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Terramechanics-Inspired Sensor Fusion for Slip and Mass Flow Estimation in Agricultural Conveyor Systems
Ruben Hefele, Timo Oksanen
TL;DR
Heterogeneous manure and slip between material and conveyor complicate accurate flow prediction. The paper combines weighing, conveyor-speed, and inertial measurements with flow and dynamics models in an EKF. In validation, estimated mass had an RMSE of 11.9 kg and integral consistency within 1.9% of observed mass loss.
Problem
Manure properties vary substantially, and slip between the material and conveyor complicates mass-flow prediction.
Source: §1 · p. 1Method
An EKF fuses load-mass, conveyor-speed, and dynamics-model-derived slip measurements with volumetric-flow and longitudinal-dynamics models.
Source: §1 · p. 2Results
11.9 kg RMSE and integral consistency within 1.9% of observed mass loss were reported for the estimated mass.
Source: §4 · p. 5Takeaways & Limitations
The resulting real-time estimates can be integrated into transport-floor speed control for variable-rate application.
Source: §6 · p. 6, §5 · p. 6The force model is only indirectly validated, material parameters were calibrated for one manure type, and start-up and near-empty phases are outside the estimator’s scope.
Source: §5 · p. 6
Abstract
from arXiv · showhide
Precision farming requires accurate knowledge of implement states. In organic fertilizer spreaders, heterogeneous material and variable field conditions complicate flow-rate prediction, and tilt angles alter the slip behaviour between transport floor and material. This paper presents a model-based sensor fusion method for slip and mass-flow estimation, integrating weighing, conveyor-speed, and inertial measurements in an Extended Kalman Filter with a volumetric flow model and a longitudinal dynamics model. Validation on real-world cattle-manure spreading shows mass estimates tracking the raw weight with an RMSE of 11.9 kg and integrated mass flow within 8.4 % of the observed mass loss.
1. INTRODUCTION
Heterogeneous manure and material–conveyor slip complicate accurate flow prediction and application control. The paper addresses the need for real-time slip and mass-flow estimates by combining a volumetric flow model and a terramechanics-based dynamics model in an EKF.
1. INTRODUCTION
- Organic fertilizer properties vary between farms and within trailer loads, with manure consistency and flow influenced by livestock type, straw, moisture, and storage time.Material cohesion and internal friction angle are identified as important for modelling solid-manure flow behaviour.Source: §1 · pp. 1–2
- Slip between manure and conveyor slats complicates mass-flow prediction, despite conveyor-speed modulation being used to control application rate.Modern spreaders may include weighing units, but real-time slip estimation remains a challenge.Source: §1 · p. 1
- Earlier mass-flow approaches lacked real-time estimates of both instantaneous flow and material–floor slip needed for dynamic variable-rate control.Kosch et al. (2004) found beater torque useful near empty states, while Balsari et al. (2015) did not account for slip and noted cattle manure may behave differently from separated pig-slurry solids.Source: §1 · pp. 1–2
- Rehman et al. (2017) fused estimated belt velocity with smoothed load-cell data for mining-conveyor mass flow, but did not account for slip.The method estimated mass flow at 10 Hz.Source: §1 · p. 2
- The paper develops and validates a real-time EKF estimator for material–conveyor slip and mass flow, using load mass, conveyor speed, and a slip signal from a longitudinal dynamics model.The drive force is modelled with a Bekker–Wong formulation adapted to conveyor–material interactions; validation uses real-world cattle-manure operating data.Source: §1 · p. 2
2. MATERIALS
The study uses a Bergmann universal spreader with a hydraulically driven chain conveyor and gate, weighing and speed sensors, and an IMU. The test material was cattle manure from a deep-litter barn.
2. MATERIALS
- The Bergmann spreader has a chain conveyor, two horizontal beaters, and a V-spread centrifugal disc unit, and was towed by a Claas Arion 550 on grassland.The conveyor and discharge gate are hydraulically driven; the gate was held at a 1.4 m clearance.Source: §2 · p. 2, Figure 1 · p. 2
- The spreader provides load-cell weight data at 10 Hz, conveyor speed at 40 Hz, and IMU roll and pitch angles at 20 Hz.The IMU measurements are internally Kalman-filtered.Source: §2 · p. 2
- The tested solid manure came from a deep-litter breeding-cow barn and had 34.19% dry matter content and 750 kg·m−3 bulk density.The manure was stored for two weeks before loading.Source: §2 · p. 2
3. METHODS
The method combines a volumetric flow model and a longitudinal material–conveyor dynamics model to estimate slip and mass flow. An EKF fuses mass, floor-speed, and model-derived slip measurements to estimate load speed and mass flow.
3. METHODS
- The EKF fuses mass, floor speed, and a model-derived slip signal to estimate load speed and mass flow, with a unit delay preventing an algebraic loop.It operates at 10 Hz, the weighing unit’s update rate.Source: §3 · p. 2, §3.3 · p. 4
3.1 Volumetric flow model
- Assuming constant bulk density and a filled gate region, the volumetric model derives mass flow from load speed through the gate opening.The outlet cross-section is bounded by gate clearance and hopper width; the material is treated as a uniform continuum, without granular fluctuations.Source: §3.1 · p. 3
3.2 Longitudinal dynamics model as a base for slip estimation
- A longitudinal force balance models the load as a point mass and requires driving force to overcome floor and wall friction, beater resistance, acceleration, and downslope gravity.Floor friction depends on pitch and the moving-floor area ratio; wall pressure is height-averaged and dynamic effects such as roll are neglected.Source: §3.2 · pp. 3–4
- The model assumes beater force is proportional to mass flow and uses flat, symmetric walls with identical lateral pressure on both sides.Wall friction acts over the effective wall area, with mean lateral pressure obtained from a height-averaged Janssen distribution.Source: §3.2 · pp. 3–4, Figure 5 · p. 3
- The Bekker–Wong formulation models transferable floor–load force as a function of slip, from zero force at zero slip to a maximum saturated value.Slip is resolved using a nominal acceleration of 0.01 m·s^-2; the effective contact area accounts for moving versus stationary floor parts.Source: §3.2 · p. 4
3.3 Extended Kalman filter
- The EKF uses states for mass, load speed, and slip, and measurements of mass, floor speed, and model-derived slip to correct its predictions.The volumetric model supplies the system dynamics; process noise and the derived-slip measurement noise are tuned on replayed field data.Source: §3.3 · p. 4
4. RESULTS
Real-world load-cycle and start-up results show the EKF tracking weight and estimating mass flow, with accuracy varying by terrain and fill state. On downhill terrain, slip-model performance is weaker than on level terrain.
4. RESULTS
- The estimator was evaluated by chronological replay of logged field measurements, using only past data at each step.The floor-speed control enforced a fixed ratio to tractor ground speed using a field-calibrated slip value and a 25 m working width.Source: §4 · p. 4
- After 4 s, estimated mass flow agreed with the noisier, delayed flow calculated from 1 s weight-signal differences.During nearly level start-up from roughly 40% fill, slip saturated at 0.5.Source: §4 · p. 4, Figure 6 · p. 5
- On level terrain, floor friction dominated the force decomposition, followed by wall friction; beater and downslope contributions were negligible.The mass estimate was smoothed compared with the raw weight signal.Source: §4 · pp. 4–5
- The mass estimate followed the overall trend with an RMSE of 11.9 kg and integral consistency within 1.9 % of observed mass loss in the nearly level start-up-to-steady-state floor-speed scenario (Tab. 3).Source: §4 · p. 5, Figure 6 · p. 5
- 20.9 kg RMSE and 22.3% integral consistency were recorded during downhill start-up.Downslope force exceeded wall friction on slopes steeper than −8°, and slip increased from 0.3 to 0.6 starting at a pitch of −6°; the authors note that level-calibrated slip parameters may need refinement for steep slopes.Source: §4 · p. 5, Figure 7 · p. 5, Table 3 · p. 5
- 16.4 kg RMSE and 8.4% integral consistency were achieved over the complete load cycle.Estimated mass flow remained mostly constant within a margin of 10 kg · s−1, while estimated slip increased as fill state decreased.Source: §4 · p. 5, Table 3 · p. 5
5. DISCUSSION
The estimator is reported to estimate slip and mass flow robustly under realistic conditions and undulating terrain, with real-time mass-flow estimates that can support transport-floor speed control. Its validation and scope remain limited by indirect force-model validation, single-manure calibration, and excluded operating phases.
5. DISCUSSION
- The estimator robustly and accurately estimates slip and mass flow under realistic operational conditions and undulating terrain.It requires only an IMU in addition to sensors commonly available on commercial spreaders.Source: §5 · p. 5
- Real-time mass-flow estimation without significant filter dynamics enables integration into transport-floor speed control for more precise application-rate control.Slope effects become relevant beyond 8°, and the slight overestimation of downslope force warrants refinement.Source: §5 · p. 6
- Validation is indirect because force-model ground truth is unavailable; parameters were calibrated for one manure type, and start-up and near-empty phases remain outside scope.Other products may need parameter adjustment, while EKF measurement fusion limits parameter sensitivity.Source: §5 · p. 6
6. CONCLUSION
The paper develops and validates a real-world EKF estimator for slip and mass flow during solid-manure unloading, adapting Bekker–Wong terramechanics to conveyor–material interaction. Its real-time 10 Hz estimates enable integration into transport-floor speed control for improved variable-rate application.
6. CONCLUSION
- The EKF-based estimator for slip and mass flow during solid-manure unloading was developed and validated on real-world data.Source: §6 · p. 6
- The key contribution adapts the Bekker–Wong terramechanics formulation to conveyor–material interaction.Source: §6 · p. 6
- Real-time 10 Hz estimates enable integration into transport-floor speed control for improved variable-rate application.Source: §6 · p. 6