Cross-Layer Reliability Analysis and Edge-Adaptive Multi-Objective Optimization Strategies for Network-Physical Modeling in Intelligent Agriculture CPS Management

Summary

This protocol presents a cross-layer cyber-physical modeling and optimization strategy for intelligent greenhouse management, enabling reproducible assessment of reliability and ecological performance.

Abstract

Growing food demand and climate stresses drive smart agriculture implementation, but existing Cyber-Physical Systems (CPS) lack dependable cross-layer integration and real-time flexibility, limiting performance in dynamic environments. This protocol aims to provide a cross-layer cyber-physical modeling and optimization strategy for intelligent greenhouse agriculture. It demonstrates potential applicability for enhancing the reliability and adaptability of agricultural Cyber-Physical Systems. The approach integrates a physical layer with the Soil-Plant-Atmosphere Continuum model and Ensemble Kalman Filter (EnKF) calibration for accurate soil moisture prediction. It includes a network layer employing multi-protocol fusion with Stochastic Petri Net modeling to evaluate communication reliability. A control layer builds on a stochastic hybrid system to coordinate joint decision-making. Reliability is further assessed through a functional-temporal-ecological indicator framework, while optimization combines multi-objective reinforcement learning with safety constraints and Bayesian meta-learning to enable rapid adaptation during crop switching. An edge-intelligent deployment ensures robust control during communication interruptions. Results from greenhouse tomato cultivation in Shouguang, China, show reproducible and stable performance in yield prediction, water use efficiency, and control latency under challenging conditions. This methodology provides a practical and replicable workflow for implementing adaptive and reliable agricultural Cyber-Physical Systems.

Introduction

The world population is growing rapidly, and resource availability is declining, which is transforming the way agriculture is developed. The conventional models of agriculture, where labor and material input are high, and the reliance on the natural circumstances is strong, cannot offer efficiency and sustainability. Smart agriculture has, in this case, become the transformative approach. It allows achieving a complete field perception, making accurate decisions, and controlling the field intelligently through the combination of the Internet of Things, big data analytics, artificial intelligence, and spatial information systems, which enhances the efficiency of the use of resources and contributes to sustainable agricultural production^1,2.

The smart agriculture market is growing exponentially across the world, and the U.S. is growing in the technologies of precision agriculture, Israel in water-saving irrigation, and Japan in the sphere of smart greenhouse systems³. In China, the national agricultural and rural informatization development 14^th five-year plan has led to the digital transformation of agriculture, which has resulted in advances in digital breeding, intelligent machinery, and scale-based smart agriculture projects⁴. Internet of Things (IoT) refers to a network of connected actuating and sensing devices that collect, exchange, and process data. However, even with these developments, there are still problems with the coverage of the IoT networks, sensor precision and dependability, information exchange among systems, and access to interdisciplinary understanding that limit extensive implementation^5,6.

The Cyber-Physical Systems (CPS) of agriculture are at the center of this landscape in connecting the perception of the environment to intelligent control⁷. CPS combined both computational and physical processes that are connected with sensors, controllers, and communication networks. Nevertheless, existing modeling methods are usually based on the independence of the physical, network, and control layers, restricting the interaction of layers and decreasing the predictive ability during dynamic disturbances⁸. Existing reliability assessments also emphasize functional and temporal dimensions, while ecological reliability, such as water use efficiency and soil salinity constraints-remains underexplored⁹. Moreover, many optimization strategies rely on offline training, leading to delays in edge-based inference and difficulties in adapting to rapid environmental or crop changes¹⁰.

Sensor-based greenhouse monitoring is gaining popularity, but is still facing numerous hindrances preventing greater acceptance. System scalability and reliability are limited by high deployment costs and uneven sensor quality. The modeling methods used in sensor-based greenhouse monitoring are based on the premise of stable environmental conditions, consistent growth patterns of crops, and reliable transmission of information through communication networks. However, these assumptions are not valid under many conditions that occur inside greenhouses. These limitations indicate that there is a requirement to design and implement a framework capable of dealing with non-constant noisy readings from sensors, fluctuations in sensor power supply during the course of use, and periods of communication loss without compromising performance quality or implementation feasibility.

To address these limitations, this protocol introduces a reproducible cross-layer modeling and optimization workflow that integrates physical, network, and control processes into a unified framework. The physical layer employs a Soil-Plant-Atmosphere Continuum model with Ensemble Kalman Filter calibration for accurate soil moisture prediction¹¹. The network layer uses multi-protocol fusion using a Stochastic Petri Net model to measure the reliability of communication. On the control level, a stochastic hybrid system allows joint cross-layer decision-making. Functional-temporal-ecological index system is used to measure reliability, multi-objective deep reinforcement learning is used to optimize that system, with safety constraints and Bayesian meta-learning, which is used to quickly adapt to crop switching. An edge-intelligent deployment also provides system robustness to system interruptions during communication. Combining these elements, the protocol offers a systematic and replicable way of improving the stability and flexibility of CPS applications in smart farming¹².

This protocol is suitable for medium- to large-scale greenhouse environments (800-1500 m²) with diverse wireless sensor networks for soil, microclimate, and CO₂ monitoring. To provide real-time control, a minimum sample resolution of 5 min is recommended, with LoRa/NB-IoT communication necessary for multi-node deployment (>200 nodes). The workflow is demonstrated for greenhouse tomato production, but it can be applied to crops like cucumber, pepper, and leafy vegetables through parameter retuning and meta-learning transfer.

The protocol is based on a sequential working cycle where physical modeling determines the soil moisture, the network layer determines data transmission stability, and the control + optimization layers produce irrigation and fertilization policies which provide ecological and operational stability. Figure 1 depicts the proposed cyber-physical system cross-layer workflow.

Protocol

It is noted that no experiments on human beings or vertebrate animals are involved in this protocol. In case of any future studies that will involve human involvement or biological samples, this has to be approved by the concerned institutional review board, and the approval number must be recorded prior to implementation.

1. Site and hardware preparation

NOTE: This step builds a standardized sensor network, which gives precise and synchronized information about the environment to be used in subsequent physical modeling and control.

1. Establish the location of the greenhouse by inputting the GPS coordinates in the monitoring software. Select the crop species from the crop library provided and establish the environmental goals (temperature: 20-28 °C, relative humidity: 50%-70%).
2. Record greenhouse dimensions, ventilation systems, and shading configuration.
3. Synchronize all devices to a unified clock using the Network Time Protocol (NTP)¹³.
4. Install soil moisture, temperature, humidity, light, and CO₂ sensors according to manufacturer specifications.
   1. Install 60 wireless soil moisture and temperature sensors (accuracy ±2%), 10 humidity and CO₂ sensors (± 30 ppm CO₂ accuracy), and 4 multispectral light sensors. Use a grid spacing of 6 m x 5 m to position soil sensors at depths of 10, 20, and 30 cm. Depending on their function, all sensors use LoRa transceivers and NB-IoT modules for wireless communication. Synchronize the gateway and meteorological sensors using NTP to achieve ±1 s timestamp accuracy.
5. Install the fixed sensors at the given depths and positions to make sure that the measurement is correct.
6. Set the data sampling rate to 5 mph and turn on the alignment of timestamps at the gateway.
7. Register all sensor nodes with unique IDs and check gateway connectivity. Conduct a 24-hour test run to evaluate packet loss and clock drift.
8. Keep the baseline log to make use of it in the future. Table 1 represents the configuration and parameter settings for the modeling steps.

2. Physical layer modeling (Soil - Plant - Atmosphere Continuum (SPAC) and Ensemble Kalman Filter (EnKF))

NOTE: This phase approximates the soil, plant, and atmospheric interactions to produce correct estimates of soil moisture that are used to control irrigation.

1. Ready input data in the SPAC model because it requires the following: the soil texture, field capacity, root distribution, meteorological drivers, and the canopy leaf area index.
2. All input datasets were resampled to a uniform 5-minute time index in Python 3.10 using the Pandas resample('5min').mean() function. Missing values were imputed using SciPy's CubicSpline, while gaps >5 minutes were reconstructed by propagating SPAC model forecasts through the EnKF prediction phase. Uncertainty flags were preserved for reliability analysis.
   1. Fill missing values using cubic spline interpolation¹⁴. Reconstruct longer gaps (> 5 min) using the EnKF prediction phase based on soil moisture and meteorological forecast. Mark all the reconstructed values for uncertainty tracking.
3. Establish the Richards equation for modeling unsaturated water flow.
    
   Where  is the rate of change of volumetric water content θ (m³) with respect to time t, h is the pressure head (cm), and K(θ) is hydraulic conductivity. The operator ∇ indicates the spatial gradient, and the expression (∇h+1) represents the total hydraulic gradient.
4. Estimate soil hydraulic parameters using the van Genuchten model:
   
   Where K_s the saturated hydraulic conductivity, S_e (θ-θ_r )/(θ_s -θ_r) is the effective saturation with θ_s and θ_x the saturated and residual water contents. l is the pore-connectivity parameter, m and n and are shape parameters related by ( with n>1). denotes the effective saturation increased to the pore-connectivity parameter l. Based on effective saturation S_e, the van Genuchten hydraulic function term  describes non-linear soil water retention behaviorand shape parameter m.
5. Couple the Richards equation with the Farquhar photosynthesis model. Integrate the Penman-Monteith transpiration model to account for the effects of light, temperature, and CO₂.
6. Initialize parameter priors and state vectors for EnKF.
   NOTE: The EnKF is a Monte Carlo data assimilation method that updates soil moisture state estimations by integrating model predictions with real-time observations from sensors and statistically estimating error covariance¹⁵.
7. Run EnKF prediction-update cycles until the root-mean-square error (RMSE) of soil moisture predictions falls below 2%, or a maximum of 50 iterations is reached.
8. Archive all calibrated parameters for subsequent analysis. Figure 2 depicts the soil moisture stabilization curve produced after SPAC-EnKF calibration.
9. Execute the numerical simulation procedure for SPAC-EnKF. Use MATLAB R2023b to compute SPAC-EnKF. Set the time step Δt = 300 s, ensemble size N = 100, and state variables θ, h, and K(θ) to their initial values. Use the Richards equation solver to carry out the forecast phase and use observational soil moisture data for the update phase. Until the convergence threshold of RMSE < 2% is reached, repeat prediction-update cycles.

3. Network layer modeling (Heterogeneous Network and Stochastic Petri Net (SPN))

NOTE: This section assesses communication dependability to enable timely and continuous data delivery for control decisions.

1. Deploy heterogeneous communication modules, including LoRa for long-range meteorological data, NB-IoT for soil sensors, and 5G for high-frequency phenotyping cameras.
   1. Allocate long-range low-bandwidth meteorological data (wind, radiation, rainfall) to LoRa modules. Enable NB-IoT modules for soil sensor nodes requiring moderate bandwidth and low power operation. Enable high-frequency phenotyping camera data using 5G NR modules for high-speed video transfer. Attach a Raspberry Pi-based edge gateway supporting multi-protocol management to each communication node.
2. Configure the system to support over 200 nodes per gateway with a 5 min sampling frequency.
3. Continuously record Received Signal Strength Indicator (RSSI), Signal-to-Noise Ratio (SNR), and battery status. Compute packet reception rates at 5 min intervals.
4. If abnormal reception is detected, inspect antenna alignment and check for potential interference sources. Define and solve the Stochastic Petri Net (SPN) communication reliability model
   1. Implement SPN using Mobius 2.0. Define three places: Normal (>95% reception), Delay (80-95%), and Interrupt (<80%). Configure transition rates λ_nd, λ_di, and λ_in as functions of SNR and remaining battery energy:
      
   2. Compute the steady-state distribution using the linear balance equation πQ = 0 to obtain the communication interruption probability P_int = π_interrupt.
5. Define a SPN model with three communication states: N normal (>95% reception), delay D (80-95%), and interrupt I (<80%). Q signifies the generating matrix of the continuous-time Markov chain.
   
   The state transitions are governed by rate parameters λ_X→Y, where X,Y∈ {N,D,I}. To ensure that every row of Q sums to zero, each diagonal element is the negative sum of the outgoing transition rates from that state.
6. Estimate transition rates based on SNR and remaining energy metrics using.
   
   Where E is the normalized residual energy (0-1), and SNR is the observed signal-to-noise ratio in decibels. k_XY is a scaling constant for the transition rate between state X to state Y, while k_s regulates the steepness of the SNR-dependent response. The SNR threshold for transition X→Y is SNR_XY. Low battery levels enhance the possibility of a transition, as captured by c_XY and p_XY.  ∈_XY is a small baseline rate ensuring non-zero likelihood of transitions. The logistic function regulating SNR sensitivity is
   
   Where  σ(u) denotes the logistic sigmoid function, and the exponential term e^-u controls the rate at which the function transitions between 0 and 1.
7. Solve the steady-state distribution to obtain the interruption probability. Define α = λ_N→D, β = λ_N→I, γ = λ_D→N, δ = λ_D→I, ε = λ_I→N, ζ = λ_I→D. The steady-state interruption probability is:
   
   where π_I shows the long-term (steady-state) probability that the system will stay in the interrupted condition. The six transition rates between the three states are represented by the parameters α, β, γ, δ, ε, and ζ. The denominator shows the overall flow balance across all transitions, whereas the numerator compiles all efficient transition pathways leading to the Interrupt state. The stationary chance of communication interruption under the specified rate structure is provided by the resultant value. Table 2 depicts the procedural data-flow transitions between modeling layers in the proposed CPS. 

4. Control layer modeling (MPC within SHS)

NOTE: This process maximizes the alternative of irrigation and fertilizing, as well as accommodating issues of communication.

1. Build a Model Predictive Control (MPC) system, with a goal to optimize the yield of crops at the end of 24 h. Execute Model Predictive Control (MPC)-based irrigation scheduling. Implement MPC in Python 3.10 / CasADi library. Define prediction horizon Hp = 24 steps, control horizon Hc = 6, and control input u(t) (irrigation flux). Optimize cost function:
   J = Σ (θ_target − θ(t))² + λu(t)²,
   using IPOPT solver with constraint bounds 0 ≤ u(t) ≤ 6 mm/h.
2. Define the variables of decision regarding the irrigation and fertilizing processes.
3. Use restraints on the moisture range of soil, root zone conductivity, and control latency.
4. Add network interruption probabilities to the MPC solver as time uncertain.
5. Use the soft constraint in the costing function using weights. Q (input)= 0.5-1.0; Q (output)= 0.3-0.7. Tune weights depending on the preliminary tests in tuning so that the predictive stability of MPC can be guaranteed.
6. When the occurrence of packet loss happens, forecast 1 h soil moisture with the SPAC model and calculate compensation irrigation.
7. Synchronize the control state immediately after communication recovery to avoid duplicated actions.
8. Combine a continuous physical system, a discrete network system, and control actions into a Stochastic Hybrid System (SHS) transition model.

5. Reliability quantification

NOTE: To evaluate the robustness of the systems in response to disturbances, this part evaluates both functional, temporal, and ecological dependability.

1. Three reliability indicators were used: (1) functional reliability quantified by yield prediction error (E_γ, %) and soil-moisture estimation RMSE; (2) temporal reliability measured by end-to-end control latency (L_e₋_e, s); and (3) ecological reliability assessed using water-use efficiency (WUE, g·kg⁻¹) and the proportion of time root-zone electrical conductivity exceeded the safety threshold (T_ec>2.5dS/m, %).
2. Build a stochastic game model, where three agents are involved: sensor (minimizing the probability of failure), attacker (maximizing the possibility of failure), and environment (adding random disturbances) to the model.
3. Define payoff functions and solve Nash equilibria to identify reliability boundaries. Perform a global sensitivity analysis using Sobol indices to rank parameter contributions¹⁶.
4. Parameter contribution was quantified using the mean of absolute elementary effects (EE, Morris sensitivity index), computed from perturbed sampling trajectories, and assessed jointly with the variance of EE to capture interaction strength and nonlinearity; parameters with the highest mean|EE| and elevated EE variance were identified as dominant contributors and selected for subsequent optimization.

6. Optimization strategy

NOTE: This part maximizes control decisions to achieve optimal productivity, cost, and ecological stability, and still, rapid adaptability when changing crops.

1. Specify the state space, which includes leaf area index, SPAC–EnKF–estimated soil moisture, and control delay recorded at the edge controller.
2. Establish the action space by defining irrigation amount, fertilization rate, and sensor sampling frequency as discrete and bounded control actions implemented at the edge controller.
3. Build a multi-objective rewarding function by integrating reliability, economic cost, and environmental performance through weighted optimization.
4. Observe Pareto-optimal policies using the NSGA-III algorithm (Table 3).
5. Provide safety limitations with control barrier functions (CBFs) by enforcing lower bounds on root-zone soil moisture and upper bounds on soil salinity to prevent drought and salt stress.
6. Provide a Lyapunov stability condition by defining a positive definite Lyapunov function on the growth state vector and enforcing its time derivative to be negative definite within the safe operating bounds.
7. Use the Bayesian meta-learning to allow the fast update of parameters in case of switching crops.
   NOTE: After this step, the workflow can be paused to validate model updates offline. Resume by reloading the latest checkpoint.
8. Adapt to the latest 7 days and have retraining time of less than 5 min. Train a compressed reinforcement model by applying pruning and post-training quantization, then fine-tune it on the edge device using locally collected interaction data.
9. Use the downgrade mechanism whenever there are communication hiccups in order to ensure that the control latency remains below 30 s. Synchronize the resume clouds with communication recovery.

Results

Soil moisture and SNR have the greatest positive SHapley Additive exPlanations (SHAP) influence on irrigation decisions, according to the SHAP summary plot (Figure 3). High latency drives the policy toward conservative fallback options, demonstrating conformity with the reliability-aware control architecture. Table 4 depicts operational instructions and configuration details for computational modules

Experimental setup

Discussion

The experimental evidence shows that the proposed CPS framework and optimization strategies excel across the three dimensions of reliability, safety, and computational efficiency. Cross-layer coupling modeling successfully overcomes the historical separation between physical and network representations. By embedding SPAC and SPN within a unified SHS framework, the system reduced yield prediction error by 32.7% and shortened delays by 45% under extreme high temperatures. Safety constraints ensured that ecological performa...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Multispectral Camera	MicaSense	RedEdge-MX	Captures canopy reflectance for LAI estimation
NVIDIA Jetson Nano	NVIDIA	945-13450-0000-100	Edge device for local AI inference
Soil Moisture Sensor	Decagon Devices	EC-5	Measures volumetric water content in soil
Weather Station	Campbell Scientific	CR300	Records temperature, humidity, and rainfall