat transfer coefficients are allowed to vary within either specified ranges or discrete sets, a multiperiod hyperstructure network representation is developed based on critical operating conditions (i.e. periods of operation) that limit the network's flexibility. This multiperiod hyperstructure includes all possible network configurations. Structural modifications, such as new stream matches, exchanger reassignments, splitting and mixing of streams are explicitly modeled either considering one-to-one or one-to-many assignment of heat exchangers to stream matches. Energy recovery and utility consumption are not predetermined but are optimized as part of a total annualized cost along with the structural modification cost in the objective function. Thus, trade-offs between operating and retrofit investment costs to improve the flexibility of a HEN are accounted for. The resulting large scale MINLP is solved with the application of the Generalized Benders Decomposition. The proposed multiperiod retrofit model can be included in a general framework to improve the operability of heat exchanger networks.     

Integrated technique assessment based on the pinch analysis approach for the design of production networks

Integrated Process Design aims at a holistic approach to process design, retrofitting, and operations planning. Cost and energy “targets” (i.e. the minimum possible values for these objectives) can be calculated based on pinch technology, which defines the enthalpy at which the hot and cold process streams are separated by the minimum temperature difference in heat exchanger networks. This approach is well established in process engineering and has recently been expanded to mass pinch analysis. The combination of engineering, process integration and Operations Research allows the consideration of a variety of economic and environmental process attributes for an integrated technique assessment, as a case study in the sector of automotive serial coating shows.     

A theory for the optimal synthesis of heat-exchanger systems

The problem of the optimal synthesis of heat exchanger systems is treated here with an entirely new approach. It is formulated, using the heat spectrum diagram, as a problem of finding the combination of heat donors and receivers that will minimize a given criterion function. This function is the cost of the heat exchanger system, assumed to be proportional to the total heat-transfer area.The problem is a combinatorial problem for continuous elements. It is solved in general by applying the maximum principle of Pontryagin. The solution for a specific problem is shown to be obtainable by a simple graphical operation.     

Evolving fuzzy rule based controllers using genetic algorithms

The synthesis of genetics-based machine learning and fuzzy logic is beginning to show promise as a potent tool in solving complex control problems in multi-variate non-linear systems. In this paper an overview of current research applying the genetic algorithm to fuzzy rule based control is presented. A novel approach to genetics-based machine learning of fuzzy controllers, called a Pittsburgh Fuzzy Classifier System # 1 (P-FCS1) is proposed. P-FCS1 is based on the Pittsburgh model of learning classifier systems and employs variable length rule-sets and simultaneously evolves fuzzy set membership functions and relations. A new crossover operator which respects the functional linkage between fuzzy rules with overlapping input fuzzy set membership functions is introduced. Experimental results using P-FCS 1 are reported and compared with other published results. Application of P-FCS1 to a distributed control problem (dynamic routing in computer networks) is also described and experimental results are presented.     

Data-driven fuzzy models for nonlinear identification of a complex heat exchanger

This paper presents and discusses experimental results on nonlinear model identification method applied to a real pilot thermal plant. The aim of this work is to develop a moderately complex model with interpretable structure for a complex parallel flow heat exchanger which is the main component of the thermal plant using a fuzzy clustering technique. The proposed Takagi–Sugeno-type (TS) fuzzy rule-based model is derived through an iterative fuzzy clustering algorithm using a set of input–output measurements. It is shown that the identified multivariable fuzzy rule-based model captures well the key dynamical properties of the physical plant over a wide operating range and under varying operating conditions. For validation, the model is run in parallel and series-parallel configurations to the real process. The experimental results show clearly the high performance of the proposed fuzzy model in achieving good prediction of the main process variables.     

A fast genetic method for inducting descriptive fuzzy models

Under certain inference mechanisms, fuzzy rule bases can be regarded as extended additive models. This relationship can be applied to extend some statistical techniques to learn fuzzy models from data. The interest in this parallelism is twofold: theoretical and practical. First, extended additive models can be estimated by means of the matching pursuit algorithm, which has been related to Support Vector Machines, Boosting and Radial Basis neural networks learning; this connection can be exploited to better understand the learning of fuzzy models. In particular, the technique we propose here can be regarded as the counterpart to boosting fuzzy classifiers in the field of fuzzy modeling. Second, since matching pursuit is very efficient in time, we can expect to obtain faster algorithms to learn fuzzy rules from data. We show that the combination of a genetic algorithm and the backfitting process learns faster than ad hoc methods in certain datasets.     

Multi-objective optimization of heat exchangers using a modified teaching-learning-based optimization algorithm

Teaching-learning-based optimization (TLBO) is a recently developed heuristic algorithm based on the natural phenomenon of teaching-learning process. In the present work, a modified version of the TLBO algorithm is introduced and applied for the multi-objective optimization of heat exchangers. Plate-fin heat exchanger and shell and tube heat exchanger are considered for the optimization. Maximization of heat exchanger effectiveness and minimization of total cost of the exchanger are considered as the objective functions. Two examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using the modified TLBO are validated by comparing with those obtained by using the genetic algorithm (GA).     

Computing latest starting times of activities in interval-valued networks with minimal time lags

This paper deals with problems of determining possible values of earliest and latest starting times of an activity in networks with minimal time lags and imprecise durations that are represented by means of interval or fuzzy numbers. Although minimal time lags are practical in different projects, former researchers have not considered these problems.After proposing propositions which reduce the search space, a novel polynomial algorithm is presented to compute intervals of possible values of latest starting times in interval-valued networks with minimal time lags. Then, the results are extended to networks with fuzzy durations.     

Temporal problems solved by dynamic fuzzy network based on genetic algorithm with variable-length chromosomes

In this paper, a dynamic fuzzy network and its design based on genetic algorithm with variable-length chromosomes is proposed. First, the dynamic fuzzy network constituted from a series of dynamic fuzzy if–then rules is proposed. One characteristic of this network is its ability to deal with temporal problems. Then, the proposed genetic algorithm with variable-length chromosomes is adopted into the design process as a means of allowing the application of the network in situations where the actual desired output is unavailable. In the proposed genetic algorithm, the length of each chromosome varies with the number of rules coded in it. Using this algorithm, no pre-assignment of the number of rules in the dynamic fuzzy network is required, since it can always help to find the most suitable number of rules. All free parameters in the network, including the spatial input partition, consequent parameters and feedback connection weights, are tuned concurrently. To further promote the design performance, genetic algorithm with variable-length chromosomes and relative-based mutated reproduction operation is proposed. In this algorithm, the elite individuals are directly reproduced to the next generation only when their averaged similarity value is smaller than a similarity threshold; otherwise, the elites are mutated to the next generation. To show the efficiency of this dynamic fuzzy network designed by genetic algorithm with variable-length chromosomes and relative-based mutated reproduction operation, two temporal problems are simulated. The simulated results and comparisons with recurrent neural and fuzzy networks verify the efficacy and efficiency of the proposed approach.     

An extension to possibilistic fuzzy cluster analysis

We explore an approach to possibilistic fuzzy clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical. Our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters, so that they are forced away from each other. We develop this approach for the possibilistic fuzzy c-means algorithm and the Gustafson–Kessel algorithm. In our experiments we found that in this way we can combine the partitioning property of the probabilistic fuzzy c-means algorithm with the advantages of a possibilistic approach w.r.t. the interpretation of the membership degrees.     

Using the Hamming distance to extend TOPSIS in a fuzzy environment

Considering the fact that, in some cases, determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data, this paper extends the TOPSIS method for dealing with fuzzy data, and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. In this approach, to identify the fuzzy ideal solution and fuzzy negative ideal solution, one of the Yager indices which is used for ordering fuzzy quantities in [0, 1] is applied. Using Yager’s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives. Then, the Hamming distance is proposed for calculating the distance between two triangular fuzzy numbers. Finally, an application is given, to clarify the main results developed in the paper.     

Optimal stopping in a fuzzy environment

The problem under consideration is that of optimally controlling and stopping either a deterministic or a stochastic system in a fuzzy environment. The optimal decision is the sequence of controls that maximizes the membership function of the intersection of the fuzzy constraints and a fuzzy goal. The fuzzy goal is a fuzzy set in the cartesian product of the state space with the set of possible stopping times. Dynamic programming is applied to yield a numerical solution. This approach yields an algorithm that corrects a result of Kacprzyk.     

Online identification of Takagi–Sugeno fuzzy models based on self-adaptive hierarchical particle swarm optimization algorithm

This paper presents an approach for online learning of Takagi–Sugeno (T-S) fuzzy models. A novel learning algorithm based on a Hierarchical Particle Swarm Optimization (HPSO) is introduced to automatically extract all fuzzy logic system (FLS)’s parameters of a T–S fuzzy model. During online operation, both the consequent parameters of the T–S fuzzy model and the PSO inertia weight are continually updated when new data becomes available. By applying this concept to the learning algorithm, a new type T–S fuzzy modeling approach is constructed where the proposed HPSO algorithm includes an adaptive procedure and becomes a self-adaptive HPSO (S-AHPSO) algorithm usable in real-time processes. To improve the computational time of the proposed HPSO, particles positions are initialized by using an efficient unsupervised fuzzy clustering algorithm (UFCA). The UFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system, enhancing the HPSO’s tuning. The approach is applied to identify the dynamical behavior of the dissolved oxygen concentration in an activated sludge reactor within a wastewater treatment plant. The results show that the proposed approach can identify nonlinear systems satisfactorily, and reveal superior performance of the proposed methods when compared with other state of the art methods. Moreover, the methodologies proposed in this paper can be involved in wider applications in a number of fields such as model predictive control, direct controller design, unsupervised clustering, motion detection, and robotics.     

Flexible Energy Management and Heat Exchanger Network Design

The design of heat exchanger networks (HEN) is a well-studied problem in process synthesis and an ideal test base to benchmark methods and techniques in the field. Despite a significant number of relevant publications, networks are still designed under assumptions of fixed operating conditions. Significant variations in supply and demand, alongside a need for efficient management in energy markets (energy grids, deregulated markets), impose limitations to this practice. Networks, designed with thermodynamic and economic efficiency under nominal operation, are known to have their efficiency dissipated and wasted in a context of similar though different conditions and demands. In a process plant, operational changes are common but designers still favor the staged approach of Pinch Technology (i.e., targeting-network development) where flexibility is not addressed properly and systematically. Alternatively, superstructure methods offer formulations with complexities hard to address by conventional algorithms. In this work, flexibility is addressed in a context amenable to targeting and network development stages, offering opportunities to visualise solutions and review options. For targeting, a dual approach is proposed that follows the framework of Hypertargets by Briones and Kokossis (1999a, 1999b, 1999c). The conceptual screening involves (i) the selection of cost-effective (primal) matches, and (ii) a model-based approach to assess the flexibility of the design options. Models and procedures are employed to assess trade-offs between operating cost (energy), capital cost (area), and the options' ability to handle variations (flexibility). Primal matches are automatically developed into network configurations with the use of mathematical models. A rigorous, superstructure-based approach is next applied to ensure the development of networks capable of handling operational variations without a need to consider exhaustive combinations of scenarios. The iterative approach incrementally augments the mathematical formulation by constraints and vertex conditions that guarantee consistency. The procedure is illustrated with two industrial problems and reports important improvements over conventional techniques.     

Sparse quadratic programming in chemical process optimization

The quadratic programming aspects of a full space successive quadratic programming (SQP) method are described. In particular, fill-in, matrix factor and active set updating, numerical stability, and indefiniteness of the Hessian matrix are discussed in conjunction with a sparse modification of Bunch and Parlett factorization of symmetric indefinite (Kuhn-Tucker) matrices of the type often encountered in optimization. A new pivoting strategy, called constrained pivoting, is proposed to reduce fill-in and compared with complete, partial and threshold pivoting. It is shown that constrained pivoting often significantly reduces fill-in and thus the iterative computational burdens associated with the factorization and solution of Kuhn-Tucker conditions within the QP subproblem. A numerical algorithm for updating the lower triangular and diagonal factors is presented and shown to be very fast, usually requiring only about 5% of the cost of refactorization. Two active set strategies are also presented. These include the options of adding inequalities either one or several at a time. In either case, the effects on matrix factor updating is shown to be small. Finally, a simple test is used to maintain iterative descent directions in the quadratic program. Our sparse symmetric indefinite QP algorithm is tested in the context of a family of SQP algorithms that include a full space Newton method with analytical derivatives, a full space BFGS method and a Range and Null space Decomposition (RND) method in which the projected Hessian is calculated from either analytical second derivatives or the BFGS update. Several chemical process optimization problems, with small and large degrees of freedom, are used as test problems. These include minimum work calculations for multistage isothermal compression, minimum area targeting for heat exchanger networks, and distillation optimizations involving some azeotropic and extractive distillations. Numerical results show uniformly that both the proposed QP and SQP algorithms, particularly the full space Newton method, are reliable and efficient. No failures were experienced at either level.     

Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays

This paper investigates delay-dependent robust exponential state estimation of Markovian jumping fuzzy neural networks with mixed random time-varying delay. In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the robust exponential state estimation of Markovian jumping Hopfield neural networks with mixed random time-varying delays. Moreover probabilistic delay satisfies a certain probability-distribution. By introducing a stochastic variable with a Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally exponentially stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay-dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally some numerical examples are provided to demonstrate the effectiveness of the proposed method.     

An architecture of fuzzy neural networks for linguistic processing

Fuzzy sets have been used successfully in order to deal with imprecise data, linguistic terms or not well-defined concepts. Recently, considerable effort has been made in the direction of combining the neural network approach with fuzzy sets. In this paper a fuzzy feed-forward neural network, able to process trapezoidal fuzzy sets, has been investigated. Normalized trapezoidal fuzzy sets have been considered. The fuzzy generalized delta rule with different back-propagation algorithms is discussed. The more interesting and characteristic property of the proposed architecture is the ability of each node to process fuzzy sets or linguistic terms, preserving the simplicity of the back-propagation algorithm. Consequently, the resulting architecture is able to cope with problems in which the input parameters and the desired targets are described by linguistic terms. This methodology has the further interesting characteristic of being able to operate at the linguistic level rather than at the numerical level, that is it can work at a higher data abstraction level. An example in computerized electrocardiography will be illustrated in order to test the proposed approach.     

A novel self-adaptive control strategy of frost prevention and retardation for air source heat pumps in winter conditions

As frost accumulates on the heat exchanger surface with time, system operating performance will be dramatically degraded, and limit its use in climates susceptible to frost formation. A novel self-adaptive control strategy of frost prevention and retardation for air source heat pumps (ASHP) is introduced in this paper. The control strategy relies on a new thermodynamic model, which involves a Dimensionless Artificial Neural Network (DANN) correlation model describing frost accumulation for ASHP on the air-side of the fin-and-tube heat exchanger. The dimensionless parameters of this DANN model, including the ambient conditions, 6 commonly used refrigerants, and the geometric parameters of the heat exchanger, are considered in the model. To enhance the reliability of DANN, we develop a self-adaptive algorithm, including determining the optimal transfer algorithm and selecting the number of neurons in the hidden layer, for the DANN model. Results show a limited relative error (7.55%) between calculated values and experimental data, which help researchers and manufacturers analyze the complicated frosting process and design the new ASHPs more reasonably in different regions with different ambient conditions.