Exact Modeling Research Articles

The exact spectral element modeling and vibration analysis of the acoustic black hole double-beam system

In this paper, we present a study of vibration characteristics of the double-beam structures combined with the concept of the acoustic black hole (ABH), which is an effective technique for vibration and noise control. In the proposed double-beam structure, the ABH beam as the vibration damper is attached to the primary uniform beam by a range of translational and rotational springs. We formulate the closed-form spectral element matrix of the double-beam structure and calculate the natural frequencies and mode shapes of the system. The results demonstrate the ABH effect of increasing the modal damping ratios. We also study the power flow and mechanical intensity of the system to offer physical insight into the vibration suppression mechanism of the ABH. A detailed parametric analysis of both translational and rotational springs is carried out. The investigation contributes to the exact dynamic modelling and analysis of the double-beam system containing ABH elements. Furthermore, the proposed ABH double-beam structure shows great potential for vibration control and energy harvesting.

Design of a Takagi–Sugeno Fuzzy Exact Modeling of a Buck–Boost Converter

DC–DC converters are used in many power electronics applications, such as switching power supply design, photovoltaic, power management systems, and electric and hybrid vehicles. Traditionally, DC–DC converters are linearly modeled using a typical operating point for their control design. Some recent works use nonlinear models for DC–DC converters, due to the inherent nonlinearity of the switching process. In this sense, a standout modeling technique is the Takagi–Sugeno fuzzy exact method due to its ability to represent nonlinear systems over the entire operating range. It is more faithful to system behavior modeling, and allows a nonlinear closed-loop control design. The use of nonlinear models allows the testing of controllers obtained by linear methods to operate outside their linearization point, corroborating with robust controllers for specific applications. This work aims to perform the exact fuzzy Takagi–Sugeno modeling of a buck–boost converter with non-ideal components, and to design a discrete proportional–integral–derivative (PID) controller from the pole cancellation technique, obtained linearly, to test the controller at different operating points. The PID control ensured a satisfactory result compared with the stationary value of the different operating points, but it did not reach the desired transient response. Since the proposed model closely represents the operation of the buck–boost converter by considering the components’ non-idealities, other control techniques that consider the system’s nonlinearities can be applied and optimized later.

Drift Reduction in Underwater Egomotion Computation by Axial Camera Modeling

Localization of autonomous underwater vehicles is essential for underwater exploration, environmental monitoring, and infrastructure inspections, as only a few examples. As wirelessly transmitted data cannot be used in underwater navigation, and equivalent sensors are costly and not readily deployable, the use of cameras as a localization aid offers an attractive alternative. Nonetheless, the utilization of cameras for underwater navigation is hindered by medium-induced visual deterioration and refraction of the incident ray. While most research has been focusing on addressing the radiometric deterioration effects, we demonstrate that the introduction of a physically aware model of the refraction effect can significantly improve the platform localization. Specifically, we develop a refraction-aware continuous formulation of the egomotion model, which computes the translational and rotational velocities using optical flow measurements. We also demonstrate that a linear model can be reached despite the nonlinear ray's path. Results show an improved navigation solution echoed by a significant reduction in the drift with more than tenfold improvement in the estimated position and angular quantities compared to state-of-the-art methods. They demonstrate the benefit of exact modeling in underwater navigation.

Geometrically Exact Beam-based Aeroelastic Modeling and Solution Of Composite Rotor Blades in Forward Flight

In this paper, the geometrically exact beam model and aeroelastic solution methods for composite rotor blades in forward flight by the latest variational asymptotic beam sectional analysis (VABS) have been employed. The geometrically exact beam equations of motion in the mixed variational form and the latest VABS are used to deal with one-dimensional blade analysis and the structural property of blade cross section, respectively. The methods can be used for the aeroelastic solution of composite rotor blades with arbitrary cross-sectional shape and material distribution, large deflections and significant nonclassical effects such as cross-sectional warping, transverse shear deformation, and elastic couplings caused by anisotropic material properties. The Peters–He finite state dynamic inflow model and the Peters finite state airloads theory are used to calculate the induced velocity and blade airloads, respectively. An auto-pilot trim scheme is used for calculating the blade pitch controls to meet the trim requirements. The convergence issue encountered when solving the geometrically exact, mixed variational aeroelastic equations in time domain has been successfully addressed. The values of the empirical parameters in the auto-pilot trim scheme for the presented aeroelastic model have been properly selected. The accuracy of the presented aeroelastic modeling and solution methods has been verified against the SA349/2 flight-test data. The influence of transverse shear deformation on the aeroelastic response of composite rotor blades was also investigated, indicating that this effect has a nonnegligible influence on the aeroelastic response of the five different kinds of elastically coupled hingeless composite rotors investigated in this paper.

Calibration of FEM models of historic masonry structures and its application on a local historic structure

Masonry structures may be of different kinds, including stone, brick and other masonry blocks assembled in different ways using mortar. For study of such structures, modelling them is necessary which can be done in two ways, either by modelling large classes of masonry as single units (Simple Model) or by regular arrangement of blocks and the interaction between blocks and mortar (Refined Model). Simple Model approach takes crude material assumptions and produces results affected by large approximations, while the second approach is sophisticated and close to reality. The present research deals with the creation of a method for modelling of Finite Element Models of masonry buildings through their fast regenerative modelling in an environment offered by Rhinoceros 3D and Grasshopper. Since exact modelling of such structures is complicated and time-consuming, macro modelling of such structures is carried out by simplistic assumptions of the structural system as load bearing walls. Simple architectural plans of each storey may be imported from AutoCAD to Rhinoceros 3D, scaled according to the dimensions. These can then be assigned as geometry in Grasshopper and extruded in Z-direction (according to storey height) to get the basic volume of the curves. The plan of each storey can then be placed on top of one another by maintaining a distance equal to the storey height and the whole 3D model may be created. These models are user friendly and consume very less time, if definitions for extrusion and openings etc. are created beforehand in Grasshopper, and can be used for multiple structures. Such macro models are then used for simple static analysis by using a similar script in Grasshopper or may be imported to other Finite Element Analysis (FEA) softwares.

The blindfolded traveler’s problem: A search framework for motion planning with contact estimates

We address the problem of robot motion planning under uncertainty where the only observations are through contact with the environment. Such problems are typically solved by planning optimistically assuming unknown space is free, moving along the planned path and re-planning if the robot collides. However this approach can be very inefficient, leading to many unnecessary collisions and unproductive motion. We propose a new formulation, the Blindfolded Traveler’s Problem (BTP), for planning on a graph containing edges with unknown validity, with true validity observed only through attempted traversal by the robot. The solution to a BTP is a policy indicating the next edge to attempt given previous observations and an initial belief. We prove that BTP is NP-complete and show that exact modeling of the belief is intractable, therefore we present several approximation-based policies and beliefs. For the policy we propose graph search with edge weights augmented by the probability of collision. For the belief representation we propose a weighted Mixture of Experts of Collision Hypothesis Sets and a Manifold Particle Filter. Empirical evaluation in simulation and on a real robot arm shows that our proposed approach vastly outperforms several baselines as well as a previous approach that does not employ the BTP framework.

Tracking Control Based on GPS Intelligent Buoy System for an Autonomous Underwater Vehicles Under Measurement Noise and Measurement Delay

This paper deals with the real-time tracking control problem for an autonomous underwater vehicle based on an acoustic-based positioning method, i.e., the so-called GPS intelligent buoy system, which causes inevitable measurement delay. The measurement delay increases the control difficulty and degrades the tracking accuracy. Additionally, the exact modeling for an autonomous underwater vehicle is difficult due to uncertain hydrodynamic parameters. Based on these findings, a model-free control scheme is proposed. In the proposed scheme, the GPS intelligent buoy system provides the position signals without velocity measurements. Considering the measurement noise, a robust exact differentiator is used instead of the traditional numerical differentiation method to obtain the derivatives of position signals, which saves the limited actuator energy of autonomous underwater vehicles. Simulations are performed to verify the validity of the proposed control scheme. The results demonstrate that the proposed control scheme can achieve high timeliness and high tracking accuracy for autonomous underwater vehicles. Compared to the conventional model predictive control, the proposed controller requires 89.7% less average calculation time. In addition, the proposed controller outperforms the conventional proportion-differentiation controller in root-mean-square error by approximately 62.3−80.7%.

On-Site Soil Monitoring Using Photonics-Based Sensors and Historical Soil Spectral Libraries

In-situ infrared soil spectroscopy is prone to the effects of ambient factors, such as moisture, shadows, or roughness, resulting in measurements of compromised quality, which is amplified when multiple sensors are used for data collection. Aiming to provide accurate estimations of common physicochemical soil properties, such as soil organic carbon (SOC), texture, pH, and calcium carbonates based on in-situ reflectance captured by a set of low-cost spectrometers operating at the shortwave infrared region, we developed an AI-based spectral transfer function that maps fields to laboratory spectra. Three test sites in Cyprus, Lithuania, and Greece were used to evaluate the proposed methodology, while the dataset was harmonized and augmented by GEO-Cradle regional soil spectral library (SSL). The developed dataset was used to calibrate and validate machine learning models, with the attained predictive performance shown to be promising for directly estimating soil properties in-situ, even with sensors with reduced spectral range. Aiming to set a baseline scenario, we completed the exact same modeling experiment under laboratory conditions and performed a one-to-one comparison between field and laboratory modelling accuracy metrics. SOC and pH presented an R2 of 0.43 and 0.32 when modeling the in-situ data compared to 0.63 and 0.41 of the laboratory case, respectively, while clay demonstrated the highest accuracy with an R2 value of 0.87 in-situ and 0.90 in the laboratory. Calcium carbonates were also attempted to be modeled at the studied spectral region, with the expected accuracy loss from the laboratory to the in-situ to be observable (R2 = 0.89 for the laboratory and 0.67 for the in-situ) but the reduced dataset variability combined with the calcium carbonate characteristics that are spectrally active in the region outside the spectral range of the used in-situ sensor, induced low RPIQ values (less than 0.50), signifying the importance of the suitable sensor selection.

Extended angular-spectrum modeling (EASM) of light energy transport in scattering media.

The exact modeling of light transport in scattering media is critical in biological imaging, free-space communication, and phosphor-converted lighting. Angular spectrum is proved to be a fast and effective approach to reconstructing the wavefront dynamics during the propagation in scattering media, however, finding it difficult in acquiring the wavefront and energy change simultaneously. Besides, conventional methods for energy tracing, such as the Monte Carlo method, are inefficient in speed and hard to simulate the wavefront change. Here, we propose an extended angular-spectrum modeling (EASM) approach using tenuous scattering approximate solutions to obtain a time-efficient and accurate method for reconstruction of energy and wavefront dynamics in various scattering media. The generality of our method is numerically simulated and experimentally verified with a set of scattering media with different properties. EASM has a time advantage under the guarantee of calculation accuracy, especially when calculating several thickness changes after the calculation model is established. Furthermore, multi-layered media can also be simulated by EASM with a good precision. The results suggest that EASM performs certain computations more efficiently than the conventional method and thus provides an effective and flexible calculation tool for scattering media.

Prediction of the rupture pressure of a corroded pipeline by ANN

This work highlights the use of artificial intelligence (AI) in fracture mechanics, in particular to solve complex problems such as the fracture of a corroded pipeline subjected to both internal pressure and axial compressive stress. The paper describes the use of artificial neural networks (ANN), a popular technique in AI, to replace the empirical expression of the DNV method with a system of simple equations based on weights and biases. The use of ANN avoids problems associated with theory, such as assumptions, boundary conditions and exact modeling. The choice of neural network structure was made on the basis of the required accuracy, measured by indicators such as the coefficient of determination R2 and the root mean square error MSE during the validation phase. The results obtained with this neural network model were satisfactory, showing good linear correlation with the target values and low divergence during the validation phase. The implementation of this model in computer applications facilitates the prediction of failure pressure without requiring in-depth expertise in finite element analysis.

Composite Learning Adaptive Interaction Control for High-DoF Collaborative Robots*

Variable impedance control is essential for improving safety and naturalness during physical human-robot interaction. However, the robot target impedance is usually difficult to be realized for existing variable impedance control methods. This paper proposes a composite learning adaptive interaction control strategy for robots to achieve target impedance under parametric uncertainty. A multi-mode adaptive control scheme is defined based on weighting functions to ensure smooth mode transitions. A composite learning technique is applied for exact robot modeling online such that target impedance can be achieved under interval excitation that is much weaker than persistent excitation. The proposed method can achieve variable stiffness and damping with guaranteed stable and safe interaction. Experiments on a collaborative robot with 7 degrees of freedom named Franka Emika Panda have validated the effectiveness and superiority of the proposed method.

Joint Graph Learning and Blind Separation of Smooth Graph Signals Using Minimization of Mutual Information and Laplacian Quadratic Forms

The smoothness of graph signals has found desirable real applications for processing irregular (graph-based) signals. When the latent sources of the mixtures provided to us as observations are smooth graph signals, it is more efficient to use graph signal smoothness terms along with the classic independence criteria in Blind Source Separation (BSS) approaches. In the case of underlying graphs being known, Graph Signal Processing (GSP) provides valuable tools; however, in many real applications, these graphs can not be well-defined <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> and need to be learned from data. In this paper, a GSP-based approach for joint Graph Learning (GL) and BSS of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smooth</i> graph signal sources is proposed, which, to the best of our knowledge, has not been addressed. The minimization of Mutual Information (MI) is exploited in our work because of its desirable advantages, such as having no local minimum and exact (not approximative) modeling of statistical independence. As well as investigating the convergence analysis and identifiability conditions and deriving Cramér-Rao Lower Bound (CRLB), comprehensive experiments of generating (cyclostationary) graph signal mixtures are provided to show the superiority over classic and also GSP-based BSS approaches in the case of the latent sources being <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smooth</i> on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unknown</i> underlying graphs. Based on the provided experimental results, our proposed method performs quite robustly in even high noise levels in both terms of source separation and recovery of underlying graphs.

Q-learning based control for energy management of series-parallel hybrid vehicles with balanced fuel consumption and battery life

The present study investigates an energy management strategy based on reinforcement learning for series-parallel hybrid vehicles. Hybrid electric vehicles allow using more advanced power management policies because of their complexity of power management. Towards this feature, a Q-Learning algorithm is proposed to design an energy management strategy. Compared to previous studies, an online reward function is defined to optimize fuel consumption and battery life cycle. Moreover, in the provided method, prior knowledge of the cycle and exact modeling of the vehicle are not required. The introduced strategy is simulated for four driving cycles in MATLAB software linked with ADVISOR. The simulation results show that in the HWFET cycle, the fuel consumption decreases by 1.25 %, and battery life increases by 65% compared to the rule-based method implemented in ADVISOR. Also, the results for the other driving cycles confirm the self-improvement property. In addition, it has been depicted that in the case of change in the driving cycle, the method performance has been maintained and gained better performance than the rule-based controller.

Protocolized Diuretic Strategy as a Treatment Algorithm for Cardiorenal Syndrome

Background: A diuretic strategy is needed that is superior to current clinical care in the management of cardiorenal syndrome. Current HF guidelines do not provide any standard protocol for diuretic dosing. Aim: To determine if a protocolized diuretic treatment strategy (ProDiuS), compared to usual care (UC), results in improved decongestion, clinical outcomes, and health-related quality of life (HRQOL), while preserving renal function in hospitalized patients with cardiorenal syndrome. Materials and Methods: This trial was a prospective randomized single-blind trial of participants hospitalized for cardiorenal syndrome from November 1, 2013 to July 9, 2015. Participants were randomized to ProDiuS vs. UC and followed daily in hospital, and at 1-month and 3-month follow-up. ProDiuS was a stepped diuretic strategy targeting daily urine output of 3-5 L/day. UC was care at the discretion of treating providers. The primary outcome, change in body weight (kg) from randomization to 96 hours (day 4), was compared between the ProDiuS and UC groups using the t-test. Data analysis for secondary outcomes between the two groups were conducted using the t-test or Wilcoxon rank sum test depending on whether data was skewed for continuous variables, as well as linear regression modeling. For ordinal variables or proportions, data were analyzed using the exact chi-square test and logistic regression modeling. For mortality, time to death was analyzed as time-to-event data, with censoring at the time of death, date of last follow-up, or the end of the study (3 month follow-up), using Kaplan-Meier curves and log-rank tests, and Cox proportional hazards models to adjust for continuous and discrete covariates in the survival analysis. Results: The study did not enroll the prespecified number of subjects due to slow recruitment. Out of 786 prescreened patients, 19 participants were included in the trial. There were no significant differences in baseline characteristics. Mean age was 68.7±7.3 years and 72.2% were male. There was borderline higher change in body weight from baseline to day 4 or discharge in ProDiuS vs. UC (-6.12 vs. -2.07 kg; p=0.05). Net negative fluid balance, length of hospitalization, HF rehospitalizations, mortality, acute kidney injury, adverse outcomes, and HRQOL scores were similar between groups. Conclusion: Due to small sample size, firm conclusions cannot be drawn. However, these findings suggest that ProDiuS results in similar clinical and HRQOL outcomes as UC in HF patients treated at a large tertiary medical center in the short term. This trial was conducted in an advanced HF population on specialized HF services, which may have attenuated the efficacy of ProDiuS vs. UC. Further studies with larger sample size and more diverse HF populations are needed to determine the efficacy and safety of ProDiuS. Several lessons learned in attempting to design a trial of protocolized diuretic strategy in the cardiorenal population are discussed.

Optimal Selection and Integration of Batteries and Renewable Generators in DC Distribution Systems through a Mixed-Integer Convex Formulation

The problem concerning the optimal placement and sizing of renewable energy resources and battery energy storage systems in electrical DC distribution networks is addressed in this research by proposing a new mathematical formulation. The exact mixed-integer nonlinear programming (MINLP) model is transformed into a mixed-integer convex model using McCormick envelopes regarding the product between two positive variables. Convex theory allows ensuring that the global optimum is found due to the linear equivalent structure of the solution space and the quadratic structure of the objective function when all the binary variables are defined. Numerical results in the 21-bus system demonstrate the effectiveness and robustness of the proposed solution methodology when compared to the solution reached by solving the exact MINLP model. Numerical results showed that the simultaneous allocation of batteries and renewable energy resources allows for the best improvements in the daily operating costs, i.e., about 53.29% with respect to the benchmark case of the 21-bus grid, followed by the scenario where the renewable energy resources are reallocated while considering a fixed location for the batteries, with an improvement of 43.33%. In addition, the main result is that the difference between the exact modeling and the proposed formulation regarding the final objective function was less than 3.90% for all the simulation cases, which demonstrated the effectiveness of the proposed approach for operating distributed energy resources in monopolar DC networks.

Thermal conductivity at elevated temperature, density and geochemical signatures for the massive rhyolites of the Bundelkhand Craton, central India

SUMMARY In spite of the fact that rhyolite constitute a vital part of the key tectonic environments, such as continental rift-arc systems and oceanic islands, the data on the thermal and physical properties are scarce, which hinders the exact thermal modelling of these regions. Here, we have investigated the thermal conductivity from room temperature (25 °C) to elevated temperatures (up to 300 °C) for 11 massive rhyolite samples, collected from the greenstone belt of the Bundelkhand Craton, central India. The petrographical, geochemical (major oxide and trace elements) and physical (density and porosity) properties have been studied to characterize the samples before measurement of thermal conductivity at elevated temperatures. Geochemical results indicate that these rhyolites are high-K (K2O: 3.6–5.4 wt. per cent), calc-alkaline in nature with enriched REE signatures {(La/Yb)N: 9.4–22.3, (Gd/Yb)N: 1.2–1.9} and are similar to FI-type Archaean rhyolites. The density of these rhyolites depicts a narrow range between 2590 and 2690 kg m−3, with an average of 2637 kg m−3 and negligible porosity. Their thermal conductivity at room temperature varies between 2.5 and 3.3 W m−1 K−1, with an average of 2.8 W m−1 K−1; the decrease in thermal conductivity from room temperature to 300 °C ranges between 16 and 32 per cent, with an average of 23 per cent; and the temperature coefficient of thermal conductivity b, in the expression λT = λRT (1 + bT)−1, varies between 0.7 × 10−3 and 1.7 × 10−3 K−1 with an average of 1.1 × 10−3 K−1. Our study reveals that the massive rhyolites have an almost similar density as their intrusive equivalent like Bundelkhand granitoids, but their thermal properties, such as thermal conductivity at room temperature (λRT), decrease in thermal conductivity with temperatures (Δλ) and the temperature coefficient of thermal conductivity (b), lies between the two extreme variety of the granitoids, that is (i) alkali feldspar granite to monzogranite and (ii) granodiorite to tonalite to quartz diorite. We suggest that the temperature coefficient of the massive rhyolite can be expressed as b = 0.81 × λRT–1.21, which will be useful in determining the thermal conductivity of such rhyolites at elevated temperatures from their thermal conductivity at room temperature (λRT). Thermal and physical parameters reported for rhyolites will provide important constraints in various geophysical and thermo-mechanical modelling for the rhyolitic terrains.

Overcoming non‐convexity of the robust nonlinear output feedback problem: An adaptive linear matrix inequality solution

AbstractThis article presents a novel solution for adaptive output feedback of uncertain nonlinear systems; it uses nonlinear controller and observer structures to drive a time‐varying function as a Lyapunov one, thus guaranteeing asymptotic stability of the system states and observation error. Exact convex modeling of available terms and polytopic embedding of unavailable ones in the Lyapunov function dynamics, allow linear matrix inequalities to be used, thus overcoming former difficulties over the non‐convex nature of the problem. Moreover, the proposal incorporates a recently appeared factorization to get rid of approximate solutions based on Lipschitz bounds and persistence of excitation. The methodology is successfully put at test against related works in a variety of examples.

Optimizing scheduling policy in smart grids using probabilistic Delayed Double Deep Q-Learning (P3DQL) algorithm

High penetration of smart devices in IoE-enabled smart grids besides decentralization originated from employing renewable resources face the power system with intricate optimization problems. Operation scheduling of energy components is one of the principal problems that need to be addressed. However, engaging with big data produced by the interconnected infrastructures, besides the high dimensional and uncertain environment, make traditional methods incapable of addressing these problems since exact modeling of the environment under uncertainties is impracticable. While learning-based methods suffer from excessive complexity and the curse of dimensionality, Deep Reinforcement Learning has recently successfully handled highly complex scheduling problems. However, biases and model efficiency are two primary considerations that need more investigation. Positive and negative biases lead to better exploration and exploitation, respectively, and their harmony, considering model efficiency, results in a better outcome. Accordingly, this research develops and introduces a novel algorithm named Probabilistic Delayed Double Deep Q-Learning, which is a combination of the tuned version of Double Deep Q-Learning and Delayed Q-Learning. The proposed algorithm makes a trade-off between overestimation and underestimation biases, guaranteeing sample complexity by applying a delay in updating the rule. Finally, the proposed algorithm is tested on three real-world datasets assessing its performance in various benchmarks. The results indicate that the developed model is thoroughly stable since both population and characteristic stability indices are less than 0.1 in all case studies. The average model's error is 0.028 showing the exactitude of the model while running time is lower than other examined methods. Utilizing the developed algorithm results in 11.1 % reduction in the average power ratio. Consequently, the peak load decreased from 8.043 kW to 5.8137 kW, resulting in a 30.1 % cost reduction.

Analysis of presence-only data via exact Bayes, with model and effects identification

This paper provides an exact modeling approach for the analysis of presence-only ecological data. Our proposal is also based on frequently used inhomogeneous Poisson processes but does not rely on model approximations, unlike other approaches. Exactness is achieved via a data augmentation scheme. One of the augmented processes can be interpreted as the unobserved occurrences of the relevant species, and its posterior distribution can be used to make predictions of the species over the region of study beyond the observer bias. The data augmentation also leads to a natural Gibbs sampler to make Bayesian inference through MCMC. The proposal shows better performance than the currently standard method based on Poisson process with intensity function depending log-linearly on the covariates. Additionally, an identification problem that arises in the traditional model does not seem to affect our proposal in the analyses of real ecological data.

Conjugate sparse plus low rank models for efficient Bayesian interpolation of large spatial data

AbstractA key challenge in spatial data science is the analysis for massive spatially‐referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance matrices that lack computationally exploitable structures. Recent developments in spatial statistics offer a variety of massively scalable approaches. Bayesian inference and hierarchical models, in particular, have gained popularity due to their richness and flexibility in accommodating spatial processes. Our current contribution is to provide computationally efficient exact algorithms for spatial interpolation of massive data sets using scalable spatial processes. We combine low‐rank Gaussian processes with efficient sparse approximations. Following recent work by Zhang et al. (2019), we model the low‐rank process using a Gaussian predictive process (GPP) and the residual process as a sparsity‐inducing nearest‐neighbor Gaussian process (NNGP). A key contribution here is to implement these models using exact conjugate Bayesian modeling to avoid expensive iterative algorithms. Through the simulation studies, we evaluate performance of the proposed approach and the robustness of our models, especially for long range prediction. We implement our approaches for remotely sensed light detection and ranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit (TIU) in a remote portion of Interior Alaska.