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Maintenance scheduling optimization for decaying performance nonlinear dynamic processes
Abstract
A first contribution of this paper is an overview of the research efforts and contributions
over several decades in the area of scheduling maintenance optimization for decaying
performance dynamic processes. Following breakthrough ideas and implementation in
the area of heat exchanger networks for optimal scheduling of cleaning actions subject to
exchanger surface fouling, these concepts were transferred successfully to the area of
scheduling catalyst replacement actions in catalytic reactor networks. This necessary
overview leads to the main, second contribution aimed with this work: its application to
restorative maintenance scheduling in the area of RON regeneration actions planning, as
well as point to new areas where this approach can be fruitfully applied to and extended
into in the near future – particularly enhancing model descriptions that include general
types of planning uncertainty. The effectiveness and efficacy of the approach is
demonstrated computationally in this work.
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Heat exchanger networks are structures composed of a set of heat exchangers interconnected in order to reduce utilities consumption. During the network operation, heat exchangers may present a decrease of their thermal effectiveness caused by fouling, which corresponds to the undesirable accumulation of deposits over their thermal surface. In this context, this paper presents a proposal to increase the energy recovered in heat exchanger networks affected by fouling through the optimization of the distribution of the flow rates of the process streams. The problem corresponds to a dynamic optimization problem, because the flow rate optimization affects the surface temperature and velocity, which modifies the fouling rate, thus demanding the simultaneous analysis of the entire time horizon. The objective function is represented by the integral of the utility consumption during the operational time horizon. The main constraints include mass and energy balances, heat exchangers equations (P-NTU method), and fouling rate modeling. The mathematical structure of the problem corresponds to a nonlinear optimization. The utilization of the optimization scheme is illustrated by the analysis of two examples of heat exchanger networks.
This article presents a novel approach for optimising maintenance scheduling and production in a process using decaying catalysts while considering uncertainties in the kinetic parameters involved. The approach formulates this problem as a multistage mixed-integer optimal control problem (MSMIOCP) and uses a solution methodology that can offer a number of potential advantages over conventional methodologies. The solution methodology involves using a multiple scenario approach to consider parametric uncertainties and formulating a stochastic version of the MSMIOCP, which is solved as a standard nonlinear optimisation problem using a technique developed in a previous work. The proposed formulation and solution methodology are applied to identify the effects on the optimal process operation, of individual uncertainty of each parameter, of simultaneous uncertainty of all parameters and of the number of scenarios generated, as four case studies. The results obtained provide insights into these aspects and indicate the approach’s capability to solve this problem.
In this work, an optimal control approach for scheduling maintenance and production in a process using decaying catalysts, originally developed in a previous study for a single reactor, is extended to parallel lines of reactors. Unlike traditional mixed-integer optimisation methods, this approach involves formulating this problem as a multistage mixed-integer optimal control problem (MSMIOCP) and using a methodology that enables solution as a standard nonlinear optimisation problem. The methodology’s features of a feasible path approach and scheduling catalyst changeovers without combinatorial optimisation techniques can be advantageous in providing reliable, robust and efficient solutions in comparison to mixed-integer methods. The MSMIOCP formulation is applied to the case study of an industrial process that operates a single feed over a set of 4 parallel reactors and produces a single product. The solutions obtained using the proposed methodology are of high quality and highlight the potential advantages of this approach over mixed-integer techniques.
Reverse osmosis (RO) is a very well established technology for water desalination. Commercial RO systems are composed of several number of RO passes with auxiliary equipment such as high pressure pumps and pressure exchanger units to facilitate the separation, and to deliver clean water. Available design models for the RO network represent mixed integer nonlinear programming (MINLP) formulations. In addition, the existing RO design MINLP models are static in nature. These models are not suitable for RO network design under time variant constraints. In this study, a multiperiod MINLP model is detailed for the RO network design. High level design decision variables are related to the RO network configuration and equipment sizing which are independent of time. These decisions are modelled by discrete and continuous variables. Low level time variant decision variables are related to the RO network operation and modelled by continuous variables. The operation decision variables are constrained by the design variables through different time periods to satisfy water demand constraints. In addition, several correlations are considered in this study to estimate water and RO transport properties during the separation process. Case studies are analyzed to show the application of the mathematical programming model.
The optimisation of the cleaning schedule in heat exchanger networks (HENs) subject to fouling is presented in which the impact of parametric uncertainty is considered. This work is based on the realisation that these HEN cleaning scheduling problems are multistage mixed-integer optimal control problems (MIOCPs) in which the controls, i.e. cleaning actions, exhibit bang-bang behaviour as they occur linearly in the system equations. A multiple scenario feasible path MIOCP approach is proposed, whereby many scenarios of the HEN multiperiod problems are stacked, sharing the same control actions. This is implemented on a 10 unit and a 25 unit HEN case studies representing crude oil refinery preheat trains (PHTs). Results show that there is a large difference in financial performance for the deterministic case versus the parametric uncertainty problem and hence it is vital that uncertainty be taken into account during the optimisation of schedules for HEN maintenance problems.
The performance and operability of heat exchanger networks (HEN) is strongly affected by fouling, the deposition of unwanted material reduces the heat transfer rate, and increases the pressure drop, the operational cost and the environmental impact of the process. Periodical cleaning and control of flow rate distribution in the HEN are used to mitigate the effects of fouling and restore the performance of the units. The optimal cleaning scheduling has been formulated as a MILP or MINLP problem and solved using various approaches. The optimal control has been formulated as a NLP and used to define the flow rate distribution of the network. In principle, the simultaneous solution of the optimal control problem and the optimal cleaning scheduling problem should provide greater savings than the independent or sequential solution of the two problems, as the interactions of the two mitigation alternatives are considered. However, these two problems have been typically considered separately due to modelling and solution challenges. Also, it is not quite clear what additional benefit a simultaneous solution may bring.. The challenges for solving the integrated problem are the large scale of the associated optimization problem and the different time scales involved in each operational layer. We proposed a general and efficient formulation using a continuous time discretization scheme for the integrated problem of scheduling and control of HEN subject to fouling. A dynamic model of heat exchangers is proposed that is sufficiently detailed to represent the physics of interest with novel modifications to address simultaneously their control and scheduling in a network. The problem is formulated as a MINLP and solved using deterministic optimization algorithms. The flexibility of the model and variations of the formulation are demonstrated with two small case studies. The formulation complexity vs. scale and advantages are analyzed. The results show that considering the two problems simultaneously has a very strong synergistic effect, with over 20% decrease in operational cost achieved in comparison with using either fouling mitigation alternative individually.
An approach for optimising the cleaning schedule in heat exchanger networks (HENs) subject to fouling is presented. This work focuses on HEN applications in crude oil preheat trains located in refineries. Previous approaches have focused on using mixed-integer nonlinear programming (MINLP) methods involving binary decision variables describing when and which unit to clean in a multi-period formulation. This work is based on the discovery that the HEN cleaning scheduling problem is in actuality a multistage optimal control problem (OCP), and further that cleaning actions are the controls which appear linearly in the system equations. The key feature is that these problems exhibit bang-bang behaviour, obviating the need for combinatorial optimisation methods. Several case studies are considered; ranging from a single unit up to 25 units. Results show that the feasible path approach adopted is stable and efficient in comparison to classical methods which sometimes suffer from failure in convergence.
An approach for optimising the cleaning schedule in heat exchanger networks (HENs) subject to fouling is presented. This work focuses on HEN applications in crude oil preheat trains located in refineries. Previous approaches have focused on using mixed-integer nonlinear programming (MINLP) methods involving binary decision variables describing when and which unit to clean in a multi-period formulation. This work is based on the discovery that the HEN cleaning scheduling problem is in actuality a multistage optimal control problem (OCP), and further that cleaning actions are the controls which appear linearly in the system equations. The key feature is that these problems exhibit bang-bang behaviour, obviating the need for combinatorial optimisation methods. Several case studies are considered; ranging from a single unit up to 25 units. Results show that the feasible path approach adopted is stable and efficient in comparison to classical methods which sometimes suffer from failure in convergence.
This work addresses the optimal planning of biopharmaceutical continuous manufacturing processes under performance decay, modelling its operational constraints in a mixed integer linear programing (MILP) model, based on a Resource Task Network (RTN) continuous single-time grid formulation. The model assesses the manufacturing constraints for the determination of the production schedule while defining the appropriate maintenance planning timing in downstream units to assure optimal process performance. An improved model approach is discussed and compared with the application results to literature-based industrial cases. In order to evaluate different solutions towards the multiple decision maker’s strategic and operational objectives, the definition of the Pareto sets for three bi-objective analyses is performed with the augmented ε-constraint method, using the profit maximisation: with the minimisation of the number of intermediate maintenance operations, the maximisation of average service level, and the maximisation of the utilisation rate of processing units.
Considering the performance decay of the chromatography resins in the downstream purification of biopharmaceutical manufacturing, the maintenance decisions should be made at appropriate times to achieve a good performance of the whole manufacturing process. In this paper, on the basis of the literature work on production planning, a mixed integer linear programming optimization model is developed to address the production and maintenance planning of biopharmaceutical manufacturing under performance decay, in which the total operating profit is maximized. The batch production profiles are tracked by binary variables introduced in the proposed model. The proposed model is then applied to two literature-based illustrative examples. Two scenarios are investigated and compared with the optimal solutions. A discussion about the effects of the maintenance duration and cost and the resins lifetime is also presented.
Due to widespread automation and the high capital tied up in production equipment, the importance of maintenance is ever increasing.
This makes maintenance an investment opportunity to be optimized, not a cost to be minimized. Academics have recognized this
and many maintenance optimization models have been published over the years. Most of these models focus on one optimization
criterion or objective, making multi-objective optimization models an underexplored area of maintenance optimization. Moreover,
there is a big gap between academic models and application in practice. It is very difficult for industrial companies to adapt
these models to their specific business context. This article reviews the literature on maintenance optimization models, with
special focus on the optimization criteria and objectives used. To overcome flaws in present optimization models, a generic
classification framework of maintenance optimization models is presented. All factors that have an influence on the optimization
model will be made explicit and their links will be established. The framework is a starting point to develop business specific
optimization models and enables decision making in e-maintenance. Moreover, it ensures a fit between the business model of
a company and the maintenance optimization model right from the beginning. Future research will be on the development of a
maintenance optimization model taking into account the most relevant optimization influence factors and criteria for a situation
at hand.
KeywordsMaintenance optimization–Maintenance optimization models–Maintenance optimization criteria–Decision support–eMaintenance
Identifying the optimal design for an RO membrane network is not straightforward when significant fouling occurs. The most robust optimal network design will feature the minimal capital and operating costs over the anticipated lifetime of the plant, and is therefore strongly dependent on the fouling behaviour and associated mitigation. This study considers the case where the likely fouling behaviour is known and investigates how to incorporate this knowledge into the design and operation of a network. The optimisation task is complicated by the highly non-linear nature of the problem owing to membrane behaviour, fouling behaviour, network interactions and operating parameter constraints (pressures and flows). In this work, fouling is modelled as an exponential decay in membrane permeability. Three optimisation approaches are used to evaluate candidate networks: (i) laborious comparison of pre-selected individual network designs; (ii) deterministic gradient search methods, and (iii) a simulated-annealing-based hybrid stochastic-deterministic method. All of the approaches consider various configurations of a two-stage network with a maximum of three membrane units in each stage, represented in a superstructure model. The results from the approaches are compared and the most effective method for network design is discussed.