Membership-set estimation using random scanning and principal component analysis

A set-theoretic approach to parameter estimation based on the bounded-error concept is an appropriate choice when incomplete knowledge of observation error statistics and unavoidable structural model error invalidate the presuppositions of stochastic methods. Within this class the estimation of non-linear-in-the-parameters models is examined. This situation frequently occurs in modelling natural systems. The output error method proposed is based on overall random scanning with iterative reduction of the size of the scanned region. In order to overcome the problem of computational inefficiency, which is particularly serious when there is interaction between the parameter estimates, two modifications to the basic method are introduced. The first involves the use of principal component transformations to provide a rotated parameter space in the random scanning because large areas of the initial parameter space are thus excluded from further examination. The second improvement involves the standardization of the parameters so as to obtain an initial space with equal size extension in all directions. This proves to largely increase the computational robustness of the method. The modified algorithm is demonstrated by application to a simple three-parameter model of diurnal dissolved oxygen patterns in a lake

Application of flexible recipes for model building, batch process optimization and control

Unlike the traditionally fixed recipes in batch process operation, flexible recipes allow the adjustment of some of its relevant recipe items. These adjustments can either be predefined in cases of planned experimentation, or suggested by a formal process optimization or control algorithm on the basis of actual information. In both the response surface methodology and the simplex evolutionary operation (EVOP), some well-known methods for empirical model building and process optimization, flexible recipes are involved. Another application of flexible recipes arises in a feedforward quality control strategy of batch processes when variations in market or process conditions are known a priori. The experimental results of these strategies are presented for the batchwise production of benzylalcohol on a pilotplant scale. Experiments have been performed to obtain a reliable model of the yield. On the basis of this model, better process conditions have been suggested, which substantially deviate from the final simplex resulted from experiments within simplex EVOP. Finally, an adaptive feedforward control strategy has been applied for a priori known disturbances in the process inputs

Uncertainty propagation and speculation in projective forecasts of environmental change: a lake-eutrophication example

The issue of whether models developed for current conditions can yield correct predictions when used under changed control, as is often the case in environmental management, is discussed. Two models of different complexity are compared on the basis of performance criteria, but it appears that good performance at the calibration stage does not guarantee correctly predicted behavior. A requirement for the detection of such a failure of the model is that the prediction uncertainty range is known. Two techniques to calculate uncertainty propagation are presented and compared: a stochastic first-order error propagation based on the extended Kalman filter (EKF), and a newly developed and robust Monte Carlo set-membership procedure (MCSM). The procedures are applied to a case study of water quality, generating a projective forecast of the algal dynamics in a lake (Lake Veluwe) in response to management actions that force the system into a different mode of behavior. It is found that the forecast from the more complex model falls within the prediction uncertainty range, but its informative value is low due to large uncertainty bounds. As a substitute for time-consuming revisions of the model, educated speculation about parameter shifts is offered as an alternative approach to account for expected but unmodelled changes in the system

Making aquaponics a business: A framework

Commercial aquaponics systems remain a challenge independent of the country, fish, plant species, or system design type. Most aquaponics systems are made by hobbyists, with aquaponics not being the main source of income. As such, scholars and practitioners have long debated the real profitability of aquaponics systems. With the growth of the aquaponics industry and commercial businesses, sustainable economic viability is necessary. Recently, considerable literature has been published around the theme of aquaponics systems design but there is a gap in the literature regarding the business aspect of this. Moreover, only by acquiring the enterprise knowledge of planning a business case, obtaining funds, and running and maintaining a business will this industry be able to grow. This paper intends to create a directory of possible considerations to plan for a viable commercial aquaponics system by uniting already established business frameworks and adapting them to the aquaponics industry. This framework proposes a guide to evaluate the economic feasibility of the enterprise depending on the revenues, costs and investments needed for the chosen system within its operations, market, and environment.publishedVersio

Carbon dynamics and energy recovery in a novel near-zero waste aquaponics system with onsite anaerobic treatment

Aquaponics is gaining renewed interest to enhance food security. This study aimed to investigate the performance of a novel off-grid aquaponics system with near-zero water and waste discharge, focusing on the carbon cycle and energy recovery that was achieved by the addition of onsite anaerobic treatment of the solid waste streams. Following a stabilization stage, the system was closely monitored for four months. Fish tank water was recirculated via solid and nitrification reactors, from which 66% was recycled to the fish tank directly and 34% indirectly through the hydroponically grown plants. Fish solid waste was anaerobically treated, energy was recovered, and the nutrient-rich supernatant was recycled to the plants to enhance production. Plant waste was also digested anaerobically for further recovery of energy and nutrients. Fish stocking density was 15.3 and over time reached approximately 40 kg/m3 where it was maintained. Feed (45% protein content) was applied daily at 2% of body weight. Typical fish performance was observed with a survival rate >97% and feed conversion ratio of 1.33. Lettuce production was up to 5.65 kg/m2, significantly higher than previous reports, largely because of high nutrients reuse efficiency from the anaerobic supernatant that contained 130 and 34 mg/L N and P, respectively. Of the feed carbon, 24.5% was taken up by fish biomass. Fish solid wastes contained 38.2% carbon, of which 91.9% was recovered as biogas (74.5% CH4). Biogas production was 0.84 m3/kg for fish sludge and 0.67 m3/kg for dry plant material. CO2 sequestration was 1.4 higher than the feed carbon, which reduced the system's carbon footprint by 64%. This study is the first to demonstrate highly efficient fish and plant production with near-zero water and waste discharge and with energy recovery that can potentially supply the system's energy demand.publishedVersio

On the sensitivity of local flexibility markets to forecast error : A bi-level optimization approach

The large-scale integration of intermittent distributed energy resources has led to increased uncertainty in the planning and operation of distribution networks. The optimal flexibility dispatch is a recently introduced, power flow-based method that a distribution system operator can use to effectively determine the amount of flexibility it needs to procure from the controllable resources available on the demand side. However, the drawback of this method is that the optimal flexibility dispatch is inexact due to the relaxation error inherent in the second-order cone formulation. In this paper we propose a novel bi-level optimization problem, where the upper level problem seeks to minimize the relaxation error and the lower level solves the earlier introduced convex second-order cone optimal flexibility dispatch (SOC-OFD) problem. To make the problem tractable, we introduce an innovative reformulation to recast the bi-level problem as a non-linear, single level optimization problem which results in no loss of accuracy. We subsequently investigate the sensitivity of the optimal flexibility schedules and the locational flexibility prices with respect to uncertainty in load forecast and flexibility ranges of the demand response providers which are input parameters to the problem. The sensitivity analysis is performed based on the perturbed Karush-Kuhn-Tucker (KKT) conditions. We investigate the feasibility and scalability of the proposed method in three case studies of standardized 9-bus, 30-bus, and 300-bus test systems. Simulation results in terms of local flexibility prices are interpreted in economic terms and show the effectiveness of the proposed approach.</p

Navigating towards decoupled aquaponic systems : a system dynamics design approach

The classical working principle of aquaponics is to provide nutrient-rich aquacultural water to a hydroponic plant culture unit, which in turn depurates the water that is returned to the aquaculture tanks. A known drawback is that a compromise away from optimal growing conditions for plants and fish must be achieved to produce both crops and fish in the same environmental conditions. The objective of this study was to develop a theoretical concept of a decoupled aquaponic system (DAPS), and predict water, nutrient (N and P), fish, sludge, and plant levels. This has been approached by developing a dynamic aquaponic system model, using inputs from data found in literature covering the fields of aquaculture, hydroponics, and sludge treatment. The outputs from the model showed the dependency of aquacultural water quality on the hydroponic evapotranspiration rate. This result can be explained by the fact that DAPS is based on one-way flows. These one-way flows results in accumulations of remineralized nutrients in the hydroponic component ensuring optimal conditions for the plants. The study also suggests to size the cultivation area based on P availability in the hydroponic component as P is an exhaustible resource and has been identified one of the main limiting factors for plant growth

Practical identifiability analysis of environmental models

Identifiability of a system model can be considered as the extent to which one can capture its parameter values from observational data and other prior knowledge of the system. Identifiability must be considered in context so that the objectives of the modelling must also be taken into account in its interpretation. A model may be identifiable for certain objective functions but not others; its identifiability may depend not just on the model structure but also on the level and type of noise, and may even not be identifiable when there is no noise on the observational data. Context also means that non-identifiability might not matter in some contexts, such as when representing pluralistic values among stakeholders, and may be very important in others, such as where it leads to intolerable uncertainties in model predictions. Uncertainty quantification of environmental systems is receiving increasing attention especially through the development of sophisticated methods, often statistically-based. This is partly driven by the desire of society and its decision makers to make more informed judgments as to how systems are better managed and associated resources efficiently allocated. Less attention seems to be given by modellers to understand the imperfections in their models and their implications. Practical methods of identifiability analysis can assist greatly here to assess if there is an identifiability problem so that one can proceed to decide if it matters, and if so how to go about modifying the model (transforming parameters, selecting specific data periods, changing model structure, using a more sophisticated objective function). A suite of relevant methods is available and the major useful ones are discussed here including sensitivity analysis, response surface methods, model emulation and the quantification of uncertainty. The paper also addresses various perspectives and concepts that warrant further development and use