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Smart meters implemented at the end-user in the energy sector create the opportunity to develop data-intelligent methods for district heating systems by using a large amount of fine-granular heat consumption time series from end-users. The current state-of-the-art methods for temperature control in district heating systems rely on predefined critical points in the network and a set reference temperature curve that expresses the minimum forward temperature as a function of the outdoor temperature at the end-users. The critical points are used to ensure that the consumers’ supply temperature requirements are met all times. To predefine the critical points at the network, the location of the lowest temperature in the grid needs to be identified at any point in time. Since the lowest temperature often varies over time, one must have a set of critical points in a district heating network. This paper proposes a method to estimate the temperature at an artificial critical point for the network using time-wise quantile estimation using smart meter data at end-users. This novel approach eliminates the need for physical critical points in the net or sensors in wells and creates the possibility of changing the critical point location if needed. The benefits for the provider of using smart meters as feedback, makes the measurement wells redundant and flexibility of the location. The location of low temperature areas in the network can change overtime hence the flexibility of being able to change where the feedback is located. The proposed method to replace the well measurements to provide feedback for temperature control at the production site groups a predefined set of smart meter readings together for each point in time. The grouping is done to have reliable measurements from each smart meter device, excluding some of the meters when a faulty reading occurs. The set of acceptable readings is used to estimate the street pipe’s temperature using the estimated quantile of the forward temperature. The approach is tested on two demo cases. The first demo consists of smart meters to estimate the forward temperature of the main street pipe. The second demo uses three smart meters at large apartment buildings as feedback for the control. Initial results show that the estimated temperature of the network can replace the well-measurements which traditionally are used as feedback for temperature control and give a better and more flexible control.

Combining forecasts from multiple temporal aggregation levels exploits information differences and mitigates model uncertainty, while reconciliation ensures a unified prediction that supports aligned decisions at different horizons. It can be challenging to estimate the full cross-covariance matrix for a temporal hierarchy, which can easily be of very large dimension, yet it is difficult to know a priori which part of the error structure is most important. To address these issues, we propose to use eigendecomposition for dimensionality reduction when reconciling forecasts to extract as much information as possible from the error structure given the data available. We evaluate the proposed estimator in a simulation study and demonstrate its usefulness through applications to short-term electricity load and financial volatility forecasting. We find that accuracy can be improved uniformly across all aggregation levels, as the estimator achieves state-of-the-art accuracy while being applicable to hierarchies of all sizes.

Membrane-based separations are proven and useful industrial-scale technologies, suitable for automation. Digital twins are models of physical dynamical systems which continuously couple with data from a real world system to help understand and control performance. However, ultrafiltration and microfiltration membrane separation techniques lack a rigorous theoretical description due to the complex interactions and associated uncertainties. Here we report a digital-twin methodology called the Stochastic Greybox Modelling and Control (SGMC) that can account for random changes that occur during the separation processes and apply it to water ultrafiltration. In contrast to recent probabilistic approaches to digital twins, we use a physically intuitive formalism of stochastic differential equations to assess uncertainties and implement updates. We demonstrate the application of our digital twin model to control the filtration process and minimize the energy use under a fixed water volume in a membrane ultrafiltration of artificially simulated lakewater. The explicit modelling of uncertainties and the adaptable real-time control of stochastic physical states are particular strengths of SGMC, which makes it suited to real-world problems with inherent unknowns. Jan Kloppenborg Møller & Goran Goranović and colleagues introduce a data-driven twin methodology which balances physical knowledge with uncertainty quantifications. The approach makes it suited to application of real world problems with inherent unknowns. They demonstrate its application in the modelling and control of membrane water ultrafiltration

Building archetypes are a common solution to study the energy demand of cities and districts. These are generally based on building information such as construction year and function. However, there can be large differences in the energy demand of buildings of the same archetype due to factors such as the preferences of occupants, quality of the building construction, and unrecorded renovations. This work uses a non-linear mixed effects model to capture these random differences. The model uses weather measurements to generate the daily heating load of buildings for the whole year. The model is generated and tested using data from 56 Norwegian apartments. Results show that 91% of measurements from an out-of-sample test set fall inside the 95% prediction interval. Additionally, the model allows us to compute a proxy of the heat loss coefficient, which characterises the heating performance of the population of apartments. Finally, two sub-categories of apartments are identified by clustering the model estimates for the studied population. The model is general, computationally light and uses existing data that are commonly collected in many buildings. The suggested method offers a more robust and reliable method to segment building archetypes using only weather data and energy demand.

A comfortable indoor environment should be one of the main services buildings provide. However, technical building systems are typically designed and operated according to fixed set-point temperatures determined by the ‘one-size-fits-all’ principle assuming universal thermal comfort requirements, which has been questioned in the last fifty years. Designing and implementing comfortable set-point modulations that consider occupant feedback would be beneficial in terms of increasing comfort, potentially reduce energy consumption and significantly support the clean energy transition. An exploratory study aimed at predicting the thermal preferences of human subjects exposed to a dynamic thermal environment is presented. Using data acquired from a laboratory experiment where subjects were exposed to precisely controlled thermal ramps in an ‘office-like’ climatic chamber, cluster-specific and population-averaged methods are designed to handle the group-level residual during the prediction of the thermal preference votes. The results show that both approaches are valid strategies for modelling thermal preference votes and are effective in supporting a concrete occupant-centric building design and the building’s operation. Furthermore, the population-averaged approach is suitable for the occupant-centric building design phase, where the target is an ‘average’ occupant. The cluster-specific method is best suited to meet the needs of a specific occupant and is suitable for implementation in the operational phase of the building.

Smart meters at consumers create opportunities to improve operation of the district heating sector using data-driven methods. Information from these meter measurements carries the potential to increase the energy efficiency of both individual houses and the utility network, for example by identifying buildings with too high return temperature, or by detecting leakage in the network. This paper proposes a method for using meter data to estimate network temperatures. Network temperatures can subsequently be used to estimate the network characteristics, namely the nonlinear relationship between network temperature and the plants’ temperature and flow. A description of the network characteristics is needed for most temperature-optimisation methods to keep the supply temperature as low as possible without violating the system constraints. Traditionally, measurement wells located in the network have been used. These wells are located at critical points in the network where the largest temperature losses occur. Since the lowest temperature often varies over time, multiple critical points are necessary. The method presented in this paper eliminates the need for these physical critical points in the network. It also makes it possible to change the location of the critical points if needed. The network temperature is estimated using a stochastic state–space model of the heat dynamics from the street level distribution pipe over the service pipe and into individual houses. The parameters in the model are estimated using a maximum likelihood approach, and the Kalman Filter is used to evaluate the likelihood function. The estimation process takes advantage of automatic differentiation using the R package Template Model Builder (TMB) to reduce the computational workload. The proposed method is validated by comparing the estimated temperature with the temperature measured from a measurement well.

Sustainable urban drainage is an economically expensive necessity, partially due to the operation of water pumps. Reliable forecasting of stormwater response following a rainfall event has the potential to reduce those expenses, because it can be used in model predictive control schemes that optimize the energy consumption of pumps significantly better than the commonly applied real-time control systems. Urban drainage systems are traditionally designed around highly complex, deterministic models where an assessment of the uncertainty of the stormwater forecast is either absent or relies on computation–heavy simulations. With offset in a Danish stormwater tunnel, we propose a much faster, but reliable, non-linear continuous-discrete-time state-space model based on stochastic differential equations which can generate probabilistic forecasts that contain complete information about the distribution of uncertainty. We explain step-by-step how the model structure is built from simple physical assumptions, then how the parameters are estimated from maximum likelihood principles and finally we demonstrate the forecasting capabilities of the model. We believe this model would be well-suited for a subsequent model predictive control scheme.

Probabilistic forecasting is becoming increasingly important for a wide range of applications, especially for energy systems such as forecasting wind power production. A need for proper evaluation of probabilistic forecasts follows naturally with this, because evaluation is the key to improving the forecasts. Although plenty of excellent reviews and research papers on probabilistic forecast evaluation already exist, we find that there is a need for an introduction with some practical application. In particular, many forecast scenarios in energy systems are inherently multivariate, and while univariate evaluation methods are well understood and documented, only limited and scattered work has been done on their multivariate counterparts. This paper therefore contains a review of a selected set of probabilistic forecast evaluation methods, primarily scoring rules, as well as practical sections that explain how these methods can be calculated and estimated. In three case studies featuring simple autoregressive models, stochastic differential equations and real wind power data, we implement, apply and discuss the logarithmic score, the continuous ranked probability score and the variogram score for forecasting problems of varying dimension. Finally, the advantages and disadvantages of the three scoring rules are highlighted, and this provides a significant step towards deciding on an evaluation method for a given multivariate forecast scenario including forecast scenarios relevant for energy systems.

Heating and ventilation strategies in buildings can be improved significantly if information about the current presence and activity level of the occupants is taken into account. Therefore, there is a high demand for inexpensive sensor-based methods to detect the occupancy or occupant activity level. It is shown that the carbon dioxide (CO2) level in a room is dependent on the activity level rather than only on just the number of people. Therefore, this study suggests a new model based on the use of CO2 trajectories to estimate the occupant activity level, trained on measurements both from a school classroom and from a Danish summerhouse. A hidden Markov-switching model was employed to identify the activity level. This modelling approach is a generalization of hidden Markov models, taking autocorrelation in the observations into account. This is done by an additional autoregressive part which models the persistence of the CO2 concentration by relating the current value to past lags. The analysis of one-step prediction residuals shows that this method inherits the dynamics of the CO2 curves much better than an ordinary hidden Markov model, and can therefore be considered a promising candidate for occupant activity estimation. Furthermore, it is shown that the presented model can be used for simulations of activity level and of the accompanying CO2 levels.

Occupant-centric data streams, and more specifically continuous subjective occupant feedback (CSOF) systems, offer the possibility for autonomous collection of occupant feedback in buildings. They are made possible by recent developments in pervasive ICT technology and can enable a continuous flow of information that may enhance human-centric building design and operation. Due to the relative novelty of these systems, no research has been developed so far to systematically evaluate whether information collected by CSOF systems is truly representative of the entire population's opinions and evaluations. In this study, we analyze how information on occupant's opinions on indoor climate collected though a multi-level CSOF system compare to the information obtained though simultaneously performed manual surveys. We used data collected from five field tests in modern office buildings with uninformed occupants, and compare a total of 317 Satisfaction evaluations, 124 Complaints, and 44 Control actions with 546 surveys. Using logistic regression techniques, we investigated the relations between the feedback information and the information from surveys. We found that cumulative link models were suitable for modeling the relationship between feedback and survey data. The Building ID tag was the most important variable for modeling Occupant satisfaction and Occupant complaint feedback. Occupant control actions was best modeled using the Workplace ID. When comparing CSOF with surveys, we found a Mean Absolute Error (MAE) of 16% and of 12%, for Occupant satisfaction and for Occupant complaint feedback, respectively. We demonstrated that the adopted methods are suitable for understanding the meaning of the collected CSOF data. Further studies based on this methodology and using a larger dataset should be carried out to deepen the understanding of CSOF feedback significance and to increase the soundness of the results obtained in this study. This is an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Home Energy Management Systems (HEMSs) are expected to become an inevitable part of the future smart grid technologies. To work effectively, HEMSs require reliable and accurate load forecasts. In this paper, two new modelling methods are presented. They are both suited for producing multivariate probabilistic forecasts, which consider the temporal correlation between forecast horizons. The first method employs point forecasts generated with Recursive Least Squares (RLS) models and subsequently analyses the forecasts’ residuals to estimate the marginal distributions and temporal correlation. The second method is based on quantile regression to estimate marginal distributions, and a Gaussian copula for linking them together. Furthermore, the application of two modelling approaches for the temporal correlation estimation are investigated for each of the two modelling methods. As a case study, a numerical experiment is designed to emulate an online HEMS operation using data from an inhabited home located in Denmark. Simulation results show a robust performance for the proposed models, with the quantile–copula ensemble outperforming the RLS-based models in predicting the marginal distributions and capturing the temporal correlation.

Heat load forecasts are crucial for energy operators in order to optimize the energy production at district heating plants for the coming hours. Furthermore, forecasts of heat load are needed for optimized control of the district heating network since a lower temperature reduces the heat loss, but the required heat supply at the end-users puts a lower limit on the temperature level. Consequently, improving the accuracy of heat load forecasts leads to savings and reduced heat loss by enabling improved control of the network and an optimized production schedule at the plant. This paper proposes the use of temporal hierarchies to enhance the accuracy of heat load forecasts in district heating. Usually, forecasts are only made at the temporal aggregation level that is the most important for the system. However, forecasts for multiple aggregation levels can be reconciled and lead to more accurate forecasts at essentially all aggregation levels. Here it is important that the auto- and cross-covariance between forecast errors at the different aggregation levels are taken into account. This paper suggests a novel framework using temporal hierarchies and adaptive estimation to improve heat load forecast accuracy by optimally combining forecasts from multiple aggregation levels using a reconciliation process. The weights for the reconciliation are computed using an adaptively estimated covariance matrix with a full structure, enabling the process to share time-varying information both within and between aggregation levels. The case study shows that the proposed framework improves the heat load forecast accuracy by 15% compared to commercial state-of-the-art operational forecasts.

EXECUTIVE SUMMARY Evaluations of improvements in long chronic-patient pathways must include both short- and long-term effects on patients; that is, effects on the full patient pathway. Otherwise, costs might be cut without considering the long-term effects and, consequently, the overall cost of the pathway could increase. Unfortunately, current methods of evaluation present several issues: (1) they do not provide valid insights regarding the effects of a given improvement effort until several years later, (2) they provide imprecise and biased results, and (3) the aggregated results are not useful for identifying and disseminating the best practices that lead to an improvement. In this article, the accelerated longitudinal design with decomposition of total costs (ALDD) method is applied to evaluate the effects of improvement efforts on inpatient utilization for long cardiac pathways at a Danish hospital. The results show that the ALDD method can deliver valid results much faster than traditional methods and can uncover hidden improvements in the local work processes of clinical teams. Application of the ALDD method at a hospital in Denmark identified a significant reduction (15.4%) in the mean total bed utilization per cardiac pathway and revealed that this reduction was caused by improvements in the work processes.

This study is a proof-of-concept of a stochastic Model Predictive Control (MPC) strategy for effluent phosphorus concentration in municipal wastewater treatment. Firstly, a simple data-driven model providing adequate predictions of phosphorus was created and demonstrated. Secondly, the model was used to find the optimal aeration control upholding legal requirements within a fixed amount of computation time. The optimal control is here considered the cheapest control in terms ofelectricity costs with variable electricity prices and effluent taxes on phosphorus. Results showed significant reductions (~ 45 %) in operational costs compared with a rule-based control.

This study presents a general model predictive control (MPC) algorithm for optimizing wastewater aeration in Water Resource Recovery Facilities (WRRF) under different management objectives. The flexibility of the MPC is demonstrated by controlling a WRRF under four management objectives, aiming at minimizing: (A) effluent concentrations, (B) electricity consumption, (C) total operations costs (sum electricity costs and discharge effluent tax) or (D) global warming potential (direct and indirect nitrous oxide emissions, and indirect from electricity production) . The MPC is tested with data from the alternating WRRF in Norre Snede (Denmark) and from the Danish electricity grid. Results showed how the four control objectives resulted in important differences in aeration patterns and in the concentration dynamics over a day. Controls B and C showed similarities when looking at total costs, while similarities in global warming potential for controls A and D suggest that improving effluent quality also reduced greenhouse gasses emissions. The MPC flexibility in handling different objectives is shown by using a combined objective function, optimizing both cost and greenhouse emissions. This shows the trade-off between the two objectives, enabling the calculation of marginal costs and thus allowing WRRF operators to carefully evaluate prioritization of management objectives. The long-term MPC performance is evaluated over 51 days covering seasonal and inter-weekly variations. On a daily basis, control A was 9–30% cheaper on average compared to controls A, D and to the current rule-based control. Similarly, control D resulted on average in 35–43% lower greenhouse gasses daily emission compared to the other controls. Difference between control performance increased for days with greater inter-diurnal variations in electricity price or greenhouse emissions from electricity production, i.e. when MPC has greater possibilities for exploiting input variations. The flexibility of the proposed MPC can easily accommodate for additional control objectives, allowing WRRF operators to quickly adapt the plant operation to new management objectives and to face new performance requirements.

Even for similar residential buildings, a huge variability in the energy consumption can be observed. This variability is mainly due to the different behaviours of the occupants and this impacts the thermal (temperature setting, window opening, etc.) as well as the electrical (appliances, TV, computer, etc.) consumption. It is very seldom to find direct observations of occupant presence and behaviour in residential buildings. However, given the increasing use of smart metering, the opportunity and potential for indirect observation and classification of occupants’ behaviour is possible. This paper focuses on the use of Hidden Markov Models (HMMs) to create methods for indirect observations and characterisation of occupant behaviour. By applying homogeneous HMMs on the electricity consumption of fourteen apartments, three states describing the data were found suitable. The most likely sequence of states was determined (global decoding). From reconstruction of the states, dependencies likeambient air temperaturewere investigated. Combined with an occupant survey, this was used to classify/interpret the states as (1) absent or asleep, (2) home, medium consumption and (3) home, high consumption. From the global decoding, the average probability profiles with respect to time of day were investigated, and four distinct patterns of occupant behaviour were observed. Based on the initial results of the homogeneous HMMs and with the observed dependencies, time dependent HMMs (inhomogeneous HMMs) were developed, which improved forecasting. For both the homogeneous and inhomogeneous HMMs, indications of common parameters were observed, which suggests further development of the HMMs as population models.

It is widely accepted today that probabilistic forecasts of wind power production constitute valuable information that can allow both wind power producers and power system operators to exploit this form of renewable energy economically, while mitigating the potential adverse effects relating to its variable and uncertain nature. In order to provide reliable wind power forecasts for periods beyond a couple of hours, forecasts of the wind speed are fundamental. In this paper, we propose a modeling framework for wind speed that is based on stochastic differential equations. We show that stochastic differential equations allow us to capture the time dependence structure of wind speed prediction errors naturally (from 1 to 24 h ahead) and, most importantly, to derive point and quantile forecasts, predictive distributions, and time-path trajectories (also referred to as scenarios or ensemble forecasts), all using one single stochastic differential equation model that is characterized by a few parameters.

Short-term (hours to days) probabilistic forecasts of wind power generation provide useful information about the associated uncertainty of these forecasts. Standard probabilistic forecasts are usually issued on a per-horizon-basis, meaning that they lack information about the development of the uncertainty over time or the inter-temporal correlation of forecast errors for different horizons. This information is very important for forecast end-users optimizing time-dependent variables or dealing with multi-period decision-making problems, such as the management and operation of power systems with a high penetration of renewable generation. This paper provides input to these problems by proposing a model based on stochastic differential equations that allows generating predictive densities as well as scenarios for wind power. We build upon a probabilistic model for wind speed and introduce a dynamic power curve. The model thus decomposes the dynamics of wind power prediction errors into wind speed forecast errors and errors related to the conversion from wind speed to wind power. We test the proposed model on an out-of-sample period of 1year for a wind farm with a rated capacity of 21MW. The model outperforms simple as well as advanced benchmarks on horizons ranging from 1 to 24h. Copyright © 2016 John Wiley & Sons, Ltd.

The increasing penetration of wind power has resulted in larger shares of volatile sources of supply in power systems worldwide. In order to operate such systems efficiently, methods for reliable probabilistic forecasts of future wind power production are essential. It is well known that the conditional density of wind power production is highly dependent on the level of predicted wind power and prediction horizon. This paper describes a new approach for wind power forecasting based on logistic-type stochastic differential equations (SDEs). The SDE formulation allows us to calculate both state-dependent conditional uncertainties as well as correlation structures. Model estimation is performed by maximizing the likelihood of a multidimensional random vector while accounting for the correlation structure defined by the SDE formulation. We use non-parametric modelling to explore conditional correlation structures, and skewness of the predictive distributions as a function of explanatory variables. Copyright © 2015 John Wiley & Sons, Ltd.

We use state-based stochastic greybox modeling - combining physics and statistics - to model the slugging phenomenon. We extend the model of DiMeglio et al. (2010) to include random components and variable flow coefficients, providing 30 seconds prediction intervals. Altogether six models, each comprising no more than ten equations, are fitted to off-shore riser training data and then cross-validated on new data sets. We use advanced statistical methods to 1) obtain optimal parameters of a given model fitted to measurements, 2) give model predictions with uncertainty intervals, and 3) quantitatively measure the relative goodness of the extended models. These features of our reductive method are general and can be applied to any data sets. For the slugging data, simpler models are preferable over the more complex ones (although the differences are minute for practical purposes in oil and gas industry) and a high statistical significance obtained on the training data does not imply improved long term prediction on independent data. Better physical (mechanistic) models to capture slugging oscillations are needed, ultimately to develop effective control strategies.

We present a new method to troubleshoot the causes of failure in complicated systems such as offshore water injection set-ups. We employ physico-chemical constraints and greybox estimates to categorize the failed modes of operations by the energy content in the modes’ spectra. Particular emphasis is given to the critical modes of failure i.e. positive feed-back loops.

It has been predicted that electric vehicles will play a crucial role in incorporating a large renewable component in the energy sector. If electric vehicles are integrated in a naive way, they may exacerbate issues related to peak demand and transmission capacity limits while not reducing polluting emissions. Optimizing the charging of electric vehicles is paramount for their successful integration. This paper presents a model to describe the driving patterns of electric vehicles in order to provide primary input information to any mathematical programming model for optimal charging. Specifically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is defined by the time-varying probabilities of starting and ending a trip, and is justified due to the uncertainty associated with the use of the vehicle. The model is fitted to data collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines.

Probabilistic forecasts of renewable energy production provide users with valuable information about the uncertainty associated with the expected generation. Current state-of-the-art forecasts for solar irradiance have focused on producing reliable point forecasts. The additional information included in probabilistic forecasts may be paramount for decision makers to efficiently make use of this uncertain and variable generation. In this paper, a stochastic differential equation framework for modeling the uncertainty associated with the solar irradiance point forecast is proposed. This modeling approach allows for characterizing both the interdependence structure of prediction errors of short-term solar irradiance and their predictive distribution. Three different stochastic differential equation models are first fitted to a training data set and subsequently evaluated on a one-year test set. The final model proposed is defined on a bounded and time-varying state space with zero probability almost surely of events outside this space. Copyright © 2014 John Wiley & Sons, Ltd.

In healthy individuals, insulin and glucagon work in a complex fashion to maintain blood glucose levels within a narrow range. This regulation is distorted in patients with diabetes. The hepatic glucose response due to an elevated glucagon level depends on the current insulin concentration and thus endogenous glucose production (EGP) can not be modelled without knowledge of the concentration of both hormones in plasma. Furthermore, literature suggests an upper limit to EGP irrespective of glucagon levels. We build a simulation model of the glucose-insulin-glucagon dynamics in man including saturation effect of EGP. Ten healthy subjects received a 1 mg subcutaneous (SC) glucagon bolus (GlucaGen®). Plasma samples were collected until 300 minutes post dose and analyzed for glucagon, insulin, and glucose concentrations. All observations were used to fit a physiological model of the glucose-insulin-glucagon dynamics using the Hovorka model with a novel multiplicative description of the effects of insulin and of glucagon on EGP. Bayesian estimation by Maximum a Posteriori using prior knowledge reported in literature was used to estimate the model parameters for each subject. Profile likelihood plots were used to investigate parameter identifiability. Unidentifiable parameters were fixed at their prior mean values. The new model enables simulations of the glucose-insulin-glucagon dynamics in humans at both low and high glucagon concentrations (180-8000 pg/mL) and physiologic insulin concentrations (1.2-81.9 mIU/L). The model can be used for simulation of glucagon bolus strategies for treatment of hypoglycemia and for in silico simulation of dual-hormone artificial pancreas algorithms.

Summary While there seems to be consensus that hydrological model outputs should be accompanied with an uncertainty estimate the appropriate method for uncertainty estimation is not agreed upon and a debate is ongoing between advocators of formal statistical methods who consider errors as stochastic and GLUE advocators who consider errors as epistemic, arguing that the basis of formal statistical approaches that requires the residuals to be stationary and conform to a statistical distribution is unrealistic. In this paper we take a formal frequentist approach to parameter estimation and uncertainty evaluation of the modelled output, and we attach particular importance to inspecting the residuals of the model outputs and improving the model uncertainty description. We also introduce the probabilistic performance measures sharpness, reliability and interval skill score for model comparison and for checking the reliability of the confidence bounds. Using point rainfall and evaporation data as input and flow measurements from a sewer system for model conditioning, a state space model is formulated that accounts for three different flow contributions: wastewater from households, and fast rainfall–runoff from paved areas and slow rainfall-dependent infiltration–inflow from unknown sources. We consider two different approaches to evaluate the model output uncertainty, the output error method that lumps all uncertainty into the observation noise term, and a method based on Stochastic Differential Equations (SDEs) that separates input and model structure uncertainty from observation uncertainty and allows updating of model states in real-time. The results show that the optimal simulation (off-line) model is based on the output error method whereas the optimal prediction (on-line) model is based on the SDE method and the skill scoring criterion proved that significant predictive improvements of the output can be gained from updating the states continuously. In an effort to attain residual stationarity for both the output error method and the SDE method transformation of the observations were necessary but the statistical assumptions were nevertheless not 100% justified. The residual analysis showed that significant autocorrelation was present for all simulation models. We believe users of formal approaches to uncertainty evaluation within hydrology and within environmental modelling in general can benefit significantly from adopting the evaluation measures applied here, so the probabilistic performance of their models can be assessed properly.

In this paper we show how the grey box methodology can be applied to find models that can describe the flow prediction uncertainty in a sewer system where rain data are used as input, and flow measurements are used for calibration and updating model states. Grey box models are composed of a drift term and a diffusion term, respectively accounting for the deterministic and stochastic part of the models. Furthermore, a distinction is made between the process noise and the observation noise. We compare five different model candidates’ predictive performances that solely differ with respect to the diffusion term description up to a 4 h prediction horizon by adopting the prediction performance measures; reliability, sharpness and skill score to pinpoint the preferred model. The prediction performance of a model is reliable if the observed coverage of the prediction intervals corresponds to the nominal coverage of the prediction intervals, i.e. the bias between these coverages should ideally be zero. The sharpness is a measure of the distance between the lower and upper prediction limits, and skill score criterion makes it possible to pinpoint the preferred model by taking into account both reliability and sharpness. In this paper, we illustrate the power of the introduced grey box methodology and the probabilistic performance measures in an urban drainage context.

Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both forecasting and control purposes. The grey-box model is based on stochastic differential equations and a key feature is the separation of the total noise into process and measurement noise. The grey-box approach is properly introduced and hypothesis regarding the noise terms are formulated. Three different hypotheses for the diffusion term are investigated and compared: one that assumes additive diffusion; one that assumes state proportional diffusion; and one that assumes state exponentiated diffusion. To implement the state dependent diffusion terms Ito's formula and the Lamperti transform are applied. It is shown that an additive diffusion noise term description leads to a violation of the physical constraints of the system, whereas a state dependent diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower flow prediction limits, because the observation noise is proportionally scaled with the modelled output. Finally it is concluded that a state proportional diffusion term best and adequately describes the one-step flow prediction uncertainty, and a proper description of the system noise is important for ascertaining the physical parameters in question. Copyright © 2011 John Wiley & Sons, Ltd.

The use of stochastic differential equations (SDEs) for the simulation of aquatic ecosystems has attracted increasing attention in recent years. The SDE setting also provides the opportunity for statistical estimation of ecosystem parameters. We present an estimation procedure, based on Kalman filtering and likelihood estimation, which has proven useful in other fields of application. The estimation procedure is presented and the development from ordinary differential equations (ODEs) to SDEs is discussed with emphasis on autocorrelated residuals, commonly encountered with ODEs. The estimation procedure is applied to a simple nitrogen-phytoplankton model, with data from a Danish estuary (1988–2006). The resulting SDE is simple enough to have a well-known stationary distribution and this distribution is presented and compared with observed phytoplankton data.

An algorithm for time-adaptive quantile regression is presented. The algorithm is based on the simplex algorithm, and the linear optimization formulation of the quantile regression problem is given. The observations have been split to allow a direct use of the simplex algorithm. The simplex method and an updating procedure are combined into a new algorithm for time-adaptive quantile regression, which generates new solutions on the basis of the old solution, leading to savings in computation time. The suggested algorithm is tested against a static quantile regression model on a data set with wind power production, where the models combine splines and quantile regression. The comparison indicates superior performance for the time-adaptive quantile regression in all the performance parameters considered.

International audience; Predictions of wind power production for horizons up to 48-72 h ahead comprise a highly valuable input to the methods for the daily management or trading of wind generation. Today, users of wind power predictions are not only provided with point predictions, which are estimates of the conditional expectation of the wind generation for each look-ahead time, but also with uncertainty estimates given by probabilistic forecasts. In order to avoid assumptions on the shape of predictive distributions, these probabilistic predictions are produced from non-parametric methods, and then take the form of a single or a set of quantile forecasts. The required and desirable properties of such probabilistic forecasts are defined and a framework for their evaluation is proposed. This framework is applied for evaluating the quality of two statistical methods producing full predictive distributions from point predictions of wind power. These distributions are defined by a number of quantile forecasts with nominal proportions spanning the unit interval. The relevance and interest of the introduced evaluation framework are discussed.

Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described.

SUMMARY A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part of the model illustrates that hysteresis effect and regime shifts can be obtained for a limited range of parameter values only. The effect of multiplicative noise components entering at different levels of the model is presented and discussed. Including noise leads to very different results on the stability of regimes, depending on how the noise propagates through the system. The dynamical properties of a system should therefore be described through propagation of the state distributions rather than the state means and consequently, stochastic models should be compared in a probabilistic framework. Copyright © 2008 John Wiley & Sons, Ltd.

Immunohistological demonstration of human placental lactogen (hPL) in non-villous, mononuclear intermediate trophoblastic cells may be of routine diagnostic value, when chorionic villi are absent in endometrial curettings from patients suspected of miscarriage of an intrauterine pregnancy. The histological presence and distribution of hPL was investigated in endometrial curettings from 90 patients studied retrospectively (47 had ectopic pregnancies, 14 miscarriages, and 29 legal abortions), and a consecutive, prospective series of 50 patients (40 had miscarriages and 10 had ectopic pregnancies) without chorionic villi in their endometrial curettings. Non-specific background staining was not a problem. The retrospective survey disclosed that hPL was a highly sensitive marker of intrauterine pregnancy (sensitivity = 0.98). In the prospective series, the predictive value of positive staining for hPL for intrauterine pregnancy was 1.00, and the sensitivity of hPL, as an indicator of uterine gestation, was 0.62. In absence of specific hPL-staining, the risk of ectopic pregnancy was about 50%. The immunohistochemical demonstration of hPL is a useful tool for identifying patients who are suspected of having had a miscarriage, but for whom evidence in the form of chorionic villi in endometrial curettings is lacking.

The environmental impact related to alternating activated sludge processes (ASP) includes both global warming potential (GWP) and eutrophication. Here we present a model predictive control approach which minimizes this impact, calculated as CO2-emissions related to electricity production, nitrous oxide emissions from the ASP and eutrophication related to discharge of ammonium and nitrate. We compare solutions for two different set of assumptions regarding released nitrous oxide and eutrophication impact. This results in controls with different resulting emissions and hence we show that the strategy can be used to prioritize environmental impacts.

Online model predictive control (MPC) of water resource recovery facilities (WRRFs) requires simple and fast models to improve the operation of energy-demanding processes, such as aeration for nitrogen removal. Selected elements of the activated sludge model number 1 modelling framework for ammonium and nitrate removal were included in discretely observed stochastic differential equations in which online data are assimilated to update the model states. This allows us to produce model-based predictions including uncertainty in real time while it also reduces the number of parameters compared to many detailed models. It introduces only a small residual error when used to predict ammonium and nitrate concentrations in a small recirculating WRRF facility. The error when predicting 2 min ahead corresponds to the uncertainty from the sensors. When predicting 24 hours ahead the mean relative residual error increases to ∼10% and ∼20% for ammonium and nitrate concentrations respectively. Consequently this is considered a first step towards stochastic MPC of the aeration process. Ultimately this can reduce electricity demand and cost for water resource recovery, allowing the prioritization of aeration during periods of cheaper electricity.

The purpose is to build a simulation model of the glucoregulatory system in man. We estimate individual human parameters of a physiological glucose-insulin-glucagon model. We report posterior probability distributions and correlations of model parameters.

Existing electricity networks need to adapt to the increasing amount of renewables to maintain a safe and stable supply. This will require massive developments in smart energy systems. Hence applications such as building heat, vehicle charging and industrial cooling have received attention in their ability to “smartly” consume/save energy in selected periods without significant loss of utility for the users. In this transformation, urban water systems can also provide an important contribution.

Wastewater treatment aeration accounts for a large amount of societal electricity consumption. This abstract suggests MPC driven by stochastic differential equations and genetic optimization, under legal and equipment constraints to prioritize aeration in selected periods. Thereby we reduce costs and empower smart use of green electricity from e.g. wind turbines.