Approximate Model Research Articles

A Sparse Approximate Factor Model for High-Dimensional Covariance Matrix Estimation and Portfolio Selection

Abstract We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model (AFM). Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard AFM. We prove the consistency of the covariance matrix estimator under the Frobenius norm as well as the consistency of the factor loadings and the factors. Our Monte Carlo simulations reveal that the SAF covariance estimator has superior properties in finite samples for low and high dimensions and different designs of the covariance matrix. Moreover, in an out-of-sample portfolio forecasting application, the estimator uniformly outperforms alternative portfolio strategies based on alternative covariance estimation approaches and modeling strategies including the 1/N-strategy.

Multidisciplinary Collaborative Design Optimization of Electric Shovel Working Devices

The development of the open-pit mining industry has set higher performance standards for mining electric shovels. Addressing issues such as low efficiency, high energy consumption, and high failure rates in working mining electric shovel devices, this paper comprehensively considers bulk mechanics, structural mechanics, and dynamics to conduct a multidisciplinary, collaborative design optimization for electric shovels by introducing the BLISCO method, which is based on an approximated model, into the structural-optimization design process of working electric shovel devices, aiming to enhance the overall performance of electric shovels. Firstly, a dynamic model of an electric shovel is established to analyze the hoist force and crowd force during the excavation process, and an accurate load input for the dynamic analysis is provided through the bulk material mechanics model. Additionally, to ensure that the stiffness of the boom meets the requirements, the maximum stress at the most critical position of the optimized boom is considered. Subsequently, the design variables are screened through experimental design, and an approximate model is established. Focusing on the hoist force, crowd force, maximum stress at the critical position of the boom, and the angle between the dipper arm and the wire rope, a mathematical model is constructed and optimized using a two-level integrated system co-optimization framework based on an approximate model (BLISCO-AM), followed by a simulation. Finally, a test bench for the electric shovel working device is constructed to compare pre- and post-optimization performance. Experimental results show that through the optimized design, the hoist force and crowd force required in a single excavation process are reduced by 6% and 8.48%, respectively, and the maximum angle between the wire rope and the dipper arm is increased by 4%, significantly improving excavation efficiency while ensuring the safety and reliability of the equipment.

Approximate modeling of cross-beam multi-axis force/moment sensor through Gaussian process and partial dependence plots for design optimization including stress topology

This study introduces a novel approximate model (AM) aimed at optimizing the design of cross-beam multi-axis force/moment sensor. It considers the characteristics of flexure hinges in elastic beams and the flexibility of beam joints, resulting in improved accuracy and broader solutions for equivalent stresses and natural frequencies compared to existing approximate models in the literature. Model validation is carried out by comparing the results with the finite element model in different cases that each case contains 1000 simulations. Validation cases combine different sensor dimensions with different forces, moments, material properties, and center hub shapes. Each validation case typically requires approximately 19 h using the finite element method (FEM) and just 1 sec with the AM. Furthermore, by using the Gaussian process and partial dependence plots, the sensitivity of the model accuracy on normalized sensor dimensions is investigated. The evaluation of model linearity and dimension normalization allows for the utilization of the novel approximate model beyond the provided dimension range, while still adhering to the normalized parameters. The implementation of AM in the design optimization problem demonstrates its suitability and advantages compared to existing literature and FEM results. When compared to finite element solutions within the sensor workspace, the approximate model exhibits a stiffness error of 5%, a strain error of 2%, a fundamental frequency error of 3%, and an equivalent stress error of 8%, while maintaining correlations of axial sensor properties above 98%.

Properties of observable mixed inertial and gravito-inertial modes in gamma Doradus stars

The space missions Kepler and TESS provided a large number of highly detailed time series for main-sequence stars, including gamma Doradus stars. Additionally, numerous gamma Doradus stars are to be observed in the near future thanks to the upcoming PLATO mission. In gamma Doradus stars, gravito-inertial modes in the radiative zone and inertial modes in the convective core can interact resonantly, which translates into the appearance of dip structures in the period spacing of modes. Those dips are information-rich, as they are related to the star core characteristics. Our aim is to characterise these dips according to stellar properties and thus to develop new seismic diagnostic tools to constrain the internal structure of gamma Doradus stars, especially their cores. We used the two-dimensional oscillation code TOP to compute sectoral prograde and axisymmetric dipolar modes in gamma Doradus stars at different rotation rates and evolutionary stages. We then characterised the dips we obtained by their width and location on the period spacing diagram. We found that the width and the location of the dips depend quasi-linearly on the ratio of the rotation rate and the Brunt-Väisälä frequency at the core interface. This allowed us to determine empirical relations between the width and location of dips as well as the resonant inertial mode frequency in the core and the Brunt-Väisälä frequency at the interface between the convective core and the radiative zone. We propose an approximate theoretical model to support and discuss these empirical relations. The empirical relations we established could be applied to dips observed in data, which would allow for the estimation of frequencies of resonant inertial modes in the core and of the Brunt-Väisälä jump at the interface between the core and the radiative zone. As those two parameters are both related to the evolutionary stage of the star, their determination could lead to more accurate estimations of stellar ages.

Multi-objective optimization design of NPR protection shell for hydrogen storage tank

In order to improve the safety of on-board hydrogen storage tanks during collision, a protective shell based on a negative Poisson’s ratio (NPR) core is designed in this paper. After analyzing and comparing the crashworthiness of three typical honeycomb structures, the concave hexagonal negative Poisson’s ratio honeycomb is selected as the energy-absorbing inner core of the hydrogen storage tank protection structure. The sensitivity analysis of the structural parameters of the NPR shell is conducted through orthogonal tests to identify parameters with a significant impact on crash performance. These parameters are then used as experimental variables for subsequent optimization design. Subsequently, a response surface approximation model between the optimization objective and the structural parameters is established based on the response surface method. Finally, the adaptive simulated annealing algorithm (ASA), neighborhood cultivation genetic algorithm (NCGA), and non-dominated sorting genetic algorithm-II (NSGA-II) are used to optimize the structural parameters, and the optimization results are verified by the whole-vehicle crash simulation. The simulation results demonstrate that all three algorithms achieve better optimization results, among which NCGA is more advantageous in improving the overall performance of the protective shell. After NCGA optimization, the specific energy absorption of the protective shell increases by 19.75%, the maximum collision force of the rigid wall decreases by 23.63%, and the maximum stress of the hydrogen storage tank body decreases by 22.77%. These findings indicate that the designed protection shell effectively improves the crashworthiness of the hydrogen storage tank during collisions.

Exploring quantum confinement signature in nitrogen-functionalized graphene quantum dots: Effective mass approximation (EMA) model insights from computational and experimental analyses

A well-established relationship between bandgap energy and Quantum Dots (QDs) dimension, predicted by Effective Mass Approximation (EMA) models, is a cost-effective and reliable method to evaluate the bandgap energy of QDs. The EMA model sheds light on linearity between bandgap energy (Egap) to their inverse square diameter (1/dn), as a signature of the quantum confinement, with the n value reflecting the dimension of the quantum confinement. This study systematically investigated the power parameter "n" dependence in the bandgap energy of Nitrogen-functionalized Graphene Quantum Dots (N-GQDs) with distinct C–N configurations, i.e., Pyridinic-N, Pyrrolic-N, Graphitic-N based on computational and experimental data. The results showed that the calculated bandgap energy values reveal a notable weakening of the size dependence in N-GQDs compared to pristine GQDs, particularly in Pyrrolic-N GQDs, indicative of a unique geometric dimensionality of confinement. This systematic exploration advances our understanding of "n" dependence and bandgap energy in N-GQDs, laying a solid groundwork for modulating the bandgap energy of N-GQDs for optoelectronics and quantum device applications.

Comparing the potential of benchtop and handheld mid-infrared spectrometers for predicting soil phosphorus (P) sorption capacity and evaluating the influence of sample preparation

Traditional soil phosphorus (P) sorption capacity is examined from a Langmuir isotherm batch technique, which is time-consuming, labour intensive and generates chemical waste. In this work, we provide an efficient and convenient technique with MIR spectroscopy to predict the Langmuir parameter of soil P sorption maximum capacity (Smax, mg·kg−1).Four spectral libraries from benchtop (Bruker) and handheld (Agilent) MIR spectrometers were built with samples in two particle size ranges, <0.100 mm (ball-milled) and <2 mm. respectively. Using an archive of samples with a database of sorption parameters, soils were classified into ‘low’ and ‘high’ sorption capacities. Chemometric regression models of partial least squares (PLS), Cubist, support vector machine (SVM) regression and random forest (RF) were evaluated for Smax prediction. Bruker spectral libraries with both soil particle sizes yielded ‘excellent models’, with SVM predicting Smax values with high accuracy (RPIQV = 4.50 and 4.25 for the spectral libraries of the ball-milled and <2 mm samples, respectively). In comparison, the Agilent handheld spectral libraries contained more noise and less resolution. For Agilent MIR spectroscopy, more homogeneous samples after ball milling resulted in a higher accurate Smax prediction. For Agilent libraries of ball-milled samples, an ‘approximate quantitative model’ (RPIQV = 2.74) was obtained from the raw spectra using the Cubist algorithm. However, for Agilent spectroscopy of <2 mm samples, the best performing Cubist algorithm can only achieve a ‘fair model’ (RPIQV=2.23) with the potential to discriminate between ‘low’ and ‘high’ Smax values.The results suggest that the benchtop spectrometer can predict the Langmuir Smax value with high accuracy without the need to ball mill samples. However, the handheld spectrometer can only make approximate quantitative predictions of Smax for ball-milled samples. For <2 mm samples, Agilent can only be used to classify ‘low’ and ‘high’ sorption capacity soils.

Connecting palettes — An integrated spectroscopic analysis and UMAP visualisation of Wu Guanzhong's paint palette and his painting

A paint palette of the 20th-century Chinese modern artist Wu Guanzhong (1919–2010) was studied with an integrated spectroscopic approach, macro-scale non-invasive techniques hyperspectral imaging (HSI) and macro X-ray fluorescence (MA-XRF), complemented with Raman spectroscopy. The palette is revealed to be comprised of synthetic inorganic and organic pigments, typical of the 20th century modern palette that is dominated by azo and phthalocyanine pigments. HSI datasets of the paint palette and those of Wu's oil painting ‘Xidi Village’ (2001) were then processed within one unsupervised Uniform Manifold Approximation and Projection (UMAP) model, in an attempt to identify connections between the artefact and the artwork, so that known pigment results of the palette may provide preliminary pigment assignment for the painting. This study describes the steps taken to establish this automated assisted pigment analysis workflow, which involves processing multiple HSI datasets within one UMAP model, density clustering, non-negative least square (NNLS) fitting to extract endmembers (EM) spectra and to generate distribution maps. The approach to perform micro-sampling pigment analysis on the artist's palette (or artist's materials) is considered less invasive to the integrity than that from artworks, the results of which have demonstrated to serve as a critical resource to support further pigment analysis studies of the artist's paintings via non-invasive analytical techniques.

Dynamic Programming-Based Track-before-Detect Algorithm for Weak Maneuvering Targets in Range–Doppler Plane

This paper focuses on detecting and tracking maneuvering weak targets in the range–Doppler (RD) plane with the track-before-detect (TBD) algorithm based on dynamic programming (DP). Traditional DP-TBD algorithms integrate target detection and tracking in their framework while searching the paths provided by a predefined model of the kinematic properties within the constraints allowed. However, both the approximate motion model used in the RD plane and the model mismatch caused when the target undergoes a maneuver can degrade the TBD performance sharply. To address these issues, this paper accurately describes the evolution of the RD equation based on Constant Acceleration (CA) and Coordinated Turn (CT) motion models with the process noise in the Cartesian coordinate system, and it also employs a recursive method to estimate the parameters in the equations for efficient energy accumulation and path searches. Facing the situation that targets energy accumulation during the DP iteration process will lead to an expansion of the target energy accumulation process. This paper designs a more efficient Optimization Function (OF) to inhibit the expansion effect, improve the resolution of the nearby targets, and increase the detection probability of the weak targets simultaneously. In addition, to search the trajectory more efficiently and accurately, we improved the process of DP multi-frame accumulation, thus reducing the computation amount of large-scale searches. Finally, the effectiveness of the proposed method for CA and CT motion target detection and tracking is verified by many of the simulation experiments that were conducted in this paper.

Uncertain vibration response of vehicles passing through barricades based on approximate models

In vibration analysis, a vehicle system encounters dimensionality issues due to its high-dimensional uncertain parameters. An approximate model offers a viable solution for analyzing such uncertain responses. This study introduces an efficient approximate model, called PCE-HDMR, which is founded on the Legendre Polynomial Chaos Expansion (PCE) and High-Dimensional Model Representation (HDMR). Specifically, the Legendre PCE in interval space is employed to delineate the lower and upper bounds of uncertain responses. At the same time, the HDMR is harnessed to develop a high-dimensional uncertainty model that approximates the dynamic response. To demonstrate the application of PCE-HDMR, a model for a vehicle with interval parameters was constructed using a 9-DOF dynamics model for testing. In this framework, all stiffness and damping parameters are treated as interval uncertainty parameters. The numerical results validate the effectiveness of the proposed method for high-dimensional uncertain parameters, demonstrating that PCE-HDMR outperforms Monte Carlo simulation (MCS) in terms of efficiency. This study advances an effective interval uncertainty analysis approach for assessing vehicle performance, particularly when dealing with high-dimensional interval uncertainty parameters. The proposed method serves as a viable alternative for interval analysis and subsequent optimization design for complex vehicle systems characterized by high-dimensional uncertain parameters.

Model of non-equilibrium near-cathode plasma layers for simulation of ignition of high-pressure arcs on cold refractory cathodes

The introduction of secondary ion-electron emission into an approximate model of non-equilibrium plasma layers on hot (thermionic) cathodes of high-pressure arc discharges allows extending the model to low cathode surface temperatures. Analysis of evaluation results shows that the extended model describes glow-like discharges on cold cathodes and thermionic arc discharges on hot cathodes, as it should. In the course of glow-to-arc transitions on cold cathodes, a transient regime occurs where a hot arc spot has just formed and a significant fraction of the current still flows to the cold surface outside the spot, so that the near-cathode voltage continues to be high. The power input in the near-cathode layer is very high in this regime, and so is the electron temperature in the near-cathode region. The mean free path for collisions between the atoms and the ions in these conditions exceeds the thickness of the layer where the ion current to the cathode is generated. A new method for evaluation of the ion current under such conditions is implemented. The developed model is applicable for cathode surface temperatures below the boiling point of the cathode material and may be used for multidimensional simulations of ignition of high-current arcs on refractory cathodes.

SA-UCBSS: Sparsity-Based Adaptive Underdetermined Convolutive Blind Source Separation

Blind source separation is the process of separating unknown source signals based only on the received mixing signals when the source signal cannot be accurately known. Traditional methods are mainly based on linear approximate transformation models that often have large systematic errors in high reverberation environments, resulting in poor separation performance. To avoid these limitations, a sparsity-based adaptive underdetermined convolutive blind source separation (SA-UCBSS) algorithm is proposed by unifying a convolutive approximate transformation model and an Lp(0<p≤1)-norm regularisation penalty. A crosstalk canceller is designed for room impulse response pretreatment with p-norm optimisation to eliminate audible echoes, and a sparse optimisation scheme is designed for the parameter initialisation to accelerate the convergence of the iterative recovery process. Subsequently, a convolutive approximate transformation model is built to achieve a more accurate estimation of the mixing system. The SA-UCBSS algorithm is proposed to achieve better source separation by adaptively tuning the value of parameter p. Experimental results including BSS of the synthesised and live-recorded speech convolutive mixtures showed that the SA-UCBSS algorithm had superior separating properties and better robustness than several popular algorithms.

Strategic Geosteering Workflow with Uncertainty Quantification and Deep Learning: Initial Test on the Goliat Field Data

Continuous integration of real-time logging-while-drilling data into a subsurface model with relevant geological uncertainties enables strategic geosteering: a field-level optimization of the well-placement strategy. Model errors arising from oversimplified conceptual geological models and imperfect simulation of measurements result in unreliable subsurface-model updates. The model errors are particularly pronounced when synthetic measurements are approximated with a fast but imperfect model, such as a deep neural network (DNN).#xD;We present a practical data-assimilation workflow consisting of offline and online phases. The offline phase involves DNN training and building an uncertain prior near-well geo-model. The online phase utilizes the flexible iterative ensemble smoother (FlexIES) to perform real-time assimilation of extra-deep electromagnetic data while accounting for the model errors in the approximate DNN model. We demonstrate the proposed workflow on historic well-log data from the Goliat Field (Barents Sea). #xD;The median of our probabilistic estimation is on par with proprietary inversion, regardless of the number of layers in the chosen prior or the approximate DNN model. By estimating model errors, FlexIES automatically quantifies the uncertainty in the boundaries and resistivities of layers, which is not standard in proprietary inversion. #xD;This capability allows us to capture uncertainties more efficiently, thus providing input for future quantitative decision support methods. We demonstrate the potential of quantitive decision support by visually estimating the ahead-of-bit risk of reservoir exit that has occurred during the considered operation.

Extending the Tight‐Binding Model by Discrete Fractional Fourier Transform

An extension of the tight‐binding approximation model using the discrete fractional Fourier transform is proposed. The quantum state between localized and delocalized states is formulated, where the intermediate state is continuously parameterized. The mixed features of the localized molecular‐like state and delocalized wave‐like state are confirmed when the wavefunction and band diagram of the intermediate state are represented. The proposed model is expected to be used to represent the quantum state with localized/delocalized features in, for example, organic semiconductors.

CFD modeling and optimal design of louvered fins heat exchangers using radical basis function

Louvered fins heat exchanger is widely applied to chemical, energy, and refrigeration industries. The manuscript proposes a way for accurately and efficiently optimizing louvered fins heat exchangers. The louvered fin pitch, louvered fin height and louvered fin length are selected as main independent variable. The optimal structural parameters were extracted by CFD simulation, RBF and MOGA. The Colborn coefficient j and resistance coefficient f need to be optimized to be optimal. Using radical basis function (RBF) to find out approximation model, and the structure size is optimized by multi-objective genetic algorithm (MOGA). It shows that Colborn coefficient j reduces by 4 %, and resistance coefficient f reduces by 43 %. And the convection heat transfer is basically unchanged, when the flow resistent index is obviously reduced. Secondly, the effect of the optimized structure is analyzed in terms of pressure, velocity and temperature, and the optimization effect is further emphasized. Finally, the good performance of the optimization structure is further verified by the field synergy theory.

Dynamic Model Reduction for Viscously Damped Structures with Statically Determinate Interfaces

A novel model reduction method for viscously damped structures with statically determinate interfaces, such as spacecraft flexible appendages, is proposed. The paper presents a derivation of the complete complex modal expansion of the interface dynamic stiffness of these structures. Based on the identity relation for all complex modes, which is obtained during the derivation, it is found that the interface acceleration impedance can be expressed as a rational fraction with high accuracy using only low-order complex modes. Using this rational fraction as an approximation model, numerical results of the frequency response can be fitted. The fitted interface acceleration impedance can be applied to real-time control as a reduced model in the form of a transfer function. Furthermore, it can be transformed into the form of system matrices by introducing auxiliary variables, which then participate in the dynamic analysis of the assembly. The reduction process circumvents complex modal analysis and necessitates only the results of frequency responses. Thanks to the powerful ability of conventional finite element software to perform frequency response analysis, this reduction method can be used for large-scale complex models in actual engineering applications.

Multi-Objective Optimization Design of Dynamic Performance of Hydrofoil with Gurney Flap

The horizontal axis tidal turbine, as a crucial device for capturing tidal energy, has gained significant attention because it has better energy efficiency performance. Enhancing the performance of foils, a vital part of tidal turbine blades, can significantly improve tidal turbine performance. Among numerous methods to enhance the foil performance, the Gurney flap has gained significant attention due to its avoidance of complex structural design. Currently, there is limited research on optimizing the design of Gurney flaps while considering the dynamic performance of foils. In this study, the S809 foil with a blade cross-section was selected as the research subject, a multi-objective optimization design platform was created by integrating a multi-objective optimization algorithm with Computational Fluid Dy-namics (CFD) numerical simulation techniques. The objective of this platform is to enhance the dynamic performance of the hydrofoil by optimizing the geometric structure of the Gurney flap. The improvement of dynamic lift and the size of the dynamic stall hysteresis loop are used as objective variables in this study to evaluate the hydrofoil’s dynamic performance. The optimal Latin hypercube design method is used in the optimization process to choose sample locations, and the Kriging approximation model is used to determine the relationship between the design variables and the objective variables. Meanwhile, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) is used to create a multi-objective optimization platform for solving the optimization problem, and the optimized results are validated using CFD. Comparative validation results show that quantifying the dynamic performance during hydrofoil pitching oscillation and using the optimal Latin hypercube design method and Kriging approximation model for optimizing the Gurney flap structure is rational and accurate. This study explores the mechanism of the Gurney flap through in-depth CFD numerical simulations and finds that the Gurney flap affects the flow characteristics at the hydrofoil’s trailing edge, thereby influencing the performance. It increases the pressure difference between the pressure and suction surfaces, thus enhancing the hydrofoil’s lift. Finally, this article provides three recommended parameters to improve the dynamic performance of the hydrofoil. This research can serve as a reference for the application of Gurney flaps in tidal turbine blade design.

Lyapunov stability of suspension bridges in turbulent flow

In the era of sleek, super slender suspension bridges, facing the issue of stability against dynamic wind actions represents an increasingly complex challenge. Despite the significant progress over the last decades, the impact of atmospheric turbulence on bridge stability remains partially not understood, evoking the need for innovative research approaches. This study aims to address a gap in current research by investigating the random flutter stability associated with variations in the angle of attack due to turbulence, which has not formally been addressed yet. The present investigation employs the 2D rational function approximation model to express self-excited forces in a turbulent flow. The application of this type of models to bridge dynamics yields a viscoelastic coupled dynamic system characterized by memory effects and driven by broad-band long-time-scale noise, described here by a linear homogeneous time-variant differential equation, which shows apparent nonlinear features, and which has rarely been matter of research. Utilizing a Monte Carlo methodology, this work innovates in applying the largest Lyapunov exponent (LE) and the moment Lyapunov exponents (MLE) to study bridge random flutter stability. The calculation of LE and MLE under diverse turbulent wind conditions uncovers lower flutter stability than without turbulence effects. In most cases, sample and low-order p-th moment stability thresholds closely align with the bridge dynamic response pattern; therefore, the flutter critical wind speed is unequivocal. However, under certain turbulence scenarios, it is necessary to resort to MLE for a complete description of stability, evoking some additional consideration of which statistical moments should be considered for the engineering assessment of the flutter limit. Finally, this work provides a qualitative insight into the instability mechanisms by approximating the random parametric excitation with a sinusoidal gust and evaluating the time-periodic system stability via Floquet theory.

Label‐Free Impedance Analysis of Induced Pluripotent Stem Cell‐Derived Spinal Cord Progenitor Cells for Rapid Safety and Efficacy Profiling

AbstractRegenerative therapies, including the transplantation of spinal cord progenitor cells (SCPCs) derived from induced pluripotent stem cells (iPSCs), are promising treatment strategies for spinal cord injuries. However, the risk of tumorigenicity from residual iPSCs advocates an unmet need for rapid SCPCs safety profiling. Herein, a rapid (≈3000 cells min‐1) electrical‐based microfluidic biophysical cytometer is reported to detect low‐abundance iPSCs from SCPCs at single‐cell resolution. Based on multifrequency impedance measurements (0.3 to 12 MHz), biophysical features including cell size, deformability, membrane, and nucleus dielectric properties are simultaneously quantified as a cell is hydrodynamically stretched at a cross junction under continuous flow. A supervised uniform manifold approximation and projection (UMAP) model is further developed for impedance‐based quantification of undifferentiated iPSCs with high sensitivity (≈1% spiked iPSCs) and shows good correlations with SCPCs differentiation outcomes using two iPSC lines. Cell membrane opacity (day 1) is also identified as a novel early intrinsic predictive biomarker that exhibits a strong correlation with SCPC differentiation efficiency (day 10). Overall, it is envisioned that this label‐free and optic‐free platform technology can be further developed as a versatile cost‐effective process analytical tool to monitor or assess stem cell quality and safety in regenerative medicine.

Selecting the number of factors in approximate factor models using group variable regularization

. We propose a novel method for the estimation of the number of factors in approximate factor models. The model is based on a penalized maximum likelihood approach incorporating an adaptive hierarchical lasso penalty function that enables setting entire columns of the factor loadings matrix to zero, which corresponds to removing uninformative factors. Additionally, the model is capable of estimating weak factors by allowing for sparsity in the non zero columns. We prove that the proposed estimator consistently estimates the true number of factors. Simulation experiments reveal superior selection accuracies for our method in finite samples over existing approaches, especially for data with cross-sectional and serial correlations. In an empirical application on a large macroeconomic dataset, we show that the mean squared forecast errors of an approximate factor model are lower if the number of included factors is selected by our method.