“System Identification” is the process of building a mathematical model of a system from experimental data.

    The mathematical model identified from data can then integrated into:
  • VIRTUAL SENSOR: calculate a value that can’t be measured directly with a physical device
  • IMU SENSOR: sensor fusion on the raw measurements for Precise Point Positioning (PPP)
  • FAULT DETECTION and PREDICTIVE MAINTENANCE: early detection of a system failure
  • FORECASTING: estimate a future state of a system (ex. Temperature in a room ) or a product property
  • MODEL-BASED PREDICTIVE CONTROLS (MPC): process optimization by a process simulation
  • QUALITY CONTROL: early detection of the deviation from the normal parameters
  • DECISION MAKING PROCESS MODEL: based on a “What If” simulation

    “System Identification” is the process of building a mathematical model of a dynamical system from experimental data. When the equations that govern the dynamical system are known it is possible to use a mathematical model based on “first principles” (equations), this approach is also known as White Box Modelling. This approach is commonly used for simple systems: the experimental data are used to perform the “parameter estimation”: to find the correct numerical values to make the simulation outcomes coincident with the measured experimental data.

    On the other side, when the equations governing the physical phenomena are partially or completely unknown a Black Box Modelling approach is required: in this case a general mathematical model like a Neural Network (NN), a Recurrent Neural Network (RNN) or a NARMAX is fitted on the experimental data.

    The physical system to be identified is driven by controlled input signals u(t) and uncontrolled disturbances v(t), y(t) are the outputs that can be measured. For example, in the case of an industrial furnace or in the case of a building the input signals u(t) can be represented by energy flows (burners, inductive heating coils) while the disturbances v(t) could be the environmental temperature and the humidity and chemical composition of the process raw material while the output y(t) will be the measured internal temperature.

    We usually adopt a Grey Box Modelling approach that is the combination of the previous two described approaches: in this way we leverage both the Engineering and the Machine Learning / Deep Learning advantages. While the equation-based part of the models are specific for any application, the Machine Learning / Deep Learning algorithms are more general: we describe some of them in the following paragraphs. For what concern the implementation of the algorithms, we rely both on high performance Open Source libraries and on internal specific implementation: as an example we use some publicly available libraries for Ensemble Methods and dimensionality reduction but at the same time we developed our specific proprietary, high performance, distributed implementation for NARMAX and NLARX algorithms.


    A Virtual Sensor is a software algorithm that calculates a value (typically a sensor reading, the property of a product or a system state) that can’t be measured directly with a physical device for many reasons. In the most common situation the physical device is too expensive, unreliable, can’t be installed in the correct position or simply doesn’t exist.

    A Virtual Sensor works by correlating the measurements of the available physical sensors to find the unknown value with the requested precision. It produces both Real-Time or future (predicted) values.


    Many industrial and consumer applications require higher accuracy than traditional GNSS provides, for example mapping, agricultural uses, marine navigation, automated vehicle parking systems and race controls. We develop accurate positioning algorithms that integrate the Precise Point Positioning (PPP) with available informations from accelerometers, gyros and wheel sensors to have a precise positioning even when the GPS signal is not available or unstable.

    This is particularly true for Attitude Heading and Reference Systems better known as AHRS where a 3-axis Inertial Measurement Unit (IMU) is combined with a 3-axis magnetic sensor. The Virtual Sensor can mix the sensor’s readings and provide highly accurate heading (yaw), pitch, and roll angles of an object moving in 3D space.

    The traditional approach relies on a Kalman filter that is used to compute the orientation solution using the six measurements. Those systems are affected by lags in the response because the Kalman filter needs time to update its parameter.

    Our solution, based on a custom neural network, is not affected by lag in the response: check our SideSlip Angle Estimator (SSE) page for additional information.


    The Fault Detection, Identification and Recovery (FDIR), is composed of three main functions: the process of determining that a fault has occurred (detection), the localization of the fault within the system (identification) and the process of enabling the service to be restored to an acceptable state (recovery). The system that implements such capabilities to achieve a low dependency on the presence of certain faults is known as fault tolerant system.

    The Virtual Sensors can be used to enable all the three described processes: a Virtual Sensor is in fact a data-based mathematical model of the system and can be used to check if the system behavior (or the behavior of any of its subsystems) diverges from the response predicted by the Virtual Sensor itself: this implements the Detection and Identification capability. The Sensors Recovery capability is implemented by temporarily use the Virtual Sensors output to provide a virtual reading of the sensor while the sensor itself is replaced.


    Forecasting estimates a future reading, a future system state or product property. In this case the Virtual Sensor is used as a Predictor. Forecasting a value can be used to control a system with a slow response as in thermal systems: a typical application is for industrial application where it is important to maintain stable a temperature, like in case of a melting furnace. Here the response of the material is very slow and a typical control can generate instability.


    These kind of controls are widely used in chemical and petrochemical plants or in other industrial applications where the effects of a variation of an input of the process (production parameters, raw material quality) are seen after a time on the process outputs. MPC uses a mathematical model of the process to simulate and predict the future effects of a certain action: an optimization loop finds the best process parameters by interactively calling the process simulator. This kind of control is computationally intensive so it has been applied just to slow processes so far (typically chemical reactors). Basically MPC has the ability to anticipate future events and can take control actions accordingly, on the contrary, standard PID and LQR controllers do not have this predictive ability.


    Production Quality Control can be reached by the continuous inspection of the production or by the continuous control of the process parameters. Usually both action are performed at the same time.

    To guarantee the maximum achievable quality the controls must be automatized: the Machine Learning and Deep Learning algorithms can be applied both to inspection and parameters controls.

    The most important inspection that can be performed with Deep Learning algorithms is the automatic visual inspection both on camera images or X-Ray images, here the Deep Learning algorithms usually perform much better that the standard vision algorithms based on fixed thresholds.

    For what concern the Process Parameters controls the standard approach is to observe just one parameter at a time. The algorithms based on Machine Learning and Deep Learning technologies instead are based on the concept of a Statistical Fingerprint of the system where multiple parameters are observed at the same time.


    A reliable mathematical model of a complex system is fundamental to optimize the system itself: the mathematical model can simulate the system under different condition and calculate its outputs under thousands of different hypotheses. By simulation it is possible to adjust a complex system with thousands of “virtual” experiments without compromising its safety and without losing production. This approach (the Model-Based Approach) can be applied to business processes as well to create powerful Business Process Model Tools.

Applications by Industry

  • automotive

    Driver Performance metrics

    The Driver Performance system is used to classify the driver’s behaviour. This measure can be used to set the proper driving style on the vehicle controls and to provide to the driver himself informative suggestions on how to improve the driving style to obtain better energy efficiency. The driver model can be used by insurance companies to predict the driver reliability and the risk of accidents or casualties.

  • automotive

    Engine Torque estimation

    There are no available sensors to directly measure the engine torque, the virtual measure is a common approach. The engine torque is a function of the engine speed, throttle, fuel rate, air pressure and temperature. Moreover other variables (like the wheels speed and accelerations) can be used to obtain a more accurate reading by correcting the low-frequency drifts.

  • automotive aerospace

    Force estimation

    A force applied to a system can be estimated both from reverting the dynamic model of the system or from indirect measures like the current requested by an electric driver. Most of the time the system is characterized by unknown energy dissipations and variable kinematics, this makes the problem highly nonlinear, in these conditions the data driven approach based on neural networks shows its superiority with respect to traditional methods

  • automotive aerospace

    Pressure estimation

    The local pressure in a given point of an hydraulic system is usually a nonlinear function of many parameters like fluid speed and temperature. Usually other phenomena like fluid aging, particle inclusions and fluid line deposits. A direct data modeling with neural networks and other machine learning algorithms is essential to take in consideration all those effects that cannot be modeled with an equation-based approach.

  • automotive consumer

    Batteries State of Charge (SOC), State of Health (SOH), Core Temperature

    Accurate estimation of SOC and SOH cannot only protect battery, prevent overcharge or discharge, and improve the battery life, but also let the system make rationally control strategies to save energy and improve the user experience. A battery is a chemical energy storage source, and the chemical parameters cannot be directly accessed. This is a typical task that can be tackled with nonparametric data models and in particular with our proprietary implementation of Nonlinear Set Membership Algorithms.

  • industry

    Ledge tickness in mettalurgic reactors

    This is usually a difficult task because the thermal contact resistance of the metallurgical reactor wall is poorly known. This is an important parameter to define a standard equation-based model of the metallurgical process. Here the black box recurrent neural network (RNN) models will outperform the standard equation based modeling or the kalman filtering approach.

  • industry

    Thermal dimensional deformation and stress

    Machining devices and tools and measuring equipment are affected by thermal deformation. This effects both the machining precision as well as the control systems of the machine. Sometimes it is not trivial to determine with good precision the deformation due to variable kinematics and uneven temperature distribution in the machinery. Our nonlinear data driven approach based on Neural Networks can give good results. Usually in this case we proceed with a preliminary study to determine which algorithms are more suitable for the specific application.

  • smart-buildings industry energy

    Energy use in building and industrial sites

    Dynamic analysis of energy data can help improve the efficiency of buildings in several ways: evaluation of proposed modifications of a building or its operation (e.g. dynamic thermostats set-points); verification of performance on the basis of short-term measurements (corrected for weather); diagnostics and optimal control of HVAC equipment. To do this kind of analysis we need an accurate thermal model of the building: this is a typical inverse problem: given actual performance data for a building, how is it possible to create an accurate mathematical model? Our methods are based on NARMAX algorithms (Nonlinear Autoregressive Moving Average with eXogenous inputs). The time-series analysis based on the NARMAX technique has an advantage over the traditional spectral method in that the latter can lead to the over-parameterization of the accompanying model. We developed a proprietary distributed implementation for NARMAX training associated with advanced pre-selection algorithms. This technology gives us a fundamental advantage over existing systems allowing us to explore feasible solutions and produce proper identified system models much faster that what the existing commercial software allow.

  • environmental

    Monitor smart irrigation, fertilization, livestock

  • automotive industry energy

    Virtual Flow Metering

    This kind of Virtual Sensor is largely applied in different fields. In automotive. Air Mass Meters are used for for determining the air aspirated by the internal combustion engine. In the Oil & Gas companies the Multiphase Flow Meters are expensive and difficult to install and maintain. In this case the Virtual flow Meters can be used both to continuously check the health status of the physical devices or to replace or integrate the physical sensors in flow assurance applications. In buildings and industrial plants the Virtual Flow meters are used to estimate the coolant flow in HVAC systems, ventilation airflow and compressed air leakages. We provide reliable algorithms for Virtual Flow Metering based on Ensembles of NARMAX models and Deep Neural Networks.

  • automotive energy

    Viscosity virtual sensor

    Thermo electrical power plants burn oil to produce electrical energy. One of the most important properties to consider to optimize the combustion is the oil viscosity: it determines the atomization effect in the oil drop size. The oil viscosity can be measured in laboratory tests but the physical (hardware) viscosity meters available to be installed on the plants are expensive and in some conditions unreliable. In internal combustion engines the oil viscosity is essential to determine the lubricating property of the fuel. In this case the oil viscosity changes due to the fluid aging (that change its chemical-physical characteristics) and because the fluid dilution with fuel and water inclusion. These effects are not predictable a-priori because depend on the engine working conditions and on the engine wearing conditions.

  • pharma

    Pharmaceutical Process Control

    In order to control quality and process variables the process conditions just be continuously measured. In theory, conventional hardware can provide this information, but existing sensors cannot measure some types of data in Real Time. Most drug makers today still rely on off-line quality testing in the laboratory, leading to delays and high cycle times. Virtual sensors allow drug makers to manage and control all critical sources of process and product variability. Virtual sensors estimate the value of primary variables that are impractical, or impossible, to measure online, such as particle size distribution, melt-flow index or chemical composition. The Virtual Sensor uses available Real Time data, to derive these values that can be used to implement an effective process control.

  • automotive

    Forecast (Nowcasting) Driver Torque Request

    One of the energy saving techniques on modern automotive engines is the cylinder deactivation: it is used to reduce the fuel consumption and emissions during light-load operation. Cylinder deactivation is achieved by keeping the intake and exhaust valves closed for a particular cylinder. By keeping the intake and exhaust valves closed, it creates an «air spring» in the combustion chamber. The transition between normal engine operation, cylinder deactivation and back is energy inefficient so, basically it is convenient to proceed with cylinder deactivation just when that condition will be maintained for more than five seconds. Our algorithms based on Ensemble Methods and Deep Autoencoders can provide a good torque request nowcasting by creating a driver’s statistical model that take in consideration driving style, road and traffic conditions.

  • automotive industry

    Electric Load Forecasting

    It is vitally important in many industrial and automotive applications for different reasons. In automotive applications the electric load forecasting is primarily devoted to optimize the overall vehicle energy management: vehicles are characterized by an electric storage capacity that increases on the new models, start and stop, hybrid solutions require bigger accumulators but also better power management. On the other side, the energy distribution geographical systems and the industrial applications are characterized by limited storage capability: since there is no “inventory” or “buffer” from generation to end users (customers), ideally, power systems have to be built to meet the maximum demand, the so called peak load. Under those assumptions is important to have state of the art statistical algorithms that can calculate the demand probability to drive the system control strategies.

  • environmental

    Marine wave nowcasting

    Wind and wave forecasting is a key aspect to support operations in the Offshore Oil & Gas development. Very short term prediction of waves at the vessel location is fundamental to improve the safety of critical marine operations, such as heavy lifting and subsea installations. In particular we developed a reliable wave nowcasting algorithm for station keeping by Dynamic Positioning (DP) during pipeline installation.

  • environmental

    River Flood forecasting

    Flood forecasting and an early warning system is an important tool to give appropriate reliable information of the incoming flood to the community. Traditional statistical methods and deterministic type models (Local Approximation) are common methods adopted for this kind of task. We can provide an alternative NARMAX and RNN (Recurrent Neural Network approach) to integrate the existing models.

  • pharma industry energy

    Model-Based Predictive Controls

    What’s unique about this approach is its continuous ability to learn. The algorithms can be fed into companies’ existing control systems to automate processes that previously required manual adjustment. Instead of reacting to problems, users can anticipate them and optimize accordingly.

  • smart-buildings

    Smart Conditioning

    Smart thermostats to control temperature based on weather forecasts, calendar, human presence sensors, price of heating, temperature sensors and sunlight sensors, in house daily activity. Using just the temperature reading of thermometers inside and outside the building create a thermodynamical model to predict the future temperature and then adjust the controlled heaters and HVAC systems to have the right perceived temperature at the time you need it.