Steady-state Conditions Research Articles

Steady-state rolling resistance prediction model of non-pneumatic tyres considering tread temperature: theory and experiment

Non-pneumatic tires have potential advantages over pneumatic tires, including lower rolling resistance. First, a non-pneumatic mechanical elastic wheel (ME-Wheel) was designed. Based on its structural characteristics, a tread temperature prediction model under steady-state rolling conditions was established, and the accuracy of the established model was verified through temperature measurement experiments. Combined with the tread temperature prediction model, a steady-state rolling resistance prediction model of ME-Wheel was established, and the basic parameters (ground length CL , ground width CW , radial stiffness SR ) required for the model were identified through experiments. Finally, the experimental data were compared with the predicted values under different speed and load conditions. The results showed that the average simulation value of the rolling resistance coefficient of ME-Wheel was 0.01853, which was positively correlated with speed and load. The test results and predicted values showed a similar trend under the same operating conditions, with a maximum error of less than 3.5%. This proved that the novel non-pneumatic tyre steady-state rolling resistance prediction model based on tread temperature could accurately predict the steady-state rolling resistance of tyres. This research addresses a significant topic in tyre technology and has the potential to influence future designs and optimizations of non-pneumatic tyres.

The Hydraulic Evolution of Groundwater-Fed Pit Lakes After Mine Closure.

Open pit mining frequently requires regional water tables to be lowered to access ore deposits. When mines close, dewatering ceases allowing the water table to recover. In arid and semi-arid mining regions, the developing pit lakes are predominantly fed by groundwater during this recovery phase and pit lakes develop first into "terminal sinks" for the surrounding groundwater system. With time, the re-establishment of regional hydraulic gradients can cause pit lakes to develop into throughflow systems, in which pit lake water outflows into adjacent aquifers. In this study, we use numerical groundwater modeling to aid process understanding of how regional hydraulic gradients, aquifer properties, net evaporation rates, and pit geometry determine the hydraulic evolution of groundwater-fed pit lakes. We find that before the recovery of the regional water table to its new equilibrium, pit lakes frequently transition to throughflow systems. Throughflow from pit lakes to downstream aquifers can develop within two decades following cessation of dewatering even under low hydraulic gradients (e.g., 5 × 10-4) or high net evaporation rates (e.g., 2.5 m/year). Pit lakes remain terminal sinks only under suitable combinations of high evaporation rates, low hydraulic gradients, and low hydraulic conductivities. In addition, we develop an approximate analytical solution for a rapid assessment of the hydraulic status of pit lakes under steady-state conditions. Understanding whether pit lakes remain terminal sinks or transition into throughflow systems largely determines the long-term water quality of pit lakes and downstream aquifers. This knowledge is fundamental for mine closure and planning post-mining land use.

Localization estimation of two leaks in pipelines through Monte Carlo simulations and hydraulic-spatial constraints

The problem of localizing two leaks using only flow rate and pressure measurements at the boundaries of a pipeline, and under steady-state flow conditions, is ill-posed due to the undetermined nature of the inverse problem, which involves two coupled equations with four unknowns associated with the presence of the leaks: two emitter coefficients and two locations. Therefore, attempting to solve this problem using any method without imposing additional constraints leads to an unbounded solution space, which contains solutions that may be physically meaningless. In this article, we propose a four-algorithm method that incorporates both spatial and hydraulic constraints to filter out physically infeasible solutions. The proposed method is based on Monte Carlo simulations, which use input data from hydraulic instruments installed at the boundaries of the pipeline, as well as random values with predefined probabilities that are bounded by the hydraulic-spatial constraints. The outputs of the method are probability distributions for the four unknowns. To demonstrate the feasibility of the method, results obtained through simulations and experimental testing on a test bed are presented.

A Study of Bidirectional Electric Vehicle Charging using MATLAB Simulink

On considering Electric Vehicles, the rise of Vehicle-to-Grid(V2G) concept has been accompanied with lots of advantages. The V2G technology ensures that no extra electricity needs to be consumed from the grid. It helps the power grid on a larger scale. It enables a bidirectional power flow between the EV battery and the grid. Bidirectional Buck- Boost Converter helps in grid stabilization, financial gains, and effective energy management. The DC-DC Converter does two functions: matching the battery voltage to the motor's rated voltage and controlling power flow under steady-state and transient conditions. The Proportional-Integral (PI) controller is used to correct the errors between commanded set point and the actual value based on feedback. The efficiency of the converter can be increased by using PI controller.

A Comprehensive Investigation of Stimulatory Agents on MAIT and Vα7.2+/CD161- T Cell Response and Effects of Immunomodulatory Drugs.

Mucosal-associated invariant T (MAIT) cells, a subset of Vα7.2+ T cells, are a crucial link between innate and adaptive immunity, responding to various stimuli through TCR-dependent and independent pathways. We investigated the responses of MAIT cells and Vα7.2+/CD161- T cells to different stimuli and evaluated the effects of Cyclosporin A (CsA) and Vitamin D3 (VitD). Peripheral blood mononuclear cells (PBMCs) from healthy donors were stimulated with various agents (PMA/Ionomycin, 5-OP-RU, 5-OP-RU/IL-12/IL-33) with or without CsA and VitD. Flow cytometric analysis assessed surface markers and intracellular cytokine production. Under steady-state conditions, MAIT cells displayed elevated expression of CCR6 and IL-13. They showed upregulated activation and exhaustion markers after activation, producing IFNγ, TNFα, and TNFα/GzB. CsA significantly inhibited MAIT cell activation and cytokine production. Conversely, Vα7.2+/CD161- T cells exhibited distinct responses, showing negligible responses to 5-OP-RU ligand but increased cytokine production upon PMA stimulation. Our study underscores the distinct nature of MAIT cells compared to Vα7.2+/CD161- T cells, which resemble conventional T cells. CsA emerges as a potent immunosuppressive agent, inhibiting proinflammatory cytokine production in MAIT cells. At the same time, VitD supports MAIT cell activation and IL-13 production, shedding light on potential therapeutic avenues for immune modulation.

Hygrothermal response to air movements in wall junctions: Comparison between two numerical approaches and experiments

Airflow in wall-to-wall junctions is known to have a major hygrothermal impact on building performance. However, current and validated modeling options to simulate such phenomena are limited. This paper develops and compares two numerical models to study the heat and moisture transfer due to air infiltrations through a prefabricated wall-to-wall junction. The first model explicitly accounts for the airflow with a pipe flow approach. The second model is a modification to a typical approach to simulate ventilated cavities in building envelope simulation tools and mimics the effect of the airflow through source terms. Both approaches were introduced in a heat and moisture transfer 2D finite element model. Additionally, laboratory measurements were conducted in a climatic chamber to validate the simulation results. Six scenarios were tested experimentally under steady-state conditions. These datasets were used to calibrate different parameters of the models, such as material properties, the junction air gap thickness, and the magnitude of the heat and moisture source terms. Both sets of numerical results provided reasonable agreement with the measurements. The first approach outputs more accurate temperature and relative humidity values than the second one. However, considering uncertainties, no method predicted a perfect fit with the relative humidity profiles. Close to the junction, the first method estimates better the relative humidity than the second one. This work provides guidelines to better model and account for wall junctions in building envelope simulators.

Design, Fabrication and Testing of A Novel Thermally-Actuated Tesla Valve (TATV): A Hybrid Microvalve

Abstract A novel thermally-actuated hybrid microvalve (similar to a Tesla Valve configuration) was designed, fabricated, assembled, and tested using soft lithography-based approaches. The modified design integrates the "normally open and closed" hybrid configurations of Tesla Valves with a thermo-pneumatic (or thermal-hydraulic) actuator microfabricated in-situ that modulates the diodicity of the microvalve apparatus in the microfluidic chip. Diodicity (Di) is defined as the ratio of flow rate in the forward direction to that of the reverse direction (for a constant value of pressure drop that is imposed on a microvalve device). The results from the study successfully demonstrated the operation of an array of Tesla Valves that are normally open in forward direction and marginally closed in reverse direction at room temperature (i.e., with Di > 1, the flow resistance values were different when the inlet and outlet ports were swapped). When the microfluidic chip was heated (at steady-state conditions with a nominal temperature of ~30°C), the diodicity virtually vanished (i.e., Di ≈ 1) resulting in both reverse and forward directions being normally open (or having the same flow resistance - irrespective of the flow direction).

On the optimality of the radical-pair quantum compass

Quantum sensing enables the ultimate precision attainable in parameter estimation. Circumstantial evidence suggests that certain organisms, most notably migratory songbirds, also harness quantum-enhanced magnetic field sensing via a radical-pair-based chemical compass for the precise detection of the weak geomagnetic field. However, what underpins the acuity of such a compass operating in a noisy biological setting, at physiological temperatures, remains an open question. Here, we address the fundamental limits of inferring geomagnetic field directions from radical-pair spin dynamics. Specifically, we compare the compass precision, as derived from the directional dependence of the radical-pair recombination yield, to the ultimate precision potentially realisable by a quantum measurement on the spin system under steady-state conditions. To this end, we probe the quantum Fisher information and associated Cramér–Rao bound in spin models of realistic complexity, accounting for complex inter-radical interactions, a multitude of hyperfine couplings, and asymmetric recombination kinetics, as characteristic for the magnetosensory protein cryptochrome. We compare several models implicated in cryptochrome magnetoreception and unveil their optimality through the precision of measurements ostensibly accessible to nature. Overall, the comparison provides insight into processes honed by nature to realise optimality whilst constrained to operating with mere reaction yields. Generally, the inference of compass orientation from recombination yields approaches optimality in the limits of complexity, yet levels off short of the theoretical optimal precision bounds by up to one or two orders of magnitude, thus underscoring the potential for improving on design principles inherent to natural systems.

The thermal and hydrodynamic analysis in a heat sink with different configurations of shark scales-based fins

The development of efficient thermal management techniques in cooling systems will lead to achieving a higher power capacity for electronic devices. Extended surfaces such as fins and riblets effectively improve the heat transfer rate in heat sinks, but they can cause increasing the friction factor. In this numerical study, a novel configuration of fins is introduced according to the shark scales’ geometry to provide a trade-off between heat transfer rate and friction losses compared to simple fins in a microchannel cooling system. Also, the cooling effect of concentrations of graphene oxide (GO)+ silver (Ag)/water (H2O) and molybdenum disulfide (MoS2) + cobalt oxide Co3O4/water (H2O) nanofluids (1, 3, and 5 wt%) are investigated for the Reynolds number ranging from 130 to 525. The geometrical parameters and different materials such as copper, nickel, and silver are evaluated by ANSYS-FLUENT under steady-state conditions. The comparison of outlet temperature, pressure drop, and temperature difference by experimental results verifies the accuracy of the numerical model. The results indicate that increasing arc width from 1 mm to 1.5 mm reduces the maximum CPU (central processing unit) temperature by 5 K while the temperature uniformity index decreased by 9.96 % at 0.3 m/s of inlet flow rate. The novel configuration of fins results in a performance evaluation criterion (PEC) greater than 1 for GO+Ag/water nanofluids in all cases compared to simple circular fins.

Adaptive extended kalman filter for PEMFC membrane water content estimation

Proton Exchange Membrane Fuel Cells are a favorite technology for decarbonizing the transportation sector. However, their large-scale democratization is hampered by their high cost compounded by their unsatisfactory lifespan. To anticipate potential degradation while keeping improving performance, it is essential to maintain an acceptable humidity range inside the cells, especially at the membrane level. However, membrane humidity level is not directly measurable, alternative techniques must be considered to recover this key variable. Here, we develop a real-time software sensor of the membrane water content at the fuel cell’s heart. We build a model describing the membrane water balance, electrochemical behavior, and species mass balance. We then reduce the model and perform an Adaptive Extended Kalman Filter. We perform sensitivity analyses in both steady-state and transient conditions. We validate the filter on a “Worldwide Harmonized Light Vehicles Test Cycles” test procedure. Finally, we obtain a fast and accurate model-based software sensor.

Model Predictive Control of a Modular Multilevel Converter with Reduced Computational Burden

Recent advances in high-power applications employing voltage source converters have been primarily fuelled by the emergence of the modular multilevel converter (MMC) and its derivatives. Model predictive control (MPC) has emerged as an effective way of controlling these converters because of its high response. However, the practical implementation of MPC encounters hurdles, particularly in MMCs featuring many sub-modules per arm. This research introduces an approach termed folding model predictive control (FMPC), coupled with a pre-processing sorting algorithm, tailored for modular multilevel converters. The objective is to alleviate a significant part of the computational burden associated with the control of these converters. The FMPC framework combines multiple control objectives, encompassing AC current, DC current, circulating current, arm energy, and leg energy, within a unified cost function. Both simulation studies and real-time hardware-in-the-loop (HIL) testing are conducted to verify the efficacy of the proposed FMPC. The findings underscore the FMPC’s ability to deliver fast response and robust performance under both steady-state and dynamic operating conditions. Moreover, the FMPC adeptly mitigates circulating currents, reduces total harmonic distortion (THD%), and upholds capacitor voltage stability within acceptable thresholds, even in the presence of harmonic distortions in the AC grid. The practical applicability of MMCs, notwithstanding the presence of a large number of sub-modules (SMs) per arm, is facilitated by the significant reduction in switching states and computational overhead achieved through the FMPC approach.

The concentration of maternal sacubitril/valsartan transferred into human milk is negligible.

Peripartum cardiomyopathy (PPCM) is a common cause of heart failure (HF) in the peripartum. Some medications are considered safe while breastfeeding. However, sacubitril/valsartan (Entresto), while efficacious, is not recommended in breastfeeding women due to concerns about adverse infant development, and no published data suggest otherwise. This study aimed to assess the transfer of sacubitril/valsartan into human milk and evaluate the infant's risk of drug exposure. The InfantRisk Human Milk Biorepository released samples and corresponding health information from five breastfeeding maternal-infant dyads exposed to sacubitril/valsartan. Sacubitril, valsartan, and LBQ657 (sacubitril active metabolite) concentrations were determined using liquid chromatography-mass spectrometry (LC/MS/MS) from timed samples 0, 1, 2, 4, 6, 8, 10, and 12 h following medication administration at steady state conditions. Valsartan levels were below the detection limit of 0.19 ng/mL in all milk samples. Sacubitril was measurable in all milk samples of the five participants, peaking 1 h after drug administration at a mean concentration of 1.52 ng/mL for a total infant dose of 0.00049 mg/kg/12 h and a relative infant dose (RID) calculated at 0.01%. The maximum concentration of its active metabolite LBQ657 in the milk samples was observed 4 h after medication administration and declined over the remaining 12-h dosing interval, for an average concentration of 9.5 ng/mL. The total infant dose was 0.00071 mg/kg/12 h, and the RID was 0.22%. Two mothers reported continuing to breastfeed while taking sacubitril/valsartan; both mothers stated observing no negative effects in their breastfed infants. The transfer of sacubitril/valsartan into human milk is minimal. These concentrations are unlikely to pose a significant risk to breastfeeding infants, with a combined calculated RID of <0.25%, which is far lower than the industry safety standards (RID <10%).

No influence of steady-state postural changes on cerebrovascular compliance in humans.

The aim of this study was to determine the effect of posture changes on vascular compliance in intracranial (brain) vs. extracranial vascular beds (forearm). Eighteen young adults (nine females) performed a supine-to-seated-to-standing protocol involving five minutes of rest in each position. Continuous blood pressure, middle cerebral artery (MCA) blood velocity, and brachial artery blood velocity were recorded at each posture. Three to five consecutive steady-state cardiac cycles at each posture were analyzed by a four-element lumped parameter modified Windkessel model to calculate vascular compliance. Mean arterial pressure (MAP) increased from supine to seated (76[9] vs 81[12] mmHg; P=0.006) and from supine to standing (76[9] vs 82[13] mmHg; P=0.034). Mean blood flow was greater in the MCA relative to the forearm (forearm: 40[5] ml•min-1, MCA: 224[17] ml•min-1; main effect P<0.001). Conversely, vascular resistance (forearm: 3.25[0.50] mmHg-1•ml•min-1, brain: 0.36[0.04] mmHg-1•ml•min-1; main effect P<0.001) and compliance (forearm: 0.010[0.001] ml•min-1•mmHg-1, brain: 0.005[0.001] ml•min-1•mmHg-1; main effect P=0.001) were greater in the forearm compared to the brain. Significant main effects of posture were observed with decreasing values in upright positions for mean blood flow (P=0.001) in both vascular beds, but not for resistance (P=0.163) or compliance (P=0.385). There were no significant interaction effects between vascular bed and posture for mean flow (P=0.057), resistance (P=0.258), or compliance (P=0.329). This study provides evidence that under steady state conditions, posture does not affect cerebrovascular compliance.

Experimental and Numerical Investigations on the Relaxation Behavior of Power Plant Flange Connections Under Steady State and Transient Conditions

Abstract An essential part of today's power plants are flanges, for example, as connection between turbine housings and pipes. They allow for revisions, inspections, and maintenance measures. Ongoing changes toward higher amounts of renewable energy sources leading to higher demands in flexibility to counterbalance weather-related fluctuations. This flexibility leads to changing load types with more frequent warm and hot starts, causing uncertainties for the design and the determination of maintenance intervals of bolted flange connections. In this context, results of a recently finished research project and ongoing numerical investigations are presented. Tests were conducted on a model of an IP turbine flange under near-to-service loads, such as internal pressure and temperature, using a test rig allowing heating on the flange's inner surface. Concerning different influences on the stress relaxation behavior, results are shown for tests with martensitic and nickel-based bolted joints. The total test time of 5000 h for each bolted joint consist of 2000 h under steady-state conditions and 3000 h under transient conditions. Comparisons of the results with the martensitic and nickel-based bolted joint show an opposite creep strain distribution in the bolt and flange. In addition, a significant influence of the already existing creep deformation from previous load periods can be observed. Comparative simulations with a modified Graham–Walles creep model are carried out. The results confirm the differences in creep behavior with both bolted joints and reproduce the observed influence of the previous creep deformation.

Using a non-precious metal catalyst for long-term enhancement of methane production in a zero-gap microbial electrosynthesis cell

Microbial electrosynthesis (MES) cells exploit the ability of microbes to convert CO2 into valuable chemical products such as methane and acetate, but high rates of chemical production may need to be mediated by hydrogen and thus require a catalyst for the hydrogen evolution reaction (HER). To avoid the usage of precious metal catalysts and examine the impact of the catalyst on the rate of methane generation by microbes on the electrode, we used a carbon felt cathode coated with NiMo/C and compared performance to a bare carbon felt or a Pt/C-deposited cathode. A zero-gap configuration containing a cation exchange membrane was developed to produce a low internal resistance, limit pH changes, and enhance direct transport of H2 to microorganisms on the biocathode. At a fixed cathode potential of –1 V vs Ag/AgCl, the NiMo/C biocathode enabled a current density of 23 ± 4 A/m2 and a high methane production rate of 4.7 ± 1.0 L/L-d. This performance was comparable to that using a precious metal catalyst (Pt/C, 23 ± 6 A/m2, 5.4 ± 2.8 L/L-d), and 3–5 times higher than plain carbon cathodes (8 ± 3 A/m2, 1.0 ± 0.4 L/L-d). The NiMo/C biocathode was operated for over 120 days without observable decay or severe cathode catalyst leaching, reaching an average columbic efficiency of 53 ± 9 % based on methane production under steady state conditions. Analysis of microbial community on the biocathode revealed the dominance of the hydrogenotrophic genus Methanobacterium (∼40 %), with no significant difference found for biocathodes with different materials. These results demonstrated that HER catalysts improved rates of methane generation through facilitating hydrogen gas evolution to an attached biofilm, and that the long-term enhancement of methane production in MES was feasible using a non-precious metal catalyst and a zero-gap cell design.

Transient behavior of the freshwater-saltwater mixing zone after land reclamation in coastal aquifers

The interaction between freshwater and saltwater in the mixing zone governs regional groundwater flow and the exchange of water and salt between groundwater and the ocean. However, previous studies have overlooked the impact of land reclamation on the transient behavior of the mixing zone. This research investigated the dynamic influence of reclamation length, reclamation material properties, and recharge rate on the transient behavior of the mixing zone and timescale of mixing zone variation (TMV) through a series of field-scale numerical simulations. In general, the width of the mixing zone (WMZ) in the upper and center regions of the aquifer exhibited initial increase followed by subsequent decrease in various scenarios, displaying a consistent trend. For reclamation lengths less than 300 m, the mixing zone reached a steady-state condition within 8,000 days, while the corresponding TMV for a 500 m-length reclamation case increased to 20,000 days. The growth rates of the WMZ in the upper and center regions of the aquifer were notably slower, requiring more time to reach steady state in low-permeability scenarios. This observation underscored that reclamation with lower permeability could significantly extend the TMV. It was noteworthy that varying the longitudinal dispersion of the reclamation area between 0.5–10 m had only a slight effect on the TMV, ranging from 8,000 to 8,500 days. The peaks of the mixing zone width showed a proportional increase with longitudinal dispersion. Furthermore, increasing the recharge rate led to a substantial decrease in the TMV, from 10,000 days to 2,000 days. The WMZ exhibited faster growth with increasing recharge rate.

Forecasting Freight on Board for Gonggong Export in Batam Using Markov Chain

As an archipelagic country, Indonesia has great potential in the fisheries sector. As a free trade zone, Batam is important in exporting fishery products. One of the fishery export products in Batam City is gonggong snails. It is a favorite seafood item in Riau Islands Province and has high economic value. However, previous studies focused more on the content of gonggong snails and their industrial feasibility; there has been no specific research on the analysis of gonggong snail exports in Batam City, even though gonggong snails are one of Batam City's export products. In this research, we will forecast the freight on board (FoB) value for gonggong exports in Batam City using a discrete-time Markov chain with two states: above and below the moving average. There are several types of moving averages, including simple moving averages and weighted moving averages. An initial analysis will determine the moving averages' type and duration following the Gonggong export FOB data in Batam. The data used is the Gonggong export FoB data for Batam City from January 2020 to November 2023. Based on this data, the transition probability matrix will be calculated based on the number of export transitions below and above the Weighted Moving Average 6 (WMA 6) value. Limiting probability from the Markov chain will be used to predict the long-term FOB value of fishery product exports up to steady-state conditions. It was found that steady-state conditions would be reached after 17 months, with a probability of FOB exports below WMA6 of 55.06% and FOB exports above WMA6 of 44.94%.

Tensile and bond properties at elevated temperatures of a PBO-FRCM composite system for strengthening concrete elements: Experimental and analytical investigations

This paper presents experimental and analytical investigations on the tensile and bond behaviour at elevated temperature of a polypara-phenylene-benzo-bisthiazole (PBO) fabric reinforced cementitious matrix (FRCM) system for strengthening concrete elements. Direct tensile (DT) and single lap direct shear tests (DS) were performed under steady-state conditions at the following temperatures: 20 °C, 85 °C, 150 °C, 230 °C and 300 °C. The results obtained were evaluated in terms of strength, stiffness, ultimate strain, load vs. slip response at the interface PBO FRCM/concrete and failure modes. Overall, the tensile and bond properties were significantly affected by the temperature increase. These results are mainly associated with the reductions of mechanical properties of the FRCM constituent materials as well as the degradation of the interaction between the fibres and the inorganic matrix at elevated temperatures. The experimental results were then used (i) to evaluate the suitability of the Aveston–Cooper–Kelly (ACK) model in describing the tensile response of FRCM at elevated temperatures and (ii) to calibrate temperature-dependent local shear bond stress vs. slip laws for the FRCM-concrete interaction.

Data-driven auto-tuning strategy for RTO-MPC based on Bayesian optimization

Real-time optimization (RTO) and model predictive control (MPC) are extensively employed in industrial processes to enhance economic objectives. However, the tuning of the system remains a challenge, in particular, for cases where an explicit model relating the RTO objective and the process dynamics is unknown. To address this issue, an online data-driven auto-tuning strategy leveraging two Bayesian optimization (BO) techniques is proposed. This strategy is useful for situations where the RTO objective and the process dynamics are detectable but their exact functional forms are unclear. The proposed strategy views the RTO objective as a black-box objective and interprets the steady-state conditions as black-box equality constraints within the RTO layer. In this context, the upper-trust-bound based constrained BO (UTB-CBO) method is adopted to optimize the setpoints and enhance solution feasibility. Additionally, the proposed approach can take into account measurable disturbance inputs explicitly and account for their consequential influence on objective optimization by considering disturbance variations as contextual information. Simultaneously, another contextual BO scheme is implemented to automatically tune the MPC controller parameters for improving tracking performance upon accepting the setpoints optimized by the RTO. Simulation results based on a continuous stirred-tank reactor system are given to illustrate the effectiveness of the proposed approach.

A multitask incremental least mean square algorithm using orthonormal codes

A new multitask incremental least mean-square (MILMS) algorithm using orthonormal codes is developed. In the multitask topology, nodes belong to different clusters, with each cluster performing its own ILMS estimation. The closed-form expressions of both the theoretical transient and steady-state mean squared deviation (MSD) are derived. The proposed MILMS algorithm is further reinforced by two combination strategies, referred to here as the combine-then-adapt (CTA), and adapt-then-combine (ATC), giving rise to two new improved algorithms, the CTA-MILMS and ATC-MILMS that substantially improve the MSD. Two further variants of these two improved algorithms are also developed based on the combination of the variable step size (VSS) and discrete cosine transform (DCT) techniques, leading to the two combined algorithms, termed here as CTA-VSSMILMS and ATC-VSSMILMS, respectively. Analysis of the first and second moments of the step size, under the transient and steady-state conditions, is also included.The problem of agent localization is solved using the MILMS algorithm by deploying a fixed number of anchors with known positions that surround agents with unknown positions. Extensive experiments were carried out to show the excellent match between the theoretical transient and steady-state expressions and their corresponding empirical results in terms of MSD performance. Moreover, we show that both the ATC-VSSMILMS and CTA-VSSMILMS algorithms improve the accuracy and computational speed of the MSD results of the proposed MILMS algorithm, thanks to the VSS-induced reduction of the number of needed steps and the DCT-induced data compression effect.