Mathematical model for monitoring mycolysis of architectural monuments wooden structures

Research article
DOI:
https://doi.org/10.60797/JAE.2024.46.5
Issue: № 6 (46), 2024
Suggested:
04.05.2024
Accepted:
20.05.2024
Published:
19.06.2024
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Abstract

The article is devoted to the urgent problem of mycological destruction of architectural monuments' wooden structures. The solution of this problem is possible through an automated system of continuous monitoring of mycolysis of architectural monuments wooden structures. In this regard, the purpose of the work is to develop a mathematical model describing the components of the monitoring system and their relations. The article proposes a top-level mathematical model and algorithm of the automated system for monitoring mycolysis of architectural monuments wooden structures, describing the components of the monitoring system and their relations. A set-theoretic approach is used in building the model. The model includes monitoring object, monitoring system infrastructure, initial data and monitoring results, relations between model components. The model allows to develop an effective and reliable system for monitoring mycolysis of architectural monuments wooden structures, allowing to detect the process of mycological destruction at the earliest stage.

1. Introduction

Wood is a valuable, renewable and most affordable building material. Its cost is comparatively lower than other building materials. Therefore, wood has become widespread in the construction of buildings and structures

,
. A significant number of surviving architectural monuments, especially in the north of Russia, are structures made of wood
,
. Wooden structures of architectural monuments in the course of their operation are subject to mycological destruction
,
, leading to partial or complete loss of monuments as objects of cultural heritage. Mycological destruction is a process of degradation of components of lignocarbohydrate complex of wood under the action of enzymes of wood-destroying fungi, leading to the formation of “wood rot” and a decrease in its strength
,
. Preservation and protection of architectural monuments wooden structures from mycological destruction is an actual and rather complicated problem. The solution of this problem is possible through automated continuous monitoring of mycolysis of architectural monuments wooden structures. To develop an effective and reliable monitoring system, it is necessary to build a mathematical model describing its components and their relations, which was the purpose of this work.

To model the automated system for monitoring mycolysis of architectural monuments wooden structures, the theoretical-multiple approach, considered in

,
,
and describing the components of the monitoring system and their relations, was used.

2. Main results and discussion

At the top level, the mathematical model of the automated system for monitoring mycolysis of architectural monuments wooden structures can be described by the tuple:

M = <O, I, D, F>,

where O is the monitoring object;

I is the infrastructure of the monitoring system;

D is the initial data and monitoring results;

F is the relations between the components of the model.

Let us consider the decomposition of the components of the proposed monitoring model.

A monitoring object can be described by a tuple:

O = <OD, ON, OZ, OM>,

where OD is the name and description of the monitored object: architectural monuments wooden structures (log construction, roofs, coverings and finishes, truss structures, etc.

);

ON is the name and description of the monitoring subject: specialists in ensuring the preservation of cultural heritage objects;

OZ is the purpose and objectives of monitoring: earlier identification of areas of architectural monuments wooden structures subject to mycological destruction, through continuous measurement and analysis of values of environmental parameters and wooden structures;

OM is the model of the monitoring object: mycological destruction of wooden structures is a biochemical process of decomposition of the main components of wood by enzymes of wood-destroying fungi, which can be described by the model

: C6H10O5 + 6O2 → 6CO2 + 5H2O. The presented model shows that mycological destruction of wooden structures is accompanied by the release of carbon dioxide and water, therefore, the criteria that can be used to identify areas of wooden structures subject to mycological destruction are changes in the content of carbon dioxide at the surface of wooden structures and their humidity.

The infrastructure of a monitoring system can be described by a tuple:

I = <ID1, ID2, ID3, IS, IR, IT, IP>,

where ID1 is the information source No. 1: sensor measuring carbon dioxide content at the surface of wooden structures;

ID2 is the information source № 2: sensor measuring absolute humidity of wooden structures;

ID3 is the information source No. 3: sensor measuring the carbon dioxide content in the air inside the premises of the architectural monument;

IS is the data storage system: controller equipped with integrated Wi-Fi module and/or 3G (4G) modem (data measured by sensors are accumulated on the controller);

IR is the infrastructure operability: energy resources (power supply of sensors and microcontroller is provided from the stationary electric network or a backup power source – accumulator batteries, which ensures their high operability for different conditions and modes of operation of the monitoring system);

IT is the data transmission system: 3G (4G) cellular network or Wi-Fi local network (data accumulated on the controller are transmitted to the computer (or mobile device) connected to the Internet via 3G (4G) cellular network or Wi-Fi local network after a certain time interval);

IP is the data processing system: computer program algorithm (the data measured by sensors are processed on the controller by a specially developed computer program algorithm: Certificate of state registration of computer program No. RU 2024618307 Program for monitoring the condition of architectural monuments wooden structures and early detection of the process of their mycological destruction, date of registration 03.04.2024).

A sensor for measuring carbon dioxide near the surface of wooden structures can be described by a tuple:

ID1 = <IDD1, IDL1>,

where IDD1 is the description: infrared carbon dioxide sensor (e.g. MH-Z19B);

IDL1 is the localization location:

1) areas of increased wood moisture (basements, attics, areas of possible leaks of atmospheric moisture);

2) areas with traces of activity of wood-destroying fungi;

3) other surfaces. The number of sensors should be at least 5-6 per roof, 2-4 for each floor of the building, and necessarily at least 12 on each group of structural elements.

The description of a sensor for measuring carbon dioxide at the surface of wooden structures can be represented by a tuple:

IDD1 = <IDDM1, IDDC1, IDDE1, IDDT1, IDDU1, IDDO1, IDDS1>,

where IDDM1 is the sensor type, model: infrared carbon dioxide sensor MH-Z19B (detects CO2 level by NDIR non-dispersive infrared radiation principle);

IDDC1 is the sensor settings: operating voltage from 4.5 V to 5.0 V, current consumption < 60 mA (150 mA at peak load), measurement range 0~5000 ppm, measurement accuracy ±50 ppm, operating temperature 0 to 50 °C, humidity 0 to 95%;

IDDE1 is the method of sensor operability support: power supply is realized from stationary electric network through power supply unit or backup power source (accumulator batteries);

IDDT1 is the method of data transmission from the sensor to another subsystem responsible for data processing: data are transmitted to the controller in the form of a digital signal;

IDDU1 is the installation method: the sensor is mounted on the outer surface of architectural monuments wooden structures;

IDDO1 is the data preprocessing method: the sensor consists of an IR radiation source, a measuring chamber where the gas mixture under test is supplied, a wavelength filter and an IR detector. When the gas enters the chamber, certain wavelengths are absorbed in the IR spectrum, filtered out by the filter and the radiation enters the photodetector. Here the light intensity is converted into a proportional signal, which is then pre-amplified;

IDDS1 is the data storage method in case the data are not immediately transferred to other subsystems: the data are immediately transferred to the controller.

A sensor for measuring the absolute moisture content of wooden structures can be described by a tuple:

ID2 = <IDD2, IDL2>,

where IDD2 is the description: electronic absolute humidity sensor (e.g. humidity sensor on LM393 comparator chip);

IDL2 is the localization location:

1) areas of high humidity of wood (basements, attics, areas of possible leaks of atmospheric moisture);

2) areas with traces of activity of wood-destroying fungi;

3) other surfaces. The number of sensors should be at least 5-6 per roof, 2-4 for each floor of the building, and necessarily at least 1-2 on each group of structural elements.

The description of a sensor for measuring the absolute moisture content of wooden structures can be represented by a tuple:

IDD2 = <IDDM2, IDDC2, IDDE2, IDDT2, IDDU2, IDDO2, IDDS2>,

where IDDM2 is the sensor type, model: electronic absolute humidity sensor on LM393 comparator chip;

IDDC2 is the sensor settings: operating voltage from 3.3 V to 5.0 V, current consumption in the mode of no signal 3 mA and in the mode of water signal 6 mA, output type discrete and analog, measurement range 0~100%, measurement accuracy ±1 %, operating temperature from 0 to 70 °С;

IDDE2 is the method of sensor operability support: power supply is realized from stationary electric network through power supply unit or backup power source (accumulator batteries);

IDDT2 is the method of data transmission from the sensor to another subsystem responsible for data processing: data are transmitted to the controller in the form of an analog signal;

IDDU2 is the method of installation: the sensor is mounted inside wooden constructions of architectural monuments at a depth of about 20 mm;

IDDO2 is the data preprocessing method: the sensor has no built-in algorithm for processing the read data;

IDDS2 is the method of data storage in case the data are not immediately transferred to other subsystems: the data are immediately transferred to the controller.

A sensor for measuring carbon dioxide in the air inside a monument room can be described by the tuple:

ID3 = <IDD3, IDL3>,

where IDD3 is the description: infrared carbon dioxide sensor (e.g. MH-Z19B);

IDL3 is the localization location: inside each room of the monument at a distance from the wooden structures.

The description of the sensor for measuring the carbon dioxide content in the indoor air of a monument can be represented by the tuplet:

IDD3 = <IDDM3, IDDC3, IDDE3, IDDT3, IDDU3, IDDO3, IDDS3>.

All components of the IDD3 sensor description fully correspond to the components of the IDD1 sensor description.

The raw data and monitoring results can be described by a tuple:

D = < DI1, DI2, DI3, DO1, DO2, DM1, DM2, DV>,

where DI1 is the data coming from information sources No. 1 (initial data): carbon dioxide content at the surface of wooden structures CO2WS;

DI2 is the data coming from information sources No. 2 (initial data): absolute humidity of wooden structures Wabs;

DI3 is the data coming from information sources No. 3 (baseline data): carbon dioxide content in the air inside the premises of the architectural monument СО2AIR;

DO1 is the data formed on the basis of data coming from information sources No. 1 and 3 (calculated data): signal about exceeding the critical value of relative deviation of carbon dioxide content at the surface of wooden structures over the content of carbon dioxide inside the room of the monument;

DO2 is the data formed on the basis of data coming from information source No. 2 (calculation data): a signal about exceeding the critical value of absolute humidity of wooden structures;

DM1 is the method by which the calculated data DO1 are obtained: comparison of the relative deviation of carbon dioxide content at the surface of wooden structures over the content of carbon dioxide in the air inside the room of the monument ΔCO2 with the critical value ΔCO2CRIT = 26%, at which the process of mycological destruction of wooden structures is identified. The relative deviation of carbon dioxide content at the surface of wooden structures over the content of carbon dioxide inside the room of the architectural monument is calculated by the expression:

ΔCO2 = (CO2WS – CO2AIR) / CO2AIR;

If ΔCO2 > ΔCO2CRIT, then it is concluded that there is a high probability of damage to the area of wooden structures by wood-destroying fungi;

DM2 is the method by which the DO2 calculation data are obtained: comparison of the initial data of absolute moisture content of wooden structures WABS with the critical value of absolute moisture content WABSCRIT = 22%, at which the process of mycological destruction of wooden structures is identified. If WABS > WABSCRIT, the conclusion is made about high probability of wood destruction by wood-destroying fungi;

DV is the ways of presenting the results to the user: text message.

The relationships between the components of the model can be described by a set:

F = {f1, f2, f3, f4, f5},

where DI1 = f1 (ID1) is the input data DI1 comes from sensor ID1: carbon dioxide content at the surface of wooden structures;

DI2 = f2 (ID2) is the input data DI2 comes from sensor ID2: absolute humidity of wooden structures;

DI3 = f3 (ID3) is the the initial data DI3 comes from the sensor ID3: the content of carbon dioxide inside the room of the monument;

DO1 = f4 (DI1, DI2, DM1) is the calculation data DO1, are formed from the initial data DI1 and DI2 using the method DM1;

DO2 = f5 (DI3, DM2) is the calculated data DO2, formed on the basis of the initial data DI3 using the method DM2.

The scheme of the monitoring algorithm is presented in Figure 1.

 Monitoring algorithm scheme

Figure 1 - Monitoring algorithm scheme

3. Conclusion

Within the framework of the conducted modeling, a mathematical model of the automated system for monitoring mycolysis of architectural monuments wooden structures has been built, which describes the components of the monitoring system and their relations quite completely. The model allows to develop an effective and reliable system for monitoring the condition of architectural monuments wooden structures, allowing to detect the process of mycological destruction at the earliest stage. The modeling results are consistent with the results of experimental studies of architectural monuments wooden structures using multisensor systems of automated remote monitoring performed by the author

,
, as well as with the results of other authors
,
.

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