Rapid Spectroscopic Analysis for Food and Feed Quality Control: Prediction of Protein and Nutrient Content in Barley Forage Using LIBS and Chemometrics

Abstract

Rapid and accurate assessment of nutritional quality, particularly crude protein content and essential nutrient concentrations, remains a major challenge in the food and feed industries. In this study, laser-induced breakdown spectroscopy (LIBS) was combined with advanced chemometric modeling to predict the levels of crude protein and key macro- and micronutrients (Ca, Mg, K, Na, Fe, Mn, P, Zn) in 61 barley forage samples composed of whole aerial plant parts ground prior to analysis. LIBS offers a compelling alternative to traditional analytical methods by enabling real-time analysis with minimal sample preparation. To minimize interference from atmospheric nitrogen, nitrogen spectral lines were excluded from the protein calibration model in favor of spectral lines from elements biochemically associated with proteins. We compared the performance of Partial Least Squares (PLSR) regression and Extreme Learning Machine (ELM) using fivefold cross-validation. ELM outperformed PLS in terms of prediction, achieving a coefficient of determination (R²) close to 1 and a ratio of performance to deviation (RPD) exceeding 2.5 for proteins and several nutrients. These results underscore the potential of LIBS-ELM integration as a robust, non-destructive, and in situ tool for rapid forage quality assessment, particularly in complex and heterogeneous plant matrices.

1. Introduction

Plants play a central role in the food chain for both humans and animals, serving as the primary source of essential nutrients such as proteins, minerals, and bioactive compounds. In animal nutrition, the quality of forage plants is critical for maintaining ruminant health, optimizing zootechnical performance, and supporting the sustainability of livestock systems. Among the key nutritional components, proteins and minerals (e.g., calcium, magnesium, potassium, phosphorus, and iron) are vital for numerous physiological processes, including metabolism, growth, reproduction, and the production of milk and meat. The concentration of these elements in plants is influenced by factors such as plant variety, environmental conditions, and agricultural practices [1]. Therefore, accurate and rapid measurement is essential for adjusting feed rations and ensuring the nutritional quality of animal products.

Barley is a strategic forage crop in the Canadian Prairies due to its nutritional value and resilience to climatic variability. As the entire plant is commonly used in ruminant diets, its comprehensive analysis is relevant for evaluating overall forage quality [2]. However, current analytical methods for determining its chemical composition remain largely conventional. For mineral analysis, techniques such as atomic absorption spectroscopy (AAS), inductively coupled plasma optical emission spectroscopy (ICP-OES), and inductively coupled plasma mass spectrometry (ICP-MS) are standard. While accurate and sensitive, these methods require acid digestion, substantial reagent use, and skilled personnel, making them unsuitable for rapid, on-site analysis. Protein content is typically assessed using the Kjeldahl or Dumas methods [3], which are also labor-intensive, costly, and require corrosive or high-purity reagents. Near-infrared (NIR) spectroscopy has emerged as an indirect method for estimating protein content, especially in homogeneous matrices such as wheat or rice [4,5], and, to some extent, in more heterogeneous matrices like woody plants [6]. However, the low spectral specificity of NIR signals and their sensitivity to matrix effects limit their performance, necessitating complex chemometric models [7] and frequent recalibration.

To address these limitations, laser-induced breakdown spectroscopy (LIBS) [8] has emerged as a promising alternative. LIBS operates by focusing a laser pulse on a sample surface, generating a plasma whose light emission contains spectral lines characteristic of the constituent elements. The presence and concentration of elements are determined from emission wavelengths and intensities, respectively. LIBS is rapid, versatile, quasi-non-destructive, and compatible with portable instrumentation, making it particularly advantageous for in situ applications where conventional techniques fall short. These strengths have propelled its adoption across diverse domains, including environmental monitoring [9], food safety [10], medicine and biology [11], and agriculture [12], especially where fast, reagent-free, and spatially resolved analyses are required.

In the agri-food sector, recent studies have explored the potential of LIBS for a variety of applications [10,13], including the analysis of medicinal plants compared with ICP-OES [14], determination of essential minerals in leafy vegetables [15], assessment of micronutrients in diverse plant species [16], detection of contaminants such as chromium in rice leaves [17], and analysis of heavy metal accumulation [18,19]. LIBS has also been used to assess plant responses to pathogens [20], evaluate nutrient levels in hydroponically grown lettuce [21], and discriminate between aromatic plants [22]. A few studies have also highlighted the feasibility of using LIBS for forage plant analyses, such as elemental detection in barley leaves [23] or metal accumulation in tall fescue [24]. In addition, LIBS has demonstrated the capacity to deliver molecular insights under controlled conditions, as evidenced by the detection of trace alcohol congeners in a gas matrix [25], the identification of hydrocarbons [26], or the analysis of explosives [27].

Several studies have reported the use of LIBS for protein-related analysis in animal-derived samples, including sheep colostrum [28], poultry meat [29], canned tuna [30], maternal milk and infant formula [31], meat product authentication [32], and discrimination of terrestrial processed animal proteins [33]. Other studies have focused on identifying blood-contained proteins [34,35], the detection of whey protein concentrate adulteration [36], and the analysis of foreign protein adulteration in milk powder [37,38]. However, with the exception of the study by Abdel-Salam et al. [28], in which a strong correlation was found between the protein content and a calcium line, as well as C₂ and CN bands, these applications have been largely limited to qualitative assessments or species classification tasks, without aiming for direct, quantitative determination of protein content. To the best of our knowledge, no prior studies have focused on determining the protein content of plant-based materials using LIBS. The only exception is [39], which attempted to directly estimate protein content in homogeneous cereal samples by using nitrogen spectral lines. However, this approach faces major limitations when applied to more complex plant matrices, such as forages, due to strong interference from atmospheric nitrogen that compromises the reliability of the nitrogen signal.

The present study is, to our knowledge, the first to propose a direct quantitative LIBS-based approach for protein prediction in plant materials that does not rely on nitrogen lines. Specifically, it focuses on heterogeneous whole-plant barley forage, offering a novel application of LIBS to complex agricultural samples. To establish robust correlations between LIBS spectral features and chemical concentrations, the application of chemometric models is essential [40]. Among these, Extreme Learning Machines (ELM) [41], a type of single-layer feedforward neural network, and Partial Least Squares (PLS) regression [42] have shown considerable promise in addressing the challenges posed by the high dimensionality and complexity of LIBS data. PLS is widely used for its capacity to manage collinear and noisy datasets [43,44,45], whereas ELM provides a compelling alternative for capturing non-linear relationships, offering significantly faster training times than traditional backpropagation-based neural networks [46,47,48].

This study aims to develop a rapid, reliable, and non-destructive method for predicting the protein and nutrient composition of barley forage using LIBS. By leveraging advanced chemometric models, specifically PLS and ELM, we evaluate the potential of this technique as a practical alternative to conventional chemical analyses for feed quality assessment.

2. Materials and Methods

2.1. Sample Preparation

A total of 61 barley forage samples were collected from various regions across the Canadian Prairies, where they were cultivated under whole-barley swath grazing systems. Post-harvest, the entire plants (including stems, leaves, and ears) were chopped, dried, and ensiled following standard long-term forage storage practices. For analysis using both LIBS and conventional techniques, the samples were further dried and ground. The entire barley plant was analyzed, as this reflects the actual form in which it is fed to animals. This approach was essential to ensure the relevance of our analysis to real-world applications in animal nutrition. For LIBS measurements, the resulting coarse powder was pressed into pellets (4 cm diameter) using a hydraulic press at 88.5 MPa for 3 min. This pressing step ensured a uniform and compact surface to minimize variations in laser focusing and to reduce crater formation caused by laser ablation [49]. Figure 1 displays an example of such a pellet, highlighting the inherent heterogeneity in fibre size and composition.

2.2. Chemical Composition

Chemical characterization of the samples was performed by Cumberland Valley Analytical Services (Waynesboro, PA, USA) [50], an accredited laboratory specializing in feed and forage analysis. These results served as reference values for calibrating and validating LIBS models.

Table 1. Summary of the protein, macronutrient, and micronutrient contents of the 61 barley samples.

Nutrients	Min	Max	Mean
Proteins (%)	10.2	19.3	12.4
Macronutrients (%)
Ca	0.16	0.43	0.31
P	0.14	0.32	0.25
Mg	0.13	0.29	0.21
K	0.48	2.86	1.87
Na	0.02	0.21	0.09
Micronutrients (ppm)
Fe	80	1521	180
Mn	20	86	35
Zn	11	34	23

presents the summary statistics (minimum, maximum, and average concentrations) for proteins, macronutrients, and micronutrients in the 61 samples. Full compositional data are provided in

Table A1. Protein and nutrient content for the 61 barley forage samples.

Samples	Protein (%)	Ca (%)	Mg (%)	K (%)	P (%)	Na (%)	Fe (ppm)	Mn (ppm)	Zn (ppm)
1	10.5	0.28	0.19	1.66	0.28	0.07	204	30	31
2	11.1	0.29	0.20	1.73	0.27	0.06	136	32	27
3	12.4	0.35	0.23	2.21	0.32	0.07	154	36	31
4	11.1	0.29	0.20	1.91	0.27	0.09	106	30	28
5	11.3	0.26	0.19	1.79	0.28	0.07	124	28	28
6	11.5	0.31	0.21	1.93	0.29	0.06	153	33	33
7	11.2	0.29	0.20	1.97	0.27	0.08	125	32	27
8	11.8	0.28	0.22	2.02	0.28	0.11	95	31	28
9	13.0	0.30	0.20	1.67	0.29	0.11	170	25	33
10	12.5	0.29	0.20	1.72	0.28	0.13	128	22	31
11	12.1	0.27	0.22	1.87	0.28	0.20	129	22	28
12	11.7	0.35	0.20	2.10	0.38	0.15	157	27	32
13	11.1	0.38	0.21	2.25	0.4	0.16	257	31	34
14	15.2	0.35	0.21	2.41	0.26	0.10	152	45	25
15	14.5	0.32	0.19	2.43	0.25	0.09	141	47	22
16	15.5	0.33	0.20	2.45	0.25	0.11	128	45	23
17	15.3	0.33	0.20	2.46	0.25	0.09	175	48	21
18	19.3	0.23	0.15	1.61	0.18	0.05	167	34	13
19	12.3	0.22	0.16	1.76	0.2	0.06	186	45	13
20	12.3	0.21	0.16	1.77	0.2	0.05	138	41	14
21	11.0	0.25	0.16	1.74	0.19	0.06	175	30	14
22	10.3	0.22	0.17	1.42	0.23	0.06	250	24	16
23	10.2	0.27	0.18	1.47	0.24	0.07	187	23	18
24	11.7	0.37	0.20	1.98	0.22	0.10	103	34	17
25	11.0	0.38	0.20	1.99	0.23	0.08	380	31	14
26	11.5	0.40	0.22	2.11	0.24	0.11	120	36	17
27	10.9	0.38	0.21	1.95	0.25	0.07	119	32	14
28	12.3	0.40	0.22	2.04	0.25	0.11	127	39	17
29	10.8	0.36	0.20	1.88	0.25	0.06	91	27	14
30	12.2	0.40	0.21	2.09	0.24	0.10	120	34	17
31	10.7	0.36	0.20	2.03	0.24	0.06	109	28	15
32	11.7	0.40	0.21	1.99	0.24	0.08	143	32	16
33	10.6	0.42	0.20	2.01	0.24	0.06	120	34	14
34	12.5	0.36	0.20	1.86	0.23	0.08	91	30	15
35	11.3	0.42	0.20	1.92	0.23	0.09	162	33	14
36	12.0	0.38	0.19	2.13	0.24	0.09	331	52	27
37	11.1	0.35	0.18	1.96	0.24	0.06	170	40	23
38	12.3	0.36	0.19	2.03	0.24	0.07	107	41	24
39	11.0	0.35	0.19	2.00	0.26	0.06	117	41	22
40	12.3	0.36	0.21	2.19	0.25	0.06	106	40	24
41	11.3	0.33	0.18	2.04	0.25	0.03	101	36	22
42	12.4	0.35	0.21	2.14	0.25	0.07	104	43	23
43	12.1	0.18	0.10	1.09	0.14	0.03	80	24	11
44	10.4	0.24	0.16	1.62	0.22	0.05	225	36	31
45	10.8	0.24	0.16	1.67	0.22	0.04	187	34	26
46	11.3	0.26	0.16	1.85	0.24	0.04	181	62	24
47	11.6	0.24	0.15	1.81	0.24	0.03	182	51	22
48	15.7	0.33	0.22	2.86	0.28	0.17	170	47	25
49	12.8	0.34	0.19	1.84	0.29	0.05	136	39	27
50	11.3	0.27	0.16	1.77	0.3	0.21	130	20	21
51	12.1	0.26	0.18	1.89	0.32	0.27	96	22	24
52	13.4	0.16	0.17	1.52	0.3	0.11	128	29	20
53	12.5	0.18	0.15	1.61	0.25	0.09	119	36	19
54	13.0	0.21	0.16	1.83	0.28	0.03	106	29	18
55	11.3	0.34	0.15	0.48	0.19	0.02	689	60	16
56	11.6	0.29	0.13	0.54	0.2	0.02	298	43	16
57	15.1	0.27	0.17	0.55	0.31	0.02	320	43	23
58	13.6	0.43	0.3	2.08	0.2	0.14	1521	86	27
59	13.5	0.35	0.28	2.05	0.2	0.13	1048	76	25
60	13.3	0.37	0.29	1.95	0.2	0.13	1303	82	24
61	10.9	0.22	0.17	1.8	0.25	0.04	185	45	23

of Appendix A. The dataset demonstrates significant nutritional richness and variability, reflecting the biochemical diversity of the forage samples.

The nutrient concentrations were determined by wet chemistry. The analytical uncertainty in crude protein concentration determined by standard wet chemistry methods (e.g., Kjeldahl or Dumas) typically ranges between ±0.1 and ±0.5 percentage points on an absolute basis, assuming that proper grinding, mixing, and subsampling techniques are followed [51]. For chemical elements, typical relative analytical uncertainties are approximately ±1% to ±5% for macronutrients and ±10% to ±20% for micronutrients, depending on the concentration and analytical method [52].

2.3. LIBS Experimental Setup

The LIBS experimental setup is illustrated in Figure 2. A QuantaRay GCR150 Q-switched Nd:YAG laser (Spectra-Physics, Mountain View, CA, USA) operating at 1064 nm, with a pulse duration of 6 ns and a repetition rate of 5 Hz, was used to deliver 35 mJ per pulse onto a spot with a diameter of ~275 µm. An argon gas stream was employed to suppress interference from ambient air and enhance signal quality [53].

Two spectrometers were employed. The primary instrument, referred to as the Modular spectrometer, was a multi-channel system consisting of eight AvaSpec-2048 CCD modules (Avantes, Apeldoorn, The Netherlands) covering the 186.75–1007.65 nm range. Spectral acquisition was conducted with a 1 µs delay and an integration time of 1 ms. A 10 × 10 mapping pattern (100 spots per sample, as shown in Figure 1) was applied, with 5 laser shots per position and a 1 mm step size. The sample was mounted on a motorized translation stage for automated scanning.

Due to reduced sensitivity in the lower UV region for the used setup in our conditions, especially near 214 nm where phosphorus and zinc lines occur, a high-resolution Echelle spectrometer Aryelle 200 (LTB Lasertechnik Berlin, Berlin, Germany) having good sensitivity in the UV region, with 200–817 nm range and 22–90 pm resolution, was also used. This spectrometer was equipped with an ICCD camera iStar DH334T (Andor Technology, Belfast, Northern Ireland, UK), using a 1 µs delay time, a 5 µs integration time, and averaging 20 spectra per spot across 11 manually selected spots per sample. Although not automated, this secondary setup allowed for specific assessment of elements poorly detected by the Modular system and enabled evaluation of sampling variability in heterogeneous matrices.

2.4. Spectral Preprocessing and Variable Selection

Preprocessing of the spectral data is critical to enhance signal quality and suppress artifacts [7,54]. Baseline correction was applied to remove background plasma emission and electronic noise using the 1st or 2nd order polynomial fittings [55]. Standard normal variate (SNV) normalization [56,57] was used to correct for sampling and instrumental variability.

Principal Component Analysis (PCA) was employed to assess spectral consistency across sampling points and identify outliers [7,54]. This multivariate technique reduces data dimensionality while preserving variance, facilitating the detection of anomalous spectra based on the first two principal components. Outlier spectra at certain locations were excluded prior to modeling to enhance prediction reliability.

Univariate calibration was found inadequate for most elements, except for iron, due to matrix effects and non-linear signal responses. To improve variable selection, we adopted a targeted approach based on known atomic transitions. First, relevant spectral lines were identified using the NIST atomic database [58], excluding those involving transitions from the ground state to mitigate self-absorption effects [49,59]. Next, Pearson correlation coefficients [60] were computed between spectral line intensities and analyte concentrations:

$$r={\displaystyle \frac{Cov(\mathbf{Y},\mathbf{Z})}{\sqrt{Var\left|\mathbf{Y}\right|Var\left|\mathbf{Z}\right|}}}$$

(1)

where $\mathbf{Y}\in {\mathbb{R}}^{N\times 1}$ is the concentration vector; $\mathbf{Z}\in {\mathbb{R}}^{N\times 1}$ is the vector of spectral line intensities, and N is the number of samples. Spectral lines exhibiting strong and statistically significant correlations with the target analytes were retained for subsequent chemometric modeling.

2.5. Quantitative Analysis: PLS and ELM Modeling

Quantitative LIBS analysis often requires advanced modeling due to complex relationships between signal intensity and element concentration. This complexity results from matrix effects and self-absorption phenomena [49,53,61], rendering univariate methods inadequate. Two multivariate approaches were evaluated for predicting protein and nutrient content: PLS regression [62] and ELM [63].

2.5.1. Partial Least Squares (PLS) Regression

PLS regression is a widely used linear chemometric technique that models the relationship between high-dimensional spectral data and target variables by extracting latent variables that maximize covariance [64]. It is especially suited for datasets with collinearity. The main hyperparameter is the number of latent components, which must be optimized to balance model complexity and predictive performance.

2.5.2. Extreme Learning Machine (ELM)

The ELM algorithm, developed by Huang [65], enables rapid training of single-layer feedforward neural networks. Unlike traditional neural networks that require iterative weight adjustment (e.g., via backpropagation), ELM randomly assigns input weights and biases and computes output weights analytically. This process allows for exceptionally fast training while preserving generalization capability.

As shown in Figure 3, the ELM network includes an input layer, a hidden layer with non-linear activation (sigmoid), and a single output neuron predicting concentration. The hidden layer output matrix H is computed from the input data X, random weight matrix W, and bias vector b. The output weights β are calculated by minimizing the least-squares error between the predicted and reference concentrations using the Moore–Penrose pseudo-inverse of H. The mathematical formulation of the ELM algorithm is provided in Appendix B.

Due to the random initialization of weights and biases, model performance may vary. To address this, we optimized the number of hidden neurons, ELM’s main hyperparameter, by testing multiple architectures and evaluating each configuration over 1000 random initializations. The model yielding the best cross-validation performance was retained. Despite the high number of iterations, the process remains computationally lightweight. While PLS is well-suited for modeling linear dependencies, ELM offers significant advantages for capturing non-linear relationships in LIBS spectra, with excellent training speed, robustness, and minimal tuning.

2.6. Model Evaluation

Model performance was assessed using three standard metrics: Root Mean Square Error (RMSE), coefficient of determination $\left(R^2\right)$ [66], and Ratio of Performance to Deviation (RPD) [67]:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2},$$

(2)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{{\sum }_{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2}},$$

(3)

$$RPD={\displaystyle \frac{SD}{RMSE}}.$$

(4)

where $y_i$and ${\widehat{y}}_i$ are reference and predicted values, respectively; ${\overline{y}}_i$is the mean of the reference values; $SD$ is the standard deviation of the reference values, and $n$ is the number of samples.

An RMSE near zero and an $R^2$ close to 1 indicates high accuracy. RPD values are interpreted as follows [67]:

• RPD < 1.5: Not usable for analysis;
• 1.5 ≤ RPD < 2.0: Fair, can distinguish high/low values;
• 2.0 ≤ RPD < 2.5: Acceptable for rough screening;
• 2.5 ≤ RPD < 3.0: Good, suitable for approximate prediction;
• RPD ≥ 3.0: Excellent, reliable for quantitative use.

Cross-validation was employed to optimize model hyperparameters and reduce the risk of overfitting [66]. To this end, the dataset was first randomly shuffled and then partitioned into six validation subsets, each containing 10 or 11 samples, with the remaining samples used for calibration. The hyperparameters of both PLS and ELM models were tuned by minimizing the following heuristic objective function:

$$\phi =0.3·{RMSE}_C+0.7·{RMSE}_V-0.3·R_C^2-0.7·R_V^2,$$

(5)

where the subscripts C and V refer to the calibration and validation sets, respectively. Although this composite parameter lacks dimensional consistency, it was found to effectively balance the trade-offs between RMSE, $R^2$, and RPD in the validation sets, while maintaining consistency with the corresponding calibration metrics. The performance metrics reported below represent the average results obtained from the cross-validation process. All models were implemented using direct programming, allowing fine control over training parameters and more precise optimization of model architecture.

3. Results

3.1. LIBS Spectra Processing and PCA Analysis

Figure 4 presents the LIBS spectra obtained from 61 barley forage samples using the Modular spectrometer. Each spectrum is an average of approximately 100 individual spectra, with each location representing the average of five consecutive laser shots. To ensure data reliability, outlier spectra were identified and removed using a PCA-based filtering approach. Specifically, spectra falling far outside the main cluster in the PCA score plot were excluded, typically fewer than six per sample, before averaging the remaining spectra. This preprocessing step effectively removed spectra exhibiting significant deviations, likely due to local inhomogeneities or acquisition artifacts.

Each channel of the Modular spectrometer was preprocessed independently to improve signal quality. This included baseline correction and standard normal variate (SNV) normalization. Additionally, spectral overlaps between adjacent channels were removed to prevent artifacts. A similar procedure was applied to spectra obtained with the Echelle spectrometer. However, due to its design, which produces a single continuous spectrum rather than eight separate channels, the preprocessing was comparatively simpler.

PCA was employed to evaluate the consistency of LIBS measurements within each sample and to assess the chemical variability between samples. For each of the 61 samples, 100 spectra were randomly divided into three subgroups of equal size. The spectra within each subgroup were averaged to generate three representative spectra per sample, thereby enabling simultaneous assessment of both intra-sample reproducibility and inter-sample differentiation. PCA was then performed on the resulting set of 183 spectra (3 × 61). To aid interpretation, Figure 5 presents the PCA score plots for a representative subset of 30 samples, comparing the results obtained with both the Modular and Echelle LIBS instruments.

As illustrated in Figure 5a, PCA applied to the Modular spectrometer data shows that the three spectra for each sample are fairly well clustered, confirming good measurement repeatability and a distinct chemical signature for each sample. Notably, samples with higher iron (Fe) and manganese (Mn) concentrations are located further from the main data cloud, suggesting that these elements significantly influence spectral variance and are, thus, key contributors to chemical differentiation. In contrast, the Echelle spectrometer data (Figure 5b) show more dispersion among the three subgroups per sample. This increased variability likely stems from the smaller number of sampling locations (11 per sample), resulting in lower representativeness of the sample’s heterogeneity.

To quantitatively assess clustering quality, silhouette coefficients were calculated. For a given spectrum i, the silhouette coefficient $s_i$ is defined as

$$s_i={\displaystyle \frac{b_i-a_i}{\mathrm{m}\mathrm{a}\mathrm{x}[a_i,b_i]}}$$

(6)

where ${\mathrm{a}}_{\mathrm{i}}$ is the average distance between spectrum i and other spectra in the same cluster, and $b_i$ is the average distance between i and the nearest spectra of neighboring clusters. Values of $s_i$close to 1 indicate well-separated, cohesive clusters, while negative values suggest poor clustering. The mean silhouette coefficient $\overline{s}$ was 0.52 for the Modular spectrometer and 0.19 for the Echelle spectrometer when using the first three principal components (PCs), confirming superior clustering performance with the Modular system. This performance gap became even more pronounced when a greater number of PCs were included, with $\overline{s}$ reaching a maximum of 0.72 for the Modular system and 0.23 for the Echelle when using nine PCs, and slowly decreasing when using more PCs.

3.2. Protein Prediction Results

In conventional analytical methods such as Kjeldahl or Dumas, protein content is estimated from nitrogen concentration using a standard conversion factor (typically 6.25). However, this approach presents significant limitations in the context of LIBS spectroscopy due to the high background contribution from atmospheric nitrogen in the laser-induced plasma. Although an argon purge was used to reduce air interference, nitrogen emission lines were still detected, even in nitrogen-free reference materials such as cellulose. This observation confirms that nitrogen lines in LIBS spectra originate not only from the sample matrix but also from the ambient atmosphere, undermining their reliability for direct protein quantification.

Consistent with these findings, no robust correlation could be established between nitrogen line intensities and measured protein concentrations. Consequently, nitrogen lines were excluded from the calibration models. Unlike Sezer [39], who used nitrogen emissions to predict protein content in relatively homogeneous cereal grains, our strategy focused on alternative elemental markers biochemically associated with proteins. Elements, such as calcium (Ca), iron (Fe), manganese (Mn), potassium (K), and sodium (Na), were selected for their known roles in protein structure, stabilization, and enzymatic function. For example, iron acts as a cofactor in metalloenzymes [68,69], calcium aids in protein folding and structural stability [68,70], manganese functions as an enzyme activator, and both potassium and sodium maintain the crucial ionic environment for protein activity and membrane protein function [68,69].

Incorporating these elements into the chemometric models enabled accurate predictions of protein content from the LIBS spectra. One notable outlier, sample 18, showed significant discrepancies in all modeling scenarios, across both instruments (Modular and Echelle) and both modeling approaches (ELM and PLS). Despite normal macro- and micronutrient levels, its reported protein concentration (19.3%) was anomalously high and could not be reproduced by any model. This suggests a possible error in the reference measurement. To preserve model robustness, sample 18 was excluded from further protein prediction analysis.

The ELM and PLS models were developed using 41 and 32 spectral input variables for the Modular and Echelle spectrometers, respectively. These correspond to emission lines from the elements listed in

Table A2. List of selected spectral variables (atomic or molecular species) used for each nutrient prediction.

Nutrient	Selected Spectral Variables
Protein	Ca, Mn, K, Na, Fe
Ca	Ca, Mn, Mg, K, Na, O, C, Fe
Mg	Mg, Ca, Mn, K, Na, C2, Fe, C
K	K, Ca, Mg, Si, H, C, Mn
Na	Na, Mg, C, Mg, Ca I, C2
Fe	Fe, Mn
Mn	Mn, Fe

of Appendix A. The number of hidden neurons in the ELM models was optimized through cross-validation by minimizing the average parameter φ (Equation (5)), resulting in 35 neurons for the Modular spectrometer and 30 for the Echelle. For partial least squares (PLS), the optimal number of latent variables was determined by cross-validation in a similar way and was found to be 28.

Cross-validation results for both models are presented in

Table 2. Cross-validation results for protein content for the PLS and ELM algorithms for both the Modular and Echelle spectrometers. The average metrics RMSE, $R^2$, and RPD for the calibration and validation sets are displayed using indices C and V, respectively.

	PLS						ELM
	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{C}}$	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{V}}$	${\mathit{R}}_{\mathit{C}}^2$	${\mathit{R}}_{\mathit{V}}^2$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{C}}$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{V}}$	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{C}}$	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{V}}$	${\mathit{R}}_{\mathit{C}}^2$	${\mathit{R}}_{\mathit{V}}^2$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{C}}$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{V}}$
	(%)	(%)					(%)	(%)
Echelle	0.75	1.18	0.67	0.44	1.63	1.50	0.62	0.81	0.74	0.58	1.87	1.76
Modular	0.43	1.06	0.82	0.53	2.51	1.62	0.50	0.56	0.84	0.74	2.80	2.01

. With the Modular spectrometer, ELM achieved an RMSE_C of 0.50% and an RMSE_V of 0.56%, with $R^2$ values of 0.84 (calibration) and 0.74 (validation), and RPDs above 2. These values reflect satisfactory and practically useful predictive performance, supporting the suitability of the model for quantitative applications. In contrast, the PLS model produced similar calibration results but weaker validation performance.

For the Echelle spectrometer, both models performed slightly worse due to lower sample representativeness (fewer acquisition spots). Nonetheless, ELM still outperformed PLS, underscoring its capacity to model non-linear relationships that linear PLS cannot capture. ELM’s flexible architecture enhances its robustness against signal variability, making it particularly suited to complex, heterogeneous samples.

A comparative analysis further confirmed the superior performance of models built using the Modular spectrometer. The improved results are attributed to the higher number of measurement points (~100 vs. 11), enabling better sampling of the forage’s heterogeneous composition. Although the Echelle spectrometer offers superior spectral resolution, its limited spatial sampling introduces variability that compromises prediction stability.

To evaluate the practical robustness and operational viability of the ELM-Modular calibration model, we performed predictions using alternative spectral averages derived from only 50 randomly selected spectra per sample, half the number used during model training. Given the inherent heterogeneity of the ground barley samples, these reduced spectral subsets provide a more stringent and realistic test of the model’s performance under suboptimal acquisition conditions. Remarkably, as shown in Figure 6, the model maintained strong predictive accuracy despite this challenging scenario, with an RMSE of 0.53%, an $R^2$ of 0.83, and an RPD of 2.51. These results underscore the model’s robustness and suggest its suitability for deployment in field or industrial settings where spectral acquisition may be constrained by time, resources, or operational variability. For comparison, PLS gives an RMSE of 0.80%, an $R^2$ of 0.64, and an RPD of 1.80.

A variable exclusion analysis was conducted using the same prediction set to evaluate the contribution of individual spectral elements to the performance of the protein prediction model.

Table A3. Impact of Spectral Element Exclusion on Protein Prediction Performance.

Element Excluded	ELM			PLS
	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathbf{R}\mathbf{P}\mathbf{D}$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathbf{R}\mathbf{P}\mathbf{D}$
	(%)	(%)		(%)	(%)
Ca	0.93	0.45	1.36	1.1	0.3	1.14
K	0.77	0.66	1.73	0.87	0.52	1.45
Na	0.73	0.69	1.81	0.82	0.54	1.62
Fe	0.99	0.43	1.34	1.11	0.32	1.1
Mn	0.88	0.56	1.52	0.98	0.43	1.4

of Appendix A presents the RMSE, $R^2$, and RPD values obtained after removing one of the five elements used for protein content determination. Comparing these results with those from the full model reveals that omitting certain elements leads to a decline in predictive accuracy, underscoring their importance. Among the elements, iron, calcium, and manganese had the greatest impact on model performance, while potassium and sodium were less influential. These findings highlight the critical role of elemental information in enhancing the accuracy of LIBS-based chemometric models for protein estimation.

To further assess the robustness and reliability of the ELM calibration model for protein prediction, a Y-randomization test was conducted. In this validation procedure, the reference concentration values were randomly reassigned among the samples while maintaining the spectral data unchanged. The test was repeated 30 times, and the reported RMSE, $R^2$, and RPD values represent the average performance across these iterations. As expected, the randomized models exhibited poor predictive ability, with a mean RMSE of 1.01, an $R^2$ of 0.40, and an RPD of 1.30. Given that RPD values below 1.5 are generally considered not suitable for analytical purposes, these results confirm that the original model’s performance was not driven by chance, but rather reflects genuine and consistent spectral–chemical relationships.

3.3. Mineral Nutrient Prediction Results

Macro- and micronutrient quantification was conducted using LIBS spectra acquired with the Modular spectrometer. Consistent with protein modeling results, the Modular spectrometer outperformed the Echelle due to its broader spatial sampling. Therefore, this section focuses on models developed from Modular spectra, with the exception of zinc (Zn) and phosphorus (P), which were analyzed using Echelle spectra due to detection limitations of the Modular instrument. As with protein, certain samples exhibited atypical behavior. Sample 43, which had the lowest measured concentrations of magnesium (Mg), calcium (Ca), and potassium (K), was a significant outlier and was excluded from macronutrient models to avoid bias. No anomalies were observed in the micronutrient dataset, and all samples were retained for analysis.

A preliminary univariate analysis was performed for each nutrient to evaluate the correlation between the intensity of individual emission lines and corresponding elemental concentrations. For each nutrient, the spectral line with the highest correlation was selected for simple linear regression. Results are summarized in

Table 3. Summary of univariate linear regressions for nutrients.

Elements	Wavelength (nm)	$\mathit{R}$2	$\mathit{R}\mathit{P}\mathit{D}$
Ca	428.936	0.53	1.47
Mg	285.212	0.42	1.18
K	769.896	0.64	1.68
Na	819.481	0.8	1.56
Fe II	275.573	0.93	3.46
Mn II	257.610	0.66	1.56
P	213.618	0.16	1.1
Zn	213.856	0.004	1.07

.

Iron (Fe) yielded the best univariate performance, with $R^2=0.93$, and an RPD exceeding 3, demonstrating a strong linear relationship between spectral intensity and concentration. However, for other elements such as Ca, Mg, Na, and K, the univariate performance was more modest ($R^2$ between 0.42 and 0.80, RPD < 2), reflecting the influence of matrix effects and inter-element interactions. Zinc and phosphorus showed particularly weak correlations ($R^2$ < 0.2, RPD ≈ 1.1), largely due to low emission line intensities, low concentrations in samples, and instrumental sensitivity constraints.

These findings confirm that univariate analysis is insufficient for reliable nutrient quantification from LIBS spectra, except for Fe. The complex, multi-elemental nature and heterogeneity of the forage matrix introduce spectral interferences and non-linear effects that necessitate a multivariate approach [49,53,71]. To address this, PLS and ELM models were developed for all nutrients. These models integrate multiple selected wavelengths per element to enhance predictive robustness. Fivefold cross-validation results presented in

Table 4. Summary statistics for calibration and validation using PLS and ELM models for nutrients.

Macronutrients	PLS						ELM
	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{C}}$	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{V}}$	${\mathit{R}}_{\mathit{C}}^2$	${\mathit{R}}_{\mathit{V}}^2$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{C}}$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{V}}$	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{C}}$	${\mathit{R}\mathit{M}\mathit{S}\mathit{E}}_{\mathit{V}}$	${\mathit{R}}_{\mathit{C}}^2$	${\mathit{R}}_{\mathit{V}}^2$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{C}}$	${\mathit{R}\mathit{P}\mathit{D}}_{\mathit{V}}$
	(%)	(%)					(%)	(%)
Ca	0.02	0.034	0.89	0.75	3.12	2.21	0.017	0.021	0.92	0.87	3.7	2.79
Mg	0.014	0.02	0.75	0.74	2.34	2.26	0.008	0.009	0.93	0.89	3.87	3.48
K	0.11	0.19	0.89	0.85	3.14	2.94	0.09	0.1	0.94	0.88	4.38	3.44
P	0.025	0.042	0.63	0.4	1.86	1.46	0.022	0.026	0.61	0.57	1.85	1.67
Na	0.014	0.024	0.89	0.84	3.13	2.85	0.01	0.012	0.93	0.92	4.68	4.64
Micronutrients	(ppm)	(ppm)					(ppm)	(ppm)
Fe	53.99	60.72	0.93	0.92	4.07	4.05	39.29	51.69	0.95	0.92	6.02	5.8
Mn	6.31	10.31	0.71	0.65	1.91	1.83	5.37	5.79	0.83	0.8	2.53	2.29
Zn	4.26	5.34	0.49	0.36	1.42	1.3	3.69	3.51	0.63	0.59	1.67	1.66

show that ELM significantly outperformed PLS for most nutrients, achieving $R^2>0.85$ and an RPD > 2.29. ELM was particularly effective for elements like Fe, Ca, K, and Na, where non-linear relationships between spectral features and concentration are prominent. PLS provided reasonable results for Fe but was limited in capturing the non-linear spectral interactions prevalent in LIBS data.

For Zn and P, both models yielded suboptimal results ($R^2$ < 0.65, RPD < 2), consistent with their low spectral signal strength and limited concentration range in the samples. Although ELM slightly improved performance over PLS, further enhancements in sampling strategy and instrument configuration are needed to improve the detection and quantification of these elements.

These results further demonstrate the robustness of the ELM models. To evaluate their generalization capability more thoroughly, nutrient concentrations were also predicted using averaged spectra, each computed from 50 randomly selected spectra per sample. Figure 7 presents the predicted versus measured concentrations for six key nutrients, Ca, Mg, Na, K, Fe, and Mn, using the optimized ELM models. The models consistently achieved good-to-excellent predictive performance across all elements, with $R^2$ ranging from 0.80 to 0.94 and RPD values between 2.29 and 4.38. Despite the good correlation observed between manganese content and its selected emission lines, the lower predictive performance obtained for Mn is likely due to its relatively low concentration and limited concentration range in the samples. This limited concentration range reduces the variability needed for the model to learn robust relationships, which may hinder accurate prediction. These findings confirm the ability of the multivariate ELM approach to effectively manage spectral variability and matrix complexity, reinforcing its suitability for accurate nutrient quantification in heterogeneous forage samples.

For nutrient prediction, the robustness of the ELM models was further examined using a Y-randomization approach. The procedure was repeated 30 times, and the average RMSE, $R^2$, and RPD values are presented in

Table 5. Predictive performance of ELM models trained with randomized concentration assignments for nutrient prediction (Y-randomization test).

Macronutrients	ELM
	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathbf{R}\mathbf{P}\mathbf{D}$
	(%)	(%)
Ca	0.05	0.41	1.32
Mg	0.025	0.43	1.34
K	0.3	0.41	1.32
Na	0.042	0.23	1.15
Micronutrients	(ppm)	(ppm)
Fe	236.7	0.18	1.12
Mn	10.67	0.35	1.26

. As anticipated, all models showed weak predictive performance, with $R^2$ values below 0.45 and RPDs consistently under 1.5, a threshold below which models are generally considered unreliable for quantitative analysis. These findings support the reliability of the original nutrient models and confirm that their predictive power arises from real spectral–chemical relationships rather than random correlations.

4. Discussion and Conclusions

This study demonstrates the strong potential of LIBS spectroscopy, when combined with advanced chemometric modeling, for accurate and non-destructive prediction of protein and mineral nutrient content in complex plant matrices such as barley forage. By shifting the focus from nitrogen to elemental markers biochemically associated with proteins, the reliability of protein prediction was significantly improved, especially when using Extreme Learning Machines (ELM) with the Modular spectrometer. Across all analyses, the ELM approach consistently outperformed Partial Least Squares (PLS), offering superior accuracy, robustness, and resilience to matrix effects inherent in heterogeneous plant samples.

To our knowledge, this study is the first to propose a direct quantitative LIBS-based approach for protein prediction in plant samples, without relying on nitrogen emission lines, which have been found to be unreliable under ambient conditions. Specifically, we focus on heterogeneous whole barley forage, a complex and representative matrix for forage analysis. Our main contribution lies in demonstrating that protein content, generally inaccessible by direct elemental detection, can be indirectly estimated using chemometric models (PLS and ELM) applied to the spectral signals of elements biochemically bound to proteins, such as calcium, manganese, potassium, sodium, and iron. This work demonstrates that LIBS, a rapid technique requiring little preparation, can provide valuable predictive information not only on elemental composition but also on broader nutritional quality indicators relevant to the agri-food sector.

Nonetheless, several limitations must be acknowledged. The fibrous and heterogeneous nature of forage introduces measurement variability due to the limited sampling volume of each laser pulse. In addition, atmospheric interference restricts the reliable use of nitrogen emission lines, precluding direct estimation of total protein via elemental nitrogen detection. While our dataset was sufficient to develop and validate robust regression models, using cross-validation, Y-randomization, and a quasi-independent test set, larger and more diverse sample sets will be essential to improve the generalizability and practical applicability of the proposed approach.

These findings open the door to the development of portable, rapid LIBS-based tools for analyzing barley and other forage crops in the field. LIBS is already a well-established technique in various industrial sectors, including metallurgy, mining, recycling, and environmental monitoring [72]. It is valued in these sectors for its speed, minimal sample preparation requirements, and ability to detect multiple elements. Continued development of portable and handheld LIBS systems demonstrates the technology’s maturity and suitability for use outside laboratory environments [73,74].

Further miniaturization, enhanced durability, and the integration of automated spectral interpretation algorithms could make such devices accessible to non-experts by providing real-time, actionable information on forage quality. To encourage widespread adoption, future efforts should prioritize developing user-friendly interfaces and embedding robust chemometric models that can translate complex spectral data into easily understandable metrics, such as nutrient concentrations or predicted feed value. This would eliminate the delays and logistical issues associated with centralized laboratory analysis.

This capability would support precision livestock feeding strategies by enabling feed rations to be adjusted according to the actual nutrient composition of crops at different growth stages or under varying environmental conditions. In the longer term, these applications could contribute to improved animal health and productivity, more cost-effective feed management, and increased sustainability in forage-based livestock systems.

Beyond immediate agricultural applications, this work aligns with broader goals of sustainability and climate resilience. Enhancing the nutritional quality of forage is a critical component of efficient and ecoresponsible livestock production. The LIBS-based approach presented here offers a promising path toward data-driven, resource-efficient practices in the agri-food sector, contributing to a more sustainable agricultural future.