Bending strength is determined by two measured inputs: load cell height and applied force. Bending stiffness is determined by three measured inputs: load cell height, applied force, and displacement. Error in each of these measured inputs can create resultant error in bending strength and bending stiffness calculations. For example, when the pivot of the DARLING is not aligned with the characteristic pivot of the stalk, then discrepancies between DARLING deflection and stalk deflection are introduced. This measurement input error (i.e., error in deflection) directly creates resultant systematic error in calculations of bending stiffness but does not affect calculations of bending strength. The discrepancy between DARLING deflection and stalk deflection is evidenced by the load cell sliding along the length of the stalk during the test. As the load cell slides along the stalk, frictional forces between the load cell and stalk generate noise in the force measured by the DARLING. This creates random error that further reduces the accuracy of bending stiffness calculations and affects bending strength calculations as well. In addition, when the DARLING’s pivot and the characteristic pivot of the stalk are not aligned then the load cell becomes non-normal to the stalk, creating forces misaligned with the measurement axis of the load cell. This introduces discrepancies between the actual force applied to the stalk and the force measured by the DARLING. Lastly, when the DARLING is not horizontally aligned with the characteristic pivot of the stalk then there is a discrepancy between the load cell height of the DARLING and the height at which loads are being applied to the stalk. This likewise produces systematic errors in both bending stiffness and bending strength. Finally, errors in load cell height can be introduced when the user incorrectly measures or records the load cell height. This can occur when the user forgets to record the height value after raising or lowering the load cell to test plants of a different height. Table 3 summarizes the effects of the DARLING pivot being misaligned with the characteristic pivot of the stalk.
Table 3
Sources of error and their observed effects on each measured input.
Measured Inputs | Vertical discrepancy between the DARLING pivot and the characteristic pivot of the stalk | Horizontal discrepancy between the DARLING pivot and the characteristic pivot of the stalk |
Applied force (F) | Non-normal forces and frictional forces are introduced from the load cell sliding | Non-normal forces and frictional forces are introduced from the load cell sliding |
Load cell height (h) | N/A | The load cell height is not equal to the height at which forces are applied to stalk |
Angular deflection (θ) | N/A | Angular deflection of DARLING differs from stalk deflection |
Bending strength and bending stiffness are primary determinants of stalk lodging resistance [42]–[44]. Unfortunately, significant amounts of human labor are required to attain measurements of bending strength and bending stiffness. The cost of attaining these measurements is often prohibitive and phenotyping for these traits has become a bottleneck limiting genetic improvement of stalk lodging resistance [45], [46]. The significant amounts of systematic and random error present in field-based measurements of bending stiffness and bending strength further exacerbates this issue. Based on the results of this study, and the authors’ prior experience using phenotyping devices like the DARLING, we suspect that most field studies regularly incur errors between 15–25% in bending stiffness and 1–10% in bending strength. One way to partially mitigate systematic and random error is to increase the number of sampled plants in a study and to calculate average or median values for each variety included in the study. Unfortunately, increasing sample size requires additional human labor inputs. In this study we sought to identify principal sources of error present in field-based measurements of stalk bending strength and bending stiffness so that they may eventually be rectified. This is the first error analysis of any field based biomechanical phenotyping methodology of which the authors are aware.
Results from this study as well as prior experience using the DARLING device over several years suggest that improvements can be made to operating procedures and phenotyping devices to mitigate systematic errors in bending strength and bending stiffness measurements. When spending long hours in the field collecting phenotyping data it is common to make mistakes when recording load cell height. In particular, we have found that users sometimes forget to record a new load cell height in the DARLING software after physically changing the height of the load cell. This can produce very large systematic error (> 100%) in bending strength and bending stiffness measurements. This type of error is difficult to detect when postprocessing the data. Training and standardizing operating protocols cannot fully eliminate this source of error. Including a load cell height sensor on the device that automatically records load cell height, or that notifies the user when the load cell has been changed is a promising approach to mitigate this source of systematic error. The amount of systematic error introduced by incorrect horizontal placement of the phenotyping device pivot can be partially mitigated by using the highest reasonable load cell height. The amount of systematic error produced by horizontal offsets is a function of the horizontal offset expressed as a percentage of load cell height. Thus a 3 cm horizontal offset will produce less systematic error when the load cell height is 75 cm than when the load cell is 45cm. This source of systematic error can also be mitigated by simply explaining the effects of horizontal placement on measurement error to device users. Additionally, this source of systematic error could be mitigated by adding an extra feature to phenotyping devices to help the user ensure the phenotyping device pivot is correctly aligned with the stalk. However, the constantly varying conditions found within agricultural plots (e.g., uneven ground, brace roots, adjacent plants etc.) make this a nontrivial design challenge. Other more complex modifications to testing equipment could minimize systematic error due to vertical discrepancies between the device pivot and the characteristic pivot of the plant being tested. Ideally the device would pivot at the characteristic pivot height of each plant. However, the characteristic pivot height is a function of the height at which the load is being applied to the stalk. Thus, the pivot height would have to change every time the load cell height was changed. Requiring users to manually change the pivot height would significantly reduce throughput. Alternatively, a mechanical linkage could be designed that would change the pivot height whenever the load cell height was changed. This linkage would increase device cost, and weight which would in turn increase user fatigue. Alternatively, one could attempt to account for and correct systematic errors due to vertically misaligned pivot points during data postprocessing. This is a promising approach but requires additional research into the large deflection response of stepped cantilever beams. Finding other ways to reduce systematic error are warranted as they will enable future researchers to utilize reduced sample sizes (and human labor inputs) in phenotyping trials.
Results indicated that random error was also a function of testing position. Random error was quantified by calculating the relative standard deviation (aka coefficient of variation) at each test location. Both random error and systematic error increase the sample size required to attain reliable average bending strength and bending stiffness values of plant varieties of interest. While the magnitude of random error was less than that of systematic error it was still significant and warrants discussion. Results demonstrated that testing at positive horizontal pivot positions (Fig. 5) resulted in the largest values of relative standard deviation for both bending stiffness and bending strength. Testing at negative horizontal positions minimized the random error but should be avoided as it introduces significant systematic error. Like systematic error, the random error was minimized when the device pivot and characteristic pivot of the stalk were vertically aligned. However, as described previously the technical challenges associated with vertical aligning the pivots for every tested sample may outweigh its benefit.
Systematic and random error was calculated at 15 different test positions in the current study. These test positions were selected based on the authors’ prior experience utilizing phenotyping devices. We estimate that it is common for users to horizontally misalign the pivot of a phenotyping device by ± 3cm which corresponds to a 6.4% offset if the load cell height is 47 cm. A 47 cm load cell height is typical when testing inbred maize stalks. We estimate that horizontally misaligning the device pivot by ± 6 cm (i.e., 12.8% of a 47 cm load cell height) is quite noticeable to most users. However, this is also somewhat common due to user fatigue and variations present in the field environment (e.g., uneven ground and other plants obstructing the phenotyping device). Horizontal placement errors greater than ± 6 cm are uncommon as beyond this range the ergonomics of the device become uncomfortable and unwieldy. We choose to select three positions for vertical offsets. A 0% vertical offset is the norm for most phenotyping devices. A 15% vertical offset was chosen as it is the approximate location of the characteristic pivot of a prismatic cantilever beam. A 7.5% vertical offset was chosen simply because it evenly separated the 0% and 15% offsets. The exact position of the characteristic pivot has not been precisely determined for stepped cantilevered beams though it is assumed to be slightly greater than 15%. Further research into the exact position of the characteristic pivot position of stepped cantilevered beams is required to calculate systematic error more accurately. The magnitudes of systematic error presented in this study should therefore be viewed as the minimum possible value. The values of load cell height utilized were also chosen based on the author’s experience. The DARLING device has a ruler engraved on it that is separated into 15 cm increments. We have observed that users typically align the load cell precisely with these markings. However, an exceptionally careless user may place the load cell 1 cm above or below a mark. A far more common type of error is for a diligent but tired user to move the load cell up or down by a 15 cm increment and forget to input the new load cell height into the DARLING. These observations led us to choose four erroneous load cell height measurements: 46cm and 48cm (error of ± 1cm ), as well as 37cm and 62cm (error of ± 15cm).
Several other sources of error are present in field based biomechanical measurements of plants stems that were not investigated in this study. For example, if plants are rapidly deflected inertial effects can introduce additional forces that are detected by the load cell. The measured force can also be significantly altered if the stalk being tested contacts adjacent plants or the ground during the test. In addition, if the top section of the stalk is not removed prior to testing it can oscillate during the test which introduces error in the measured force. To prevent the tested stalk from contacting adjacent plants the leaves and the top portion of the stalk are often removed immediately prior to testing [47]. When doing so care should be taken to either leave the leaf sheath completely intact or to remove it completely. Several studies have shown that the leaf sheath contributes significantly to bending strength and bending stiffness [48], [49]. The types of devices investigated in this study often assume the stalk is rigidly anchored in the soil. However, if the soil is loose or wet the stalk and root structure may rotate in the soil. This does not alter bending strength measurements, but it can drastically alter bending stiffness measurements. Lastly, any electronic or analog sensor has inherent limits, resolution, and accuracy. Low-cost sensors are appealing but they are often unreliable. For example, low-cost load cells are widely available, but their readings can be significantly affected by temperature, relative humidity, and electronic noise. Simultaneously accounting for and mitigating all these sources of error can be especially challenging. Ideally researchers with agricultural, genetic, or biological backgrounds should collaborate with individuals who possess expertise in metrology, or engineering when conducting biomechanical phenotyping studies. Doing so will improve the accuracy and reliability of measured quantities (e.g., [50], [51]). Metrology and engineering expertise can also be leveraged to establish regular and standardized calibration routines for biomechanical phenotyping devices.