Minimum Entropy Research Articles

A novel adaptive noise cancellation method based on minimization of error entropy for electrocardiogram denoising

<span>In this paper, we use an adaptive method that conforms to the error entropy criterion in order to eliminate noise from cardiac signals electrocardiogram (ECG). In previous works, the mean squared error (MSE) criterion has been used to adaptive noise cancelation of ECG signals, which only has the ability to minimize the second moment of error. The MSE criterion only works optimally on systems with Gaussian noise and stationary signals, so this is not suitable for ECG signals that are non-stationary and have non-Gaussian noise. In contrast, the use of error entropy-based algorithms like minimum error entropy (MEE) is very useful in ECG noise cancelation. The results of the proposed algorithm indicate a significant advantage in terms of signal-to-noise ratio (SNR) and convergence value compared to the algorithm based on MSE criteria.</span>

Denoising Method of Hydro-turbine Vibration Signal Based on Joint WOA-VMD and Improved Wavelet Threshold

Comparing to the untreated signal, the traditional wavelet thresholding functions decomposed and reconstructed signal has a constant error. Variational mode decomposition (VMD) sets different penalty factor α and mode decomposition layer K during signal processing will lead to the final noise reduction results. Therefore, this paper introduces the Whale Optimization Algorithm (WOA)-VMD and improved wavelet threshold denoising for oscillation signal disposal of hydraulic turbine. Firstly, WOA was used to optimize the VMD decomposition parameters α and K with the local minimum of envelope entropy as the objective function, and the optimal noise reduction effect was obtained. Secondly, the vibration signals with noise were deconstructed into K intrinsic mode functions (IMF) after VMD, and their thresholds were set. Furthermore, the IMF component below the threshold value is denoised again by improving the wavelet threshold value. Finally, the IMF reorganization after de-noising is used to obtain the final noise reduction signal. Through the verification analysis, the combination of WOA-VMD and improved wavelet threshold function denoising method could effectively filter the noise in the signal and significantly improve the noise reduction effect of the hydraulic turbine vibration signal.

Fixed Pattern Noise Removal Based on a Semi-Calibration Method.

Due to the manufacturing imperfections, nonuniformities are ubiquitous in digital sensors, causing the notorious Fixed Pattern Noise (FPN). The ability of modern digital cameras to take images under low-light environments is severely limited by the FPN. This paper proposes a novel semi-calibration-based method for the FPN removal that utilizes a pre-calibrated Noise Pattern. The key observation of this work is that the FPN in each shot is actually a scaled Noise Pattern with an unknown scale parameter, since each pixel in the array generates a characteristic amount of dark current which is fundamentally determined by its physical properties. Given a noised image and the corresponding Noise Pattern, the scale parameter is automatically estimated, and then the FPN is removed by subtracting the scaled Noise Pattern from the noised image. The estimation of the scale parameter is based on an entropy minimization estimator, which is derived from the Maximum Likelihood principle and is further justified by subsequent analysis that minimizing the entropy uniquely identifies the true parameter. Convergence issues, as well as the optimality of the proposed estimator, are also theoretically discussed. Finally, some applications are given, illustrating the performance of the proposed FPN removal method in real-world tasks.

Unsupervised Domain Adaptation of Auto-Segmentation on Multi-Source MRIs

Deep learning has achieved great success in medical image segmentation. Most existing deep learning (DL) approaches make no adjustments to the model prior to inference. These models can perform well on the data of the same distribution, but their performance usually degrades when applied to the images from different source, i.e., different scanners. To tackle the problem caused by domain shift, we proposed an unsupervised domain adaptation (UDA) method based on entropy minimization and physical consistency constraints. The proposed method combines feature-level and instance-level domain adaptation techniques to transfer knowledge from the source to the target domain. Specifically, the feature-level adaptation technique uses a graph-based entropy minimization to reduce the discrepancy between the source and target domains. The instance-level adaptation technique employs a novel consistency loss to regularize the physical consistency of the same object, such as volume, length, and centroid, thus improving the segmentation accuracy of the target domain. A collection of 93 abdominal MR images, comprising 45 cases from a 0.35T MRI scanner (TRUFI) and 48 cases from a 1.5T MRI scanner (T2), was utilized to evaluate the effectiveness of the proposed method. The contours of 6 organs-at-risk were delineated by a senior radiation oncologist, serving as the ground truth. Three models, the source model (SRC) trained on the source domain, the target model (TGT) trained on the target domain, and the UDA model adapted from the source domain to the target domain, were compared on the target domain using the Dice Similarity Coefficient (DSC). In the experiment of 0.35T-to-1.5T, the proposed UDA method outperformed the source model, achieving an average DSC score of 0.82 ± 0.11, compared to 0.58 ± 0.23 (SRC) and 0.85 ± 0.09 (TGT), respectively. In the inverse experiment 1.5T-to-0.35T, the UDA model achieved an average DSC score of 0.79±0.13, compared to DSCs of 0.52 ± 0.25 and 0.81 ± 0.11 for the SRC and TGT respectively. The UDA method yielded a significant improvement of 46%, compared to the SRC. Particularly, OARs (organ at risk) with higher deformability such as the stomach and duodenum achieved a 58% and 63% improvement in performance, respectively. This work presents a compelling approach of UDA for auto-segmentation on multi-source MRIs. Experimental results demonstrate that the UDA effectively improve the segmentation performance of the source model in the target domain, resulting in a more robust segmentation model.

Minimum entropy production by microswimmers with internal dissipation

The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles.

Pressure plateau of separation induced by shock impingement in a Mach 5 flow

Separation induced by impinging shock is a fundamental feature in supersonic and hypersonic flows; however, it is difficult to predict the pressure plateau due to a limited theoretical understanding of the effect of impinging shock strength. In this study, the evolution of the separation configuration and pressure distribution with changes in impinging shock angle is examined, and a theoretical equation for predicting the pressure plateau based on minimum entropy production is proposed. For validation, an experimental device that can measure wall pressure in the separation region at high spatiotemporal resolution is developed, and schlieren visualization is employed to capture the flow structure. Accordingly, the fine characteristics of pressure distributions along the centreline of the separation region as well as the reattachment region induced by shock impingement at various angles ( $8.5^\circ$ to $30.5^\circ$ ) are obtained in a flow of Mach number 5 and Reynolds number ${\approx }1.4\times 10^7\ {\rm m}^{-1}$ . The experimental results agree well with the theoretical results; both indicate that the pressure distribution is strongly related to the impinging shock strength and that there is a critical flow deflection angle $\alpha ^\ast$ ( ${\approx }20.8^\circ$ for Mach 5). The pressure in the separation region grows nearly linearly with increasing impinging shock strength when the flow deflection angle of the impinging shock is less than $\alpha ^\ast$ ; the pressure stops growing and resides in a small range when the flow deflection angle is larger than $\alpha ^\ast$ . Therefore, the impinging shock strength should be considered a main factor when predicting the pressure plateau.

FBG strain monitoring data denoising in wind turbine blades based on parameter-optimized variational mode decomposition method

Herein, we aimed to solve the problem of difficulty in filtering the noise components in the monitoring of strain on wind turbine blades using fiber bragg grating, a denoising method based on parameter-optimized variational mode decomposition (VMD) is proposed. This method uses the minimum envelope entropy as the fitness function and the slime mould algorithm for self-adaptive optimization to find the optimal combination of modal decomposition components K and the quadratic penalty factor α of VMD. The optimized VMD was used to decompose the strain data of wind turbine blades over time into K intrinsic mode components, and the noise mode was removed using the sample entropy to obtain the effective signal. The proposed method was compared to ensemble empirical mode decomposition and complementary ensemble empirical mode decomposition using the simulated signals and engineering data. The experimental results show that the proposed method can effectively remove noise from the strain data of wind turbine blades and has better denoising performance than the other two methods, which provides a reliable basis for analyzing the strain data of wind turbine blades.

Increasing energy efficiency of hydrogen refueling stations via optimal thermodynamic paths

This work addresses the energy efficiency of hydrogen refueling stations (HRS) using a first-principles model and optimal control methods to find minimal entropy production operating paths. The HRS model shows good agreement with experimental data, achieving maximum state of charge and temperature discrepancies of 1 and 7%, respectively. Model solution and optimization is achieved at a relatively low computational time (40 s) when compared to models of the same degree of accuracy. The entropy production mapping indicates the flow control valve as the main source of irreversibility, accounting for 85% of the total entropy production in the process. The minimal entropy production refueling path achieves energy savings from 20 to 27% with respect to the SAE J2601 protocol, depending on the ambient temperature. Finally, the proposed method under near-reversible refueling conditions shows a theoretical reduction of 43% in the energy demand with respect to the SAE J2601 protocol.

Quantized minimum error entropy with fiducial points for robust regression

Minimum error entropy with fiducial points (MEEF) has received a lot of attention, due to its outstanding performance to curb the negative influence caused by non-Gaussian noises in the fields of machine learning and signal processing. However, the estimate of the information potential of MEEF involves a double summation operator based on all available error samples, which can result in large computational burden in many practical scenarios. In this paper, an efficient quantization method is therefore adopted to represent the primary set of error samples with a smaller subset, generating a quantized MEEF (QMEEF). Some basic properties of QMEEF are presented and proved from theoretical perspectives. In addition, we have applied this new criterion to train a class of linear-in-parameters models, including the commonly used linear regression model, random vector functional link network, and broad learning system as special cases. Experimental results on various datasets are reported to demonstrate the desirable performance of the proposed methods to perform regression tasks with contaminated data.

Experimental study of the thermal characteristic of a double tube heat exchanger with tapered wire coil inserts using PCM-dispersed mono/hybrid nanofluids

ABSTRACT An experimental study involving tapered wire coil inserts in a double-tube heat exchanger using water-based phase change material (PCM)-dispersed mono/hybrid nanofluids is conducted. The effects of the wire coils (WC) with nanofluids on the hydrothermal performance of this system are studied for different coil arrangements: converging wire coils (CWC), diverging wire coils (DWC), and converging-diverging wire coils (CDWC) and different Reynolds numbers. The experimental results indicate that among all the tested coil arrangements, the DWC presents a higher thermal performance factor (TPF) than the other arrangements. Using the DWC, the TPF of the Al2O3+PCM hybrid nanofluid is augmented by 3.98%, 9.61%, and 3.04% as compared to that for the plain wire coil (PWC), CWC, and CDWC, respectively. Besides, the DWC configuration exhibits the minimum entropy generation among all arrangements. For the Al2O3+PCM hybrid nanofluid using the DWC, the entropy generation is decreased by approximately 13.36%, 9.78%, and 5.78% as compared to that of the PWC, CWC, and CDWC at a volumetric flow rate of 15 lpm.

Characterization of flux pump-charging of high-temperature superconducting coils using coupled numerical models

Flux pumps provide a promising solution for contactless charging of high-temperature superconducting (HTS) coils, eliminating the need for bulk current leads and reducing the heat burden for the cryogenic system. Characterizing the nonlinear effects of an HTS coil charged by a flux pump and understanding the dynamics of the charging process is essential for promoting the practical application of flux pumps. Numerical models provide a fast and cost-effective way of achieving this. In this study, we propose a methodology for coupling HTS coil and flux pump models using an electrical circuit, resulting in reduced computation costs. We validate the effectiveness of our approach against the experimental results of an HTS coil charged by a dynamo-type flux pump. Specifically, we obtain the voltage produced by the HTS dynamo using a 3D model based on the minimum electromagnetic entropy production method and apply this voltage to the load HTS coil using a formulation finite-element method model coupled via an electrical circuit. The simulated charging current shows good agreement with experimental observations, validating our modeling strategy. The results demonstrate that the flux flow state in the HTS coil is the primary factor limiting the charging performance of the HTS dynamo as the charging current approaches the coil’s critical current. Furthermore, based on the simulation, we demonstrate that, when using flux pumps, it is advisable to leave a margin between the operating current and the critical current of the coil. Overall, our approach has the potential to be applied to HTS coils charged by any device.

Surrogate Modeling of the Relative Entropy for Inverse Design Using Smolyak Sparse Grids.

Relative entropy minimization, a statistical-mechanics approach for finding potential energy functions that produce target structural ensembles, has proven to be a powerful strategy for the inverse design of nanoparticle self-assembly. For a given target structure, the gradient of the relative entropy with respect to the adjustable parameters of the potential energy function is computed by performing a simulation, and then these parameters are updated using iterative gradient-based optimization. Small parameter updates per iteration and many iterations can be required for numerical stability, but this incurs considerable computational expense because a new simulation must be performed to reevaluate the gradient at each iteration. Here, we investigate the use of surrogate modeling to decouple the process of minimizing the relative entropy from the computationally demanding process of determining its gradient. We approximate the relative-entropy gradient using Chebyshev polynomial interpolation on Smolyak sparse grids. Our approach potentially increases the robustness and computational efficiency of using the relative entropy for inverse design, primarily for physically informed potential energy functions that have a small number of adjustable parameters.

Minimum total complex error entropy for adaptive filter

As a powerful tool, the minimum error entropy (MEE) criterion has aroused extensive attention within the field of adaptive filtering recently. However, most MEE-based methods cannot be applied to the complex domain. Although the maximum total complex correntropy (MTCC) algorithm has been applied in errors-in-variables (EIV) model successfully when the noise is impulsive, it would degenerate obviously in some non-Gaussian noise cases, especially in the multi-peak distributed noise case. In this paper, we take the EIV model and complex domain into consideration and then propose a minimum total complex error entropy (MTCEE) algorithm. More importantly, the local stability and steady-state behavior of MTCEE are analyzed theoretically. Finally, we apply the MTCEE algorithm to the system identification and channel estimation, considering situations where noise affects both input and output. Through these applications, we demonstrate the effectiveness and superiority of MTCEE under EIV model in complex domain.

Computational assessment of MHD Carreau tri-hybrid nano-liquid flow along an elongating surface with entropy generation : A comparative study

This research looks at the incompressible, viscous, steady-state laminar stagnation-point-flow of a Carreau ternary-hybrid nano-liquid towards a convectively heated expanding surface, taking into account first-order slippage and Ohmic dissipation. Viscous dissipation and the effects of Lorentz forces are also considered. It is discussed how thermal radiation and heat absorption/generation contribute to the heat transport process. Minimizing entropy during the transport of a Carreau ternary hybrid nano-liquid has also been studied. In addition, convective circumstances are used conceptually in the numerical solution of the current model. tiny-particles of silver (Ag), molybdenum disulfide (MoS2), and multi-wall carbon nanotubes (MWCNT) are analyzed in this work’s flow study. As a base fluid, carboxymethyl cellulose (CMC-water) is used. With the use of appropriate similarity trans-formations, the standard model equations are transformed into dimensionless form. Finding solutions for momentum and heat fields using the Runge–Kutta-Fehlberg technique and a shooting strategy. The figures depict a wide range of characteristics, including fluid flow velocity, temperature, skin friction, the Nusselt number, entropy minimization, and the Bejan number. Key results from the present model include the fact that the velocity curve flattens down as Weissenberg number increases.

Singular Points of the Tremor of the Earth’s Surface

A method for studying properties of the Earth’s surface tremor, measured by means of GPS, is proposed. The following tremor characteristics are considered: the entropy of wavelet coefficients, the Donoho–Johnston wavelet index, and two estimates of the spectral slope. The anomalous areas of tremor are determined by estimating the probability densities of extreme values of the studied properties. The criteria for abnormal tremor behavior are based on the proximity to, or the difference between, tremor properties and white noise. The greatest deviation from the properties of white noise is characterized by entropy minima and spectral slope and DJ index maxima. This behavior of the tremor is called “active”. The “passive” tremor behavior is characterized by the maximum proximity to the properties of white noise. The principal components approach provides weighted averaged density maps of these two variants of extreme distributions of parameters in a moving time window of 3 years. Singular points are the points of maximum average densities. The method is applied to the analysis of daily time series from a GPS network in California during the period 2009–2022. Singular points of tremor form well-defined clusters were found. The passive tremor could be caused by the activation of movement in fragments of the San Andreas fault.

High Precision Motion Compensation THz-ISAR Imaging Algorithm Based on KT and ME-MN

In recent years, terahertz (THz) radar has been widely researched for its high-resolution imaging. However, the traditional inverse synthetic aperture radar (ISAR) imaging algorithms in the microwave band perform unsatisfactorily in the THz band. Firstly, due to THz radar’s large bandwidth and short wavelength, the rotation of the target will result in serious space-varying(SV) range migration and space-varying phase error. Furthermore, it is challenging to accurately estimate the rotational velocity and compensate for phase errors in the presence of severe range migration effects. Therefore, in this paper, a high-precision THz-ISAR imaging algorithm is proposed. The algorithm includes the following step: First, the SV first-order range migration(FRM) is corrected using keystone transform (KT); then, the minimum entropy based on modified newton (ME-MN) is used to estimate the rotational velocity roughly, and the remaining SV second-order range migration(SRM) is corrected to obtain the range profile with the envelope alignment. Finally, the echo after the envelope alignment is processed for the second time based on ME-MN. The target rotation velocity is accurately estimated, and the phase error is compensated to obtain a well-focused imaging result. The validity of the proposed method is verified by numerical simulation and electromagnetic calculation data.

Partial Self-Testing and Randomness Certification in the Triangle Network.

Quantum nonlocality can be demonstrated without inputs (i.e., each party using a fixed measurement setting) in a network with independent sources. Here we consider this effect on ring networks, and show that the underlying quantum strategy can be partially characterized, or self-tested, from observed correlations. Applying these results to the triangle network allows us to show that the nonlocal distribution of Renou etal. [Phys. Rev. Lett. 123, 140401 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.140401] requires that (i)all sources produce a minimal amount of entanglement, (ii)all local measurements are entangled, and (iii)each local outcome features a minimal entropy. Hence we show that the triangle network allows for genuine network quantum nonlocality and certifiable randomness.

State of charge estimation of lithium-ion batteries using improved BP neural network and filtering techniques

The state of charge (SOC) is a critical parameter in the battery management system (BMS), and its accurate estimation is essential for ensuring the safety and reliability of batteries. This paper presents a lithium-ion battery SOC estimation method that combines an improved neural network with a filtering algorithm. Firstly, the backpropagation (BP) algorithm is chosen as the architecture of the neural network in the hybrid method due to its strong nonlinear approximation ability, and the particle swarm optimization (PSO) algorithm is used to optimize it to avoid falling into local optimal solutions. By combining the search ability of PSO with the learning ability of the BP neural network, the accuracy of the neural network model is improved. The proposed method integrates the PSO-BP model with the extended Kalman filter based on minimum error entropy (MEE-EKF). PSO-BP is utilized as the measurement equation for MEE-EKF, while the ampere-hour integration method is employed as the state equation to achieve closed-loop SOC estimation. Finally, experimental validation is conducted under four typical operating conditions and one random condition across a wide temperature range. The results demonstrate that the proposed method achieves high accuracy across all conditions compared with the results of other algorithms, with a maximum absolute error of not exceeding 3.13%, a mean absolute error of less than 0.54%, and a root mean square error of no more than 0.66%.

Topologically Optimized Anode Catalyst Layers of Proton Exchange Membrane Water Electrolyzers

Climate change and global warming are ongoing global problems that will severely impact the environment if they are not addressed seriously. Replacing traditional fossil fuels with clean and sustainable energy from renewable energy sources, such as wind and solar, is necessary to reduce carbon emissions. However, these renewable energy sources are intermittent and thus require a system to help stabilize power generation. In this regard, hydrogen, the most sustainable form of clean energy, is proposed as a potential energy carrier. In such a system, water electrolyzers are used together with fuel cells. This allows hydrogen to be produced and stored in times of excess power generation. When there is demand and insufficient power generation, the produced hydrogen will be converted into electricity using fuel cells, resulting in a stable power grid. Although fuel cells have been improving significantly, water electrolyzers are an essential bottleneck for the widespread commercialization of the hydrogen economy.Due to the intermittency of renewable energy, the water electrolysis system applied to renewable energy should be able to turn on and off depending on renewable energy sources. As a result, low-temperature water electrolysis has gained widespread attention. Due to its potentially high-performance and high-purity hydrogen gas, the proton exchange membrane water electrolyzer (PEMWE) is one of the most promising technology for producing clean hydrogen. However, concerning widespread industrial use, PEMWE is affected by high costs due to its high loadings of expensive iridium-based catalysts. Therefore, it is necessary to improve its performance. As PEMWE technology grows, the working current density is inevitably higher. When the current density is higher, the amount of oxygen and hydrogen that must be removed from the cell must be more significant to deliver water to the reaction site efficiently. To meet the demands of the application, it is crucial to design an efficient electrode, especially at the anode, where the water must be supplied to the catalyst layer, and, at the same time, it is necessary to transfer oxygen gas from the reaction area to the flow channel.Topology optimization, an emerging tool to optimize physical systems, has recently been applied to systems with multi-physics. However, attempts to implement the approach in the system with reactions still lacked in the literature. Only a few studies were interested in utilizing such an approach in electrochemical energy device applications. Roy et al. [1] used topology optimization to develop the porous electrode. According to the findings, the developed electrode outperformed the traditional electrode. However, topology optimization is just a numerical approach. Our research group showed how a topologically optimized structure of porous reactors connected to the situation of the most uniform and minimum entropy generation [2]. To utilize topology optimization with PEMWE, a model for the anode catalyst layer is necessary. Although there are existing models to simulate the phenomena of PEMWE [3,4], to the best of our knowledge, studies have yet to look into how to model the phenomena inside the anode catalyst layer of the PEMWE.Therefore, the main goal of this study is to develop a model to simulate the physics of the anode and utilize it in topology optimization to search for the optimal structure of the anode catalyst layer. The optimization problem was formulated to maximize the cell performance by controlling the volume fractions of ionomer and catalyst materials. Figure 1a-c displays the heterogeneous structure obtained by topology optimization. The electrochemical reaction increased by approximately 40% compared to a case with the homogeneously distributed electrode. The topologically optimized structure was similar to the structure proposed by Dong et al. [5], where their ordered structure with Ir loading of 0.2 mg cm−2 can significantly decrease the overpotentials compared with conventional MEA with an Ir loading of 2 mg cm−2. Therefore, such a structure might be a way forward for high-performance PEMWE system. Acknowledgment The authors would also like to express their gratitude to Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation (OPS MHESI) (Grant No. RGNS 65-084), Thailand Science Research and Innovation (TSRI) and King Mongkut’s University of Technology Thonburi. This work was partially supported by Grant-in-Aid for JSPS Fellows number 22J20603 and JSPS KAKENHI Grant number 21H04540 References [1] Roy, T., et al., Struct. Multidiscipl. Optim. 65 (2022) 171.[2] Charoen-amornkitt, P., et al., Int. J. Heat Mass Transf. 202 (2023) 123725[3] Lopata, J., et al., J. Electrochem. Soc., 168 (2021) 054518.[4] Lopata, J.S., et al., Electrochim. Acta, 424 (2022) 140625[5] Dong, S., et al., Nano Lett. (2022) (In Press) Figure 1

Experimental and numerical investigation of a single-phase microchannel flow under axially non-uniform heat flux

The design of microchannel based heat sinks for advanced electronic component continues to receive research interest, especially with the ever-increasing density of advanced chips with concomitant increase in heat generation. One aspect of microchannel heat sink design objectives is the optimum employment of non-uniform heat dissipation through the channel length. Two dominant schools in the performance optimization of non-uniform heat sinks are: 1) entropy minimization and 2) thermal resistance minimization. These two approaches usually result in contradictory conclusions: one recommending the use of increasing heat flux, the other recommending a decreasing heat flux. The current study seeks to explain this discrepancy by experimentally and numerically studying the heat transfer mechanisms in a single microchannel tube under the effect of non-uniform heat flux. This study presents an experimental framework capable of generating a wide range of pre-specified heat flux profiles over a single microchannel, mimicking actual heat flux profiles observed in thermo-electronic devices. We employ three flux profiles: 1) hotspots located at different locations with uniform background heat flux, 2) linearly ascending heat flux, and 3) linearly descending heat flux. The results show good agreement between numerical simulations and experimental measurements and provide insights into the microchannel tube's fundamental heat transfer mechanisms. Based on these insights, the study provides design guidelines to enhance microchannel heat sink performance under non-uniform axial heat fluxes. Finally, the discrepancy between entropy and heat resistance minimization approaches is explained.