Input Parameters Research Articles

Real-Time Lithology Prediction at the Bit Using Machine Learning

Real-time drilling analysis requires knowledge of lithology at the drill bit. However, logging-while-drilling (LWD) sensors in the bottom hole assembly (BHA) are usually positioned 2–50 m (7–164 ft) above the bit (called the sensor offset), leading to a delay in real-time drilling analysis. The current industry solution to overcome this delay involves stopping drilling to perform a bottoms-up circulation for cuttings evaluation—a process that is both time-consuming and costly. To address this issue, our study evaluates three methodologies for real-time lithology prediction at the bit using drilling and petrophysical parameters. The first method employs a petrophysical approach, which involves using bulk density and neutron porosity predicted at the bit. The second method combines unsupervised and supervised machine learning (ML) for prediction. The third method employs classification algorithms on manually labeled lithology data from mud log reports, a novel approach used in this work. Our results show varying degrees of success: the bulk density versus neutron porosity cross-plot method achieved an accuracy of 58% with blind-well test data; the ML approach improved accuracy to 66%; and the Random Forest (RF) classification with manual labeling significantly increased accuracy to 86%. This comparative analysis of three different methodologies for lithology prediction has not been previously explored in the literature. While clustering and classification methods have been regarded as the most effective, our study demonstrates that they do not always yield the best result. These findings demonstrate that ML models, particularly the manual labeling approach, substantially outperform the petrophysical method. This new algorithm, designed for real-time applications, uses selected input parameters to effectively minimize problems associated with the sensor offset of LWD tools. It rapidly adapts to changes, offering a quicker and more cost-effective interpretation of lithology. This eliminates the need for time-consuming bottoms-up circulation to evaluate cuttings. Ultimately, this approach enhances drilling efficiency and significantly improves the accuracy of lithology prediction, notably in identifying interbedded geological layers.

Design optimization of inner and outer‐rotor PMSGs for X‐ROTOR wind turbines

AbstractThis article presents an analytical design approach for the inner and outer rotor Permanent Magnet Synchronous Generators (PMSGs) that are a key component of wind turbines. By developing the analytical model, sensitivity analysis has been performed to determine the effect of some important geometrical and electromagnetic parameters on the generator's output characteristics. The GA optimization algorithm was used to find optimized designs in terms of efficiency, weight, cost, and temperature rise. In order to find the global optimization solution within the allowed variable range and in accordance with the constraints, a combined objective function has also been defined. In order to validate the analytical model, ANSYS electromagnetic and thermal simulations have been used. With this approach, the designer is provided with a good understanding of the input parameters and constraints in light of the application requirements.

Multi-objective Optimization of Diesel Engine Operating Parameters Under Highway Drive Conditions

Abstract Experimental and optimization work is carried out to study the effects of fuel injection pressure, boost pressure, pilot injection timing, pilot injection quantity and main injection timing as input parameters. A four-cylinder, automotive model direct injection diesel engine, incorporated with a variable-geometry turbocharger, was chosen for the experiment. Engine test runs are conducted at a driving condition of 80.3 Nm torque and an engine speed of 1750 rpm, respectively, corresponding to highway driving conditions, using 10 % of exhaust gases recirculated. The Response Surface Methodology is employed to design experiments and analyze the experimental data to optimize engine parameters, considering the mentioned parameters as input parameters. A multi-objective response approach is adopted to optimize engine-operating parameters to obtain desired performance and engine-out emissions. Confirmatory tests are conducted at design conditions to validate the results predicted by the model. It is observed that for the chosen engine configuration, the optimum performance and emission characteristics could be obtained with 120 kPa boost pressure, 61.1 MPa fuel injection pressure, and 11.5 % of total fuel amount as pilot injection and remaining as main injection quantity at 332° and 359° crank angle, respectively. Overall. fairly better engine performance was observed with the use of selected ranges. It is noted that with the procedures adopted, improved engine performance and a significant reduction in harmful emissions are obtained without using major add-ons. The investigation revealed excellent potential for a diesel engine to be an effective prime mover.

GenoTriplo: A SNP genotype calling method for triploids.

Triploidy is very useful in both aquaculture and some cultivated plants as the induced sterility helps to enhance growth and product quality, as well as acting as a barrier against the contamination of wild populations by escapees. To use genetic information from triploids for academic or breeding purposes, an efficient and robust method to genotype triploids is needed. We developed such a method for genotype calling from SNP arrays, and we implemented it in the R package named GenoTriplo. Our method requires no prior information on cluster positions and remains unaffected by shifted luminescence signals. The method relies on starting the clustering algorithm with an initial higher number of groups than expected from the ploidy level of the samples, followed by merging groups that are too close to each other to be considered as distinct genotypes. Accurate classification of SNPs is achieved through multiple thresholds of quality controls. We compared the performance of GenoTriplo with that of fitPoly, the only published method for triploid SNP genotyping with a free software access. This was assessed by comparing the genotypes generated by both methods for a dataset of 1232 triploid rainbow trout genotyped for 38,033 SNPs. The two methods were consistent for 89% of the genotypes, but for 26% of the SNPs, they exhibited a discrepancy in the number of different genotypes identified. For these SNPs, GenoTriplo had >95% concordance with fitPoly when fitPoly genotyped better. On the contrary, when GenoTriplo genotyped better, fitPoly had less than 50% concordance with GenoTriplo. GenoTriplo was more robust with less genotyping errors. It is also efficient at identifying low-frequency genotypes in the sample set. Finally, we assessed parentage assignment based on GenoTriplo genotyping and observed significant differences in mismatch rates between the best and second-best couples, indicating high confidence in the results. GenoTriplo could also be used to genotype diploids as well as individuals with higher ploidy level by adjusting a few input parameters.

Radiative signatures of circumplanetary disks and envelopes during the late stages of giant planet formation

During the late stages of giant planet formation, protoplanets are surrounded by a circumplanetary disk and an infalling envelope of gas and dust. For systems with sufficient cooling, material entering the sphere of influence of the planet falls inward and approaches ballistic conditions. Due to conservation of angular momentum, most of the incoming material falls onto the disk rather than directly onto the planet. This paper determines the spectral energy distributions of forming planets in this stage of evolution. Generalizing previous work, we consider a range of possible geometries for the boundary conditions of the infall and determine the two-dimensional structure of the envelope, as well as the surface density of the disk. After specifying the luminosity sources for the planet and disk, we calculate the corresponding radiative signatures for the system, including the emergent spectral energy distributions and emission maps. These results show how the observational appearance of forming planets depend on the input parameters, including the instantaneous mass, mass accretion rate, semimajor axis of the orbit, and the planetary magnetic field strength (which sets the inner boundary condition for the disk). We also consider different choices for the form of the opacity law and attenuation due to the background circumstellar disk. Although observing forming planets will be challenging, these results show how the observational signatures depend on the underlying properties of the planet/disk/envelope system.

Impact of Biotransformation on Internal Concentrations and Specificity Classification of Organic Chemicals in the Zebrafish Embryo (Danio rerio).

Internal concentrations (ICs) are crucial for linking exposure to effects in the development of New Approach Methodologies. ICs of chemicals in aquatic organisms are primarily driven by hydrophobicity and modulated by biotransformation and efflux. Comparing the predicted baseline to observed toxicity enables the estimation of effect specificity, but biological processes can lead to overestimating ICs and bias the specificity assessment. To evaluate the prediction of a mass balance model (MBM) and the impact of biotransformation on ICs, experimental ICs of 63 chemicals in zebrafish embryos were compared to predictions with physicochemical properties as input parameters. Experimental ICs of 79% (50 of 63) of the chemicals deviated less than 10-fold from predictions, and the remaining 13 deviated up to a factor of 90. Using experimental ICs changed the classification for 19 chemicals, with ICs 5 to 90 times lower than predicted, showing the bias of specificity classification. Uptake kinetics of pirinixic acid, genistein, dexamethasone, ethoprophos, atorvastatin, and niflumic acid were studied over a 96 h exposure period, and transformation products (TPs) were elucidated using suspect- and nontarget screening with UPLC-HRMS. 35 TPs (5 to 8 TPs per compound) were tentatively identified and semiquantified based on peak areas, suggesting that biotransformation may partly account for the overpredictions of ICs.

An Intelligent System for Determining Driver Anxiety Level: A Comparison Study of Two Fuzzy-Based Models

While driving, stress and frustration can affect safe driving and pose the risk of causing traffic accidents. Therefore, it is important to control the driver’s anxiety level in order to improve the driving experience. In this paper, we propose and implement an intelligent system based on fuzzy logic (FL) for deciding the driver’s anxiety level (DAL). In order to investigate the effects of the considered parameters and compare the evaluation results, we implement two models: DAL Model 1 (DALM1) and DAL Model 2 (DALM2). The input parameters of DALM1 include driving experience (DE), in-car environment conditions (IECs), and driver age (DA), while for DALM2, we add a new parameter called the accident anxiety state (AAS). For both models, the output parameter is DAL. We carried out many simulations and compared the results of DALM1 and DALM2. The evaluation results show that the DAL is very good for drivers’ ages between 30 to 50 years old. However, when the driver’s age is below 30 or above 50, DAL tends to decline. With an increase in DE and IECs, the DAL value is decreased. But when the AAS is increased, the DAL is increased. DALM2 is more complex because the rule base is larger than DALM1, but it makes a better decision of DAL value.

Machine learning approach for predicting the machining characteristics of additive manufactured ABS material

An Additive manufacturing process offers advantage for the production of intricate designs with increased efficiency and reduced material waste. In this research, an experimental and analysis work has been conducted to identify the significant 3-D printed input parameters effecting the output response characteristics as kerf width. The correlation between experimental and predicted values has been established through the application of Artificial Neural Network (ANN), Support Vector Machine Regression (SVMR), and Response Surface Methodology (RSM) techniques. The validation of predicted models conducted with the help of mean prediction error, maximum error and minimum error. The performance of ANN model was analyzed by feedforward-propagation method using Levenberg- Marquardt algorithm. The maximum prediction error investigated by ANN, SVM, and RSM were noted as 4.28, 5.18, and 5.84 respectively. The optical micrographs have been investigated to understand the hole and crater formation phenomenon.

Binning Metagenomic Contigs Using Contig Embedding and Decomposed Tetranucleotide Frequency.

Metagenomic binning is a crucial step in metagenomic research. It can aggregate the genome sequences belonging to the same microbial species into independent bins. Most existing methods ignore the semantic information of contigs and lack effective processing of tetranucleotide frequency, resulting in insufficient and complex feature information extracted for binning and poor binning results. To address the above problems, we propose CedtBin, a metagenomic binning method based on contig embedding and decomposed tetranucleotide frequency. First, the improved BERT model is used to learn the contigs to obtain their embedding representation. Secondly, the tetranucleotide frequencies are decomposed using a non-negative matrix factorization (NMF) algorithm. After that, the two features are spliced and input into the clustering algorithm for binning. Considering the sensitivity of the DBSCAN clustering algorithm to input parameters, in order to solve the drawbacks of manual parameter input, we also propose an Annoy-DBSCAN algorithm that can adaptively determine the parameters of the DBSCAN algorithm. This algorithm uses Approximate Nearest Neighbors Oh Yeah (Annoy) and combines it with a grid search strategy to find the optimal parameters of the DBSCAN algorithm. On simulated and real datasets, CedtBin achieves better binning results than mainstream methods and can reconstruct more genomes, indicating that the proposed method is effective.

Finite Element Analysis of Electrostatic Coupling in LISA Pathfinder Inertial Sensors

In the LISA Pathfinder (LPF) mission, electrostatic noise can reach the femto-Newtonian level despite the fact that the LPF’s sensors are equipped with potential shielding. Most of the existing simulation studies focus on the electrostatic edge effect and related fields, while the simulation study of the patch effect is neglected. For that reason, this paper analyzes the basic principle of electrostatic noise and constructs a simulation model for studying the coupling effects of a TM’s residual charge and stray bias voltage. The patch effect and other perturbation factors are simulated by the simulation model with finite element operation, focusing on the suppression effect of the protective ring on the edge effect, the realization of the patch effect in the simulation model, and the possible influence. The results show that electrode area and the spacing between the electrode and the TM together limit the suppression effect of the protective ring on the edge effect. The spatial and temporal variations of the patch effect significantly affect the distributed electric field between the electrodes and the TM, as well as the charge distribution density of the TM. In the worst-case scenario of LPF electrostatic input parameters, the electrostatic noise is about 1.03 × 10−15 m/s2/√Hz at 1 mHz, which is about 6% different from the expected performance estimate. Finally, considering the limitations of multiple environmental factors on the inertial sensors, the present model will be useful to explore the interactive effects of multi-field coupling and to further investigate the impact of low-energy electron charging on the performance of the inertial sensors.

Higher-order sensitivity analyses to understand the role of FE input parameters on the simulation of composites in progressive fracture tests

With the rise of data-driven engineering methods, such as machine learning, a comprehensive understanding of the underlying data fed into these algorithms is required for effectively applying these methods. This study presents two highly efficient Finite Element (FE) models that operate at different length scales, based on Continuum Damage Mechanics (CDM). The combination with Random Sampling-High Dimensional Model Representation (RS-HDMR) enables the determination of influential FE input parameters and their correlations to simulate Fibre Reinforced Polymer (FRP) composites subjected to a variety of progressive fracture tests in tension and compression. The results indicate that laminate-based models utilise the FE input parameters efficiently where all parameters are found to be influential. On the other hand, only fibre-related properties are relevant in ply-based FE models, with all input parameters related to transverse properties deemed to be non-influential. The findings of this study aid in identifying suitable fracture tests for a meaningful calibration and validation of CDM-based FE models. Moreover, the study lays the foundation for understanding the role of input parameters within data-driven methods, and for developing efficient reduced-order models or surrogates for uncertainty quantification on the damage tolerance of FRP composites.

Uncertainty Propagation of Monte Carlo Cross-Section Generation for Graphite-Moderated Pebble Bed Reactors

Monte Carlo codes have become increasingly popular for generating homogenized few-group cross-section data, especially for advanced reactor designs that have complex geometries and nontraditional compositions. However, the stochastic nature of Monte Carlo processes has the potential to introduce additional statistical uncertainties in the overall uncertainty in the prediction of core behavior. The work performed in this research quantified the additional uncertainty introduced by the use of Monte Carlo multigroup cross sections into the analysis of graphite-moderated pebble bed reactors. In this research, the objective was achieved by performing uncertainty quantification for the key output parameters in deterministic steady-state and transient safety calculations. The results show that when the homogenized multigroup cross sections are generated with a sufficient number of neutron histories in the Monte Carlo calculation, the uncertainties in the subsequent deterministic simulations caused by the Monte Carlo cross-section uncertainty are negligible compared to the contributions from the uncertainties of other input parameters.

New structure for better thermal resistance of building with phase change material: Response to milder thermal change than common walls

By adding the insulation with phase change material (PCM), the building's thermal resistance was enhanced. Relying on the capabilities of DesignBuilder, 3584 different cases were defined to determine the effect of different input parameters on energy consumption. The results showed that instead of using insulation or PCM, it is better to use a combination of insulation and PCM. The location of PCM + insulation has a great impact on the energy consumption of the building. For the supposed climate zones, the best installation location was different. For the city of Jeddah, PCM with a temperature of 28 °C was suitable, but for Riyadh, with the increase of the setpoint temperature, it is required to install PCM with a higher phase change temperature. By choosing the best layout from the combination of PCM and insulation, the building energy consumption was reduced by 36 % and 41 %, respectively.

An investigation on anisotropic soil slope stability by LS-SVM and LEM approaches

Purpose This study aims to use regression Least-Square Support Vector Machine (LS-SVM) as a probabilistic model to determine the factor of safety (FS) and probability of failure (PF) of anisotropic soil slopes. Design/methodology/approach This research uses machine learning (ML) techniques to predict soil slope failure. Due to the lack of analytical solutions for measuring FS and PF, it is more convenient to use surrogate models like probabilistic modeling, which is suitable for performing repetitive calculations to compute the effect of uncertainty on the anisotropic soil slope stability. The study first uses the Limit Equilibrium Method (LEM) based on a probabilistic evaluation over the Latin Hypercube Sampling (LHS) technique for two anisotropic soil slope profiles to assess FS and PF. Then, using one of the supervised methods of ML named LS-SVM, the outcomes (FS and PF) were compared to evaluate the efficiency of the LS-SVM method in predicting the stability of such complex soil slope profiles. Findings This method increases the computational performance of low-probability analysis significantly. The compared results by FS-PF plots show that the proposed method is valuable for analyzing complex slopes under different probabilistic distributions. Accordingly, to obtain a precise estimate of slope stability, all layers must be included in the probabilistic modeling in the LS-SVM method. Originality/value Combining LS-SVM and LEM offers a unique and innovative approach to address the anisotropic behavior of soil slope stability analysis. The initiative part of this paper is to evaluate the stability of an anisotropic soil slope based on one ML method, the Least-Square Support Vector Machine (LS-SVM). The soil slope is defined as complex because there are uncertainties in the slope profile characteristics transformed to LS-SVM. Consequently, several input parameters are effective in finding FS and PF as output parameters.

Comparative effectiveness and cost‐effectiveness of endoscopic nasopharyngectomy versus intensity‐modulated radiotherapy in the treatment of recurrent nasopharyngeal carcinoma: A microsimulation analysis

AbstractBackgroundNasopharyngeal carcinoma (NPC) is a significant health concern in southern China, like Guangdong and Hong Kong. This study aims to predict the effectiveness and cost‐effectiveness of two prevalent NPC treatments, intensity‐modulated radiotherapy (IMRT) and endoscopic nasopharyngectomy (ENPG).MethodsA microsimulation model was developed to project the long‐term outcomes of IMRT and ENPG, simulating 5000 patients with hypothetical locally recurrent NPC for each treatment option. The tumors of patients confined to the nasopharyngeal cavity, the post‐naris or nasal septum, the superficial parapharyngeal space, or the base wall of the sphenoid sinus. Analyses were performed from the healthcare system perspectives of Mainland China and the healthcare provider perspective of Hong Kong, with input parameters sourced from the existing literature and databases. The robustness of findings was evaluated through one‐way and probabilistic sensitivity analyses.ResultsFor DFS, ENPG showed a 29% reduction in risk with an HR of 0.71 (95% CI: 0.64–0.77) compared to IMRT. ENPG demonstrated a significant survival benefit in OS with an HR of 0.59 (95% CI: 0.54–0.65), equating to a 41% reduction in mortality risk. In Hong Kong, IMRT and ENPG yielded QALY gains of 4.59 and 6.29, respectively, with ENPG exhibiting an incremental cost‐effectiveness ratio (ICUR) of USD 13 057 per QALY. For Mainland China, ENPG denominated the IMRT and the ICUR was USD −1450 QALY. Probabilistic sensitivity analysis showed a 100% probability of ENPG being cost‐effective at the willingness‐to‐pay thresholds of USD 130 490 per QALY in Hong Kong and USD 12 741 per QALY in Mainland China.ConclusionThe analysis confirms that ENPG is more effective and cost‐effective than IMRT for treating recurrent NPC in both Hong Kong and Mainland China.

Research on temperature performance prediction of vortex tubes based on artificial neural networks

Abstract This study constructs a hybrid neural network model by integrating the physical constraints of the Bernoulli equation and Nikolaev's formula. The model is designed to explore and predict the variation pattern of the cold end temperature in a vortex tube. The input parameters include inlet pressure, inlet temperature, and cold mass fraction, with the cold end temperature as the output parameter. The network employs a multilayer feedforward model and the Levenberg-Marquardt learning algorithm, using a hyperbolic tangent function as the activation function. To evaluate the statistical validity of the developed model, the coefficient of determination (R²) and root mean square error (RMSE) are utilized, along with an analysis of the model's uncertainty and robustness. The hybrid model achieves an R² of 0.9936 and an RMSE of 0.3392, demonstrating strong performance in terms of uncertainty and robustness. These results indicate that the model accurately predicts the cold end temperature variation in the vortex tube. Furthermore, the findings reveal an optimal pressure range (0.49 MPa to 0.76 MPa) and cold mass fraction range (0.1 to 0.2) that minimize the cold end temperature.

The prediction of bolted joint loosening state under transverse load based on a data-driven model

The impact of transverse load results in the loosening of bolted joints. The loosening condition is determined based on the transverse load and relevant parameters of the bolted joint. To efficiently forecast the loosening state of bolts under various transverse loads and relevant parameters, this study proposes a predictive model for the loosening state of bolted joints. Initially, the relationship between the loosening criteria and relevant parameters is established according to the bolt’s force conditions. Through elementary effect analysis, the high-dimensional representation model is improved, breaking down the loosening criteria function with high-dimensional parameter inputs into a series of low-dimensional functions. Subsequently, the prediction of the loosening state is achieved by training artificial neural networks to approximate multiple low-dimensional functions. The improved predictive model is utilized to determine the critical load for bolted joint loosening. Validation indicates the accuracy of the proposed model. Notably, the influence of the bearing friction coefficient and preload on the critical transverse load is more pronounced compared to the thread friction coefficient.

Damage-free hole making using microwave drilling in flax/PP composite

ABSTRACT The current study focused on the examination of hole quality in microwave drilling of microwave cured natural flax and polypropylene composites. The effect of two input parameters, i.e. microwave power and feed rate of the concentrator were investigated to evaluate HAZ, circularity error, and overcut of the hole. Stereomicroscopic images were used for examination of the response parameters. The full factorial design of the experiments was carried out with two factors and four levels. It was found that flax/PP composite drilled at 180 W of microwave power and 130 mm/min of feed rate resulted in a minimum overcut and circularity error of 9 µm and 138.5 µm, respectively. Also, 360 W of microwave power and 130 mm/min of feed rate showed a reduced HAZ of 67.5 mm2. There was no fiber delamination observed during hole formation. Regression analysis was done in order to establish a relationship among responses and process parameters. Additionally, an ANOVA was undertaken to determine the significance of the model. Over 95% of the correlation between the experimental data and the projected model outcomes was observed. Combined interaction of both the input parameters was shown through surface and contour plots.

Hybrid artificial neural networks-based approaches predicting the heat transfer and flow characteristics of manifold microchannels

Aiming at meeting the requirement of high heat flux electronics cooling, the geometric complexity of manifold microchannels as an energy-saving technique has been increasing rapidly. It is well worth exploring optimal prediction models for the heat transfer and flow characteristics of manifold microchannels to reduce computing resources and time costs in the optimization process. In this paper, hybrid prediction approaches based on artificial neural networks are proposed for manifold microchannels. Four optimization algorithms, namely, genetic algorithm, particle swarm optimization algorithm, artificial hummingbird algorithm, and zebra optimization algorithm were adopted to enhance the prediction performance. Initially, all prediction models were trained and tested by a numerical database including six input parameters, and the thermal resistance and pumping power were taken as the target outputs. Compared to the original method, hybrid prediction models show higher accuracy and reliability on the numerical data with regression coefficients beyond 0.987. The prediction model optimized by the artificial hummingbird algorithm shows the best performance with the mean average error for thermal resistance and pumping power decreased by 88.7% and 81.4% respectively. Additionally, the runtime of all prediction models is compared and the model optimized by the zebra optimization algorithm takes the longest time, but is still two orders of magnitude shorter than that of the traditional simulation method. Finally, the generalizability of all prediction models is further validated by a database amassed from six experimental studies on manifold microchannels. The results showed that three hybrid models can provide accurate outputs with regression coefficients beyond 0.84 which differs from the poor prediction of the original method. The model optimized by the zebra optimization algorithm shows superior prediction performance for six individual studies, two fluids, three fin shapes, and wide flow rate conditions. The trained hybrid prediction models in this study perform higher accuracy and can be cost-effective and reliable prediction tools for the rapid optimization process of various manifold microchannel applications.

Optimizing High-Performance Predictive Modeling of the Medium-Speed WEDM Processing of Inconel 718

The purpose of this research was to create a predictive model for a medium-speed wire electrical discharge machine (WEDM) utilizing an artificial neural network (ANN). Medium-speed WEDM experiments were developed based on the I-optimal mixture design for machining, the Inconel 718 superalloy. During the experiment, the input parameters were the spark ontime, spark offtime, wire feed, and current, with the material removal rate (MRR) and surface roughness (Ra) selected as performance indicators. The ANN model was trained on experimental data and built using a feed-forward backpropagation neural network with a (4-8-2) structure and the Bayesian regularization (BR) learning approach. The model correctly predicted the relationship between the medium-speed WEDM’s primary process parameters and machining performance. An integrated ANN model and the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) were used to determine the ideal parameters for the MRR and Ra, resulting in a set of Pareto-optimal solutions. The confirmation experiment revealed that the mean prediction error between the experimental and ideal solutions had a maximum error percentage of 1% for the MRR and 2% for the Ra, which are within acceptable ranges. This showed that the best process–parameter combinations were better for the MRR and Ra.