Error Adjustment Research Articles

A new method of hierarchical time series prediction based on adjustable error

In the area of big data, hierarchical time series prediction (HTSP) has attracted extensive attention. For the traditional HTSPs, the uncertainty of model selection cannot be alleviated due to the shortcomings of data information loss. This article proposes a new HTSP method based on the adjustable error to deal with the above issue. Detailly speaking, in the essential prediction stage, the adjustable prediction error, including all data information, is introduced to improve the current prediction. By comparison of four cases of optimal single prediction, optimal combined prediction, optimal single prediction under the new method, and optimal combined prediction under the new method, the two assertions are obtained: (1) the prediction accuracy of this new method is significantly improved compared with the widely used methods such as bottom-up, generalized least squares; (2) the uncertainty of model selection is greatly reduced. The method’s validity is verified by the examples of American clothing retail and the Germany national electricity consumption.

The role of age and sex in non-linear dilution adjustment of spot urine arsenic

BackgroundPrevious research introduced V-PFCRC as an effective spot urinary dilution adjustment method for various metal analytes, including the major environmental toxin arsenic. V-PFCRC normalizes analytes to 1 g/L creatinine (CRN) by adopting more advanced power-functional corrective equations accounting for variation in exposure level. This study expands on previous work by examining the impacts of age and sex on corrective functions.MethodsLiterature review of the effects of sex and age on urinary dilution and the excretion of CRN and arsenic. Data analysis included a Data Set 1 of 5,752 urine samples and a partly overlapping Data Set 2 of 1,154 combined EDTA blood and urine samples. Both sets were classified into age bands, and the means, medians, and interquartile ranges for CRN and TWuAs in uncorrected (UC), conventionally CRN-corrected (CCRC), simple power-functional (S-PFCRC), sex-aggregated (V-PFCRC SA), and sex-differentiated V-PFCRC SD modes were compared. Correlation analyses assessed residual relationships between CRN, TWuAs, and age. V-PFCRC functions were compared across three numerically similar age groups and both sexes. The efficacy of systemic dilution adjustment error compensation was evaluated through power-functional regression analysis of residual CRN and the association between arsenic in blood and all tested urinary result modes.ResultsSignificant sex differences in UC and blood were neutralized by CCRC and reduced by V-PFCRC. Age showed a positive association with blood arsenic and TWuAs in all result modes, indicating factual increments in exposure. Sex-differentiated V-PFCRC best matched the sex-age kinetics of blood arsenic. V-PFCRC formulas varied by sex and age and appeared to reflect urinary osmolality sex-age-kinetics reported in previous research.V-PFCRC minimized residual biases of CRN on TWuAs across all age groups and sexes, demonstrating improved standardization efficacy compared to UC and CCRC arsenic.InterpretationSex differences in UC and CCRC arsenic are primarily attributable to urinary dilution and are effectively compensated by V-PFCRC. While the sex and age influence on V-PFCRC formulas align with sex- and age-specific urinary osmolality and assumed baseline vasopressor activities, their impact on correction validity for entire collectives is minimal.ConclusionThe V-PFCRC method offers a robust correction for urinary arsenic dilution, significantly reducing systemic dilution adjustment errors. Its application in various demographic contexts enhances the accuracy of urinary biomarker assessments, benefiting clinical and epidemiological research. V-PFCRC effectively compensates for sex differences in urinary arsenic. Age-related increases in TWuAs are exposure-related and should be additionally accounted for by algebraic normalization, covariate models, or standard range adjustments.

Impact of the Minimization of Standard Deviation Before Zeroization of the Mean Bias on the Performance of IOL Power Formulas.

In cataract surgery, accurate intraocular lens (IOL) power calculations are crucial for optimal postoperative refractive outcomes. This study explores the impact of prioritizing the reduction of the standard deviation (SD) of prediction errors before mean prediction error (PE) adjustment on IOL calculation formula precision and accuracy. We conducted a retrospective analysis of 4885 eyes from 2611 patients, all implanted with the same IOL model, comparing four traditional IOL power calculation formulas: SRK/T, Holladay 1, Haigis, and Hoffer Q. We introduced new constants aiming to minimize the SD of PE (new_const) against traditionally optimized constants (classic_const), using a heteroscedastic statistical method for comparison. Validation of precision improvements used a secondary dataset of 262 eyes from 132 patients. We observed significant reductions in mean absolute error (MAE) across training and test sets for Hoffer Q, Holladay, and Haigis formulas, indicating accuracy enhancements. Optimized constants significantly reduced SDs for Haigis from 0.3255 to 0.3153 and for Hoffer Q from 0.3521 to 0.3387. These optimizations also increased the proportion of eyes achieving PE within ±0.25D. SRK/T showed improved SD from 0.3596 to 0.3585. However, Holladay 1 showed minimal change with no significant improvement. In the test dataset, significant reductions in SD were observed for Haigis and Hoffer Q. Prioritizing SD minimization before adjusting mean PE significantly improves the precision of selected IOL power formulas, enhancing postoperative refractive outcomes. The effectiveness varies among formulas, underscoring the need for formula-specific adjustments. The study presents a novel two-step approach for optimizing IOL power calculations.

The calculation and evaluation of acceleration errors produced by position movement of acceleration sensors on the seat of a human centrifuge

Abstract With the increasing requirement for pilot anti-overload ability training, the man-machine engineering problems caused by the existing seat on a human centrifuge are becoming increasingly prominent, making it challenging to meet actual requirements and needing to be upgraded. After upgrading, the seat can be quickly adjusted in front, back, up and down. Acceleration sensors fixed on the seat will also generate displacement, which will result in errors. Three-axis acceleration values are a crucial technical index in human centrifuge systems, and their errors need to be within a certain accuracy range in order to make the system operate normally. Otherwise, the system will produce serious consequences such as alarm and shutdown. Analysis shows that the position movement of acceleration sensors on the seat has no impact on the control system, mainly affecting the safety system. This study discusses the situation when acceleration errors in seat adjustment reach the maximum values, and calculates the three-axis acceleration errors in detail. It is observed whether the values are within the set limits by the safety system in order to evaluate whether they have an impact on the safety of the entire system. The result indicates that the acceleration errors caused by the adjustment of the upgraded seat are within a controllable range and will not have any adverse effect on the safety system of the human centrifuge. Therefore, the acceleration errors will not have any adverse effect on the safety of the whole system.

Adaptive positioning of large-scale aircraft components using a simplified image-based visual servoing via online measurement of ball-head center

In digital alignment systems, ensuring fast and accurate alignment between the ball head on large aircraft components and the ball socket of the positioner is the key to aircraft assembly efficiency and quality. Image-based visual servoing is one of the most advanced techniques with high efficiency and positioning accuracy, but it does not account for measuring the ball-head position. Moreover, variable target positions, similar feature interference, and poor lighting conditions pose great challenges to the fast and robust visual measurement of ball-head position. Hence, an online visual measurement method is introduced to measure the absolute position of the ball head in real time. An adaptive region of interest extraction algorithm and an improved edge following method are introduced to extract the elliptical contour from the ball-head image, and ellipse detection is achieved through a simple triplet selection algorithm. A geometric model based on the perspective projection of the sphere is established for estimating the ball-head center. Then, the simplified image-based visual servoing method is developed by constantizing the image Jacobian matrix. Next, an adaptive positioning method of large-scale aircraft components with multiple ball heads is proposed from a holistic perspective. Finally, experiments show that the final positioning accuracy of each ball head in the X/Y plane is less than ± 0.05 mm, with an efficiency almost ten times that of the conventional method. After adaptive adjustment, the position and angle errors of the simulated component are reduced within 0.6 mm and 0.3°, respectively.

Impacts of Backcalculation Software Selection on Airport Flexible Pavements Using the Aircraft Classification Rating/Pavement Classification Rating Method

From November 2024, the aircraft classification rating/pavement classification rating (ACR/PCR) method will be accepted by civil aviation authorities to notify the bearing capacity of airport pavements. Structural characteristics are necessary to calculate the parameters relating to this method, such as the modulus of elasticity which, in the case of existing pavements, can be obtained by backcalculation. However, the results of this procedure may vary depending on the type of method and algorithms used to minimize adjustment errors between the deflection basins adopted in the software. Given the above, this article aims to evaluate whether the choice of backcalculation software affects the resistance classification and admissibility of aircraft on airport pavements using the ACR/PCR method based on the backcalculated elastic moduli. The elastic modulus values of the materials from two runways were backcalculated using BAKFAA, BackCAP, BackMedina, and ELMOD software, and then used to calculate the PCR. The results of the backcalculation showed differences in the elastic moduli obtained by the software, mainly in the subgrade. It was found that the backcalculation software used can limit the type of aircraft and the runway resistance. Therefore, the choice of software for backcalculation of deflection basins can influence the results of the ACR/PCR method because of divergences in determining the resistance of the pavement’s bearing capacity and the admissibility of aircraft operations in the analyzed structures.

Improved PID based Adaptive Controllers for Denoising Biomedical Signals

Biomedical signal processing is one of the most popular research domains. Very fine features in biomedical signals carry important information regarding patient’s health. So, it is necessary to have noise free biomedical signals for the correct diagnosis. The major trouble for biomedical equipment is Power Line Interference (PLI) which impairs the signals. An adaptive filter can be one of the possible solutions for the removal of non-stationary noise, but maintaining the system stability along with a high convergence rate is a critical issue. The adaptive algorithm works on the principle of minimization of error for optimized coefficients updating while PID controller attempts to minimize the error over time by adjusting the control variables. In this paper, these two different approaches are combined to get an efficient solution for adaptive PLI cancellation and two new algorithms namely PID-based Response Adjustment for Reducing Error (PID-RARE) and PID-based Coefficient Adjustment for Reducing Error (PID-CARE) are proposed. The integration of NSLMS adaptive algorithm with PID controller in the proposed algorithms are found to be an effective solution to adaptive PLI cancellation and have shown quite better performance in terms of SNRout, correlation coefficient, mean square error thereby providing more cleaner signal at lesser convergence rate.

On the use of hindcast skill for merging NMME seasonal forecasts across the western U.S.

Abstract Multi-model ensemble forecasts have gained widespread use over the past decade. A yet unresolved issue is whether forecast skill benefits from the use of prior skill from each model in providing a weighted combination. Here we use the available seasonal ensemble forecasts of six models from the North American Multi-Model Ensemble (NMME) to study various aspects of prior skill-based weighting schemes and explore ways to merge multi-model forecasts. First, we post-process each NMME model through quantile mapping and a simple spread error adjustment. Then, using an equal weighted combination as the baseline forecast, we test merging the models together through skill-based weights by varying the prior skill metric and varying how the metrics are aggregated across the different subbasins and time of year. Results confirm prior work that the combined forecasts do outperform individual models. When evaluating prior skill, equal weighting generally performed as well or slightly better than all weighting schemes tried. The skill of the weighting scheme was not found to be strongly dependent on prior metric but did improve when aggregating all forecasted months and subbasins together to provide one overall weight to each model. Also, we found that including an offset to the prior metric that nudged the weights closer to equal weighting improves skill especially at longer leads where individual model skill is low. Results also show that the weighting schemes performed better than regression-based techniques including multiple linear regression and random forest.

Variable selection and estimation for recurrent event model with covariates subject to measurement error

This article focuses on variable selection in the Andersen–Gill model for recurrent event analysis, particularly when covariates are subject to measurement errors. We propose a comprehensive three-stage procedure that incorporates simulation–extrapolation with various penalty functions. This approach allows for the simultaneous selection of significant covariates, estimation of regression parameters, and adjustment for measurement errors. Through extensive simulation studies, we demonstrate that our method outperforms approaches that fail to account for measurement errors or the need for variable selection. Specifically, our procedure excels in removing unimportant error-prone covariates and accurately estimating the coefficients of important variables. The results also reveal that the magnitude of measurement error has a substantial negative impact on variable selection outcomes. Additionally, we apply our method to a real-world dataset, further illustrating its practical effectiveness and robustness.

Research on a Novel Citrus Reticulata ‘Chachi’ Orientation Adjustment Mechanism (COAM) and Machine Vision Guidance Control

The initial processing of Citrus Reticulata ‘Chachi’ involves peeling as a crucial step. Currently, there is some semi-automatic peeling equipment available. However, due to the requirement of adjusting the orientation of Citrus Reticulata ‘Chachi’ to ensure the stem (or navel) is facing upwards before peeling and because the peeling process must retain the stem as a marker for fresh fruit picking, the loading of Citrus Reticulata ‘Chachi’ for peeling still solely relies on manual operation, resulting in low efficiency and poor standardization. With the rapid growth of the pericarp of the Citrus Reticulata ‘Chachi’ industry, semi-automatic processing equipment is no longer able to meet production demands. The loading issue before peeling Citrus Reticulata ‘Chachi’ is a complex hand–eye coordination problem. In response to this issue, this paper proposes a novel Citrus Reticulata ‘Chachi’ orientation adjustment mechanism (COAM). This mechanism utilizes frictional force to adjust the orientation of Citrus Reticulata ‘Chachi’. First, the conceptual design and kinematic modelling analysis of the mechanism were conducted. Next, the omnidirectional friction-driven wheels were optimized in design. Subsequently, a prototype was manufactured and assembled to conduct validation tests on its open-loop motion performance. Finally, a visual feedback-guided algorithm was introduced to complement the kinematic model, enabling the automatic and rapid adjustment of Citrus Reticulata ‘Chachi’ orientation. The experimental results indicate that the COAM designed in this study can effectively and rapidly adjust the orientation of Citrus Reticulata ‘Chachi’ fruits of different sizes and shapes. It demonstrates strong adaptability, and under visual feedback guidance, the orientation adjustment error is less than 10% of the fruit’s diameter. This meets the requirements for automated production in the initial processing of Citrus Reticulata ‘Chachi’. The research presented in this paper also provides new insights for the orientation adjustment and loading of similar spherical fruits.

Distributed avoidance-accommodating flexible performance approach for adaptive formation tracking of underactuated surface vehicles against moving obstacles

A novel strategy for formation tracking of multiple uncertain underactuated surface vehicles is introduced in this study, to maintain the prescribed formation performance in the presence of moving obstacles with unknown velocities. Unlike the existing methods for prescribed formation performance control, our key contribution is the development of distributed avoidance-accommodating flexible performance functions (FPFs). These functions prevent deviation from the prescribed performance bounds while navigating around moving obstacles, considering input saturation and model uncertainties. We design local adaptive formation controllers by using distributed posture errors and avoidance-accommodating FPFs. Auxiliary signals that facilitate adjustment of the posture errors and performance functions during obstacle avoidance are derived using a recursive design that ensures Lyapunov stability. Additionally, command filters for virtual control laws are redesigned as saturation-compensating filters to solve the input saturation problem. Consequently, the proposed controller ensures the prescribed distributed formation performance, even in scenarios involving moving obstacles and input saturation, a capability lacking in conventional prescribed performance-based formation controllers, which can become unstable in such scenarios. The theoretical findings of this study are validated through comparative simulations.

Experimental and numerical study on data-driven prediction for wildfire spread incorporating adaptive observation error adjustment

In recent wildfire prediction research, data assimilation (DA) methods like Ensemble Kalman filtering have gained traction for integrating observation data to enhance prediction accuracy. Most previous studies trusted that the observation data were accurate, and set a small observation error, which causes unreliable predicted results for scenarios with large observation error. To tackle this, our study introduced a method that iteratively adjusted the potential range of observation errors by comparing observation and simulation data over time. We conducted a 30-m experiment and kilometer-scale numerical simulations. Unlike prior research, we adopted larger error ranges (the similarity index with true data ranges from 0.6 to 1) for both real and synthetic observation data. In the experiment, to increase the complexity of fire spread, a heterogeneous fuel arrangement was employed. Irregular flame fronts appeared due to incomplete combustion and were difficult to replicate in simulations. Better accuracy was achieved using real observation data to revise predictions. Furthermore, to improve the applicability of the algorithm, numerical simulations were designed to consider observation error changing over time or not. The Root Mean Square Errors for the fire front prediction using the proposed method remained lower than that of the traditional DA approach.

Prediction of Dynamics of Riverbank Erosion: A Tale of the Riverine Town Chandpur Sadar

River channel migration often occurs inside the floodplain areas of the river. The structural changes occurring in rivers within floodplain zones serve as a significant ecological signal of their tremendous impact on both ecological and human survival. The aim of the research is to assess the spatial and temporal fluctuations of the Meghna River's bankline from 1990 to 2020 (for 30 years), and to predict the future bankline position. The Landsat imageries from USGS were used for this study. The bankline was extracted from satellite imageries (Landsat) using Modified Normalized Difference Water Index (MNDWI) indices. The variations in bankline dynamics were assessed through the application of Net Shoreline Movement (NSM) and End Point Rate (EPR) analyses using the Digital Shoreline Analysis System (DSAS). Predictive modeling was conducted utilizing the Modified EPR Model, with validation performed via the Root Mean Square Error (RMSE) technique. Adjustment of errors was achieved by employing error coefficients tailored to each individual transect. Over the past three decades, the cumulative river erosion in Chandpur Sadar amounted to 18.03 square kilometers, with the highest Net Shoreline Movement (NSM) recorded at −1979.62 m during the study period. The forecasted maximum Net Shoreline Movement (NSM) is anticipated to be −495.79 m, signifying that the transect is associated with erosion, resulting in landward movement. Conversely, the minimum NSM is projected to be −1.01 m. The most significant movement is expected to occur in Puran Bazar, while the least movement is foreseen in Bakharpur. On average, the NSM across all transects is predicted to be −76.25 m. This study presents a cost-effective approach for evaluating the changes in river erosion over time. This technique may be valuable for policymakers in developing effective plans to reduce the negative impacts of erosion-related risks.

Analysis of driving left-turn errors of young and older drivers at urban intersections

Numerous traffic crashes occur at intersections in urban areas. Understanding the mechanism of driving errors at intersections and providing effective solutions will significantly reduce traffic injuries. The objective of this study is to examine the age and hazard level’s effects on driver left-turn errors at urban intersections. In order to achieve this goal, this study customized the cognitive reliability and error analysis method (CREAM) for left-turn driving task at intersections, and driver error profiles were investigated using a driving simulation experiment as a case study. The results showed that age did not significantly affect drivers’ left turn error probability, while the error probability of both groups of drivers increased with the hazard level. Drivers were most likely to have inadequate monitoring and misjudgment in left-turn maneuvers, more so in the older group. Young drivers were more likely to make planning, decision-making, and adjustment errors compared to older drivers. In addition, observation errors were the most likely cognitive (74.5%). This study achieves the common and characteristic performance of human errors under the three hazardous intersections for the two age groups, and provides a basis for the design of effective training modules and driver assistance systems.

XNLI: Explaining and Diagnosing NLI-Based Visual Data Analysis.

Natural language interfaces (NLIs) enable users to flexibly specify analytical intentions in data visualization. However, diagnosing the visualization results without understanding the underlying generation process is challenging. Our research explores how to provide explanations for NLIs to help users locate the problems and further revise the queries. We present XNLI, an explainable NLI system for visual data analysis. The system introduces a Provenance Generator to reveal the detailed process of visual transformations, a suite of interactive widgets to support error adjustments, and a Hint Generator to provide query revision hints based on the analysis of user queries and interactions. Two usage scenarios of XNLI and a user study verify the effectiveness and usability of the system. Results suggest that XNLI can significantly enhance task accuracy without interrupting the NLI-based analysis process.

The Adjustment Analysis Method of the Active Surface Antenna Based on Convolutional Neural Network

Active surface technique is one of the key technologies to ensure the reflector accuracy of the millimeter/submillimeter wave large reflector antenna. The antenna is complex, large-scale, and high-precision equipment, and its active surfaces are affected by various factors that are difficult to comprehensively deal with. In this paper, based on the advantage of the deep learning method that can be improved through data learning, we propose the active adjustment value analysis method of large reflector antenna based on deep learning. This method constructs a neural network model for antenna active adjustment analysis in view of the fact that a large reflector antenna consists of multiple panels spliced together. Based on the constraint that a single actuator has to support multiple panels (usually 4), an autonomously learned neural network emphasis layer module is designed to enhance the adaptability of the active adjustment neural network model. The classical 8-meter antenna is used as a case study, the actuators have a mean adjustment error of 0.00252 mm, and the corresponding antenna surface error is 0.00523 mm. This active adjustment result shows the effectiveness of the method in this paper.

Well logs reconstruction of petroleum energy exploration based on bidirectional Long Short-term memory networks with a PSO optimization algorithm

During petroleum energy exploration, estimating missing well logs from existing logging data is very meaningful. Due to a highly nonlinear relationship between various logging data and a challenge to express the complexity of underground geological conditions by deterministic functions, traditional methods are difficult to meet the need of accurate interpretations of log data and fine descriptions of reservoirs. Nevertheless, deep learning method provides an advanced means for reconstructing well logs, and can directly map existing logging data to missing well logs. In this paper, we adopt the PSO-BiLSTM network that combines the BiLSTM (Bidirectional Long Short-term Memory) network with the PSO (Particle Swarm Optimization) algorithm. BiLSTM is an excellent data-driven method that can extract bidirectional temporal well logging data. PSO algorithm enhances the performance of BiLSTM model in predicting missing well logs through hyperparameter optimization, global search capability, and adaptive learning. At the same time, RMSE, MAE, and MAPE are used as indicators to evaluate the performance of PSO-BiLSTM model. The results show that when a PSO-BiLSTM model is applied to well logs reconstruction experiments, the reconstructed value of a log curve is in good agreement with its real value. Compared to LSTM and BiLSTM models, a PSO-BiLSTM model provides the best accuracy and stability in predicting missing well logs. The PSO-BiLSTM model strengthens the extraction of relevant logging information and reduces the error of parameter adjustment. It has an important reference significance for the reconstruction of well logs in complex formations.

Design of Soft Microjoint to Improve Robotic Cell Micromanipulation Flexibility

Dexterity micromanipulation is a significant topic in the field of robotics. Herein, a novel robotic rotating microjoint controlled by an exogenous magnetic field based on magnetic programmable soft materials, which brings more dexterity to the micromanipulation task is proposed. First, the magnetic soft material is synthesized and the microjoint is manufactured. The maximum rotation angle and response time are characterized. Then the force analysis of the microjoint in a uniform magnetic field is performed and the relationship between the deformation bending angle of a microjoint and the magnetic field magnitude is first proposed. A sliding mode controller based on the deformation mechanism of microjoints and radial basis function neural network (DMRSMC) is proposed to achieve robust deformation control of the microjoint. The experiment that depicts the microjoint is able to achieve a maximum rotation angle of 22.16° and a response time of 16 ms. The DMRSMC controller performs angle control with higher accuracy than conventional SMC and PID controllers. Finally, a dexterous suction mechanism is developed by combining the microjoint with a soft micropipette needle to achieve dexterous grasping of zebrafish embryos with a 97% success rate and an orientation adjustment error is 1.36°.

Longitudinal method comparison: modeling polygenic risk for post-traumatic stress disorder over time in individuals of African and European ancestry.

Cross-sectional data allow the investigation of how genetics influence health at a single time point, but to understand how the genome impacts phenotype development, one must use repeated measures data. Ignoring the dependency inherent in repeated measures can exacerbate false positives and requires the utilization of methods other than general or generalized linear models. Many methods can accommodate longitudinal data, including the commonly used linear mixed model and generalized estimating equation, as well as the less popular fixed-effects model, cluster-robust standard error adjustment, and aggregate regression. We simulated longitudinal data and applied these five methods alongside naïve linear regression, which ignored the dependency and served as a baseline, to compare their power, false positive rate, estimation accuracy, and precision. The results showed that the naïve linear regression and fixed-effects models incurred high false positive rates when analyzing a predictor that is fixed over time, making them unviable for studying time-invariant genetic effects. The linear mixed models maintained low false positive rates and unbiased estimation. The generalized estimating equation was similar to the former in terms of power and estimation, but it had increased false positives when the sample size was low, as did cluster-robust standard error adjustment. Aggregate regression produced biased estimates when predictor effects varied over time. To show how the method choice affects downstream results, we performed longitudinal analyses in an adolescent cohort of African and European ancestry. We examined how developing post-traumatic stress symptoms were predicted by polygenic risk, traumatic events, exposure to sexual abuse, and income using four approaches-linear mixed models, generalized estimating equations, cluster-robust standard error adjustment, and aggregate regression. While the directions of effect were generally consistent, coefficient magnitudes and statistical significance differed across methods. Our in-depth comparison of longitudinal methods showed that linear mixed models and generalized estimating equations were applicable in most scenarios requiring longitudinal modeling, but no approach produced identical results even if fit to the same data. Since result discrepancies can result from methodological choices, it is crucial that researchers determine their model a priori, refrain from testing multiple approaches to obtain favorable results, and utilize as similar as possible methods when seeking to replicate results.

Triplet Epipolar Images for Spaceborne Three Linear Cameras

Abstract. Epipolar images can reduce conjugate points searching from a two-dimensional to a one-dimensional space, which significantly improves the robustness and efficiency of dense matching. However, two images matched the lack of redundancy and suffered from occlusions. The third image could introduce two more stereos and improve the accuracy and completeness of the three-dimension reconstruction, which were adopted by spaceborne three linear cameras (TLCs), the ALOS PRSIM and ZY-3. In this study, we propose a new triplet epipolar images generation method for spaceborne TLCs. Triplet epipolar images were defined as any two of the three epipolar image pairs. The triplet epipolar geometry requires the imaging rays of any conjugate point to be coplanar. For high-resolution satellite images, parallel projection can be used to approximate the imaging geometry of satellite images. Therefore, a coplanar principal optical axis is a fundamental requirement for spaceborne TLCs. We propose a general workflow to generate triplet epipolar images (TEIs), which includes free-net bundle adjustment of TLCs, building a triplet epipolar geometry, correcting the y-parallaxes, and generating a rational function model (RFM) for TEIs. The ZY3-02 satellite images were used to validate the proposed method. The root means square error (RMSEs) of the free-net bundle adjustment in the image space was 0.185 pixels, which proved the fine intrinsic accuracy. After compensation, the RMSEs of the y parallaxes of the three epipolar image pairs were 0.295, 0.310, and 0.370 pixels. Owing to the simple geometry of the TEIs, the RMSEs of the RFM replacements were within 0.001 pixels.