Minimum Root Mean Square Research Articles

Free vibration analysis and prediction modeling of delaminated tapered FRP composite plates

Delamination (the separation between plies) is a common failure in Fiber Reinforced Polymer (FRP) laminated composites. The presence of delamination reduces the structural stiffness and changes in dynamic responses. The change in dynamic parameters can be successfully used for assessing structural health monitoring (SHM) for composite structures. SHM requires large amount of numerical/experimental data. This study focuses on the influence of the delamination parameters (size and in-plane location) on vibration behavior of a laminated tapered fiber reinforced polymer (FRP) composite plate with ply drop-off. Furthermore, developing a surrogate model as a fast-executing model to predict the shift in the natural frequency to reduce the computational effort for solving forward problems. The layerwise theory (LWT) has been used, and the delamination is modeled by “constrained mode” were solved using the finite element method (FEM). The numerical model was validated with an experimental modal analysis of tapered plates without delamination to make the model more robust. The effect of delamination was studied using surface plots produced using response surface methodology (RSM). The results show that the delamination size and location significantly affect the natural frequency shift. The RSM and ANN models were considered as surrogate models, and it was evaluated using an experimental modal analysis. The results shows that the single-output ANN model can predict the shift in the natural frequency with a minimum Root Mean Square Error (RMSE).

Prediction of diffuse solar radiation by integrating radiative transfer model and machine-learning techniques

Diffuse radiation is a major component of solar radiation that is important in carbon exchanges and material, energy, and information flows in agricultural ecosystems; however, measuring diffuse radiation is difficult and expensive, leaving only few stations in China that can record diffuse radiation. Therefore, five high-speed and highly accurate hybrid models were developed and compared to simulate diffuse radiation based on the aerosol optical properties and radiation parameters provided by the Aerosol Robotic Network (AERONET), Baseline Surface Radiation Network (BSRN), Wuhan University, Chinese Ecosystem Research Network (CERN), GLASS surface albedo data, and combined radiative transfer model (RTM) with machine learning (ML) models that include random forest (RF), extreme gradient boosting (XGBoost), multi-layer perceptron (MLP), deep neural networks (DNN), and convolutional neural network (CNN). Furthermore, the uncertainty in the simulated diffuse radiation due to the measurement uncertainties of aerosol optical properties and land surface albedo was quantified, and the relative contributions of multiple variables to diffuse radiation were analyzed. The results showed that RTM-RF was the most successful, with determination coefficients (R2) of 0.95, 0.94, and 0.98, and minimum root mean square errors (RMSE) of 9.56, 10.05, and 13.27 W m−2 at the Lulin, Wuhan, and Xianghe sites, respectively. The largest measurement uncertainty in the aerosol optical depth (AOD) was found at the Lulin site, while that of the single-scattering albedo led to the largest errors in Wuhan and Xianghe. AOD, solar zenith angle (SZA), and single-scattering albedo contributed significantly more than the asymmetry factor, land surface albedo, precipitable water vapor, and ozone. This was especially true for AOD, which was higher than 28 % at all sites. Overall, the proposed RTM-RF method exhibited superior performance, therefore we recommend it for estimating diffuse radiation in China.

Tool life prognostics in CNC turning of AISI 4140 steel using neural network based on computer vision

One of the essential requirements for intelligent manufacturing is the low cost and reliable predictions of the tool life during machining. It is crucial to monitor the condition of the cutting tool to achieve cost-effective and high-quality machining. Tool conditioning monitoring (TCM) is essential to determining the remaining useful tool life to assure uninterrupted machining to achieve intelligent manufacturing. The same can be done by direct and indirect tool wear measurement and prediction techniques. In indirect methods, the data is acquired from the sensors resulting in some ambiguity, such as noise, reliability, and complexity. However, in direct methods, the data is available in images resulting in significantly less chances of ambiguity with the proper data acquisition system. The direct methods, which provide higher accuracy than indirect methods, involve collecting images of worn tools at different stages of the machining process to predict the tool life. In this context, a novel tool wear prediction system is proposed to examine the progressive tool wear utilizing the artificial neural network (ANN). Experiments were performed on AISI 4140 steel material under dry cutting conditions with carbide inserts. The cutting speed, feed, depth of cut, and white pixel counts are considered as input parameters for the proposed model, and the flank wear along with remaining tool life is predicted as the output. The worn tool images were captured using an industrial camera during the turning operation at regular intervals. The ANN training set predicts the remaining useful tool life, especially the sigmoid function and rectified linear unit (ReLU) activation function of ANN. The sigmoid function showed an accuracy of 86.5%, and the ReLU function resulted in 93.3% accuracy in predicting tool life. The proposed model’s maximum and minimum root mean square error (RMSE) is 1.437 and 0.871 min. The outcomes showcased the ability of image processing and ANN modeling as the potential approach for developing a low-cost industrial tool condition monitoring system that can measure tool wear and predict tool life in turning operations.

Formula for wave transmission at submerged homogeneous porous breakwaters

A new formula is introduced to determine the wave transmission at submerged porous breakwaters highlighting the effect of the wave-induced pore pressure distribution inside the breakwater, applicable for both regular and random waves. A CFD numerical wave flume based on the Stokes-Cnoidal wave theory for regular waves and Pierson-Moskowitz spectrum theory for random waves combined with the Forchheimer formula is calibrated using an experimental dataset from Calabrese et al. (2002). The proposed formula for the wave transmission coefficient has been obtained by means of dimensional analysis and incomplete self-similarity, and it has been calibrated using the results of the numerical experiments. The new formula has been verified using a large database on wave transmission coefficient yield fairing good predictions for a wide range of wave conditions and breakwater geometries.The proposed formula has been compared with other existing formulae applying to 2336 data of the existing wave transmission coefficient dataset where the proposed formula giving the minimum root mean square error Erms = 12.6% showed the maximum accuracy among all other existing formulae for determining the wave transmission coefficient over the submerged porous breakwaters.

Stride frequency derived from GPS speed fluctuations in galloping horses

Changes in gallop stride parameters prior to injury have been documented previously in Thoroughbred racehorses. Validating solutions for quantification of fundamental stride parameters is important for large scale studies investigating injury related factors. This study describes a fast Fourier transformation-based method for extracting stride frequency (SF) values from speed fluctuations recorded with a standalone GPS-logger suitable for galloping horses. Limits of agreement with SF values derived from inertial measurement unit (IMU) pitch data are presented. Twelve Thoroughbred horses were instrumented with a GPS-logger (Vbox sport, Racelogic, 10 Hz samplerate) and a IMU-logger (Xsens DOT, Xsens, 120 Hz samplerate), both attached to the saddlecloth in the midline caudal to the saddle and time synchronized by minimizing root mean square error between differentiated GPS and IMU heading. Each horse performed three gallop trials with a target speed of 36miles per hour (16.1 ms−1) on a dirt racetrack. Average speed was 16.48 ms−1 ranging from 16.1 to 17.4 ms−1 between horses. Limits of agreement between GPS- and IMU-derived SF had a bias of 0.0032 Hz and a sample-by-sample precision of +/−0.027 Hz calculated over N = 2196 values. The stride length uncertainty related to the trial-by-trial SF precision of 0.0091 Hz achieved across 100 m gallop sections is smaller than the 10 cm decrease in stride length that has been associated with an increased risk of musculoskeletal injury. This suggests that the described method is suitable for calculating fundamental stride parameters in the context of injury prevention in galloping horses.

Ionospheric TEC Forecasting over an Indian Low Latitude Location Using Long Short-Term Memory (LSTM) Deep Learning Network

The forecasting of ionospheric electron density has been of great interest to the research scientists and engineers’ community as it significantly influences satellite-based navigation, positioning, and communication applications under the influence of space weather. Hence, the present paper adopts a long short-term memory (LSTM) deep learning network model to forecast the ionospheric total electron content (TEC) by exploiting global positioning system (GPS) observables, at a low latitude Indian location in Bangalore (IISC; Geographic 13.03° N and 77.57° E), during the 24th solar cycle. The proposed model uses about eight years of GPS-TEC data (from 2009 to 2017) for training and validation, whereas the data for 2018 was used for independent testing and forecasting of TEC. Apart from the input TEC parameters, the model considers sequential data of solar and geophysical indices to realize the effects. The performance of the model is evaluated by comparing the forecasted TEC values with the observed and global empirical ionosphere model (international reference ionosphere; IRI-2016) through a set of validation metrics. The analysis of the results during the test period showed that LSTM output closely followed the observed GPS-TEC data with a relatively minimal root mean square error (RMSE) of 1.6149 and the highest correlation coefficient (CC) of 0.992, as compared to IRI-2016. Furthermore, the day-to-day performance of LSTM was validated during the year 2018, inferring that the proposed model outcomes are significantly better than IRI-2016 at the considered location. Implementation of the model at other latitudinal locations of the region is suggested for an efficient regional forecast of TEC across the Indian region. The present work complements efforts towards establishing an efficient regional forecasting system for indices of ionospheric delays and irregularities, which are responsible for degrading static, as well as dynamic, space-based navigation system performances.

Statistical Analysis of Alpha Power Exponential Parameters Using Progressive First-Failure Censoring with Applications

This paper is an endeavor to investigate some estimation problems of the unknown parameters and some reliability measures of the alpha power exponential distribution in the presence of progressive first-failure censored data. In this regard, the classical and Bayesian approaches are considered to acquire the point and interval estimates of the different quantities. The maximum likelihood approach is proposed to obtain the estimates of the unknown parameters, reliability, and hazard rate functions. The approximate confidence intervals are also considered. The Bayes estimates are obtained by considering both symmetric and asymmetric loss functions. The Bayes estimates and the associated highest posterior density credible intervals are given by applying the Monte Carlo Markov Chain technique. Due to the complexity of the given estimators which cannot be compared theoretically, a simulation study is implemented to compare the performance of the different procedures. In addition, diverse optimality criteria are employed to pick the best progressive censoring plans. Two engineering applications are considered to illustrate the applicability of the offered estimators. The numerical outcomes showed that the Bayes estimates based on symmetric or asymmetric loss functions perform better than other estimates in terms of minimum root mean square errors and interval lengths.

A compact 90–96 GHz 6‐bit passive vector modulator phase shifter in 28‐nm CMOS for phase array applications

AbstractThis letter presents a 90–96 GHz 6‐bit digital control passive vector modulator phase shifter (PS) in a 28‐nm complementary metal–oxide–semiconductor for phase array application. In PS, a full differential directional coupler as a quadrature generator (QG) is proposed, which achieves wide bandwidth and a high‐performance orthogonal network by introducing more pole‐zero pairs. In the vector modulator, two 6‐bit binary‐weighted vector modulators, respectively scale the quadrature signal generated by QG to achieve a high‐resolution vector phase. The measured PS cover and the minimal root mean square (RMS) phase error is and RMS gain error 0.3 dB at 93 GHz, respectively. The fabricated PS occupies excluding pads with no power consumption.

Non-invasive thermal energy flow rate sensor for turbulent pipe flows

A non-invasive thermal energy flow rate sensor based on a combination of transient heat flux and temperature measurements has been developed. A heat flux sensor and a thin-film thermocouple are covered by a thin-film electric heater and clamped onto the outer surface of a pipe. A one-dimensional transient thermal model is applied before and during activation of the external heater to provide estimates of the fluid heat transfer coefficient and thermal resistance. A parameter estimation code is used to estimate the unknown parameters by using the minimum root mean square error between the analytical and experimental sensor temperature values. The sensor was tested with two different fluids (water and diesel oil) and with two different pipe diameters (d=25.4mm and d=12.7mm). Experiments were completed over a range of Reynolds number from 2000 to 25,000 and a range of fluid temperature from 20 °C to 50 °C. Correlations for the fluid temperature and the fluid velocity were within ±0.13 K and ±5% of the direct measurements. The resulting non-invasive thermal energy flow rate sensor can be used to estimate a fluid velocity and a fluid temperature in heating and cooling pipe applications.

Four Severity Levels for Grading the Tortuosity of a Retinal Fundus Image.

Hypertensive retinopathy severity classification is proportionally related to tortuosity severity grading. No tortuosity severity scale enables a computer-aided system to classify the tortuosity severity of a retinal image. This work aimed to introduce a machine learning model that can identify the severity of a retinal image automatically and hence contribute to developing a hypertensive retinopathy or diabetic retinopathy automated grading system. First, the tortuosity is quantified using fourteen tortuosity measurement formulas for the retinal images of the AV-Classification dataset to create the tortuosity feature set. Secondly, a manual labeling is performed and reviewed by two ophthalmologists to construct a tortuosity severity ground truth grading for each image in the AV classification dataset. Finally, the feature set is used to train and validate the machine learning models (J48 decision tree, ensemble rotation forest, and distributed random forest). The best performance learned model is used as the tortuosity severity classifier to identify the tortuosity severity (normal, mild, moderate, and severe) for any given retinal image. The distributed random forest model has reported the highest accuracy (99.4%) compared to the J48 Decision tree model and the rotation forest model with minimal least root mean square error (0.0000192) and the least mean average error (0.0000182). The proposed tortuosity severity grading matched the ophthalmologist’s judgment. Moreover, detecting the tortuosity severity of the retinal vessels’, optimizing vessel segmentation, the vessel segment extraction, and the created feature set have increased the accuracy of the automatic tortuosity severity detection model.

State of charge estimation for lithium-ion batteries based on fractional order multiscale algorithm

The accuracy of state of charge (SoC) plays a critical role in lithium-ion batteries management system, whereas it gradually reduces as ohmic internal resistance growing and maximum available capacity decreasing with battery aging, which is still an open and challenging problem in SoC estimation. To tackle this issue, a multi-scale estimation algorithm is proposed by incorporating fractional order adaptive extended Kalman filter and variable forgetting factor recursive least square (FOAEKF-VFFRLS). Firstly, in order to describe the physicochemical reactions inside battery accurately, a fractional order model of lithium-ion battery with its discrete form is introduced, and the resistor-capacitor (RC) values as well as the order of capacitors are obtained by employing ant colony algorithm (ACA). Secondly, for enhancing SoC estimation accuracy, a fractional order adaptive extended Kalman filter algorithm (FOAEKF) is proposed to continuously modify the noise statistical characteristics while utilizing observation data information. Thirdly, to predict ohmic internal resistance and maximum available capacity for battery, a variable forgetting factor recursive least square algorithm (VFFRLS) is established based on the fact that forgetting factor determined by individual data error would be suddenly changes in the case of inaccurate or perturbed data. Besides, to further improve the accuracy of SoC estimation, a multi-scale estimation approach is proposed in light of the slow variation of battery internal resistance and the fast change of SoC. Finally, through comparative experiments, it is proved that the proposed approach has comprehensive strengths. First, the minimum root mean square error (RMSE) of SoC estimation error is controlled within 0.52 %. Second, terminal voltage error is kept small while limiting SoC errors within narrow ranges. Third, favorable robustness in terms of SoC estimation is achieved despite SoC initial value is mis-initialized.

Lithium-Ion Battery Degradation and Capacity Prediction Model Considering Causal Feature

Accurate life prediction of lithium-ion batteries is essential for the safety and reliability of smart electronic devices, and data-driven methods are one of the mainstream methods nowadays. However, existing prediction methods suffer from the problems such as lack of practical meaning of features and insufficient interpretability. To address this problem, this article proposes a battery degradation and capacity prediction model based on the Granger causality (GC) test and the long short-term memory network. First, initial health indicators are set from the monitoring data of the battery. Second, the vector autoregressive model and the GC test are used to select causal features that are associated with capacity degradation. Then, the impulse response analysis approach is proposed for the first time to analyze the exact influence of the features on capacity degradation and combine the battery aging mechanism, further clarifying the interpretability of the selected features. Finally, using the causal features as model input, a prediction model based on the long short-term memory network is constructed. The experimental results of the two datasets show that the minimum root mean square error is 0.0093 Ah and 0.9635 mAh with the mean relative errors of 0.25% and 0.13%, which verifies the validity and accuracy of the proposed method.

Predicting Patient Wait Times by Using Highly Deidentified Data in Mental Health Care: Enhanced Machine Learning Approach.

BackgroundWait times impact patient satisfaction, treatment effectiveness, and the efficiency of care that the patients receive. Wait time prediction in mental health is a complex task and is affected by the difficulty in predicting the required number of treatment sessions for outpatients, high no-show rates, and the possibility of using group treatment sessions. The task of wait time analysis becomes even more challenging if the input data has low utility, which happens when the data is highly deidentified by removing both direct and quasi identifiers.ObjectiveThe first aim of this study was to develop machine learning models to predict the wait time from referral to the first appointment for psychiatric outpatients by using real-time data. The second aim was to enhance the performance of these predictive models by utilizing the system’s knowledge while the input data were highly deidentified. The third aim was to identify the factors that drove long wait times, and the fourth aim was to build these models such that they were practical and easy-to-implement (and therefore, attractive to care providers).MethodsWe analyzed retrospective highly deidentified administrative data from 8 outpatient clinics at Ontario Shores Centre for Mental Health Sciences in Canada by using 6 machine learning methods to predict the first appointment wait time for new outpatients. We used the system’s knowledge to mitigate the low utility of our data. The data included 4187 patients who received care through 30,342 appointments.ResultsThe average wait time varied widely between different types of mental health clinics. For more than half of the clinics, the average wait time was longer than 3 months. The number of scheduled appointments and the rate of no-shows varied widely among clinics. Despite these variations, the random forest method provided the minimum root mean square error values for 4 of the 8 clinics, and the second minimum root mean square error for the other 4 clinics. Utilizing the system’s knowledge increased the utility of our highly deidentified data and improved the predictive power of the models.ConclusionsThe random forest method, enhanced with the system’s knowledge, provided reliable wait time predictions for new outpatients, regardless of low utility of the highly deidentified input data and the high variation in wait times across different clinics and patient types. The priority system was identified as a factor that contributed to long wait times, and a fast-track system was suggested as a potential solution.

Adjustment Method of “FAST” Active Reflector Based on Optimal Fitting Strategy

The adjustment method of the fast active reflector of “Chinese heavenly eye” is studied. Firstly, this paper studies the offset characteristics of fast main cable node position, combined with the position of the celestial body to be measured, the follow-up coordinate system is established, and the optimal fitting model of active reflector adjustment based on discrete main cable node is established by using the idea of optimal fitting of the ideal surface. Secondly, the genetic algorithm is used to solve the minimum root mean square error (RMSE). The offset of the triangular reflector is driven by the offset of the main cable node, so that the working area is closer to the ideal paraboloid, and the maximum electromagnetic wave signal receiving ratio is achieved. Finally, rotate the coordinate data of each main cable node according to the known celestial body angle and use the Lagrange operator method to obtain the shortest distance from the actual offset point to the ideal paraboloid as the objective function, with the radial expansion range of the actuator and the variation range of the distance between adjacent points as constraints, and the size of the electromagnetic wave contact area is the basis for judging the amount of information, and a reflector adjustment model for the optimal displacement strategy of discrete main cable nodes is established. Through the test, concluded that the optimal fitting strategy is ideal, the model can accurately obtain the fast active reflector adjustment method under the constraint conditions. Through the test, the conclusion that the optimal fitting strategy is ideal is obtained, and the fast active reflector adjustment method that the model can accurately obtain under the constraints is verified.

Application of Suggested Three Parameters Collective Rotational Model to Superdeformed Thallium Odd-Mass Nuclei

The superdeformed rotational bands (SDRB’s) of axial symmetric Tl odd-A nuclei are described within the framework of the suggested model as an extended version of Bohr-Moltelson (BM) model. The suggested model has three parameters rather than the BM model’s two parameters. The model is employed to calculated the transition energies and therefore the unknown level spins within the three pairs of signature partners 191Tl (SD1, SD2), 193Tl (SD1, SD2) and 195Tl (SD1, SD2). The optimized model parameters and therefore the unknown spins for every band are adjusted by employing a computer simulated search program to induce a minimum root mean square deviation between the calculated theoretical and experimental transition energies Eγ (I). The most effective adopted model parameters and spins are wont to calculate the kinematic J (1) and dynamic J (2) moments of inertia, and rotational frequency ħω,. The calculated results agree excellently with the experimental ones. The behaviour of J (1) and J (2) with ħω is examined and discussed. Also, the calculated transition energies and spins are accustomed investigate and exhibit the ΔI = 1 staggering effects in transition energies between each pair of the signature partners. This can be done by considering three staggering indices looking on the dipole γ-transitions between the 2 bands of the signature partners and therefore the quadrupole γ-transitions within each band. All the studied three signature partner pairs showed an oversized amplitude staggering pattern. The ΔI = 1 energy staggering also appears within the transition energies after subtracting a rigid rotor reference when plotted versus spin. The phenomenon of identical bands (IB’s) is additionally investigated within the two pairs [193Tl (SD1), 195Tl (SD1)] and [193Tl (SD2), 195Tl (SD2)] by using the concept of incremental alignment.

A new hybrid method to estimate the single-diode model parameters of solar photovoltaic panel

Today, photovoltaic (PV) panels represent a large part of total power generation. Photovoltaic cells and modules parameter estimation is a relevant field of research that plays a critical role in PV system modeling and simulation. This paper presents a new simple and accurate hybrid method to estimate the five parameters of the single-diode model. The proposed method aims to build a set of equations as functions of the five unknown parameters based on the three remarkable points and the PV datasheet's information. These equations will be used to derive a closed form expression for I0, Iph, Rsh, and Rs. This paper also presents a new simple iterative approach to better estimate the fifth parameter, the ideality factor (n), using only datasheet information. The novelty of this study is to use a new effective simple hybrid method that combines the analytical and the iterative approaches based on the increment of the ideality factor by step of 0.01Vt to achieve the minimum Root Mean Square Error possible. The results reveal that the proposed method outperforms a large number of analytical, numerical, and even the most powerful meta-heuristic algorithms in terms of accuracy, simplicity and reliability.

A Simplified Real-Time Digital Control Scheme for ZVS Four-Switch Buck–Boost With Low Inductor Current

In this article, the four-switch buck–boost (FSBB) converter is a preferred choice for the dc–dc applications where the step-up and step-down are needed. In order to reduce the inductor size and improve the efficiency, the zero-voltage switch (ZVS) control schemes with four segments inductor current for FSBB have been investigated in numerous publications. Among these ZVS control schemes, the optimized control variable stored as the huge look-up table data achieved minimum root-mean-square (RMS) inductor current, and the complex real-time calculation is avoided. However, for the purpose of matching the wide input and output voltage ranges, an external flash is needed for storing the look-up table data; And the large time consumption for invoking the data hazard the dynamic performance significantly. To reduce the storage device cost and meet the demand of transient, a simplified real-time control algorithm is proposed by dividing the operation into the defined Discontinuous Conduction Mode (DCM) and Continuous Conduction Mode (CCM) operation featuring the minimum RMS inductor current and ZVS operation during the whole voltage range without complex calculation and mode transient. Finally, a 300 W dc–dc prototype is built to verify the theoretical analysis and proposed control scheme with a low-cost real-time digital controller.

New Generalized Regression Estimators Using a Ratio Method and Its Variance Estimation for Unequal Probability Sampling without Replacement in the Presence of Nonresponse

One of the most important problems for planning in economics is that reliable data can be difficult to obtain either because it has not been recorded or because of nonresponse in surveys. This paper is aimed at proposing new generalized regression estimators using the ratio method of estimation for estimating population mean and population total and also variance estimators of the proposed generalized regression estimators in the presence of uniform nonresponse of a study variable. We show in theory that the proposed estimators are almost unbiased under unequal probability sampling without replacement when nonresponse occurs in the study. In the simulation studies, the performances of the proposed estimators were better when compared to the existing ones in terms of minimum relative bias and relative root mean square error. In an application to Thai maize in Thailand with 2019 data, we can see that the proposed estimators gave smaller variance estimates when compared to the existing estimators

A novel method of curvature demodulation for Mach-Zehnder interferometer optical fiber curvature sensors

This paper constructs a novel curvature demodulation method for Mach-Zehnder interferometer (MZI) optical fiber sensors. The method is composed of two parts: spectral curve decomposition and support vector machine regression (SVR) of curvature. The authors fabricated the MZI fiber optic curvature sensor and carried out curvature loading experiments. The curvature demodulation method proposed in this paper includes the following steps: spectral data acquisition, data normalization, coefficient vectors calculation, and curvature calculation. The minimum root mean square errors (RMSE) of the curvature demodulation method is 0.02133 m−1. This method has two characteristics: wide curvature demodulation range and unitive curvature regression expression. The curvature demodulation method is not only limited to the MZI sensor curvature demodulation but also applicable to the demodulation of other physical quantities with the spectral data as input. This paper provides a new idea for solving similar demodulation problems.

A 24 GHz Self-Calibrated All-Digital FMCW Synthesizer With 0.01% RMS Frequency Error Under 3.2 GHz Chirp Bandwidth and 320 MHz/µs Chirp Slope

A 24 GHz self-calibrated all-digital frequency-modulated continuous-wave (FMCW) synthesizer is presented in this article. A multi-bank digitally controlled oscillator (DCO) is employed to provide adequate frequency tuning range and high frequency resolution. A full background self-calibration scheme is proposed to linearize the DCO tuning curve for highly linear and fast chirp generation. An overlap compensator based on an adaptive lookup table (LUT) is utilized to eliminate the frequency overlaps between adjacent DCO tuning bands. The compensation words in the LUT are altered by least-mean-square (LMS) algorithm for robust and precise matching. A ramp tracker, which features real-time ramp tracking with zero steady-state phase error, is employed to estimate and stabilize the frequency ramp. Implemented in 40 nm bulk CMOS, the FMCW synthesizer prototype consumes 28 mW with a 0.26 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> core area. The maximum chirp bandwidth is 3.2 GHz, corresponding to 13.33% of the center frequency. Measurement results show that the root-mean-square (RMS) frequency error is reduced by 1/10 with self-calibration after 2 ms convergence time. The maximum chirp slope is up to 320 MHz/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> with 309 kHz RMS frequency error. The minimum RMS frequency error is 7.35 kHz under 5 MHz/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> chirp slope, corresponding to 0.0002% of the chirp bandwidth.