How software-based models increase transparency: Virtual sensors for digital twins

Digital twins are regarded as a key technology for digital production and services, but they are heavily reliant on extensive sensor technology. To ensure they remain affordable and maintainable, physical measurement systems are being supplemented or partially replaced by virtual sensors. This raises fundamental questions regarding the reliability, integration and systematic evaluation of these software-based models.

What is a digital twin?

A digital twin is the digital representation of a physical system. This can be components, industrial plants or entire real-world processes. The aim of a digital twin is to replicate its real-world counterpart as accurately as possible in order to simulate its behaviour and make statements about the state of the system.

The key difference from traditional computer simulations is that the digital twin is in constant contact with the physical world and thus continuously adapts its model of the object or process. This creates a data-driven basis for decision-making. This enables routine tasks, such as maintenance work, to be predicted more accurately. Furthermore, efficiency improvements, energy optimisations for processes or general control adjustments can be simulated, tested and implemented [1].

The basic structure of a digital twin is shown in Figure 1. Physical components continuously supply sensor data to the digital model. This uses the data to simulate the current state of the system and derive optimisations or forecasts from it.

With the increasing digitalisation of industrial and everyday processes, the importance of such digital representations is growing. They create transparency in complex systems and support more precise control of systems such as production and energy systems.

Fig. 1: Structure and application of a digital twin

Why are sensors so crucial?

For a digital twin to function reliably, it requires a continuous supply of up-to-date, high-quality data. Sensors act as the interface between the physical or chemical parameters of the system and a digital model by making these state variables electronically measurable. As system complexity increases, so does the need for measurement points. Modern production, logistics and waste treatment facilities, as well as energy infrastructures, are equipped with extensive sensor networks to continuously monitor operating conditions, environmental conditions and performance parameters.

This development brings with it challenges. Physical sensors incur purchase and installation costs, require maintenance and regular calibration, and are subject to a risk of failure. Furthermore, many relevant state variables cannot be measured directly. Variables such as material fatigue, the remaining service life of components or internal thermal conditions can often only be derived indirectly from other measured variables.

This creates a tension between the need to monitor a system and the economic cost of additional sensor technology. The question therefore arises as to how such data can be obtained without the costs of installation and maintenance rising disproportionately.

The solution from software engineering

Against this backdrop, virtual sensors are gaining in importance. A virtual sensor, also known as a ‘soft sensor’ (from software sensor), is a software-based model that calculates additional state variables from existing sensor data. It combines real measured values with algorithmic models. These models can be created from fundamental physical laws, statistical procedures or machine learning methods [2], [3].

Instead of, for example, installing an additional sensor to determine the wear status of a car tyre, a virtual sensor can derive this status from existing measured variables such as driving speed, duration of use and tyre pressure using a physical model. This increases the information content of a system without installing new hardware.

Figure 2 illustrates this principle. Whilst physical sensors provide directly measurable quantities, virtual sensors can calculate additional state variables from these measurements. This expands the system’s information base without the need to install additional hardware.

Fig. 2: Extension of physical measurement parameters using virtual sensors

This approach can offer significant advantages, particularly in industrial plants and energy systems. In a large photovoltaic plant, for example, it would be technically and economically impractical to equip every single solar module with additional sensors. Virtual sensors nevertheless make it possible to assess the condition of individual components more accurately. By combining irradiance data, ambient temperature and electrical output, it is possible to calculate the energy yield that would be expected under ideal conditions. If the actual output deviates from this, it may indicate soiling or a fault. This provides plant operators with early warnings of problems and enables them to plan maintenance work more effectively. Table 1 shows the key differences between the two approaches. Below, we will present a concrete example of virtual sensors.

Table 1 Comparison of physical vs. virtual sensors

Example from the energy industry

A specific area of application for virtual sensors is the monitoring of photovoltaic power plants. In their report [4] , Redondo et al. describe how a virtual sensor is used to determine the degree of soiling on photovoltaic modules and to derive optimal cleaning times from this.

The accumulation of dust, sand or other particles on solar modules is referred to as soiling. These deposits reduce the amount of radiation reaching the solar cells and thus the electrical power generated. Studies show that this can result in average energy losses of around 3–4%.

The authors calculate that cleaning a reference plant with a capacity of 100 MW costs between 45,000 and 90,000 euros, consuming 250–600 m³ of water and 1,500–2,000 litres of diesel. This clearly demonstrates that the degree of soiling on the modules should be measured as accurately as possible so that the plant remains efficient, but no unnecessary, costly cleaning is carried out.

In large photovoltaic parks, physical soiling sensors are sometimes used. Figure 3 shows a typical soiling sensor for photovoltaic systems. These typically consist of two reference modules, one of which is cleaned regularly. By comparing the output of both modules, the so-called soiling ratio can be determined, which describes the ratio between the current output of a soiled module and the expected output of a clean module.

Fig. 3: Soiling sensor (Source: https://www.sevensensor.com/automatic-soiling-sensor)

However, such sensors are costly, require regular maintenance and provide only spot measurements within a large plant. Furthermore, reference modules must be cleaned manually, resulting in additional maintenance work. To circumvent these limitations, the authors developed a virtual sensor that models the degree of soiling of the modules based on environmental and operational data. The underlying model describes the increase in soiling over time as an exponential function of the time elapsed since the last cleaning:

Here, SL describes the percentage loss of performance due to soiling, t the time elapsed since the last cleaning, and k a constant describing the average dust deposition rate at the respective location.

The virtual sensor utilises various input variables, including:

• Time since the last cleaning of the plant
• Precipitation data for modelling natural cleaning effects
• Dust concentrations in the air
• Local weather conditions

Using this data, the sensor can continuously estimate the degree of soiling and forecast future developments.

Figure 4 shows a comparison between a physical soiling sensor (blue) and the developed virtual sensor (magenta). Both curves follow a very similar trajectory, particularly during dust events. This demonstrates that the virtual sensor can replicate the degree of soiling with a high degree of accuracy.

Fig. 4: Soiling of the photovoltaic system measured using a physical soiling sensor (blue) and the virtual sensor (magenta)

The model was validated using operational data from five photovoltaic parks in Spain with a total capacity of around 200 MW. The average difference between the virtual sensor and the physical soiling sensors was just 0.71%. Interestingly, this error was smaller than the deviation between two physical sensors within the same plant.

This demonstrates that virtual sensors are capable of complementing or partially replacing physical measurement systems whilst offering additional forecasting capabilities.

Upcoming challenges: trust and quality

This example shows that virtual sensors are already capable of providing precise estimates today. At the same time, it highlights a key challenge: the quality of a virtual sensor depends on the quality of the underlying model, whereas physical sensors have clearly defined technical specifications.

A key problem in industrial applications is so-called sensor drift. Physical sensors can gradually lose their calibration over extended periods of operation due to ageing, contamination or thermal stress. This results in measurement errors that are often difficult to detect.

In such cases, virtual sensors can serve as a reference. In gas turbines or chemical plants, for example, temperatures are frequently estimated using model-based virtual sensors. These utilise other process variables such as pressure, flow rate or rotational speed to calculate the expected temperature. If the physical sensor deviates persistently from this model value, this may indicate a drift or a malfunction of the sensor.

For industrial applications, this therefore raises the question of how the quality of such models can be systematically assessed. Typical criteria include, for example, the mean model deviation from reference measurements (e.g. Mean Absolute Error), robustness against measurement noise, or the stability of the model under changing operating conditions. Long-term effects such as model drift also play an important role, as real-world plants can change over time.

A practical aim of our current research is the development of methods for the continuous validation and recalibration of virtual sensors. These include methods for monitoring model errors, adaptive models, or hybrid approaches that combine physical models with data-driven methods.

Only if virtual sensors function transparently, traceably and reliably can they be used as a trustworthy source of information in industrial applications. In combination with physical sensors, they enable more comprehensive monitoring of complex systems, thereby improving the basis for analysis, optimisation and predictive maintenance.

References

[1]    P. D. S. Grösser, ‘Definition: Digital Twin’, https://wirtschaftslexikon.gabler.de/definition/digitaler-zwilling-54371. Accessed: 13 March 2026. [Online]. Available at: https://wirtschaftslexikon.gabler.de/definition/digitaler-zwilling-54371

[2]     P. Kadlec, B. Gabrys, and S. Strandt, ‘Data-driven Soft Sensors in the process industry’, Comput. Chem. Eng., Vol. 33, No. 4, pp. 795–814, Apr. 2009, doi: 10.1016/j.compchemeng.2008.12.012.

[3]   Y. Jiang, S. Yin, J. Dong, and O. Kaynak, ‘A Review on Soft Sensors for Monitoring, Control, and Optimization of Industrial Processes’, IEEE Sens. J., Vol. 21, No. 11, pp. 12868–12881, June 2021, doi: 10.1109/JSEN.2020.3033153.

[4]    M. Redondo, C. A. Platero, A. Moset, F. Rodríguez, and V. Donate, ‘Soiling Modelling in Large Grid-Connected PV Plants for Cleaning Optimisation’, Energies, Vol. 16, No. 2, p. 904, Jan. 2023, doi: 10.3390/en16020904.