Use Of Proper Orthogonal Decomposition Research Articles

Fluid-reduced-solid interaction (FrSI): Physics- and projection-based model reduction for cardiovascular applications

Fluid-solid interaction (FSI) phenomena play an important role in many biomedical engineering applications. While FSI techniques and models have enabled detailed computational simulations of flow and tissue motion, the application of FSI can present challenges, particularly when data for constraining models is sparse and/or when fast computational simulations are required for assessment. In this paper, we propose a novel method for flexible-wall fluid dynamics in an ALE framework applicable for cardiovascular applications where adaptive fluid motion that emulates patient data is required. Efficiency and model simplicity are gained by a physics-based reduction to solid membrane formulations at the fluid-tissue interface combined with a Galerkin projection to a subspace spanned by boundary motion modes, leveraging snapshots observed from imaging data by use of Proper Orthogonal Decomposition (POD). The resulting fluid-reduced-solid interaction (FrSI) model is verified for a series of examples, illustrating efficacy and efficiency. Focusing on an idealized left ventricle model, we demonstrate homogenization of transmural active stress along with the capacity to accommodate prestress in the FrSI model, accounting for whole cycle mechanics by coupling to 0D pre- and afterload models (showing end-diastolic and end-systolic projected endocardial surface position errors of less than 1.5% and 3.5%, respectively). Further, we present strategies to compensate for the inherent approximation errors of the FrSI model, allowing for minimizing both the integral and spatial error between reduced and full-order model by re-calibrating parameters that govern diastolic and systolic function. Finally, the ability of FrSI to extrapolate to impaired system states (increased afterload, localized region of infarct) is shown, providing a simple yet effective strategy to enhance the POD subspace to further reduce errors. These results illustrate the potential of FrSI to streamline the simulation of hemodynamics in the heart and cardiovascular system.

Realistic turbulent inflow conditions for estimating the performance of a floating wind turbine

Abstract. A novel method for generating turbulent inflow boundary conditions for aeroelastic computations is proposed, based on interfacing hybrid hot-wire and particle image velocimetry measurements performed in a wind tunnel to a full-scale load simulation conducted with FAST. This approach is based on the use of proper orthogonal decomposition (POD) to interpolate and extrapolate the experimental data onto the numerical grid. The temporal dynamics of the temporal POD coefficients is driven by the high-frequency hot-wire measurements used as input for a lower-order model built using a multi-time-delay linear stochastic estimation (LSE) approach. Being directly extracted from the data, the generated three-component velocity fields later used as inlet conditions present correct one- and two-point spatial statistics and realistic temporal dynamics. Wind tunnel measurements are performed at a scale of 1:750, using a properly scaled porous disk as a floating wind turbine model. The motions of the platform are imposed by a linear actuator. Between all 6 degrees of freedom (DOFs) possible, the present study focus on the streamwise direction motion of the model (surge motion). The POD analysis of the flow, with or without considering the presence of the surge motion of the model, shows that a few modes are able to capture the characteristics of the most energetic flow structures and the main features of the wind turbine wake, such as its meandering and the influence of the surge motion. The interfacing method is first tested to estimate the performance of a wind turbine in an offshore boundary layer and then those of a wind turbine immersed in the wake of an upstream wind turbine subjected to a sinusoidal surge motion. Results are also compared to those obtained using the standard inflow generation method provided by TurbSim available in FAST.

Particle image velocimetry in the impeller of a centrifugal pump: A POD-based analysis

The flow field within the channels of a centrifugal pump impeller is usually complex, containing turbulent structures in a wide range of time and length scales. Identifying the different structures and their dynamics in this rotating frame is, therefore, a difficult task. However, modal decomposition can be a useful tool for detecting coherent structures. In this paper, we make use of proper orthogonal decomposition (POD) of time-resolved flow fields in order to investigate the flow in a centrifugal pump. For that, we carried out experiments using time-resolved particle image velocimetry (TR-PIV) in a pump of transparent material operating at different conditions and obtained the statistical characteristics of the turbulent flow from phase-ensemble averages of velocities and turbulent kinetic energy. The results reveal that at the pump’s best efficiency point (BEP) the flow is well-organized, with no significant flow separation. For flow rates below the BEP, flow separation and vortex structures appear in the impeller channels, making the flow unstable. At flow rates above the BEP, intense jets appear close to the suction blades, while small instabilities occur on the pressure side. The POD analysis shows that at low flow rates, the flow is dominated by large-scale structures with intense energy levels, while at the BEP and higher flow rates, the flow is dominated by small-scale structures. Our results shed light on the turbulence characteristics inside the impeller, providing relevant information for reduced-order models capable of computing the flow in turbomachinery at much lower costs when compared to traditional methods.

Non-Gaussian buffeting analysis of large structures by means of a Proper Orthogonal Decomposition

Proper Orthogonal Decomposition is implemented in a Bispectral Stochastic Analysis of large MDOF structures. Although Higher Order Stochastic Analysis has been introduced few decades ago, its establishment has found place only in a theoretical way, or applied to very small systems. Its heavy computational cost as well as resource consumption burden has let it aside for practical civil engineering applications. Nevertheless, in wind engineering, the community is increasingly considering the importance of non-Gaussian nature of wind induced vibrations. This is of interest for the extreme value analysis, for which many theoretical and empirical models exist for non-Gaussian random processes. In this context, a (bi-)spectral approach is realized in a 2-D frequency space where the bispectrum is computed then the 3rd statistical moment is obtained by means of a twofold integration. These operations are quite heavy as soon as the dimension of the problem increases. A novel algorithm implementation is proposed. It hinges on (i) the use of Proper Orthogonal Decomposition and the (ii) development of an optimized numerical method. The proposed algorithmic arrangement minimizes the number of operations, and consequently saves time and memory, while conserving precision in estimating 3rd order statistical moments of structural responses.

Conditions for the convergence of proper orthogonal modes to linear vibration modes

Considerable attention has been given to the use of proper orthogonal decomposition (POD) as a tool for modal analysis. Much of this work hinges on early theoretical developments that conclude that the resulting proper orthogonal modes (POMs) converge to the linear vibration modes (LVMs) as the number of samples increases. The purpose of the present work is to clarify the conditions under which the POMs of a linear, undamped, and unforced mechanical system converge to the system’s LVMs. To that end, it presents a rigorous proof of convergence that demonstrates that increasing the number of samples (i.e., the sampling rate) alone is insufficient; instead, convergence is shown to require increasing both the sampling rate and the duration of the sampling.

Characterization of the Unsteady Wake Aerodynamics for an Industry Relevant Road Vehicle Geometry Using LES

A wall-resolved large eddy simulation (WRLES) study of the flow around a 15% scale model of the Nissan NDP, an electric concept vehicle developed by Nissan, at Re_H=100{,}000 is presented. First, wake asymmetries and the associated possibility of wake bimodality occurring are investigated by comparing the flow fields around “squareback” and cavity variants of the Nissan NDP. It is highlighted that there is no noteworthy long-term wake asymmetry in the spanwise direction for both configurations and that there is, instead, symmetric spanwise vortex shedding, as highlighted through the use of proper orthogonal decomposition (POD) post-processing. One can, therefore, exclude the existence of classical wake bimodality in the spanwise direction that has been observed for the Ahmed body. However, the wake does explore the vehicle’s rear space in the spanwise direction rapidly over non-dimensional time intervals of {mathcal {O}}(10). Meanwhile, there is a strong wake tilt in the vertical direction due to the presence of a ground, the vehicle geometry’s vertical asymmetry, and the detachment of a powerful hairpin vortex from the vehicle’s roof. When looking at POD of the flow field in a vertical plane, asymmetric vortex shedding, similar to that observed for the Ahmed body by Hesse and Morgans (2021) in the spanwise plane, is found. This suggests that wake bimodality in the vertical direction could occur for the Nissan NDP—the presented results are not conclusive, as the provided non-dimensional simulation duration of t^* sim 60 is insufficient for the bimodal phenomenon that occurs at t^* sim 1000. Additionally, the discernible impact of having a cavity at the rear of the NDP is to allow the wake to explore a larger vehicle base space (i.e. the wake is able to move more freely). This, coupled to a 5% reduction in rear base area, translates to a drag reduction compared to the “squareback” variant of 13.6%. Second, in a more qualitative analysis of simulation results, the effect of using a moving ground in simulation as compared to a stationary ground is assessed. This is only done for the cavity variant of the Nissan NDP. It is found that, for this vehicle geometry, a stationary ground is associated with the occurrence of low pressure clockwise rotating (when looking into the page of the vertical plane) vortices near the ground caused by the flow deceleration just aft of the vehicle base, where the flow moves from the vehicle under-body toward the wake’s far-field region. The consequence of this flow phenomenon is to simulate a 3.3% higher drag value with the stationary ground simulation as compared to the moving ground simulation. Thus, although the moving ground should be more representative of the real-world, the stationary ground simulation is more conservative in aerodynamic terms and should be used if developing the NDP vehicle completely digitally using a virtual twin. By over-design, the stationary ground variant namely ensures that the drag key performance indicator (KPI) is met.

POD-Kalman filtering for improving noninvasive 3D temperature monitoring in MR-guided hyperthermia.

BackgroundDuring resonance frequency (RF) hyperthermia treatment, the temperature of the tumor tissue is elevated to the range of 39–44°C. Accurate temperature monitoring is essential to guide treatments and ensure precise heat delivery and treatment quality. Magnetic resonance (MR) thermometry is currently the only clinical method to measure temperature noninvasively in a volume during treatment. However, several studies have shown that this approach is not always sufficiently accurate for thermal dosimetry in areas with motion, such as the pelvic region. Model‐based temperature estimation is a promising approach to correct and supplement 3D online temperature estimation in regions where MR thermometry is unreliable or cannot be measured. However, complete 3D temperature modeling of the pelvic region is too complex for online usage.PurposeThis study aimed to evaluate the use of proper orthogonal decomposition (POD) model reduction combined with Kalman filtering to improve temperature estimation using MR thermometry. Furthermore, we assessed the benefit of this method using data from hyperthermia treatment where there were limited and unreliable MR thermometry measurements.MethodsThe performance of POD–Kalman filtering was evaluated in several heating experiments and for data from patients treated for locally advanced cervical cancer. For each method, we evaluated the mean absolute error (MAE) concerning the temperature measurements acquired by the thermal probes, and we assessed the reproducibility and consistency using the standard deviation of error (SDE). Furthermore, three patient groups were defined according to susceptibility artifacts caused by the level of intestinal gas motion to assess if the POD–Kalman filtering could compensate for missing and unreliable MR thermometry measurements.ResultsFirst, we showed that this method is beneficial and reproducible in phantom experiments. Second, we demonstrated that the combined method improved the match between temperature prediction and temperature acquired by intraluminal thermometry for patients treated for locally advanced cervical cancer. Considering all patients, the POD–Kalman filter improved MAE by 43% (filtered MR thermometry = 1.29°C, POD–Kalman filtered temperature = 0.74°C). Moreover, the SDE was improved by 47% (filtered MR thermometry = 1.16°C, POD–Kalman filtered temperature = 0.61°C). Specifically, the POD–Kalman filter reduced the MAE by approximately 60% in patients whose MR thermometry was unreliable because of the great amount of susceptibilities caused by the high level of intestinal gas motion.ConclusionsWe showed that the POD–Kalman filter significantly improved the accuracy of temperature monitoring compared to MR thermometry in heating experiments and hyperthermia treatments. The results demonstrated that POD–Kalman filtering can improve thermal dosimetry during RF hyperthermia treatment, especially when MR thermometry is inaccurate.

Reduced order modelling of nonlinear cross-diffusion systems

In this work, we present reduced-order models (ROMs) for a nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The formation of the patterns of the SKT equation consists of a fast transient phase and a long stationary phase. Reduced order solutions are computed by separating the time into two time-intervals. In numerical experiments, we show for one- and two-dimensional SKT equations with pattern formation, the reduced-order solutions obtained in the time-windowed form, i.e., principal decomposition framework, are more accurate than the global proper orthogonal decomposition solutions obtained in the whole time interval. The finite-difference discretization of the SKT equation in space results in a system of linear-quadratic ordinary differential equations. The ROMs have the same linear-quadratic structure as the full order model. Using the linear-quadratic structure of the ROMs, the computation of the reduced-order solutions is further accelerated by the use of proper orthogonal decomposition in a tensorial framework so that the computations in the reduced system are independent of the full-order solutions. Furthermore, the prediction capabilities of the ROMs are illustrated for one- and two-dimensional patterns. Finally, we show that the entropy is decreasing by the reduced solutions, which is important for the global existence of solutions to the nonlinear cross-diffusion equations such as the SKT equation.

Partially-averaged Navier–Stokes simulations of turbulent flow past a square cylinder: Comparative assessment of statistics and coherent structures at different resolutions

Scale-resolving simulations of the turbulent wake behind a square cylinder are performed at Re = 22 000 using the partially averaged Navier–Stokes (PANS) k-ω closure model at different degrees of resolution (cut-off scales) corresponding to the unresolved-to-total kinetic energy ratio fk ∈ [0.10, 0.50]. The two principle objectives of the study are to (i) establish the degree of resolution required for an accurate computation of different quantities of interest ranging from flow statistics to coherent structures and (ii) develop a protocol for a quantitative assessment and comparison of the large-scale coherent structures simulated at different degrees of resolution. Straightforward use of proper orthogonal decomposition (POD) to assess and compare large-scale coherence at different resolution levels can prove difficult as small-scale features can affect the POD mode shape and amplitude. To overcome this difficulty, two methods of quantifying coherent structures in the wake are proposed. These methods are based upon the incorporation of Fourier and Chebyshev decompositions with spectral proper orthogonal decomposition, respectively. We examine the first-mode energy spectra and the corresponding streamwise mode shapes using the results generated from PANS simulations at different degrees of resolution. It is demonstrated that increasingly finer resolutions are needed for integral quantities, one-point statistics, frequency spectra, and coherent structures, in that order. The underlying physics is explicated.

The use of proper orthogonal decomposition for the simulation of highly nonlinear hygrothermal performance

In this paper, the use of proper orthogonal decomposition for simulating nonlinear heat, air and moisture transfer is investigated via two applications: HAMSTAD benchmarks 2 and 3. Moreover, the potential of the reduced models constructed by proper orthogonal decomposition for simulating new problems with longer simulation periods is assessed. To illustrate the feasibilities of proper orthogonal decomposition method in the field of building physics, the accuracies of the reduced models are compared with the standard finite element method. The outcomes show that with a sufficient number of construction modes and a relatively large amount of snapshots, proper orthogonal decomposition method can deliver accurate results. In addition, guidelines on selecting an appropriate amount of simulation snapshot and construction modes are provided.

Low-Order Velocity Estimation and Acoustic Noise Generation by a Turbulent Wall Jet

A method for estimating the velocity fluctuations, hydrodynamic pressure fluctuations, and far-field acoustic pressure in a planar turbulent wall jet is examined. The Reynolds number based on nozzle height and exit velocity is 25,500. Streamwise-aligned, two-component particle image velocimetry and surface pressure measurements are obtained synchronously along the center line of the wall jet. Modified stochastic estimation is used to estimate a low-dimensional representation of the time-dependent velocity field, and performance metrics for the evaluation of the estimates are presented. The use of proper orthogonal decomposition in the estimation is evaluated against the estimation of individual velocity vectors from the measurements to investigate the filtering effect of using a subset of proper orthogonal decomposition modes in the velocity reconstruction. The velocity estimates are used to solve Poisson’s equation for the time-dependent hydrodynamic pressure fluctuations. Curle’s acoustic analogy is evaluated using the estimated velocity and pressure and compared with far-field acoustic measurements via a phased array of microphones. The estimated acoustic spectrum scaled by spanwise integration width is comparable to scaled measurements of the acoustic spectrum. The estimation method highlights the importance of the interaction between the pressure and velocity fields to the acoustic generation process.

An aeroacoustic study of a leading-edge slat: Beamforming and far field estimation using near field quantities

The leading edge slat of a high-lift system is a large contributor to the overall radiated acoustic field from an aircraft during the approach phase of the flight path. This is due to the unsteady flow field generated in the slat-cove and near the leading edge of the main element. In an effort to understand the noise-source mechanisms, a suite of experimental measurements has been performed on a two-dimensional multi-element MD-30P30N airfoil, including PIV, steady and unsteady surface pressure, and phased microphone array measurements. Acoustic trends are given with angle of attack and flow speed which corresponds to a stowed chord Reynolds number range of 1.2 × 106 ≤ Rec ≤ 1.71 × 106. Spatially integrated beamforming is used to isolate the slat noise, while Kevlar sidewalls are utilized to minimize environmental influence. In addition, temporally-resolved estimates of a low-dimensional representation of the velocity vector fields are obtained through the use of proper orthogonal decomposition and spectral linear stochastic estimation and show good agreement with independent phase-locked PIV measurements. A time-resolved estimate of the pressure field is then computed via solution of the pressure Poisson equation. From this, Curle's acoustic analogy scaled for the frequency-dependent spanwise coherence length projects the time-resolved pressure forces in the slat region to the acoustic far field for comparison to the array measurements. The favorable results establish the connection between the dominant unsteady flow structures most responsible for the radiated noise and provide insight for future noise reduction efforts.

Linear Parameter-varying Approach for Modeling and Control of Rapid Thermal Processes

In the present paper, a new approach is presented to model and control single wafer rapid thermal processing (RTP) systems. In the past decade, RTP has achieved acceptance as the mainstream technology for semiconductor manufacturing. Thermal processing is one of the most efficient ways to control the phase-structure properties. Moreover, the time duration of RTP systems reduces the so-called thermal budget significantly compared to the traditional methods. RTP implementation is based on the use of light from heating lamps to provide a heat flux. This process is highly nonlinear due to the radiative heat transfer and material properties. By invoking the first principles-based models, we develop in this paper a linear parameter-varying (LPV) model to directly account for the nonlinearities within the system. The model is then discretized into a high-order LPV model; thereafter, principal component analysis (PCA) method is utilized to reduce the number of LPV model’s scheduling variables, followed by the use of proper orthogonal decomposition (POD) for model order reduction. Using the reduced order model, we then design a gain-scheduled controller to satisfy an induced L2 gain performance for tracking of a temperature profile and show improvement over other controller design methods suggested in the literature.

Modal analysis of wingtip vortices by means of Proper Orthogonal Decomposition

AbstractThis paper discusses the influence of different wingtip geometries on the first eigenmodes of wingtip vortices. With the use of Proper Orthogonal Decomposition (POD) of a turbulent velocity field, a modal decomposition of coherent structures, high energetic eigenmodes are determined. Based on the results found by Fabre et al. [1], these eigenmodes may be a key factor for the stability analysis. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of a pitching and plunging airfoil using experimental flow field and load measurements

The main goal of the current paper is to outline a low-order modeling procedure of a heaving airfoil in a still fluid using experimental measurements. Due to its relative simplicity, the proposed procedure is applicable for the analysis of flow fields within complex and unsteady geometries and it is suitable for analyzing the data obtained by experimentation. Currently, this procedure is used to model and predict the flow field evolution using a small number of low profile load sensors and flow field measurements. A time delay neural network is used to estimate the flow field. The neural network estimates the amplitudes of the most energetic modes using four sensory inputs. The modes are calculated using proper orthogonal decomposition of the flow field data obtained experimentally by time-resolved, phase-locked particle imaging velocimetry. To permit the use of proper orthogonal decomposition, the measured flow field is mapped onto a stationary domain using volume preserving transformation. The analysis performed by the model showed good estimation quality within the parameter range used in the training procedure. However, the performance deteriorates for cases out of this range. This situation indicates that, to improve the robustness of the model, both the decomposition and the training data sets must be diverse in terms of input parameter space. In addition, the results suggest that the property of volume preservation of the mapping does not affect the model quality as long as the model is not based on the Galerkin approximation. Thus, it may be relaxed for cases with more complex geometry and kinematics.

The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations

The main aim of this paper is to develop a fast and efficient local meshless method for solving shallow water equations in one- and two-dimensional cases. The mentioned equation has been classified in category of advection equations. The solutions of advection equations have some shock, thus, especial numerical methods should be employed for example discontinuous Galerkin and finite volume methods. Here, based on the proper orthogonal decomposition approach we want to construct a fast meshless method. To this end, we consider shallow water models and obtain a suitable time-discrete scheme based on the predictor-corrector technique. Then by applying the proper orthogonal decomposition technique a new set of basis functions can be built for the solution space in which the size of new solution space is less than the original problem. Thus, by employing the new bases the CPU time will be reduced. Some examples have been studied to show the efficiency of the present numerical technique.

Use of Proper Orthogonal Decomposition for Extraction of Ocean Surface Wave Fields from X-Band Radar Measurements of the Sea Surface

Radar remote sensing of the sea surface for the extraction of ocean surface wave fields requires separating wave and non-wave contributions to the sea surface measurement. Conventional methods of extracting wave information from radar measurements of the sea surface rely on filtering the wavenumber-frequency spectrum using the linear dispersion relationship for ocean surface waves. However, this technique has limitations, e.g., it isn’t suited for the inclusion of non-linear wave features. This study evaluates an alternative method called proper orthogonal decomposition (POD) for the extraction of ocean surface wave fields remotely sensed by marine radar. POD is an empirical and optimal linear method for representing non-linear processes. The method was applied to Doppler velocity data of the sea surface collected using two different radar systems during two different experiments that spanned a variety of environmental conditions. During both experiments, GPS mini-buoys simultaneously collected wave data. The POD method was used to generate phase-resolved wave orbital velocity maps that are statistically evaluated by comparing wave statistics computed from the buoy data to those obtained from these maps. The results show that leading POD modes contain energy associated with the peak wavelength(s) of the measured wave field, and consequently, wave contributions to the radar measurement of the sea surface can be separated based on modes. Wave statistics calculated from optimized POD reconstructions are comparable to those calculated from GPS wave buoys. The accuracy of the wave statistics generated from POD-reconstructed orbital velocity maps was not sensitive to the radar configuration or environmental conditions examined. Further research is needed to determine a rigorous method for selecting modes a priori.

Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters

In this paper, an approach based on the synergistic use of proper orthogonal decomposition and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of a structure is obtained during an (offline) initial training stage of monitoring; afterward, effective estimations of a possible structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first (extended) one to deal with the time evolution of a joint state vector, gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations. Results are reported for a (pseudo-experimental) benchmark test on an eight-story shear building. Capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms of the reduced-order model, identified damage location and speed-up of the whole health monitoring procedure.

A Numerical Approach to Possible Identification of the Noisiest Zones of a Wall Surface with a Flow Interaction

This paper examines the use of proper orthogonal decomposition (POD) and singular value decomposition (SVD) to identify zones on the surface of the source that contribute the most to the sound power the source radiates. First, computational fluid dynamics (CFD) is used to obtain the pressure field at the surface of the blade in a subsonic regime. Then the fluctuation of this pressure field is used as the input for the loading noise in the Ffowcs Williams and Hawkings (FW&H) acoustic analogy. The FW&H analogy is used to calculate the sound power that is radiated by the blade. Secondly, the most important acoustic modes of POD and SVD are used to reconstruct the radiated sound power. The results obtained through POD and SVD are similar to the acoustic power directly obtained with the FW&H analogy. It was observed that the importance of the modes to the radiated sound power is not necessarily in ascending order (for the studied case, the seventh mode was the main contributor). Finally, maps of the most contributing POD and SVD modes have been produced. These maps show the zones on the surface of the blade, where the dipolar aeroacoustic sources contribute the most to the radiated sound power. These identifications are expected to be used as a guide to design and shape the blade surface in order to reduce its radiated noise.

An efficient goal‐based reduced order model approach for targeted adaptive observations

SummaryAn efficient adjoint sensitivity technique for optimally collecting targeted observations is presented. The targeting technique incorporates dynamical information from the numerical model predictions to identify when, where and what types of observations would provide the greatest improvement to specific model forecasts at a future time. A functional (goal) is defined to measure what is considered important in modelling problems. The adjoint sensitivity technique is used to identify the impact of observations on the predictive accuracy of the functional, then placing the sensors at the locations with high impacts. The adaptive (goal) observation technique developed here has the following features: (i) over existing targeted observation techniques, its novelty lies in that the interpolation error of numerical results is introduced to the functional (goal), which ensures the measurements are a distance apart; (ii) the use of proper orthogonal decomposition (POD) and reduced order modelling for both the forward and backward simulations, thus reducing the computational cost; and (iii) the use of unstructured meshes.The targeted adaptive observation technique is developed here within an unstructured mesh finite element model (Fluidity). In this work, a POD reduced order modelling is used to form the reduced order forward model by projecting the original complex model from a high dimensional space onto a reduced order space. The reduced order adjoint model is then constructed directly from the reduced order forward model. This efficient adaptive observation technique has been validated with two test cases: a model of an ocean gyre and a model of 2D urban street canyon flows. Copyright © 2016 John Wiley & Sons, Ltd.