Variable Velocity Research Articles

Analysis of the magnetohydrodynamic effects on non-Newtonian fluid flow in an inclined non-uniform channel under long-wavelength, low-Reynolds number conditions

Abstract This study utilises mathematical modelling and computations to analyse the magnetohydrodynamic (MHD) effects on non-Newtonian Eyring–Powell fluid flow in an inclined non-uniform channel under long-wavelength, low Reynolds number conditions. The governing equations are solved by applying slip boundary conditions to determine the velocity, temperature, concentration, and streamline profiles. The key findings show that the magnetic parameter dampens the flow rate. The relationship between the variable viscosity, velocity, and temperature is nonlinear. The wall rigidity parameter and axial velocity are directly proportional until a threshold. Increasing inclination angles distorts streamlines. The magnetic field alters concentration contours and thermal transport. MATLAB parametric analysis explores MHD effects. This study enhances the understanding of inclined channel fluid dynamics, offering insights into variable viscosity, magnetic fields, wall properties, and impacts of inclination angles on non-Newtonian flow characteristics. This knowledge can optimise industrial MHD conduit/channel transport applications.

An Improved Scheme for the Finite Difference Approximation of the Advective Term in the Heat or Solute Transport Equations

AbstractTransport equations are widely used to describe the evolution of scalar quantities subject to advection, dispersion and, possibly, reactions. Numerical methods are required to solve these equations in applications, adopting either the advective or conservative formulations. Conservative formulations are usually preferred in practice because they conserve mass. Advective formulations do not, but have received more mathematical attention and are required for Lagrangian solution methods. To obtain an advective formulation that conserves mass, we subtract the discretized fluid flow equation, multiplied by concentration, from the conservative form of the transport equation. The resulting scheme not only conserves mass, but is also elegant in that it can be interpreted as averaging the advective term at cell interfaces, instead of approximating it at cell centers as in traditional centered schemes. The two schemes are identical when fluid velocity is constant, and both have second-order convergence, but the truncation errors are slightly different. We argue that the error terms appearing in the proposed scheme actually imply an improved representation of subgrid spreading/contraction and acceleration/deceleration caused by variable velocity. We compare the proposed and traditional schemes on several problems with variable velocity caused by recharge, discharge or evaporation, including two newly developed analytical solutions. The proposed method yields results that are slightly, but consistently, better than the traditional scheme, while always conserving mass (i.e., mass at the end equals mass at the beginning plus inputs minus outputs), which the traditional centered finite differences scheme does not. We conclude that this scheme should be preferred in finite difference solutions of transport.

Data-Driven Sparse Sensor Placement Optimization on Wings for Flight-By-Feel: Bioinspired Approach and Application.

Flight-by-feel (FBF) is an approach to flight control that uses dispersed sensors on the wings of aircraft to detect flight state. While biological FBF systems, such as the wings of insects, often contain hundreds of strain and flow sensors, artificial systems are highly constrained by size, weight, and power (SWaP) considerations, especially for small aircraft. An optimization approach is needed to determine how many sensors are required and where they should be placed on the wing. Airflow fields can be highly nonlinear, and many local minima exist for sensor placement, meaning conventional optimization techniques are unreliable for this application. The Sparse Sensor Placement Optimization for Prediction (SSPOP) algorithm extracts information from a dense array of flow data using singular value decomposition and linear discriminant analysis, thereby identifying the most information-rich sparse subset of sensor locations. In this research, the SSPOP algorithm is evaluated for the placement of artificial hair sensors on a 3D delta wing model with a 45° sweep angle and a blunt leading edge. The sensor placement solution, or design point (DP), is shown to rank within the top one percent of all possible solutions by root mean square error in angle of attack prediction. This research is the first to evaluate SSPOP on a 3D model and the first to include variable length hairs for variable velocity sensitivity. A comparison of SSPOP against conventional greedy search and gradient-based optimization shows that SSPOP DP ranks nearest to optimal in over 90 percent of models and is far more robust to model variation. The successful application of SSPOP in complex 3D flows paves the way for experimental sensor placement optimization for artificial hair-cell airflow sensors and is a major step toward biomimetic flight-by-feel.

High-resolution observations of the ocean upper layer south of Cape St. Vincent, the western northern margin of the Gulf of Cádiz

Abstract. This article presents an Eulerian physical and biogeochemical dataset from the Iberian Margin Cape St. Vincent Ocean observatory (IbMa-CSV), a facility of the European Multidisciplinary Seafloor and water column Observatory European Research Infrastructure Consortium (EMSO-ERIC), located 10 nautical miles south of Cape St. Vincent (Portugal), the southwest tip of the Iberian Peninsula and western limit of the northern margin of the Gulf of Cádiz (GoC). The observatory was installed on the shelf break, and the data time series spans 4 months for most of the variables. The upper 150 m were sampled intensively with a wave-powered vertical profiler at an average rate of 4.5 profiles per hour recording at 2 Hz when ascending at an approximate velocity of 0.2 m s−1 and 10 Hz when descending at a variable velocity. The vertical resolution was always higher than 0.2 m. Measured channels were conductivity, temperature, pressure, chlorophyll a, dissolved O2 concentration, and turbidity. Derived channels are sea pressure, depth, salinity, speed of sound, specific conductivity, dissolved O2 saturation, density anomaly, spiciness, and Brunt–Väisälä frequency. The acquired dataset includes the flow velocity and direction along the water column, taken from an upward-looking 300 kHz acoustic Doppler current profiler (ADCP) recorded every hour for 3 m depth bins extending the same depth range of the vertical profiler. A standard quality-control scheme was applied to the dataset. The dataset is preserved for multiple use and is accessible in the Sea Open Scientific Data Publication (SEANOE) repository via the following address: https://doi.org/10.17882/94769 (Rautenbach et al., 2022).

Spatiotemporal coupling deep neural network for time-resolved flow field reconstruction around a circular cylinder

We propose a spatiotemporal coupling deep neural network approach for time-resolved reconstruction of the velocity field around a circular cylinder. The neural network leverages two distinct data types: (1) non-time-resolved velocity field around the cylinder, consisting of fixed frequency sampling and variable frequency sampling velocity field, and (2) the time-resolved surface pressure sequence around the cylinder. The deep neural network comprises two sub-networks: a convolutional autoencoder (CAE) for nonlinear mode extraction and a Transformer for sequence-to-sequence learning. We refer to this architecture as CTNet (CAE-Transformer Network). The encoder in the CAE maps non-time-resolved velocity field to a latent vector, enabling the extraction of nonlinear modal coefficients. An appropriate time window length for the surface pressure sequence is then selected to establish a Transformer sequence learning model, using the chosen sequence as input to predict the corresponding nonlinear modal coefficients. Once the Transformer is well trained, the time-resolved nonlinear modal coefficients of velocity field can be achieved. Along with the well-trained decoder in the CAE, the time-resolved velocity field can be reconstructed from the output of the Transformer. We verify the performance of CTNet by a simulated dataset at a representative Reynolds number of 3900. The results show a relative reconstruction error of just 6.3% for the time-resolved velocity field, demonstrating high reliability in the reconstruction. We further compare the reconstructed velocity field obtained with and without the utilization of variable frequency sampling velocity field. Notably, the inclusion of variable frequency sampling velocity field significantly improves the reconstruction quality.

Non-similar analysis of heat generation and thermal radiation on Eyring-Powell Hybrid nanofluid flow across a stretching surface

This paper portrays a two-dimensional mathematical model developed for the analysis of Eyring-Powell hybrid nanofluid flow, incorporating variable temperature and velocity profiles. This study investigates the flow through a porous media with a mixture of hybrid nanoparticles (copper dioxide, magnetite) integrated into ethylene glycol ([Formula: see text]) across a stretching sheet. The model takes magnetic effects, heat generation, and thermal radiation into account. Additionally, nonsimilar partial differential equations (PDEs) are transformed into ordinary differential equations using the local nonsimilarity approach. These equations are then numerically solved using the built-in Matlab function bvp4c. To examine the effects of adjusting parameters on heat, mass transfer, and skin friction, the results are displayed graphically. With an increase in the given values of magnetic field [Formula: see text], the velocity profile [Formula: see text] is seen to decay. Moreover, it is observed that the hybrid nanofluid density and dynamic viscosity increase as the volume fraction rises. It is estimated that the thermal conductivity and viscosity of the [Formula: see text] hybrid nanofluid are expected to increase to 4.1% and 12.35%, respectively, and to 71.55% and 78.01%, respectively, for volume concentrations ranging from 0.02% to 0.05%. It is also concluded that the local skin-friction coefficient has the opposite trend while the local Nusselt number rises monotonically with both the slip velocity parameter and the surface convection parameter. This research has broad applications In the glass and polymer industries, metallic plate cooling, plastic sheet contractions, etc.

Online Propeller Fault Detection with Variable Sliding Window and Adjustable Gain under Variable Velocity and Current Conditions

Online Propeller Fault Detection with Variable Sliding Window and Adjustable Gain under Variable Velocity and Current Conditions

Deep neural helmholtz operators for 3D elastic wave propagation and inversion

Summary Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a Helmholtz neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.

Heterogeneous high frequency seismic radiation from complex ruptures

Fault geometric heterogeneities such as roughness, stepovers, or other irregularities are known to affect the spectra of radiated waves during an earthquake. To investigate the effect of normal stress heterogeneity on radiated spectra, we utilized a poly(methyl methacrylate) (PMMA) laboratory fault with a single, localized bump. By varying the normal stress on the bump and the fault-average normal stress, we produced earthquake-like ruptures that ranged from smooth, continuous ruptures to complex ruptures with variable rupture propagation velocity, slip distribution, and stress drop. High prominence bumps produced complex events that radiated more high frequency energy, relative to low frequency energy, than continuous events without a bump. In complex ruptures, the high frequency energy showed significant spatial variation correlated with heterogeneous peak slip rate and maximum local stress drop caused by the bump. Continuous ruptures emitted spatially uniform bursts of high frequency energy. Near-field peak ground acceleration (PGA) measurements of complex ruptures show nearly an order-of-magnitude higher PGA near the bump than elsewhere. We propose that for natural faults, geometric heterogeneities may be a plausible explanation for commonly observed order-of-magnitude variations in near-fault PGA.

Optimized multi-head self-attention and gated-dilated convolutional neural network for quantum key distribution and error rate reduction

ABSTRACT Quantum key distribution (QKD) is a secure communication method that enables two parties to securely exchange a secret key. The secure key rate is a crucial metric for assessing the efficiency and practical viability of a QKD system. There are several approaches that are utilized in practice to calculate the secure key rate. In this manuscript, QKD and error rate optimization based on optimized multi-head self-attention and gated-dilated convolutional neural network (QKD-ERO-MSGCNN) is proposed. Initially, the input signals are gathered from 6G wireless networks which face obstacles to channel. For extending maximum transmission distances and improving secret key rates, the signals are fed to the variable velocity strategy particle swarm optimization algorithm, then the signals are fed to MSGCNN for analysing the quantum bit error rate reduction. The MSGCNN is optimized by intensified sand cat swarm optimization. The performance of the QKD-ERO-MSGCNN approach attains 15.57%, 23.89%, and 31.75% higher accuracy when analysed with existing techniques, like device-independent QKD utilizing random quantum states, practical continuous-variable QKD and feasible optimization parameters, entanglement and teleportation in QKD for secure wireless systems, and QKD for large scale networks methods, respectively.

Thermal modeling of variable process parameter effects in powder bed fusion using electron beam

Purpose This study aims to develop a novel thermal modeling strategy to simulate electron beam powder bed fusion at part scale with machine-varying process parameters strategy. Single-bead and part-scale experiments and modeling were studied. Scanning strategies were described by the process controlling functions that enabled modeling. Design/methodology/approach The finite element analysis thermal model was used along with the powder bed fusion with electron beam experiments. The proposed strategy involves dividing a part into smaller sections and creating meso-scale models for each subsection. These meso-scale models take into consideration the variable process parameters, including power and velocity of the moving heat source, during part building. Subsequently, these models are integrated to perform partscale simulations, enabling more realistic predictions of thermal accumulation and resulting distortions. The model was built and validated with single-bead experiments and bulky parts with different features. Findings Single-bead experiments demonstrated an average error rate of 6%–24% for melt pool dimension prediction using the proposed meso-scale models with different scanning control functions. Part-scale simulations for three different geometries (cantilever beams with supports, bulk artifact and topology-optimized transfer arm) showed good agreement between modeled temperature changes and experimental deformation values. Originality/value This study presents a novel approach for electron beam powder bed fusion modeling that leverages meso-scale models to capture the influence of variable process parameters on part quality. This strategy offers improved accuracy for predicting part geometry and identifying potential defects, leading to a more efficient additive manufacturing process.

Determination of Local Heat Transfer Coefficients and Friction Factors at Variable Temperature and Velocity Boundary Conditions for Complex Flows

Transient conjugate heat transfer measurements under varying temperature and velocity inlet boundary conditions at incompressible flow conditions were performed for flat plate and ribbed channel geometries. Therefrom, local adiabatic wall temperatures and heat transfer coefficients were determined. The data were analyzed using typical heat transfer correlations, e.g., Nu=CRemPrn, determining the local distributions of C and m. It is shown that they are closely linked. A relationship lnC=A−mB is observed, with A and B as modeling parameters. They could be related to parameters in log-law or power-law representations for turbulent boundary layer flows. The parameter m is shown to have a close link to local pressure gradients and, therewith, near wall streamlines as well as friction factor distributions. A normalization of the C parameter allows one to derive a Reynolds analogy factor and, therefrom, local wall shear stresses.

Perturbation method for laminar flow of viscous incompressible fluid between two porous boundary walls

The present study focuses on the investigation of the velocity profile of viscous fluid between two parallel porous walls while fluid is being ejected from both channel walls at the same rate. The distributions of velocity, pressure and shear stress were determined theoretically for incompressible, steady, fully developed laminar flow past a porous boundary wall. Due to the pressure difference across the porous wall, there is ejection or injection into the wall. The velocity specified as the boundary condition at the wall has been used to explore fluid flow phenomena in porous tubes and ducts. The variable wall velocity is based on the pressure differential across the wall, the fluid characteristics, the thickness of the wall, and the permeability of the structure. An appropriate wall condition must take these factors into account. This paper discusses a Reynolds number solution. We seek formulas for the velocity component. The perturbation approach is used to solve the governing differential equation and the general solution of the velocity is obtained for higher terms of Re. Fifth term of perturbation is used in the perturbation method. The velocity of the fluid is analyzed for different values of Re for a boundary condition. Finally, the result is analysis graphically for the range of Re from .1 to 50. In addition, another strategy is used to keep the Reynolds number constant when the diameter of the hole in the porous wall changes, i.e., changing the value of λ.

Combining evolutionary computation with machine learning technique for improved short-term prediction of UT1-UTC and length-of-day

Over the years, prediction techniques for the highly variable angular velocity of the Earth represented by Earth's rotation (UT1-UTC) and length-of-day (LOD) have been continuously improved. This is because many applications like navigation, astronomy, space exploration, climate studies, timekeeping, disaster monitoring, and geodynamic studies, all rely on predictions of these Earth rotation parameters. They provide early warning of changes in the Earth's rotation, allowing various industries and scientific fields to operate more precisely and efficiently. Thus, in our study, we focused on short-term prediction for UT1-UTC (dUT1) and LOD. Our prediction approach is to combine machine learning (ML) technique with efficient evolutionary computation (EC) algorithms to achieve reliable and improved predictions. Gaussian process regression (GPR) is used as the ML technique with genetic algorithm (GA) as the EC algorithm. GA is used for hyperparameter optimization of GPR model as selecting appropriate values for hyperparameter are essential to ensure that the prediction model can accurately capture the underlying patterns in the data. We conducted some experiments with our prediction approach to thoroughly test its capabilities. Moreover, two forecasting strategies were used to assess the performance in both hindcast and operational settings. In most of the experiments, the data used are the multi-technique combinations (C04) generated by International Earth Rotation and Reference Systems Service (IERS). In one of the experiments, we also investigated the performance of our prediction model on dUT1 and LOD from four different products obtained from IERS EOP 20 C04, DTRF20, JTRF20 and USNO. The prediction products are evaluated with real estimates of the EOP product with which the model is trained. The combined excitations of the atmosphere, oceans, hydrology, and sea level (AAM + OAM + HAM + SLAM) are used as predictors because they are highly correlated to the input data. The results depict the highest performance of 0.412 ms in dUT1 and 0.092 ms/day in LOD, on day 10 of predictions. It is worth noting that the later predictions were obtained by incorporating the uncertainty of the input data as weights in the prediction model, which was a novel approach tested in this study.Graphical

A nonlocal convection–diffusion model with Gaussian‐type kernels and meshfree discretization

AbstractNonlocal models have demonstrated their indispensability in numerical simulations across a spectrum of critical domains, ranging from analyzing crack and fracture behavior in structural engineering to modeling anomalous diffusion phenomena in materials science and simulating convection processes in heterogeneous environments. In this study, we present a novel framework for constructing nonlocal convection–diffusion models using Gaussian‐type kernels. Our framework uniquely formulates the diffusion term by correlating the constant diffusion coefficient with the variance of the Gaussian kernel. Simultaneously, the convection term is defined by integrating the variable velocity field into the kernel as the expectation of a multivariate Gaussian distribution, facilitating a comprehensive representation of convective transport phenomena. We rigorously establish the well‐posedness of the proposed nonlocal model and derive a maximum principle to ensure its stability and reliability in numerical simulations. Furthermore, we develop a meshfree discretization scheme tailored for numerically simulating our model, designed to uphold both the discrete maximum principle and asymptotic compatibility. Through extensive numerical experiments, we validate the efficacy and versatility of our framework, demonstrating its superior performance compared to existing approaches.

Causality and stability in relativistic hydrodynamic theory - a choice to be endured

In this work, it has been indicated that the key features requisite for preserving causality and stability of the popularly existing relativistic hydrodynamic theories, can be translated into each other. It has been shown here, that a generic ‘fluid frame transformation’ including all orders of gradient corrections can recast a stable-causal hydrodynamic theory that (i) only includes fundamental fluid variables (velocity and temperature) but requires to be in a general hydrodynamic frame other than the Landau or Eckart, to a theory that is (ii) pathology free in Landau frame but needs newer degrees of freedom. Since frame choice provides the first principle field definitions and degrees of freedom indicate the number of conserved quantities, the causality and stability of a theory seem to require a consensus between the two unless the derivative correction goes to infinity. The key finding of this work is to indicate a connection between these different formalisms, that lead to a causal and stable hydrodynamic theory.

Parameterized physics-informed neural networks (P-PINNs) solution of uniform flow over an arbitrarily spinning spherical particle

Neural network-based approaches have emerged as alternatives to conventional computational fluid dynamics (CFD) in solving multiphase flow problems. However, most of these approaches are based on data-driven machine learning methods that require training datasets prepared beforehand through CFD simulations or experiments and cannot be used independently. This study presents an unsupervised parameterized physics-informed neural networks (P-PINNs) approach for obtaining the full flow field information over a multi-dimensional parametric space. This approach is then applied to solve the three-dimensional flow around an arbitrarily rotating sphere subjected to a cross-flow. This solution is obtained for a continuous range of three parameters: the Reynolds number based on cross-flow (Re∈[1,400]), non-dimensional streamwise and spanwise angular velocity components (Ωx∗,Ωy∗∈[−3,3]). The predictions from the P-PINNs model are compared against particle-resolved direct numerical simulation (PR-DNS) results, demonstrating that the neural network model predicts all flow variables (velocity, pressure, and their spatial derivatives) accurately with R2≳0.9. The force and torque on the particle obtained from the P-PINNs model are also compared well against the corresponding PR-DNS results with R2>0.94. The key observation is that the computational cost of the unsupervised parameterized neural network model training and deployment is substantially lower than performing numerous conventional CFD simulations to systematically vary the parameters. Furthermore, once trained, the resultant neural network model is substantially more compact than the huge database of discretized numerical solutions. The P-PINNs model is then used to reveal several interesting flow features and phenomena about the rotating sphere, including flow symmetry, secondary drag and lift, critical Reynolds number, flow bifurcation, and flow separation. This study presents P-PINNs as an efficient alternative for solving parameterized flow problems, demonstrating its practical usage in flow physics discovery with the example of flow past an arbitrarily rotating sphere.

Influence of the Presence of Different Signatures on the Heat Transfer Profile of Laminar Flow Inside a Microchannel

Abstract The process of transferring heat and mass involves a high-pressure decline. Hence microchannels are utilized in extremely efficient heat and mass transfer processes, such as in the systems of the lungs and kidneys. Due to their high surface-to-volume ratio and compact volume, microchannels have demonstrated superior thermal performance. In this work, micro-fins of different topologies and arrangements were used inside microchannels for modulating heat transfer from the surface of the fins, in the presence of flowing media. The influx of media was simulated in sinusoidal form, reproducing simplified form of physiological circulatory blood flow. The study was conducted in numerical domain, while heat transfer and mass transfer equations were solved using pardiso solver. Temperature modulation at the fin surfaces was conducted to examine the transient profile of heat transfer, as function of both variable fluid velocity as well as variable feeding heat sources. In case of different input boundary conditions, the effect of heat distributions on fluid flow with respect to spatial distribution of micro-fins within a microchannel was evaluated. Results revealed the difference in heat transfer profiles in microchannels in presence of different sets of fin configurations. It was found that rectangular fins have the highest heat transfer in fluid at all its spatial configurations; while semi-ellipsoidal-shaped fins had shown the least heat transfer profile at same surface area. At the same time, it was also observed that the rate of heat dissipation was faster and limited in semi-ellipsoidal-shaped fins configuration; while the heat transfer rate was found symmetrical and low in presence of rectangular fins. Hence, this article emphasizes the modulation of temperature and velocity variations within the working fluid by emphasizing the thermo-fluid coupling effects in microchannels.

A feature sample screening and local outlier factor fusion method for detecting tidal stream turbine blade impact fault

The impact fault caused by ocean creatures poses a risk to the safe operation of tidal stream turbine blades. However, it is difficult to detect the weak impact fault directly because the collected signal is disturbed by the waves, turbulence, and continuously variable flow velocity. To solve this problem, a fusion method of feature sample screening and local outlier factor is proposed in this paper. This method consists of three main parts. First, the Teager–Kaiser energy operator and the sliding window technique are introduced to extract the envelope statistical features from the current signal. Second, a parameter optimized density-based spatial clustering of applications with noise (DBSCAN) algorithm is proposed to perform feature sample screening before detecting. Notably, the conventional DBSCAN algorithm is sensitive to the parameter selection and lacks the capability of adaptive screening, so this paper proposes an adaptive sand cat swarm optimization algorithm to optimize the parameters. Finally, the local outlier factor is utilized to detect faults based on the screened feature samples. The experimental results show that the proposed method stands out in reducing the false alarm rate compared with traditional methods. Specifically, within the flow velocity ranges of 1.0–1.3 m/s and 1.3–1.6 m/s, the false alarm rates can reach 0% and 0.17%, respectively.

An EGF technique to infer the source parameters of a circular crack growing at a variable rupture velocity

Circular crack models with a constant rupture velocity struggle to effectively model both the amplitude and duration of first P-wave pulses generated by small magnitude seismic events. Assuming a constant rupture velocity is unphysical, necessitating a deceleration phase in the rupture velocity to uphold the causality of the healing process. Moreover, a comprehensive failure model might encompass an initial nucleation phase, typically characterized by an increase of the initial rupture velocity. Studies have demonstrated that quasi-dynamic circular crack models featuring variable rupture velocities can accurately model the shape of the observed first P-wave pulse. Based on these principles, an Empirical Green’s function (EGF) approach was previously formulated to estimate the source parameters of small magnitude earthquakes, called MAIN. In addition to determine the source radius and stress drop, this method also enables the inference of the temporal evolution of rupture velocity. However, this method encounters difficulties when the noise-to-signal ratio in the recordings of smaller earthquakes used as EGF exceeds 5%, a common situation when employing regional-scale recordings of small-magnitude earthquakes as EGF. Through synthetic tests, we demonstrated that, in such instances, the problem of this technique is that the alignment between the onset of P waves of EGF and MAIN is not rightly recovered after the initial inversion step. Consequently, a novel inversion method has been developed to address this issue, enabling the identification of the optimal alignment of P-wave arrivals in EGF and MAIN across all stations. A Bayesian statistical approach is proposed to meticulously investigate the solutions of model parameters and their correlations. Using the new technique on a small magnitude earthquake (ML = 3.3) occurred in Central Italy enabled us to identify the most likely rupture models and examine the issue of correlation among model parameters. Application of Occam’s Razor Principle suggests that, for the investigated event, a circular crack model should be favored over a heterogeneous rupture model.