Approximation model (IH)

Appearance of the approximation model launching block

Approximation model (IH) block is intended for use within the library Isothermal hydraulics of the set approximation models:

1. Neural networks, which are part of the algorithms of machine learning;

2. Gaussian processes;

3. Linear and nonlinear regression models.

Approximation Models can contain any nonlinear relations between the input parameters of the Model and calculation results that are difficult to describe by a software algorithm and require modern approaches such as neural networks and other machine learning methods.

The block is designed to call (Inference) approximation model and enabl communication with other blocks of library Isothermal hydraulics.

Approximation model (TL) block loads the model from the neutral format ONNX.

Note

The External models library contains the Approximation model block, which is used to call ML models during modeling and exchange data with the Automation library blocks and other blocks containing the port type Automation.

1.  Requirements for an approximation model interacting with Isothermal hydraulics library blocks

Important

The basic requirements for the approximation model are presented in the description of a similar block of the library External models.

1.1.  Requirements for formulating an approximation problem

The approximation model must describe the physical process of fluid motion in the simulated system, expressing the dependence of the mass flow rate \( \dot{\mathbf m_i}\) on the pressures \(\mathbf P_{i}\) (1).

Node must be a component of the approximation model. Each node \(i\) must include a pressure parameter \(\mathbf P_{i}\) and a mass flow rate calculation result \(\dot{\mathbf m_i}\).

(1)\[\dot{\mathbf m_i} = f(\mathbf P_{i})\]

in dependence (1) index \(i\) denotes the serial number of the model node.

The approximation model must contain at least one node with a pressure parameter \(\mathbf P_{1}\) and a calculated mass flow rate \( \dot{\mathbf m_1}\).

Sign convention for flow rate calculations

Positive direction

Positive direction of mass flow is accepted in the approximation model node.

Negative direction

Flow directed from a model node is considered negative.

The diagram below shows two nodes of the approximation model with positive direction of the calculated values ​​of mass flow rates.

Sign rule for calculating mass flow rates for an approximation model with two nodes.

The diagram above uses the following notations.

Designations	Description
Blue circles	Model nodes with pressure parameters \(\mathbf P_{i}\)
Blue vectors	Positive directions of mass expenditures of the \(\dot{\mathbf m_i}\) model

Option for calculating mass flow from one node to another

The approximation model can contain two nodes, calculating one value of the mass flow rate \(\dot{\mathbf m}\), directed from node 1 to node 2 according to the diagram given below.

Calculation of mass flow from node 1 to node 2 of an approximation model with two nodes.

In the case given above, the mass flow rate directed to node 2 is \(\dot{\mathbf m}\), and the mass flow rate of node 1 is taken to be \( - \dot{\mathbf m}\).

Option for calculating mass flow rates in three nodes

The approximation model can contain three or more nodes, calculating the values ​​of mass flow rates \(\dot{\mathbf m_i} = f(\mathbf P_{i})\), in each of the model nodes.

Calculation of mass flow rates in three nodes of the approximation model.

1.2.  Requirements for the parameters of the approximation model

An approximation model that interacts with the blocks of the Isothermal hydraulics library must:

1. The input parameters are the pressure values ​​(P₁,P₂,Pₙ in the figure below) at the nodes of the modeled system element;

2. As a result of the calculation, the model should provide the values ​​of the mass flow rates of the liquid (m₁, m₂, mₙ in the figure below) at each node of the modeled system.

flowchart LR inputs["P₁, P₂, P₃, ... , Pₙ"] model("Approximation model") outputs["m₁, m₂, m₃, ... , mₙ"] inputs --> model --> outputs

Исходные данные и результаты расчёта Аппроксимационной модели (ИГ)

The following notations are used in the figure above.

Designation	Dimension	Description
P₁, … , Pₙ	Pa	Initial values ​​of pressures in the nodes of the approximation model
m₁, … , mₙ	\(kg/s\)	Results of calculation of liquid mass flow rates

The physical quantities of the initial data and the results of the approximation model calculations must be presented in the SI system of units.

2.  Properties

No

3.  Inputs and outputs

Parameters	Input/Output	Description	Units of measurement	Port type
Pressure	Input	The list of input ports is generated based on information about the set of input parameters of the model from the ONNX file	Pa	Isothermal hydraulics
Expenses	Output	The list of output ports is generated based on information about the set of output parameters (calculation results) of the model from the ONNX file	\(kg/s\)	Automation

The block output ports are required to obtain the results of mass flow calculations in the model nodes, as well as to transfer the calculation results to the Outport block.

Important

The Meter block does not support displaying the calculation results of the Approximation model (IH) block.

In order to see the connection capabilities of the block, you need to go to page Description of block ports