Prediction of Tuber Damage from Harvesting and Processing Machine Working Units Based on the Recording of Impact Parameters

Abstract

The paper presents the development of an empirical mathematical model of the potato tuber damage index that considers the relationship between impact parameters, such as peak acceleration, velocity change, and the experimental coefficient. This coefficient was developed using statistical analysis methods for four isolated surfaces and two potato varieties, Hermes and Saturna. The IRD 400 device was used to measure impacts, which recorded peak accelerations and changes in impact velocity at initial velocities in the 2.43–4.43 m·s⁻¹ range. The study’s results indicate that the variety, type of surface, and initial impact velocity had a statistically significant effect on the tuber damage index; the type of surface and initial impact velocity had a statistically significant effect on the peak acceleration values (p < 0.05). The increase in peak acceleration with increases in the impact velocity confirms the hypothesis that the maximum force and the resulting internal stresses of the tuber are key elements causing damage due to the impact. The highest values of the tuber damage index occurred during impacts with steel surfaces and conveyor bars. The developed model allows for the faster prediction of potential damage in harvesting and post-harvest processing conditions than traditional measurement methods. To fully use the proposed model in Agriculture 4.0, further research should be conducted to improve recording devices for the measurement of impact parameters in real time.

1. Introduction

During harvest and post-harvest processing, mechanical damage to potato tubers occurs due to impacts on machine elements when they change direction or fall from conveyors onto various surfaces [1,2]. One way to minimize damage in these operations is to identify and improve the elements causing damage using knowledge of the threshold values of bruise-inducing forces. Many researchers have used electronic impact recorders to monitor and assess areas during potato harvesting, transport, and processing where there is a risk of damage due to impacts with complex objects [1,2,3,4,5,6,7,8]. The location of the risk zone can be determined precisely by interpreting the recorded data. As a result, the intervention reduces the risk of damage to the tubers.

One of the significant changes introduced during harvest and processing that influence the development of bruising is the height of the tuber drop and its corresponding initial impact velocity. This has been well documented in research articles [9,10,11,12]. According to Noble [13], low initial impact velocities cause blackspot damage, while high initial impact velocities cause more bruising due to shattering. In practice, the immediate assessment of damage to potato tubers following impact is not possible, especially when tissues under the skin are damaged. Damaged tuber tissues begin to produce pigment that causes discoloration of the flesh within 0.5 h. These changes may not be noticeable until 3–6 h after impact; the discoloration may not fully develop into blackspot until 6 to 48 h [14]. This creates a long delay between taking samples for damage assessment and adjusting machine settings based on the damage results. The answer to this problem may be to use an electronic device to assess the location in which the damage occurs, simulating the potential of the destructive impact force for a single tuber as it moves through sets of harvesting machines and processing devices. This would require the prior calibration of readings concerning the damage index determined due to impacts with contact surfaces.

Most electronic recorders can measure peak acceleration, velocity change, and impact times [15], although not all versions include changes in velocity [16]. Currently available electronic devices can record high accelerations (up to 500 g) at high sampling rates (up to 10 kHz). The relationship between the impact parameters recorded by electronic recorders and the degree of damage is insufficiently understood. Scientists have so far used different recording devices, leading to results that are difficult to compare. Many studies in the literature describe the use of impact recorders to locate the risk of damage in the potato processing process. The recorders that allow for measuring pressure during impact [17] and those that measure changes in acceleration [18] have been extensively described. Newer versions of these recorders are devices equipped with three-axis accelerometers, such as PTR 200, IRD 400, Smart Spud and Tuber Log, have been described by many authors [6,19,20]. The latest version of wireless impact recorders includes a measurement system that allows for the assessment of acceleration during impacts in real time. One device, with acceleration sensors and a built-in radio transmitter, was developed and tested by Vallone et al. [21] at critical points in a citrus fruit packaging line.

Data loggers have been used for many years to collect information on impact energy; attempts have been made to predict damage from these loggers. It is possible to predict potato tuber damage based on measurements of both forces from the PMS 60 data logger and accelerations from the IS 100 by establishing a relationship between readings from the measuring instruments and damage [22]. Hyde et al. [2] observed apparent differences between the motion of the actual tubers and the recorder. Similarly, Molema et al. [3] found that the number of impacts during harvest significantly exceeded the number of potato tuber impacts occurring in practice. To estimate potential damage on in-line equipment, Thomson and Lopresti [7] correlated the impact accelerations from the IS 100 with the frequency and severity of damage. This study also determined the effects of tuber mass and temperature on the damaged surface. Van Canneyt et al. [4] developed two models that combined sensor index values with dry matter content and tuber temperature to predict discoloration. These models showed moderate coefficients of determination. In a study by Bentini et al. [1], peak acceleration and integral average acceleration recorded by an electronic device were used to assess potato damage resulting from dynamic impacts during combined harvesting in various conditions. The study allowed for the influence of variety, soil type and combine harvester operating speeds on tuber damage during harvesting to be determined. The impact recorders have been widely used in studies conducted by Mathew and Hyde [10], Bajema and Hyde [23], and Rady and Soliman [24] to determine damage thresholds (bruising). It should be noted that other factors with respect to the physical and biological properties of tubers may affect bruising thresholds [25,26], including, as follows: the variety [27]; tuber hydration [28]; and tuber flesh temperature [12,29].

Electronic recorders mimic the potential of impact damage to a single tuber as it moves through harvesting and post-harvest processing machines; however, they do not measure tuber characteristics. Therefore, the penetration of the tubers into the material they impact, and the resulting peak acceleration, will be smaller compared to impacts caused by electronic recorders. This can cause difficulties in determining the exact relationships between the recorded parameters and tuber damage, as was confirmed in tests conducted by Surdilovic et al. [30] and Molema et al. [3]. In one study [6], it was shown that electronic recorders with synthetic housings produced higher peak force values than real potatoes with an implanted acceleration measuring unit. Despite many studies, the relationship between the parameters registered by recorders and the degree of damage is still poorly understood. Predicting the probability of bruising on tubers based on measurements from these devices is based on the determining the relationship between impact acceleration and product damage. Changes in velocity, as the second recorded parameter (change in velocity), also occur during impacts with varied initial velocities.

Typically, this parameter has been used to characterize the impact surface. Despite the wide use of recorders in various potato tuber studies, no direct relationship exists between the acceleration and velocity changes recorded by impact recorders and the damage rate.

This study aimed to determine the effect of the initial impact velocity and the type of impact surface on the potential damage to potato tubers during free-fall tests, and to answer the question of how the impact parameters, peak acceleration and the change in velocity during the impact, recorded with a device imitating a potato tuber with a piezoelectric sensor, can be related to the tuber damage index.

2. Materials and Methods

2.1. Research Conditions

This study used Hermes and Saturna potato tubers, which are varieties used in the production of chips, grown in the field of the Agricultural Experimental Station of the Warsaw University of Life Sciences in Obory. From the batch of potatoes dug out manually for the tests, tubers free of diseases and damage, of a similar size (average weight (175 ± 25 g) and shape were selected, which helped to minimize the influence of the shape and weight of individual tubers on the extent of the damage. The average specific gravity was 1.089 ± 0.06 kg·m⁻³ for the Hermes variety and 1.084 ± 0.1306 kg·m⁻³ for the Saturna variety. Until the experiment was conducted, the tubers were stored for 5 days at a temperature of 18–20 °C, at 82–85% humidity.

2.2. Free-Fall Test Stand

The free-fall test stand (Figure 1a) was used to determine the degree of damage to potato tubers when the tubers were dropped from 0.30–1.00 m onto four different bases.

The minimum height of the tuber drop was established, based on data in the literature, as the height at which bruises may occur. The upper limit of the drop height corresponded to the height from which potatoes fall when loaded onto trailers and box pallets.

The interchangeable surfaces were as follows: a 5 mm-thick steel plate; a 50 mm-thick concrete plate; bulk potatoes (potatoes in a filled box measuring 600 × 400 × 240 mm); and 10 mm diameter steel bars in a 2 mm thick PVC casing with a 25 mm bar pitch corresponding to the pitch used in most potato harvester sieving conveyors [31]. Before each test, individual tubers were weighed and, during the test, were placed at a height corresponding to a given initial impact velocity. The tuber was positioned so that its most susceptible bud end (as reported by McGarry et al. [32]) was facing downward; this part of the tuber was identified as the area of potential damage.

To eliminate tuber rotation during free-fall onto the tested surface, the tuber was punctured with a needle on the opposite side of the bud end and the thread was pulled until the needle was released from the tuber. The drops were performed in a controlled manner. To prevent a second impact after the tuber bounced off the surface, the tuber was grabbed by hand. The required height of the drop was determined by adding the tuber dimension between the bud end and stem end and the distance between the locating plate and the impact surface. The tuber was measured with an electronic caliper (range 150 mm, accuracy 0.1 mm); the distance between the plate and the surface was measured with a Bosch GLM40 laser rangefinder (Bosch, Stuttgart, Germany) with a range from 0.05 m to 50 m and an accuracy of 2.0 mm.

The differentiation of the maximum drop height limit was dictated by the need to achieve different levels of tuber damage for the impact surfaces used. This stand was also used to determine the impact parameters of the IRD 400 electronic recorder from Techmark Inc. (Lansing, MI, USA) on the same surfaces and at the same drop heights as those used in the case of the tubers. During the test, the IRD was placed at a height corresponding to the initial velocity set for potato tubers so that its upper surface was in contact with the strip. The drop height was determined, and the tube was then dropped onto the ground. The impact parameters were recorded in the device’s memory when it fell onto the impact surface. After the impact tests, the tubers were stored for 7 days at 20 °C to develop damage symptoms and assess them fully.

2.3. Impacts Recording

Impacts were recorded using the Impact Recording Device IRD 400 (Techmark Inc., Lansing, MI, USA) (Figure 1b). The spherical device, with a diameter of 89 mm and a mass of 373 g, is equipped with a three-dimensional accelerometer sensor used to measure and record peak acceleration a (in m·s^–2) in multiples of the gravitational acceleration g, changes in impact velocity Δv (in m·s^–1), and impact duration. Acceleration measurements were taken in the range of 0–500 g (with an accuracy of ±3%) at a sampling rate of 3906 Hz.

The recorded impacts were sent to the processor unit. After the impact data collection was completed, the collected data in the IRD 400 memory were downloaded to a computer for analysis. During data collection, the unit was programmed with a 30 g threshold so that impacts with accelerations lower than 30 g were not recorded. According to Hyde et al. [2], these are unlikely to cause damage to potatoes under regular harvesting and handling conditions.

2.4. Damage Assessment

Due to the nature of blackspot or shatter bruise damage, the damage was not always visible on the periderm surface. Therefore, the depth of the damage was used to assess the size of the damage. For this purpose, each tuber was cut with a knife through the bud end perpendicularly to the contact surface of the tuber during the impact. Then, the tuber halves were cut into 2 mm-thick slices. The maximum value of the measured damage visible in the cross-section of the slices was considered as the depth of the damage (Figure 2).

The depth of the damage was measured with an accuracy of 0.1 mm using a caliper LIMIT (Luna Sverige AB, Alingsås, Sweden) with a range of 150 mm.

To assess the tuber damage, the damage index (DI) was used, taking into account the determined depth and rank of the damage with weighting factors, according to the following formula [33]:

$$DI={\displaystyle \sum }_{i=0}^3\left(N_i W_i\right)$$

(1)

where N₀, N₁, N₂, and N₃ represent the share of the mass of tubers that is undamaged, damaged slightly, having medium damage, or severely damaged, respectively, %; and W_i is weight assigned to each damage class (W₀ = 0, W₁ = 0.1, W₂ = 0.3, W₃ = 1).

Damage was classified as slight when the damage depth did not exceed 1.7 mm. Medium damage was considered a damage depth between 1.7 mm and 5.1 mm, while values above 5.1 mm were classified as severe damage.

The Fisher–Snedecor test was used for the statistical evaluation of the obtained test results using the Statistica v.13 package. In the damage index prediction model, the selected parameters were acceleration and velocity change during the impact, which are measured by most electronic crash recorders. The basic criterion for determining the parameters for the model was the possibility of conveniently recording the crash data used later for fast damage assessment.

3. Results and Discussion

3.1. Correlations Between Damage Index and Impact Parameters

The electronic impact recorder (IRD 400) was used in this study to determine the relationship between the impact parameters and the damage index in harvesting and processing potatoes by modifying the type of impact surface, the height of the tuber drop, and the related impact velocities. The results of comparative studies on the impacts of tubers of two potato varieties (Saturna, Hermes) and the IRD 400 device with different surfaces (bulk potatoes, rod conveyor, concrete plate, steel plate) for the initial impact velocity in the range of 2.43–4.43 m·s⁻¹ are presented in

Table 1. Analysis of variance of factors influencing tuber damage index for Saturna and Hermes potato varieties and peak acceleration of IRD 400 device at impact with the surface (bulk potatoes, rod conveyor, concrete plate, steel plate) at initial impact velocity in the range of 2.43–4.43 m·s⁻¹.

Variable	Tuber Damage Index		Peak Impact Acceleration of the IRD 400
Factor	Fisher–Snedecor coefficient, F	critical significance level, p	Fisher–Snedecor coefficient, F	critical significance level, p
Variety	102.17	<0.0001	–	–
Surface	470.08	<0.0001	1443.45	<0.0001
Impact velocity	148.86	<0.0001	147.72	<0.0001

,

Table 2. Detailed statistical analysis using Duncan’s test for tuber damage index and peak acceleration of IRD 400 impacts with division into homogeneous groups for initial impact velocity, potato variety, and type of surface.

Factor	Factor Level	No.	Tuber Damage Index, %	Peak Impact Acceleration
Impact velocity, m·s−1	2.43	120	0.65 a ± 1.12	142.0 a ± 5.3
	2.80	160	14.2 b ± 0.94	209.0 b ± 4.5
	3.13	120	22.5 c ± 1.12	242.2 c ± 5.3
	3.43	160	23.7 c ± 0.94	271.8 d ± 4.5
	3.71	120	28.6 d ± 1.12	293.5 e ± 5.3
	3.96	160	30.5 d ± 0.94	296.0 e ± 4.4
	4.20	100	34.4 e ± 1.23	309.0 f ± 5.3
	4.43	140	42.9 f ± 1.02	318.5 g ± 4.5
Variety	Saturna	540	21.0 a ± 0.53	–
	Hermes	540	28.4 b ± 0.54	–
Surface	Bulk potatoes	160	0.4 a ± 1.02	67.4 a ± 4.8
	Rod	320	20.1 b ± 0.67	214.4 b ± 3.2
	Concrete	300	37.1 c ± 0.69	370.7 c ± 3.2
	Steel	300	41.2 d ± 0.69	388.4 d ± 3.2

^a–g different letters within a value represent a significant difference at p < 0.05 using Duncan’s test.

,

Table 3. Dependence of the peak acceleration of the IRD 400 device on the change in impact velocity for different surfaces together with its statistical evaluation using the coefficient of determination R².

Surface	Model	R-Squared (R2)
Concrete	a = 55.12 Δv + 13.77	0.959
Rod	a = 95.32 Δv − 128.13	0.810
Steel	a = 60.41 Δv − 29.23	0.961
Bulk potatoes	a = 18.70 Δv + 18.21	0.963

and

Table 4. Dependence of the peak acceleration of the IRD 400 device (a) on the initial impact velocity (v) for different surfaces together with its statistical evaluation using the coefficient of determination R².

Surface	Model	R-Squared, (R2)
Steel	a = −21.10v2 + 237.78v − 195.15	0.662
Concrete	a = −71.22v2 + 575.43v − 723.75	0.750
Rod	a = −16.38v2 + 201.63v − 282.31	0.755
Bulk potatoes	a = −2.3626v2 + 42.965v − 44.56	0.444

. Based on the analysis of variance, it can be concluded that the variety, surface, and initial impact velocity had a highly statistically significant effect on the variations in the tuber damage index and the peak acceleration of the IRD 400 device (Table 1). The critical significance level was significantly lower (p < 0.0001) than the accepted α = 0.05 or even α = 0.01.

Confirmation of these results can be found in the work of Deng et al. [34], who, based on orthogonal tests, ranked the factors influencing the depth of tuber damage in the following order: drop height (initial velocity), impact surface, number of impacts, and potato mass. In other studies [11], Partington et al. found that the factor contributing to the susceptibility to damage is the biochemical composition of the tubers, which differs between varieties.

Therefore, damage during the harvest and post-harvest processing of potatoes can be minimized by reducing the drop height and the associated initial impact velocity, as well as by using shock-absorbing impact surfaces. Used simultaneously, these two methods can reduce the risk of impact damage [35].

The observed regularities inspired us to find a relationship linking the tuber damage index with the characteristic impact parameters recorded by the IRD 400 device (peak acceleration, change in velocity during impact) (Table 2).

In the study, Saturna variety tubers were less damaged, with an average damage index lower by 7.4% than that of the Hermes variety. This difference may have been due to the slightly different physical and biochemical properties of the tubers of these varieties. The highest damage rate occurred when falling onto hard steel and concrete surfaces because these generated higher impact forces, leading to more severe damage than soft surfaces. The key factor is the energy that the tuber absorbs relative to the surface. In turn, the plastic coating on the rods deforms on impact, reducing the energy transferred to the tuber, resulting in a lower damage rate than rates observed with steel and concrete surfaces.

In similar studies, the depth of the damage to Kexin potatoes after impact with plastic rubber-coated steel rods was shown to be less than that after impact with an uncoated rod [36]. The cushioned impact surface of the rod did not significantly reduce the tuber damage index because there was a high-stress concentration due to the smaller tuber–rod contact area during the impact. A study by Molema et al. [3] showed that steel coating materials, such as PVC, provide a slight cushioning effect. A low damage rate was obtained when tubers collided with each other because the elastic surfaces of the tubers had a better ability to absorb and dissipate energy and were more easily deformed without damage during the impact. Using a damage index based on damage depth, Krzysztofik and Sułkowski [37] assessed the damage of 22 potato varieties. This rate was 54.17% after the potatoes had passed through the line of harvesting, transport, separation, and loading of the pile.

Peak acceleration (a) is expressed as a multiple of the acceleration of gravity for the maximum acceleration during the impact. Taking into account the differences in the peak acceleration values of the impact for the tested surfaces, separate regression models were developed depending on the change in velocity during the impact of the IRD 400 device (Table 3). These were characterized by a high degree of fit, as is demonstrated by the high values of the determination coefficients, which explain 81% to 96.3% of the variability between the peak acceleration a and the change in velocity Δv.

Deng et al. [34] and Thomson and Lopresti [7] considered the mass of the tubers, the height of the fall, and the type of impact surface as the main factors influencing the peak accelerations and velocity changes at the moment of impact. The increase in peak acceleration with increasing impact velocity or drop height is a well-known phenomenon observed in many other impact tests [26]. Results from a study on the impact of potato tubers with rods [12] indicated that a higher peak acceleration induced more extensive tuber damage. Studies by Hendricks et al. [8] showed that 22.7 kg of potatoes placed on the bottom of a cardboard box with a drop height of 15 cm and dropped onto a concrete floor reached a peak acceleration of 200 g.

The increase in peak acceleration, including the peak force with increasing impact velocity, supports the hypothesis that peak force and the resulting internal stresses are key elements causing impact damage [38]. The relationship between the IRD 400 peak impact acceleration and the initial impact velocity can be represented by a parabolic formula (Table 4).

The evaluation of these regression models is at a lower level because the coefficient of determination values are in the range of 44.4–75.5%. Although a measurement method was developed, there is still a particular risk of random factors reducing the accuracy of the measurement. The change in velocity is an important indicator characterizing the hardness of the contact surface of the impact. It is related to the characteristics of energy absorption by the impact surface. Calculated based on the area under the acceleration curve as a function of time, it characterizes the type of impact surface and the force and acceleration of the impact [3,24,35]. It follows that the value of the impact force causing the damage will be influenced by the change in velocity and the peak acceleration.

Taking into account the relationships between the peak acceleration a and the change in impact velocity Δv (Table 3), and the peak acceleration a and the initial impact velocity v (Table 4), attention was paid to the possibility of a relationship between the initial event velocity v and the product of the peak acceleration and the change in impact velocity for the surfaces and potato varieties (a × Δv). For this purpose, a correlation analysis was carried out between these features (

Table 5. Results of correlation analysis between initial impact velocity v, peak acceleration a, velocity change Δv, product of peak acceleration and impact velocity change (a × Δv) for surfaces (bulk potatoes, rod conveyor, concrete plate, steel plate) and potato varieties (Saturna, Hermes).

Characteristic	Surface	Impact Velocity, v	Peak Acceleration, a	Change in Velocity, Δv	Damage Index, DI	a × Δv
Saturna Variety
Impact velocity, v	Concrete	1
Peak acceleration, a	Concrete	0.8064	1
Change in velocity, Δv	Concrete	0.7938	0.7534	1
Damage Index, DI	Concrete	0.5944	0.5412	0.5322	1
a × Δv	Concrete	0.8415	0.9165	0.9474	0.5518	1
Impact velocity, v	Rod	1
Peak acceleration, a	Rod	0.8387	1
Change in velocity, Δv	Rod	0.6240	0.6632	1
Damage Index, DI	Rod	0.8466	0.7758	0.5007	1
a × Δv	Rod	0.7667	0.9074	0.8928	0.6633	1
Impact velocity, v	Steel	1
Peak acceleration, a	Steel	0.8069	1
Change in velocity, Δv	Steel	0.8598	0.7456	1
Damage Index, DI	Steel	0.9020	0.7943	0.8046	1
a × Δv	Steel	0.8785	0.9343	0.9247	0.8325	1
Impact velocity, v	Bulk potatoes	1
Peak acceleration, a	Bulk potatoes	0.6653	1
Change in velocity, Δv	Bulk potatoes	0.8592	0.5739	1
Damage Index, DI	Bulk potatoes	0.2047	−0.0206	0.1841	1
a × Δv	Bulk potatoes	0.8336	0.8993	0.8424	0.0854	1
Hermes Variety
Impact velocity, v	Concrete	1
Peak acceleration, a	Concrete	0.7806	1
Change in velocity, Δv	Concrete	0.7836	0.7521	1
Damage Index, DI	Concrete	0.4147	0.5402	0.4206	1
a × Δv	Concrete	0.8240	0.9134	0.9481	0.4817	1
Impact velocity, v	Rod	1
Peak acceleration, a	Rod	0.8103	1
Change in velocity, Δv	Rod	0.5894	0.6789	1
Damage Index, DI	Rod	0.7787	0.5647	0.4659	1
a × Δv	Rod	0.7491	0.9089	0.8918	0.5701	1
Impact velocity, v	Steel	1
Peak acceleration, a	Steel	0.8061	1
Change in velocity, Δv	Steel	0.8702	0.7337	1
Damage Index, DI	Steel	0.9477	0.7284	0.8155	1
a × Δv	Steel	0.8877	0.9340	0.9180	0.8203	1
Impact velocity, v	Bulk potatoes	1
Peak acceleration, a	Bulk potatoes	0.6653	1
Change in velocity, Δv	Bulk potatoes	0.8592	0.5739	1
Damage Index, DI	Bulk potatoes	0.2668	0.3174	0.2420	1
a × Δv	Bulk potatoes	0.8336	0.8993	0.8424	0.3947	1

). Based on the analysis, a strong consistency was found between the initial impact velocity v, the peak acceleration a, the change in velocity Δv, and the damage index (this effect was explained in the analysis of variance and the detailed analysis using Duncan’s test). However, the strongest consistency was observed between the initial impact velocity v and the product of the peak acceleration and the change in impact velocity (a × Δv). The correlation coefficient values for these last two factors are in the range of 0.7491–0.8887. Collinearity between these explanatory variables can lead to instability in the solution space. Therefore, the product a × Δv was used in a further analysis, which correlated quite well with the tuber damage index DI.

Taking these considerations into account and assuming the hypothesis that there is a relationship between the value of the tuber damage index and the peak acceleration and velocity change during the impact recorded by the IRD 400 device, the following model was formulated:

$$DI={\lambda }_{m}a\Delta v$$

where: DI tuber damage index, %; λ_m is the experimental coefficient, %·s·m⁻¹; a is the peak impact acceleration (in times the acceleration of gravity g); and Δv is the change in velocity during the impact, m·s⁻¹.

The unknown values of the λ_m coefficient were developed using statistical analysis methods.

Table 6. Summary of the values of the experimental coefficients λ_m for the regression models relating the damage index of the Saturna and Hermes potato tuber varieties with the parameters of the IRD 400 impact recording device DI = λ_maΔv for different surfaces, along with a statistical evaluation.

Variety	Surface	Coefficient λm,%·s·m−1	Determination Coefficient R2, %	The Root Mean Squared Error (RMSE), %
Saturna	bulk potatoes	0.0057	49.87	3.15
	rod	0.02821	77.22	13.23
	concrete	0.0132	87.03	12.58
	steel	0.0163	93.02	10.91
Hermes	bulk potatoes	0.0145	55.31	7.21
	rod	0.0415	76.76	19.72
	concrete	0.0158	87.57	15.33
	steel	0.0205	92.91	13.41

presents the values of the λ_m regression coefficients together with their statistical evaluation for the selected surfaces and potato varieties. The values of the determination coefficients are varied. The lowest evaluation of the regression models (R² in the range of 49.87–55.31%) was obtained for the tuber drop and the IRD 400 device on bulk potatoes. This is logical because the impacts of tubers or devices with bulk potatoes are characterized by the greatest randomness, resulting from central and eccentric impacts. The best evaluation of the regression models (R² in the range of 92.91–93.02%) was obtained for impacts with a steel surface.

Bulk potatoes had relatively the lowest values of λ_m coefficients, especially for the Saturna variety (0.0057). The highest values of λ_m coefficients were obtained for tuber impacts with a rod conveyor. For the Saturna and Hermes varieties, the values of this coefficient were 0.0282 and 0.0415, respectively. The higher the value of the λ_m coefficient, the greater the probability of damage to potato tubers from the surface.

The values of the root mean square error (RMSE) and coefficients of determination (R²) given in Table 6 were used to assess the accuracy of the developed model. The RMSE error for the Saturna variety was relatively low for the steel (10.91%) and concrete (12.58%) surfaces, indicating that the model is accurate for these bases. For the Hermes variety, the RMSE error was higher for all surfaces than that of the Saturna variety. For the steel surface, the RMSE was 13.41% and that for the concrete was 15.33%, suggesting that the Hermes variety model has a slightly larger error. However, the more significant RMSE errors for this variety may not be due to model errors but to the larger values of the damage index that the model is trying to predict.

The model predicts the damage less accurately for the rods, achieving higher errors (19.72% for the Hermes variety and 13.23% for Saturna variety). These may be due to the greater variability in terms of the damage, as demonstrated by the lower R². The probability of a central impact on the rods is lower than that on flat surfaces, which means that eccentric impacts can occur. The low RMSE for the prism for both variants suggests that the model predicts the damage very well but does not explain the variability in the data in this case (low R²).

There is, therefore, no basis for rejecting the adopted hypothesis. The relationship between the potato tuber damage index, the peak acceleration, and change in velocity during an impact was justified. This is an existence hypothesis formulated for the first time by the authors. The values of the experimental coefficient have not yet been determined.

Typically, the damage potential is interpreted based on the acceleration of the impact [7,10]. This approach is justified if similar surfaces are present. Different velocity changes are generated if the impacts occur on different surfaces, which provide additional damage data. The determined values of the coefficient λ_m reflect the importance of the relationship between the peak acceleration and change in velocity during an impact on the tuber damage index.

Due to the limited data range, the empirical model is only verifiable within a specific range of variables (i.e., for a given surface, type, and initial impact velocity). Using the model with a broader range may lead to a loss of model accuracy. Damage estimation may be unreliable for significant impacts with accelerations greater than 500 g. The accuracy of the empirical model may also be limited due to the measurement resolution of the device (10 points for a single impact).

3.2. Damage Prediction Based on Impact Parameters

The study of potato tuber damage from the working units of machines for the harvesting or the post-harvest processing of potatoes is usually challenging; the measurements of peak acceleration and changes in impact speed recorded with the IRD 400 electronic device should facilitate the prediction of damage. Based on the developed mathematical model, surface graphs were drawn up linking the tuber damage index DI of the Saturna and Hermes potato varieties with the acceleration and changes in velocity Δv of the impacts of the IRD 400 device with various surfaces (Figure 3). Based on the comparative graphs, it can be concluded that significantly lower values of damage indices were characteristic of Saturna potato tubers than those of the Hermes variety. The average values for these varieties were 21.0% and 28.4%, respectively (Table 2); therefore, the difference in the value of the tuber damage index was 7.4%. The most significant difference, more than twofold, in the dynamics of changes in the tuber damage index between varieties was found during their decline in bulk potatoes (Figure 3a,b). However, the damage index values were the lowest, ranging from 5 to 13%.

The results confirm research on tuber damage conducted by Rady and Soliman [24], who found that steel surfaces and coated steel bars caused more extensive damage than the two-layer potato surface. Moreover, the absorbed energy required to obtain the minimum breakage or fracture surface volume on the tested tubers was higher for the two-layer potato surface than for the other surfaces.

The highest values on the tuber damage index were calculated for their free-fall onto a rod conveyor (Figure 3c,d) and a steel plate (Figure 3g,h); for the Saturna and Hermes varieties, these values were 68% and 99%, and 76% and 96%, respectively. The minor differences in the tuber damage index values (12%) between the Saturna and Hermes varieties were recorded during the free-fall of samples onto a concrete surface (Figure 3g,h); the maximum values for this index were 60% and 72%, respectively. Based on all the research results in this field, it can be concluded that the IRD 400 device impacts, characterized by low peak acceleration values a, up to 50 g, and velocity changes Δv, up to 2.5 m·s^–1, and the corresponding free-falls of tubers onto bulk potatoes or a rod conveyor, generated tuber damage in which the index did not exceed values of 2% and 5%, respectively (Figure 3a–d). Hyde et al. [2] and Mathew and Hyde [10] also found a positive correlation between increasing impact acceleration and damage severity. Hyde et al. [2] reported that the potential for damage to potato tubers was high when the peak acceleration exceeded 100 g, and that peak accelerations above 375 g were likely to cause visible damage. The authors used these threshold values (from 100 to 375 g) in their study to determine the risk of bruising depending on the type of packaging material, drop height, and impact force. In a study by Thomson and Lopresti [7], accelerations exceeding 196 g on a sorting line caused damage of at least 10 mm in diameter.

During the impacts on samples with a concrete or steel plate, the minimum peak acceleration exceeded the value of 200 g. The change in the impact velocity Δv was greater than 3.4 m·s^–1, resulting in damage to the tubers, in which the index value was at least 10% (Figure 3e–h). This means that even the lowest height of the free-fall of the tubers (0.30 m) onto the concrete or steel plate was too high. To not exceed the permissible damage index of 10%, falls onto this type of surface should be reduced, or the external surfaces should be covered with an elastic material, e.g., rubber or soft plastic, characterized by a high value for the elasticity coefficient. In a similar study, Rady and Soliman [24] reported that single-tuber drop heights exceeding 15 cm on steel surfaces caused damage. However, when the steel surface was covered with rubber, drop heights could be increased to 25 cm before damage occurred.

Statistical models linking the readings of the PRT-200 electronic device, biological conditions, and seasonality with the discoloration of potato tuber tissues were the result of research by Van Canneyt et al. [4]. These models are a source of information on the relationship between the energy recorded by the device and the actual tissue damage, taking into account the sensitivity of the product. Due to the limited number of factors in the models and the not very high determination coefficients, the areas of damage prediction are quite broad, which limits the statistical power of these models. Taking into account the formulated mathematical model between the potato tuber damage index and the peak acceleration and changes in the impact velocity of the IRD 400 device, this electronic device can be used to assess the work of the combine harvester or potato processing line working units under the conditions of bench or field tests. This will help to minimize quantitative and qualitative losses of tubers during harvesting and preparation for further processing.

Concerning potato harvesting and processing conditions, the model may be less precise when stones appear in the harvested material. Further research should be conducted in actual field conditions to fully evaluate the model in a broader scope, considering dynamic interactions.

Applying the developed empirical mathematical model of the tuber damage indicator in the context of Agriculture 4.0 will require further work on measuring the impact parameters in real time. Using the damage indicator model, automatic harvesters equipped with sensors and actuators can then dynamically adjust working speeds and control mechanisms based on the predicted impact parameters. This will reduce tuber damage caused by working units. By adapting appropriate control systems in processing lines, the model can be used to optimize the settings of the sorting line (e.g., conveyor speed, impact force) depending on the types of soil and the potato variety.

Further research should be conducted to continuously monitor impact parameters and provide immediate feedback to operators or automated systems. This will enable ongoing adjustments to maintenance processes, minimizing damage as it occurs. A continuous flow of measurement data will improve the accuracy and reliability of the real-time damage index model.

4. Conclusions

Impact parameter data obtained from the free-fall of the IRD ball onto different surfaces and at varying initial impact velocities can be used to determine the damage index for selected potato varieties. Tuber damage studies have shown that the impact surfaces of concrete, steel plates, and steel rods cause a higher damage index than bulk potatoes. The hypothesis of a relationship between the value of the tuber damage index and the peak acceleration and change in velocity during impact was substantiated. The peak acceleration included in the model reflects the force of impact, which allows for the assessment of the intensity of the impact; the change in velocity demonstrates the amount of energy transferred from the tuber to the tested impact surface, which is crucial for understanding how susceptible a given potato variety is to damage. The developed mathematical model can be used to predict tuber damage from the internal working units of harvesting and processing machines, which has been difficult to assess in agricultural practice. This prediction will be made possible based on the measurement of peak acceleration and changes in impact speed recorded by the IRD 400 electronic device. Further research should be conducted towards continuously monitoring impact parameters to enable the ongoing adjustment of service processes, minimizing damage at the time of its occurrence. This will allow for broader use of the developed model.