Time Grid Research Articles

Study on numerical PMM test and its application to KCS hull

· A numerical moving tank was applied for the various PMM tests of the KCS model. · Numerical sensitivity of time window, grid resolution, and time step was systematically examined. · The wave patterns and vortices around ship was observed in various PMM test conditions. · A complete set of hull manoeuvring coefficients was obtained. · The manoeuvring coefficients were successfully applied for the prediction of turning tests. The planar motion mechanism (PMM) test is among the most popular methods to evaluate ship manoeuvrability due to its ability to generate manoeuvring coefficients through a series of captive tests. As a replacement for conventional towing tank facilities, the present work applies an open-source-based computational fluid dynamics (CFD) solver to conduct numerical tests, including the static drift, pure sway, pure yaw, and combined drift-yaw tests. The test model is the KRISO container ship (KCS), which has a highly-curved hull with sharp edges and extruded bulbous bow. The original k-ω SST turbulence model has been enhanced to stabilize the turbulence fields near the free surface as well as the hull, and the bow and stern vortices that occur during the ship's PMM motions are displayed in the present CFD analysis. For both the static and dynamic tests, the force and moment predicted by the present CFD solver agree well with the experimental measurements. The numerical PMM tests have generated a complete list of manoeuvring coefficients for the bare hull, and the further application to ship 35° turning circle test has demonstrated a reasonable agreement with the direct free-running experiments.

Discrete Time Sequence Reconstruction of a Signal Based on Local Approximation Using a Fourier Series by an Orthogonal System of Trigonometric Functions

The article considers the development of mathematical and algorithmic support for the sample’s reconstruction in problem sections of a discrete sequence of a continuous signal. The work aimed to ensure the reconstruction of lost samples or sections of samples with a non-constant distorted time grid when sampling a signal with a uniform step and at the same time to reduce the computational complexity of digital reconstruction algorithms. The solution to the stated problem is obtained based on the local approximation method. The specific of this method application was the use of two subsequences of samples located symmetrically concerning the reconstructed section of the sequence. The approximating model is a Fourier series on an orthogonal system of trigonometric functions. The optimal solution to the approximation problem is based on the minimum square error criterion. Mathematical equations are obtained for this type of error. They allow us to estimate its value depending on the model order and the samples number in the subsequences used in the reconstruction process. The peculiarity of the mathematical equations obtained in this paper for signal reconstruction is that they do not require the preliminary calculation of the Fourier series coefficients. They provide a direct calculation of the values of reconstructed samples. At the same time, when the number of samples in the subsequences used for reconstruction will be even, it is not necessary to perform multiplication operations. All this made it possible to reduce the computational complexity of the developed algorithm for signal reconstruction. Experimental studies of the algorithm were carried out based on simulation modeling using a signal model that is an additive sum of harmonic components with a random initial phase. Numerical experiments have shown that the developed algorithm provides the reconstruction result of signal samples with a sufficiently low error. The algorithm is implemented as a software module. The operation of the module is carried out on the basis of asynchronous control of the sampling reconstruction process. It can be used as part of metrologically significant software for digital signal processing systems.

Resource Orchestration of Cloud-Edge–based Smart Grid Fault Detection

Real-time smart grid monitoring is critical to enhancing resiliency and operational efficiency of power equipment. Cloud-based and edge-based fault detection systems integrating deep learning have been proposed recently to monitor the grid in real time. However, state-of-the-art cloud-based detection may require uploading a large amount of data and suffer from long network delay, while edge-based schemes do not adequately consider the detection requirement and thus cannot provide flexible and optimal performance. To solve these problems, we study a cloud-edge based hybrid smart grid fault detection system. Embedded devices are placed at the edge of the monitored equipment with several lightweight neural networks for fault detection. Considering limited communication resources, relatively low computation capabilities of edge devices, and different monitoring accuracies supported by these neural networks, we design an optimal communication and computational resource allocation method for this cloud-edge based smart grid fault detection system. Our method can maximize the processing throughput of the system and improve resource utilization while satisfying the data transmission and processing latency requirements. Extensive simulations are conducted and the results show the superiority of the proposed scheme over comparison schemes. We have also prototyped this system and verified its feasibility and performance in real-world scenarios.

Research on efficient and accurate computing strategies for complex optimal control problems

In this study, grid refinement strategies are studied to improve computing accuracy and efficiency of the complex optimal control problems. Firstly, a solution method based on multiple variable time nodes was proposed for the optimal control problem with Bang-Bang characteristics. The problem was transformed into the Mayer formula by adding relaxed variables to eliminate integral terms. And the implementation procedure for the algorithm was also defined. Then, for optimal control problems with continuous slope changes and key switching points, a slope-based adaptive grid refinement strategy was also proposed. The time grids were able to automatically increase or decrease based on the slope information, and a new technique was used to judge the switching points and refine the corresponding time grids. Finally, the performances of the proposed methods were verified with six classical examples. The results demonstrate that they comprehensively surpass traditional methods in computing accuracy and efficiency.

Adaptive control arc length-based time grid refinement control parameterisation method for unmanned hypersonic vehicle reentry trajectory optimisation

An adaptive control arc length-based trajectory optimisation approach, which combines the control vector parameterisation (CVP) method with Gauss time grid distribution and adaptive grid refinement strategy, is proposed to further improve the downrange of unmanned hypersonic vehicles. Firstly, the Gauss time grid strategy is introduced to obtain a nonuniform Gauss time grid to calculate the original control profiles. By employing the curve integral formula to analyse the control arc length, an adaptive time grid refinement concept is proposed and the refinement process is derived in detail. The initial time grid nodes are then adaptively subdivided and combined. Finally, the control arc length-based nonuniform time grid refinement optimisation method is implemented. Numerical tests are carried out on common aero hypersonic vehicles and comparisons are made with other CVP methods. The test results reveal that the proposed approach can efficiently improve the downrange and decrease the path constraint oscillation.

Математическое моделирование динамики тепловых ударных волн в нелинейных локально-неравновесных средах

We performed a mathematical simulation of heat transfer in a local non-equilibrium medium whose transfer characteristics are functions of the temperature distribution. A homogeneous polynomial of arbitrary degree represents nonlinearities in thermal conductivity and thermal diffusivity. The mathematical model consists of a hyperbolic nonlinear heat transfer wave equation, initial conditions and nonlinear boundary conditions of the second and first kind. To solve this problem, we used a conservative homogeneous finite-difference scheme along the upper time grid line (implicitly). We then used the tridiagonal matrix algorithm of the second order in the spatial variable and of the first order in time to solve the resulting system of linearised algebraic equations. A periodic series of rectangular temperature or heat flux pulses form the boundary conditions of the first and second kind. Computation results reveal ultimate propagation rates of temperature and heat fronts featuring pronounced first-kind discontinuities with attenuating magnitudes. As the process unfolds, the initial pulses heat the region between the boundary and the heat wave front, while the subsequent pulses traverse this region at a higher velocity due to thermal diffusivity being a function of temperature, their fronts "catching up" with the previous fronts, increasing the discontinuity magnitude at the initial pulse front, that is, forming a thermal shock wave front similar to that of a shock wave in gas dynamics. We obtained such thermal shock waves for boundary conditions of both the first and the second kind. We also analysed kinematic and dynamic characteristics of thermal waves

Stability of Variable-Step BDF2 and BDF3 Methods

We prove that the two-step backward differentiation formula (BDF) method is stable on arbitrary time grids; while the variable-step three-step backward differentiation formula scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the severe mesh restrictions in the literature and provide a new understanding of variable-step BDF methods. Our main tools include the discrete orthogonal convolution kernels and an elliptic type matrix norm.

How innovations in methodology offer new prospects for volume electron microscopy

Detailed knowledge of biological structure has been key in understanding biology at several levels of organisation, from organs to cells and proteins. Volume electron microscopy (volume EM) provides high resolution 3D structural information about tissues on the nanometre scale. However, the throughput rate of conventional electron microscopes has limited the volume size and number of samples that can be imaged. Recent improvements in methodology are currently driving a revolution in volume EM, making possible the structural imaging of whole organs and small organisms. In turn, these recent developments in image acquisition have created or stressed bottlenecks in other parts of the pipeline, like sample preparation, image analysis and data management. While the progress in image analysis is stunning due to the advent of automatic segmentation and server‐based annotation tools, several challenges remain. Here we discuss recent trends in volume EM, emerging methods for increasing throughput and implications for sample preparation, image analysis and data management.

A multi-objective approach to determine time series aggregation strategies for optimal design of multi-energy systems

The optimal topology and operation of multi-energy systems (MES) can be determined by mathematical programming models, which are commonly difficult to solve due to the complex structures of the models and large-scale time-series data. The time series aggregation (TSA) strategies are usually adopted to reduce the complication of the data input and thus improve the solution efficiency. Nevertheless, for the optimal design of MES, significant differences exist in the structures and performances of the systems resulting from different TSA strategies. It is crucially important to determine appropriate TSA strategies in the optimal design of MES. In this work, a two-step method was proposed to determine TSA strategies based on a multi-objective optimization framework. In the first step, the preliminary design for the multi-energy system was obtained by different TSA strategies for the optimal design and operation of MES. In the second step, the total annual cost and loss of load probability (LSLP) of the system were taken as two objectives, and a multi-objective optimization approach was established to determine the appropriate TSA strategy for the optimal design of the MES, where the structure and performance of the system were considered simultaneously. The implementation and effectiveness of the proposed method were demonstrated by the optimal design of an MES with energy storage. The deviations of the design scheme and system performance obtained by different TSA strategies were comprehensively compared and analyzed. The results indicate that the feasibility of the optimal design schemes of the MES can be verified by using the original full-time series data, and the deviation of the results obtained by different TSA strategies can be quantified. The reduction of LSLP is at the expense of the increase of the costs. In the multiple time grids strategy (TG1) with the number of time steps (TS) 730, the TAC of the system increases from $9.79 × 107 to $1.56 × 108 when the LSLP of the system decreases from 7.90% to zero. The determination of the strategy based on the result of the minimum LSLP is critical to meet the demand in the energy system. The appropriate TSA strategies for the optimal design of MES can be selected and determined in compliance with specific requirements.

A Kinetic Performance-Informed Technoeconomic Assessment-Life Cycle Assessment Model of Ce and V Redox Flow Batteries

The EIA projects that 60% of cumulative capacity additions in the U.S. by 2050 will be renewable electric generating technologies.1 The use of intermittent renewable energy in the U.S. electricity grid requires energy storage. NREL predicts that for a scenario in which 80% of electricity in the U.S. comes from renewable energy by 2050, 120 GW of energy storage would be needed,2 yet as of 2020, the U.S. has only 24 GW of storage capacity.3 Redox flow batteries (RFBs) are a useful technology for ensuring the smooth integration of renewable energy into the U.S. electricity grid because of their long lifecycles and discharge times. RFBs are currently too expensive for market deployment, however, with the all vanadium RFB (VRFB) costing double the DOE target.4,5 One way to improve the cost effectiveness of RFBs is to explore chemistries that increase the voltage window. The replacement of the VO2+/ VO2 + chemistry at the positive electrode of a VRFB with the Ce3+/Ce4+ chemistry would result in an increased theoretical voltage, but it is unclear how the kinetic, ohmic, and mass transport overvoltages would change. Additionally, studies of the environmental burdens of life cycle phases of Ce RFBs are limited. To advance the most cost effective and least environmentally harmful RFB, in this study, we develop a combined Technoeconomic Assessment-Life Cycle Assessment (TEA-LCA) model that is informed by our performance measurements to compare the levelized cost of electricity (LCOE) and levelized greenhouse gas (LGHG) emissions of VRFBs and Ce-V RFBs.The TEA-LCA model allows the user to select from a list of positive and negative electrode redox chemistries, solvents, electrode materials, and electricity grid generation profiles to calculate the LCOE and LGHG emissions of the battery for the delivery of 1 kWh of energy. A solver function optimizes the current density that minimizes either LCOE or LGHGs. The TEA-LCA model uses a bottom-up approach, in which energy- and power-dependent capital costs and environmental burdens are calculated by converting the amount of material to a kWh basis. Cost estimates are sourced from vendors and GHG emissions are pulled from the GREET database and literature. The amount of active species required to deliver 1 kWh of electricity at a specified discharge time is calculated using the redox couple properties, including redox potential, exchange current density, and limiting currents. These performance parameters are based on measurements collected in lab. The use phase burdens are calculated using the roundtrip efficiency of the battery and the price and GHGs associated with the electricity grid generation mix. End-of-life costs consist of the economic and environmental burdens of recycling and disposing of the battery material and are collected from vendors and GREET.The TEA-LCA model answers important questions related to the optimal operating conditions of an RFB. In addition to comparing the economic and environmental performances of the VRFB and Ce-V RFB, it demonstrates how different electricity grid mixes influence total cost and emissions and highlights the difference in optimal operating current density if cost or GHG emissions are prioritized, e.g., lower current density results in fewer emissions but higher cost in carbon-intensive electricity grid profiles. Preliminary results using literature values show that the Ce-V RFB has an LCOE that is 45% lower than the VRFB LCOE, with capital costs dominating. We will present the finalized LCOE for the VRFB and Ce-V RFB, as well as LGHGs, as a function of discharge time and electricity grid mix. Sensitivity analyses of the input parameters found that for both RFBs, the discount rate, discharge faradaic efficiency, and lifetime of battery had the most influence on LCOE, with a 20% decrease in discharge faradaic efficiency resulting in a 16% increase in LCOE for the VRFB. The results of this TEA-LCA model show that the use of cerium is a viable option for reducing the cost of RFBs to advance their use in renewable energy storage grid applications. Additionally, this model is generalizable to other batteries and electrochemical systems, such as CO2 conversion. Thus, the development of this TEA-LCA model represents not only an advancement to the field of redox flow batteries but also the wider field of electrochemistry. U.S. EIA. Annual Energy Outlook. (2021).Mai, T. et al. Renewable Electricity Futures Study. NREL. (2012).CSS University of Michigan. U. S. Grid Energy Storage Factsheet. (2021).Mongird, K. et al. 2020 Grid Energy Storage Technology Cost and Performance Assessment. (2020).Weber, A. Z. et al. J. Appl. Electrochem. 41, 1137–1164 (2011).Smith, G. F. & Getz, C. A. Ind. Eng. Chem. Res. 10, 191–195 (1938).

Error estimate of the fast L1 method for time-fractional subdiffusion equations

This paper analyzes the convergence of the fast L1 method for the semi-linear time-factional subdiffusion equations. The tool we use is the generalized discrete Gronwall inequality. We show that the difference between the solution of the L1 method and the solution of the fast L1 method can be arbitrarily small and is independent of the sizes of the time and/or space grids. Our proof is very simple and is helpful to be used to simplify the convergence analysis of the fast methods for time-fractional evolution equations.

Global superconvergence analysis of nonconforming finite element method for time fractional reaction-diffusion problem with anisotropic data

In this paper, a class of two-dimensional (2-D) time fractional reaction-diffusion equation is considered. The solution usually exhibits singularity at the initial moment and anisotropic behavior in the spatial direction. In response to these problems, we provide an effective numerical framework for analyzing the L2-norm error, H1-norm superclose property and H1-norm global superconvergence result. This framework combines the high-precision L2-1σ scheme on non-uniform time grids and the anisotropic nonconforming quasi-Wilson finite element method (FEM) in space. Some numerical experiments are presented to illustrate our theoretical findings.

Sufficient Conditions for the Existence and Uniqueness of the Solution of the Dynamics of Biogeochemical Cycles in Coastal Systems Problem

The article considers a three-dimensional mathematical model of population dynamics based on a system of non-stationary parabolic advection-diffusion-reaction equations with lower derivatives describing the advective motion of the aquatic environment and non-linear source functions. In contrast to the previous authors’ works devoted to the description of this model and its numerical implementation, this article presents the results of an analytical study of the initial-boundary value problem corresponding to this model. For these purposes, the original initial-boundary value problem is linearized on a single time grid—for all nonlinear sources, their final spatial distributions for the previous time step are used. As a result, a chain of initial-boundary value problems is obtained, connected by initial—final data at each step of the time grid. For this chain of linearized problems, the existence and uniqueness of the solution of the initial-boundary value problem for the system of partial differential equations in the Hilbert space were researched. Numerical experiments were performed for model problems of the main types of phytoplankton populations in coastal systems under the influence of dynamically changing biotic and abiotic factors, the results of which are consistent with real physical experiments. The developed model, including the proposed model of biological kinetics, allows for the study of the productive and destructive processes of the shallow water body biocenosis to assess the state of the processes of reproduction of valuable and commercial fish participating in the food chain with selected species of summer phytoplankton.

Features of solving the problem of condensation of vapor containing solid particles on the edge

THE PURPOSE. To evaluate the effect on the condensation process of contaminants contained in the steam and deposited on the surface of the cooled fins, for which to formulate a mathematical model of the process, to investigate its properties and to obtain quantitative estimates of the characteristics.METHODS. The equations of the mathematical model are based on the laws of conservation of energy and mass, their study and evaluation are carried out using analytical methods of the theory of differential equations, methods of similarity theory and dimensions, as well as numerical methods for solving boundary value problems.RESULTS. The formulation of the problem of condensation of vapor containing solid particles on the edge is formulated. The presence of a self-similar solution is revealed, which is represented as a dimensionless function of one variable, uniform for all sets of initial parameters. The relations describing the distributions of the thickness δ(x, τ) of the sediment and the temperature ϑ(x, τ) on a straight edge of unlimited height (l = ∞) with an initially clean surface (h0 = 0) are obtained. These relations also almost accurately describe the initial stage of such a process on a straight edge of a finite height l, until a sediment of noticeable thickness covers the entire surface of the rib, as well as the initial moments in the case of an edge on a round pipe, until the width of the sediment zone with a noticeable thickness is significantly less than the radius of the pipe.CONCLUSION. Using these distributions as the initial ones for edges of limited height instead of, for example, introducing a uniform initial layer h0, will allow achieving high accuracy of numerical calculations without excessive thickening of the grid in coordinate and time.

Fully implicit local time-stepping methods for advection-diffusion problems in mixed formulations

This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite element method, in which the flux variable represents both the advective and diffusive flux, and the Lagrange multiplier arising from the hybridization is used for the discretization of the advective term. Based on global-in-time and nonoverlapping domain decomposition, we propose two implicit local time-stepping methods to solve the semi-discrete problem. The first method uses the time-dependent Steklov-Poincaré type operator and the second uses the optimized Schwarz waveform relaxation (OSWR) with Robin transmission conditions. For each method, we formulate a space-time interface problem which is solved iteratively. Each iteration involves solving the subdomain problems independently and globally in time; thus, different time steps can be used in the subdomains. The convergence of the fully discrete OSWR algorithm with nonmatching time grids is proved. Numerical results for problems with various Peclét numbers and discontinuous coefficients, including a prototype for the simulation of the underground storage of nuclear waste, are presented to illustrate the performance of the proposed local time-stepping methods.

A second-order scheme with nonuniform time grids for Caputo–Hadamard fractional sub-diffusion equations

In this paper, a second-order scheme with nonuniform time meshes for Caputo–Hadamard fractional sub-diffusion equations with initial singularity is investigated. Firstly, a Taylor-like formula with integral remainder is proposed, which is crucial to studying the discrete convolution kernels and error estimate. Secondly, we come up with an error convolution structure (ECS) analysis for Llog,2−1σ interpolation approximation to the Caputo–Hadamard fractional derivative. The core result in this paper is an ECS bound and a global consistency analysis established at an offset point. By virtue of this result, we obtain a sharp L2-norm error estimate of a second-order Crank–Nicolson-like scheme for Caputo–Hadamard fractional differential equations. Ultimately, an example is presented to show the sharpness of our analysis.

Remote Geotechnical Monitoring of a Buried Oil Pipeline

Extensive but remote oil and gas fields in Canada and Russia require extremely long pipelines. Global warming and local anthropogenic effects drive the deepening of seasonal thawing of cryolithozone soils and enhance pathological processes such as frost heave, thermokarst, and thermal erosion. These processes lead to a reduction in the subgrade capacity of the soils, causing changes in the spatial position of the pipelines, consequently increasing the number of accidents. Oil operators are compelled to monitor the daily temperatures of unevenly heated soils along pipeline routes. However, they are confronted with the problem of separating anthropogenic heat losses from seasonal temperature fluctuations. To highlight heat losses, we propose a short-term prediction approach to a transformed multidimensional dataset. First, we define the temperature intervals according to the classification of permafrost to generate additional features that sharpen seasonal and permafrost conditions, as well as the timing of temperature measurement. Furthermore, linear and nonlinear uncorrelated features are extracted and scaled. The second step consists of selecting a training sample, learning, and adjusting the additive regression model. Forecasts are then made from the test sample to assess the accuracy of the model. The forecasting procedure is provided by the three-component model named Prophet. Prophet fits linear and nonlinear functions to define the trend component and Fourier series to define the seasonal component; the third component, responsible for the abnormal days (when the heating regime is changed for some reason), could be defined by an analyst. Preliminary statistical analysis shows that the subsurface frozen soils containing the oil pipeline are mostly unstable, especially in the autumn season. Based upon the values of the error metrics, it is determined that the most accurate forecast is obtained on a three-month uniform time grid.

Semiparametric distributed lag quantile regression for modeling time-dependent exposure mixtures.

Studying time-dependent exposure mixtures has gained increasing attentions in environmental health research. When a scalar outcome is of interest, distributed lag (DL) models have been employed to characterize the exposures effects distributed over time on the mean of final outcome. However, there is a methodological gap on investigating time-dependent exposure mixtures with different quantiles of outcome. In this paper, we introduce semiparametric partial-linear single-index (PLSI) DL quantile regression, which can describe the DL effects of time-dependent exposure mixtures on different quantiles of outcome and identify susceptible periods of exposures. We consider two time-dependent exposure settings: discrete and functional, when exposures are measured in a small number of time points and at dense time grids, respectively. Spline techniques are used to approximate the nonparametric DL function and single-index link function, and a profile estimation algorithm is proposed. Through extensive simulations, we demonstrate the performance and value of our proposed models and inference procedures. We further apply the proposed methods to study the effects of maternal exposures to ambient air pollutants of fine particulate and nitrogen dioxide on birth weight in New York University Children's Health and Environment Study (NYU CHES).

A framework for randomized time-splitting in linear-quadratic optimal control

Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal control. In our proposed framework, the linear dynamics of the original problem is replaced by a randomized dynamics. To obtain the randomized dynamics, the system matrix is split into simpler submatrices and the time interval of interest is split into subintervals. The randomized dynamics is then found by selecting randomly one or more submatrices in each subinterval. We show that the dynamics, the minimal values of the cost functional, and the optimal control obtained with the proposed randomized time-splitting method converge in expectation to their analogues in the original problem when the time grid is refined. The derived convergence rates are validated in several numerical experiments. Our numerical results also indicate that the proposed method can lead to a reduction in computational cost for the simulation and optimal control of large-scale linear dynamical systems.

MO903: Associations of Serum Sodium With Mortality in Patients on Maintenance Haemodialysis Treatment

Abstract BACKGROUND AND AIMS Chronic HD-patients have a 50% 5-year survival and unphysiological fluid and sodium shifts are key pathophysiological contributors. Several studies have shown that hyponatremia is associated with worse outcomes in haemodialysis patients. However, the association of all-cause mortality with volume status in hyponatremic patients is uncertain. Body composition monitoring has provided a more precise tool to estimate fluid status in dialysis patients. The primary aim of this international observational study performed in a large patient database (EUCLID5) was to quantify the association between salt exposure, fluid overload (FO) and mortality risk in haemodialysis patients. METHOD We included 71 706 incident haemodialysis patients from 1 January 2010 to 4 December 2020 in an extended Cox regression model for a time to death analysis. Exposure variables were defined as predialysis serum sodium and fluid overload (in liters as determined by the BCM—Body Composition Monitor using bioimpedance spectroscopy) on a monthly time grid. Effect modifiers, mediators, confounders and predictors were defined a priori. Adults were included with at least one valid BCM measurement within 3 months from first haemodialysis treatment and followed up until death or administrative censoring. All patients included in the study cohort were treated in the NephroCare–FMC dialysis centre network operating in 26 countries. Data were retrieved from the central EuCliD5 database. RESULTS In hyponatremic patients (serum sodium < 135 mmol/L), the association to the risk of death doubled [(HR = 1.97 (1.82–2.12)] in overhydrated patients (relative FO defined as 13% in men, and 15% in women >90th percentile of physiological hydration), was increased by 56% [HR = 1.56 (1.27–1.93)] in underhydrated patients (<–7% <10th percentile of normohydration) and was modestly higher in states of isovolemia (–7%–13% in women and 15% in men). The associated risk of death in states of overhydration decreased [HR = 1.50 (1.27–-1.76)] when patients were hypernatremic (serum sodium >142 mmol/L), (Table 1). Generally, the risk increased with rising FO and declining sodium concentration. CONCLUSION The observed associations to the risk of death reflecting the interplay between states of hypo-, iso- and hypernatremia and states of under, normal and over hydration deserve further study to understand the underlying complex mechanisms and identify therapeutic approaches. When assessing the risk level of different sodium concentrations, fluid status should be taken into account.