Planning and Repairing Bridges with Robotic and Automation Technology

Abstract

Today, the maintenance of valuable buildings is carried out continuously and with the help of automated technologies that aim to streamline project activities. The technological innovations are the new machine-robots of Conject technology, and the organisational innovations are the new iterative formula equations of procedures. Thus, the method of dynamic structural programming (DSP) with vectorial methods of norms (VN) and a modified Gaussian S-curve (MGSC) ensures investment planning with modern scientific procedures. In other words, the above automation processes are a development of the rationality of society and provide opportunities for further scientific research in the field of AI systems depending on the wave frequency of their construction.

1. Introduction

Planning is an organisational and managerial function that is essential for the realisation or maintenance of a given project. It enables the optimal and cyclical planning of project activities and the allocation of all resources with the possibility of controlling and regulating the system of project implementation. In practise, this function is often vague and imprecise due to outdated standards. For example, the maintenance of bridges [1] or valuable buildings, for example, is still continuously carried out with new automated robotics, internet communication technology (ICT) and integrated information technology (IIT). That is, digitalised communication with modern management is supported by the IIT management system, but the construction industry systems do not show significant improvements in the economic principles for certain projects. For the sustainability of the transport infrastructure system, it is necessary to respond to the automation of technology with the automation of logistics, that is, with the management of contractor systems in the whole enterprise. The softwareisation of existing organisational and management processes has a problem with static and outdated normative data for the execution of certain activities in the construction process, and the new ICT and IIT technologies do not have a greater impact on the rationalisation of large infrastructure projects. Therefore, it is necessary to replace the old organisation with innovations in organisational management that are translated into new formulas and procedural equations, as technology has done with vector systems for design, dimensioning and robotic execution with cyclic iterative processes. Vector and iterative methods are thus proposed to round off the investment using scientific procedures that should help improve economic indicators not only for the company but also for the state institutions. Looking at the problem of maintenance or reconstruction of buildings from a layman’s point of view, the statement that it is cheaper to build a new building than to repair an old one is true. It would be the same for bridges, but bridges are valuable objects of cultural heritage and represent the tourist potential of any place. Therefore, the continuous replacement of quickly worn-out structural elements prevents the deterioration of the main structural elements, reducing the essential costs and significantly extending the useful life and profitability of the investment. Every realisation is a production. It is a function of technology, organisation, management and ICT. The technology uses differential equations, while the other components run behind the mathematical modelling of these processes. Therefore, software models and simulations such as BIM and Digital Twins appear today as tools that seek to supplement the lack of decision-making in processes. Thus, the need for vector [2] or parametric [3] modelling and the transformation of POG and PMD documentation into scientific documentation emerges. However, today’s ICT digital technology also provides automation of the work, for which the GPS technology was developed, which converts manual collection into automatic data collection in the field and automatically sends it to central data processing in the company’s IIS system. However, the key to solving the problem lies not only in automating existing administration but also in standardising new models, construction standards and cost items. This is how the method dynamic structural programming (DSP) or iterative double COD, which creates the iterative differential of cyclical production processes, came into being. Here, mathematical and cybernetic methods are used to transform organisational structures into differential organisational structures as the main components of the AI system. The purpose of automation is softwareisation, that is, the model standardisation of production processes using mathematical and statistical methods to replace routine and dangerous operations with robots. The goal is to establish new vector norms with statistical modelling of modern project planning and control and process automation for all routines, especially dangerous work, to free people from hard and dangerous work. This leads to model standardisation and normalisation of construction activities and at the same time of all economic activities.

2. Conject robot technology of hydrodemoling

Bridge rehabilitation works in the Republic of Croatia are carried out using today’s most advanced technology. Modern hydrodemolition technology with Conjet robots and high-pressure hydro pumps in Figure 1 accelerates the investment cycle in the sustainable development of construction and socio-economic livelihood cycles.

Figure 1.

Hydrodemolition of bridge deck with Conjet robots.

Svedise Innovation Technology’s Conjet [4] concrete hydrodemolition robots use a high-pressure water jet of up to 1500 bar (22,000 psi) that travels at a constant speed over the concrete surface, taking advantage of the concrete’s permeability to create positive pressure that breaks it up. The automation of the hydrodemolition robots allows operators to easily perform both selective and non-selective removal. Automated Concrete Removal (ACR™) is a concrete removal method that uses robotic technology to remove concrete from structures such as bridges, parking decks, dams and tunnels using high pressure water (hydrodemolition). The hydrodemolition technology ensures that no micro-cracks occur during concrete removal and provides an ideal surface for the bonding of new concrete, while the robot ensures the quality and consistency of the concrete removal. The Conjet ACR™ robot removes the same amount of concrete as 20–25 workers with jackhammers. Even better, the ACR™ robot significantly reduces the noise of concrete demolition. Djelovanje mlaza na konstruktivne elemnte stavara prostorne sile koje se trigonometrijom proraunavaju u vektorskom prostornom i frekvencijskom polju. The Conjet robot with a pump over 1000 bar or > 100 N/mm² and a remote-controlled programme automatically hydrodemolishes concrete, which is usually designed for strength C 30/37 or 30 N/mm². The generation of pressure by the pump three and more times than necessary to destroy the concrete is demonstrated in Figure 2.

Figure 2.

Schematic representation of the effect of pressures and frequencies [5, 6].

3. Vectoral norms or effects

The methods of technical standardisation [7] and measurement of time consumption are the methods of timekeeping, photo-inspection, recording, ongoing observations and technical records. Using the method of the work diary, that is, technical records, the statistical distribution curve of the effect of the robot in Figure 3 was determined from the analytical data Table 1 by observing and recording the process of hydrodemolition at the bridge in Zagreb over the Sava.

Figure 3.

Discrete frequency of the effect partial and cumulative by effect from monitoring the variables of Conject robots 364 operations at level 5/7.

datum	RN	pumpa	robot	strojar 1	strojar 2	operacija	smjena	dubina	širina	duljina	m+	efektivni radni sati	norma sati
28.11.2007	111.752	364	364	Kovačić.Z	Ivšić	staza	2	0.2	0.3	35.7	2.14	11	0.19
17.11.2007	111.752	364	364	Šobak	Osti	popravci	1	0.06	2	10	1.20	11	0.11
27.11.2007	111.752	364	364	Glavica	Butorac	popravci	1	0.06	2	26	3.12	7	0.45
12.11.2007	111.752	364	364	Damjanović	Drljan	ploča 5/7	2	0.06	2	24	2.88	3	0.96
13.11.2007	111.752	364	364	Palijan	Butorac	ploča 5/7	1	0.06	2	55	6.60	11	0.60
13.11.2007	111.752	364	364	Damjanović	Drljan	ploča 5/7	2	0.06	2	53	6.36	11	0.58
14.11.2007	111.752	364	364	Palijan	Butorac	ploča 5/7	1	0.06	2	55	6.60	11	0.60
14.11.2007	111.752	364	364	Miličević	Krivokuča	ploča 5/7	2	0.06	2	51	6.12	11	0.56
15.11.2007	111.752	364	364	Palijan	Butorac	ploča 5/7	1	0.06	2	66	7.92	11	0.72
15.11.2007	111.752	364	364	Miličević	Krivokuča	ploča 5/7	2	0.06	2	60	7.20	12	0.60
16.11.2007	111.752	364	364	Palijan	Butorac	ploča 5/7	1	0.06	2	55	6.60	11	0.60
16.11.2007	111.752	364	364	Miličević	Krivokuča	ploča 5/7	2	0.06	2	34	4.08	10	0.41
17.11.2007	111.752	364	364	Miličević	Krivokuča	ploča 5/7	2	0.06	2	50	6.00	10	0.60
18.11.2007	111.752	364	364	Butorac	Osti	ploča 5/7	1	0.06	2	48	5.76	11	0.52

Table 1.

Schedule of work of machinists on robots and pumps for water demolition.

These measurements were transformed into a discrete function, which is approximately replaced by the exponential Weibull distribution derived from the Erlang distribution [8], which is typical for work and service activities. The given discrete plotted example was transformed into a function of the event frequency density of the robot work effect so that the effect and the norm, that is, the expected duration of the process, are determined.

In column Table 2, P(x), that is, the probability of occurrence of the robot’s effect frequency, was defined to determine the mathematical expectation of the statistical effect variable for a given robot 364 activity. It follows that E(x) (Eq. 1) is 0.646, that is, 0.65 m³/h for the robot and the pump operated by the Table 1 mechanism.

sum	24	1	0,646
t	n		E(x) = 0,65
x	y	Px	x*Px
0,1	0	0,00	0,000
0,2	0	0,00	0,000
0,3	0	0,00	0,000
0,4	3	0,13	0,050
0,5	4	0,17	0,083
0,6	6	0,25	0,150
0,7	5	0,21	0,146
0,8	3	0,13	0,100
0,9	2	0,08	0,075
1	1	0,04	0,042

Table 2.

Effect frequencies of E(x) robot 364 on the Zagreb-Zaprešić bridge.

$$E\left(x\right)=\sum _{X}x\ast P\left(x\right)$$E1

The second method of functional connection of the effect using the modified Erlang curve gives an approximate result (Eq. 2).

$$y\left(x\right)=\lambda {\left(\mathit{\lambda x}\right)}^k{e}^{-\mathit{\lambda x}}/k!$$E2

$E\left(x\right)={\int }_{-\infty }^{\infty }x\left({\mathrm{y}}_{\mathrm{x}}\right)\mathrm{d}x$ The mathematical expectation value of the Erlang distribution is known by k and λ (Eqs. 3 and 4).

$$E\left(y_x\right)={\int }_{-\infty }^{\infty }x\left(y_x\right)\mathrm{d}x$$E3

$$E\left(x\right)=\left(k+1\right)/\lambda$$E4

The parameters k and λ are discrete values of a sample for whose values the Erlang function approximates the distribution of observations of the effects of a given robot. By using the Matcad tool and assigning certain parameter values, we define and observe whether the curve corresponds to our selective distribution. The modified Erlang curve has an exponent for the variable x k − 1 instead of k (Eq. 5). The variable x is in the interval [1,2,−10], k = 6 and λ = 0.96, and the Erlang curve in Figure 4 is defined as E(x) = 0.7 m³/h, that is, the expected effect of the observed hydrodemolition robot.

Figure 4.

Modified Erlang labour distribution of machinists on hydrodemolition robots and pumps.

$$f\left(x\right)=1/k!\left({\lambda }^{k+1}{x}^{k-1}{e}^{-\mathit{kx}}\right)$$E5

Modified Erlang work allocation of machinists on hydrodemolition robots and pumps.

It can be seen that the mathematical expectation of the standard for the definition of a continuous event is higher than for the definition of a discrete event, since the continuous line fills the gaps of the discrete distribution (Eq. 6).

$$E\left(y_x\right)={\int }_{-\infty }^{\infty }x\left(y_x\right)\mathit{dx}>\sum _i\left(x_i{y}_i/\sum _i{y}_i\right)$$E6

Thus, the approximate solution for the expected performance of the robot can also be determined by the third common data correlation method, the Gaussian sum of least squares method [9, 10]. The given curve is parabolic and resembles the Gaussian distribution density function (Eqs. 7–10), with input variables and matrix b and matrix kooeficijent for robot performance. The matrix variables for the given Gaussian system are the matrix t with the frequency of the effect and the matrix x with the numerator of the effect value of the machine, which is replaced by a vector with unit numbers of the effect multiplied by 10. The number of measurements is n = 10 and the result is Figure 5.

Figure 5.

Modified parabolic distribution of machinists’ work on hydrodemolition robots and pumps.

$$x=\left[\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\\ 6\\ 7\\ 8\\ 9\\ 10\end{array}\right],t=\left[\begin{array}{c}0\\ 0\\ 0\\ 3\\ 6\\ 4\\ 5\\ 3\\ 2\\ 1\end{array}\right]$$E7

$$b=\left[\begin{array}{c}b1\\ b2\\ b3\end{array}\right]b1=\sum _{x=1}^{n}x,b2=\sum _{x=1}^n\mathit{xtb}3=\sum _{x=1}^n{x}^{2}t$$E8

$$\left[\begin{array}{ccc}n& \sum _{x=1}^{n}x& \sum _{x=1}^n{x}^2\\ \sum _{x=1}^{n}x& \sum _{x=1}^n{x}^2& \sum _{x=1}^n{x}^3\\ \sum _{x=1}^n{x}^2& \sum _{x=1}^n{x}^3& \sum _{x=1}^n{x}^4\end{array}\right]\times \left[\begin{array}{c}{X}_1\\ X_2\\ X_3\end{array}\right]=\left[\begin{array}{c}b1\\ b2\\ b3\end{array}\right]$$E9

$$X=b{A}^{-1}X=\left[\begin{array}{c}-\mathrm{3,883}\\ \mathrm{2,645}\\ -\mathrm{0,216}\end{array}\right]$$E10

The variable r replaces x, and by correcting the obtained equation, we approximate the quadratic equation with the product 1/25 and get the distribution in Table 3. From this approximation, it follows that E(x) is 0.619, or 0.6 m³/h, taken for the Conject 364 robot.

sum	18,1	1	0,619
t	n		E(x) = 0,6
x	y	Px	x*Px
0,1	0	0,00	0,000
0,2	0,5	0,03	0,006
0,3	1.5	0,08	0,025
0,4	2,3	0,13	0,051
0,5	2,8	0,15	0,077
0,6	2,9	0,16	0,096
0,7	2,8	0,15	0,108
0,8	2,3	0,13	0,102
0,9	2	0,11	0,099
1	1	0,06	0,055

Table 3.

Frequencies of the effect with E(x) of robot 364 on the Zagreb-Zaprešić bridge when returning from a quadratic function.

Sort the given database with various queries from the given variables that influence the effect is most often the depth of hydrodestruction, which depends on the brand of concrete. Before the hydrodemolition, the bridge was divided into fields, and the strength of the fields was determined using a sclerometre (Table 4).

X,C \ T	T1	T2	T3	T4	T5	T6
C	34,2	40,32	34,2	38,88	31,32	34,2
X	34	37,4	33,4	36,6	32,4	34
efect	0,96	0,59	0,58	0,66	0,5	0,6
28	2	0	2	0	1	0
30	1	0	1	0	4	2
32	1	0	2	2	2	3
34	1	1	2	0	1	1
36	1	5	1	3	0	3
38	1	0	0	3	1	2
40	2	4	2	2	1	0

Table 4.

Frequencies of the strength of the concrete on the Zagreb-Zaprešić bridge by field.

Discard the min and max performance data and brand of concrete, the proportionality of the dependence of these data is visible in Figure 6.

Figure 6.

Hydrodemolition of bridge deck with Conjet robots.

His is the definition of the equation used to determine the dimensional coefficient kd, the concrete strength kdc. The base or unit is taken for C 30/35. The solution of the curve as a function of the action variable t and the concrete strength variable x is obtained by linear Gaussian regression (Eqs. 11–13) Input variables with matrix b and linear matrix systems are defined in Figure 7.

Figure 7.

Dependence of the thickness of the bridge deck on the panel thickness and the robot performance.

$$x=\left[\begin{array}{c}0,59\\ 0,69\end{array}\right],t=\left[\begin{array}{c}37,4\\ 32,17\end{array}\right],b=\left[\begin{array}{c}b1\\ b2\end{array}\right],b1=\sum _{x=1}^{n}x,b2=\sum _{x=1}^n\mathit{xt}$$E11

$$\left[\begin{array}{cc}n& \sum _{x=1}^{n}x\\ \sum _{x=1}^{n}x& \sum _{x=1}^n{x}^2\end{array}\right]\times \left[\begin{array}{c}{X}_1\\ X_2\end{array}\right]=\left[\begin{array}{c}b1\\ b2\end{array}\right]$$E12

$$X=b{A}^{-1}X=\left[\begin{array}{c}-\mathrm{3,883}\\ \mathrm{2,645}\\ -\mathrm{0,216}\end{array}\right]$$E13

This results in the functional dependence of the dimensional coefficient, that is, the concrete strength kdc, represented by the assumed linear function (Eq. 14). With the given coefficients, kdc is decimally reduced by the numerator n, which follows the series of concrete strengths of + C 5.

$$k_{\mathit{dc}}=-0,1n+1,2$$E14

Thus, the numerator n has the interval [1, 2, 3, 4, 5], bat C [30, 35–50]. Through the one-year study of robotic work on over 1700 m³ of concrete and over 3200 hours effectively spent, it was found that the shift work does not have much effect, while the width of the work is equal to the depth. The depth observations show that they depend on the brand of concrete. Thus, it can be seen that for d > 20, the effect is approximately constant, and they are beams of stable concrete brand C 40/50, while for smaller thicknesses for slabs where the concrete has failed (the effect of salt on the bond between the reinforcement and the concrete), the dispersion of the effects is approximately equal to that of the strength of the concrete. The mathematical expectation technically lies approximately in the middle of the Erlang distribution, so it is satisfactory to use this point as the average mathematical expectation effect of the robot for calculation and planning procedures. By testing the given Erlang distributions with the chi-square test for α = 0.05 and 2 degrees of freedom, χ2 < χ2 α, the given curves are valid for a random sample, since the deviations of the empirical distribution from the Erlang distribution are not significant in a tabular representation of the mathematical performance expectation of the processed robots in Table 5.

Robot	E(x)			X	χ^2 < χ^2α
		d ≤ 20 cm	d > 20 cm		5,99
361	0,7	0,8	0,48	0,54	5,75
364	0,6	0,65	0,45	0,56	2,84

Table 5.

Mathematical expected performance of all robots on the Zagreb-Zaprešić bridge in 1 month.

With several considerations of the mathematical expectation E(x) through Table 2 and the simplified linear method of the arithmetic mean, one obtains the average effect of the resource, which becomes a vector effect variable in Figure 8.

Figure 8.

Vectorial effect of water destruction by Conjet robots.

Substitutes for the graphical representation are the equations of the base and other graphs, that is, the water destruction of plates, bars or vertical structures. Thus, the equation of the basic graph for water destruction of plates (Eq. 15) is.

$$U_{k,r,\mathit{ko},\mathit{kd}}=k_{\mathit{dc}}{k}_o{U}_{k,r}$$E15

where k_dc is the coefficient of the construction dimension C for the of concrete, the base coefficient ko which is a function of the structural element, and the equation of the effect U_kr which is a function of the resource r and the structural element k. For the base effect, the listed coefficients are uniform so that the equation takes the form of a function of the water destruction effect of the C35 plate. The reciprocal of the effect [m³/h] gives the standard [h/m³] (Eq. 16) (Figure 9).

Figure 9.

Vector norm of water destruction by Conjet robots.

$$N=\frac{1}{U_{k,r,\mathit{ko},\mathit{kd}}}=1/k_{\mathit{dc}}{k}_o{U}_{k,r}$$E16

It can be seen that the slab is easier to hydrodemolish than the beam and especially the wall due to the effect of the forces acting most strongly in the direction of gravity.

4. Planning with the DSP method

4.1 Software tools for planning

For the realisation of the project, it is important to prepare the work, that is, to plan the development of the production process of the object and the management to regulate the production processes, which are the function of the technology, the organisation, the management and the ITC system with daily system management, which enables the daily regulation of the system (Figure 10) [11, 12].

Figure 10.

Regulating of the system.

Software tools for planning outside the IIS system (Figure 11) are developed on the method CPM from Superproject to Perimavera and MSP. Nevertheless, planning in construction is at a low level due to outdated standards. Therefore, the introduction of dynamic or parametric vector standards is recommended to increase the accuracy of planning and thus the costing of projects. Therefore, relational databases create a vector organisational structure [13] of the company, which is introduced into the matrix organisational structure on the third axis, that is, the resource variable stored in the database with histograms.

Figure 11.

IIS construction companies with a vector data model structure.

Integration is done using the foreign software tools for using ODBC databases or the new XML Internet technology. There are also other possible solutions based on operational research through software combinatorics. However, the graphics functions used by indigenous engineers are inferior to those mentioned above. Therefore, Microsoft graphics have been integrated into indigenous software and a report produced in combination with Microsoft tools is shown in Figure 12.

Figure 12.

Project monitoring and cash flow report of the Zagreb-Zaprešić bridge.

The system allows monitoring of resource efficiency by activity and on a daily basis through the presented data model. Monitoring of normative and financial indicators is enabled alternately, which leads to an increase, that is, streamlining, of the control of resources of projects that were previously monitored on a periodic financial basis, from now on on a daily basis and in the future on the basis of normative indicators. This addition is beneficial not only for a company but also for society (the wider community). A rational decision-making process combined with the new scientific approach to the component that is crucial in any society, namely, the value of human labour, would lead to more humanistic outcomes. Once the standards are objectively set, humanistic solutions are yet to be achieved as we enter the realm of humanism and humanity, qualities we lack today. The DSP method paves the way for the standardisation of models through the production of bills of quantities, draft bids and standards.

4.2 Model’s standardisation of the bid construction

By harmonising the description of the item in the tender construction, that is, the text of the bill of quantities, that is, the standard, a unique code is created to define the construction product. A product record is formed by layers and distribution of complex processes to procedures, and the construction production record is modelled by the combinatorics and linking of these records through model standardisation (Figure 3). A record of the elements is given by the project MSP (Eqs. 17 and 18), definition of the structure with a given resource and a description of the operational elements, from activities, processes and procedures for construction production and other more advanced production to the movement of robotisation of production, the equation of model standardisation of production (Figure 13).

$$\mathit{MSP}=\sum A=\sum \mathit{Pe}=\sum O=\sum \mathit{Pd}=\sum M$$E17

$$\mathit{MSP}=\sum p=\sum c=\sum r=\sum d$$E18

Figure 13.

Standardisation of activities: elements of the description of delivery items in construction [14].

Here, MSP forms the left side of the picture with the variables activity A, process Pe, operation O, procedure Pd and movement M, while p is the project, c the construction, r the resources and d the dimension [15]. Modular and variant components can simulate all practical processes and operations up to the procedure through CPS, MindJet graphics technology or the software method DSP.

4.3 DSP COD

DSP code is created by combining dynamic programming with object or structural programming. It is very interesting because resource consumption in multiple processes can be recorded simultaneously, assuming that the given capacity is used. When we consider a multi-process system, we can define a set of vectors x. The optimisation determines which process we need to allocate more resources to in order to obtain a greater profit. To obtain this solution, it is necessary to write down all possible distributions of resources through all processes, that is, to write down and calculate all possible paths. The recordings can be made using cybernetic equations (Eq. (19)).

$$F\left(X_j\right)=\sum _{j=1}^n{g}_j\left(x_j\right),S=\sum _{j=1}^n{x}_{j}0\le x_j\ge S$$E19

That is, by the method of recurrent equations, whose characteristic is the iteration of the functional equations of the state of the system f_n (S_n) in the sum of the observed function g_n and the function of the previous state f_n-1 (S – x_n) with all possible changes in the value of the variables in the given functions or processes (Eq. (20)).

$$f_n\left(S_n\right)={\mathit{max}}_{0\le x_n\le S}\left(g_n\left(x_n\right)+f_{n-1}\left(S-x_n\right)\right)$$E20

For multidimensional vector dynamic programming, the equations are identical, only with more variables (x,y). The organisational differential is marked as follows in Figure 14.

Figure 14.

DSP vector iteration organisational differential.

The mathematical methods of logic and inductive optimisation and the programming methods define the dual DSP structure. Baumholz plus the induction equation, that is, dynamic programming with object programming, defines the idea of the DSP equation to model the production process, that is, construction bid construction with DSP code (5) and TROSKO code. By linking and extending the above models with iteration software technology, a DSP model has been developed to help solve the problem of defining production and products. Thus, the product of the bid construction and the item element are defined as MSP = Σ Fn(S) = f(T,O), as a function of the record of technology (design) and execution organisation, and T ≈ O = f(A,R,D), that is, as a function of the variables A—activities, R—resources and D—dimensions of design and resource performance. The greatest influence is the standardisation of records of bid or bill of quantities items as a recurring form (Eqs. 21 and 22).

$$\mathit{BC}=U\left[f_n\left(T_n,O_n\right)=f_{n+1}\left(T_{n+1},O_{n+1}\right)\right]$$E21

or

$$\mathit{DSP}\mathit{COD}=U\left[f_n\left(\left[A\left|R\left|D\right|\right|\right]\right)=f_{n+1}\left(\left[\begin{array}{c}A\end{array}\left|R\left|D\right|\right|\right]\right)\right]$$E22

While substituting identical structures T O the iteration DSP CODE of the product (Figure 15) results.

Figure 15.

BC-DSP COD in the MindJet software.

4.4 Planning with the code DSP

Planning with the DSP code uses a combinatorial Eq. (15) to define all paths in product creation. The DSP code is a universal equation that can be used for all equations, including CPM equations or DSPiP in Figure 16.

Figure 16.

DSPIP in the Delphy software.

5. Simulations with MGSC for water breakage

More recently, probabilistic forecasts of project performance and the use of stochastic S-curves with a stochastic S-curve generation software package and simulation approach have defined the dispersion variance of finances and time of the modified Gaussian S-curve (MGSC) project as a function of the density distribution of cost and time. Expected monetary value (EMV) or S-charts are widely used today and are complemented by functional MGSK [16, 17] (Eq. 23), (Figure 17).

Figure 17.

MGSK project Zagreb-Zaprešić.

$$\mathit{\text{skvGr}}\left(x,T\right)=\mathit{\lambda kv}·{\int }_0^x\frac{1}{\left(a·T+b\right)·\sqrt{2·\pi }}·e^{\frac{-{\left(x-\mu \right)}^2}{\mathit{kv}·\left(a·T+b\right)}}\mathit{dx}$$E23

The levelling and fitting of the curves, that is, the modification of the Gaussian curve, refers to the introduction of a constant kv parameter in the value of 10,000 units. The investment value for the reconstruction of the Zagreb-Zaprešić bridge is visible in the MSP case stream and amounts to HRK 12325579. In the software budget, the cost axis is in thousands, so T = 1233 × 10⁴. The number of working months for the project is n = 5, which defines the variable x, and the expectation on the variable x is x/2. The constant variable kv is 104, and λkv is assumed to be 3.375.

The Dis S-curve has monthly rates for the investment distributed within 1.2 to 4.5 million in Figure 18, which is much more optimal for the S-curve of the Gantt chart than the flow curve of the case from the SME Gantt chart.

Figure 18.

Simulation of project management with MGSC for the Zagreb-Zaprešić project.

6. Automation and AI systems for hydrodemolition

By linking the production engineering structures to the organisational process and creating a functional definition of the structures with a cybernetic record of all combinations, we obtain the DSP -e model of the product definition, that is, the cybernetic system [18, 19, 20, 21] of the product definition in Figure 19.

Figure 19.

Sayber product system [18].

By defining the structure of the product with technology T and organisation O, the equation of the product and the cost of the code are defined, which allows the logical function of defining a specific action in the project. In this way, we arrive at the automation or fragmentation of parts of the product defined by the bid code (Eq. 24) (Figure 20).

Figure 20.

Sayber product system.

$$\mathit{\text{Constructionbid}}=f\left(T,O,M,\mathit{ICT}\right)$$E24

The equation defines the iteration equation of the Sayber system to define the construction bid construction, that is, the product, that is, the execution object. By supplementing the dynamic programming equation with structural or object programming, DSP CODE, or the DSP method of product definition, is developed. The MGSC statistical method, the least squares method and the structural modelling and combination method are used to optimise the creation of a proposal design. The given equation primarily enables the calculation of the quotation construction, and with the filling of the unit price, it enables the system to calculate the critical planning path using combinatorial records of all states and rotational links. Thus, linking the organisational component of the standard or effect to the concrete strength (Eq. 25) opens the field for frequency calculation on the bridge during hydrodemolition, because the frequency of the structure (Eq. 26) is also a function of the concrete strength variable, which is replaced by the strength function as a function of the robot’s performance using Eq. (24). Thus, the frequency within the audible radio waves [22, 23] (Eq. 27) (Figure 21), is obtained as a function of the thickness of the structure and the strength of the concrete.

Figure 21.

Frequency of the bridge plate from the hydrodemolition action of the Conject robot.

$$f_c=-52,3x+68,25$$E25

$$f_x=\frac{\sqrt{\frac{\sigma 3I}{m}}}{2\pi }$$E26

$$f_x=\frac{\sqrt{\frac{f_{c}3I}{m}}}{2\pi }$$E27

If one enters the values for the standard physical dimensions of the mass of the structure for reinforced concrete 25 kN/m³, the moment of inertia of the slab 10 cm high and the Ludolf number constant from the circumference of the circle and the strength ab. Construction replaced by the power equation, the result is a matrix of the bridge frequency with about 1000 Hz. However, larger absorption plates with a height of up to 90 cm also generate radio waves.

The given equations connect organisation and technology, that is, economic and physical processes. If you further complete the method DSP by planning a three-level set of permutations and variations, the form of the equations shows the software code of loops over the variables within the matrix structure, which has no standard mathematical properties but is software mathematics. Combinatorics creating a data set of all Croatian lottery combinations opens up the possibility of defining permutations, variations and combinations given by the equation (Eq. 28) in a few minutes. Such combinatorial iterative equations are suitable for computers. Permutations can also be represented graphically by adding the next number to all intermediate columns and the first and last columns of the previous data set. An iterative software equation defines a series of records of all combinations or variations using a matrix representation [24].

$$K=\left[\begin{array}{c}{n}_1\to k_{\mathit{max}}-1\\ \overleftarrow{n_{\mathit{max}}}\end{array}\left|\begin{array}{c}{n}_2\to 1\\ \overleftarrow{n_1-k_i}\end{array}\left|\begin{array}{c}{n}_i\to n_i+1\to \overleftarrow{}{n}_k-1\\ \overleftarrow{n_1-k_i}\end{array}\left|\begin{array}{c}\begin{array}{c}\begin{array}{c}{n}_k\to n_1+1\\ \overleftarrow{n_{\mathit{max}}}\end{array}\end{array}\end{array}\right|\right|\right|\right]$$E28

Today, Mathcad has also developed greatly and can also write matrices graphically using software mathematics so that such matrices or determinants can be called software matrices.

7. Conclusions

Optimal investment and maintenance of bridges are the result of new techniques in organisation, management and ITC methods. Operational research with software technology is developing new mathematical models that simulate investment costs for optimal, rational management of capital projects. Any improvement in the organisational or technological cycle is an important component for the profitability of the investment. This requires a new model of standardisation with the vector form of VN-KOD standards defined by DSP code that enables the automation of building products from project documentation to production. Combinatorics and functional linkage connect all branches of science. Just as theory complements practise and vice versa, organisation appears as progress in technology and vice versa. It is a path to AI systems and a great contribution of digitalisation to daily management, that is, the creation of profit within software-mathematical organisational problems. This leads to system automation at the system level of physical processes and controls and the establishment of intelligent project management [25] with the ambition to define AI [26] with simultaneous management. Thus, Android technologies communicatively unite the concept of the fourth industrial revolution through the cloud of the internet and virtual technology [27]. AI systems with model standardisation and vector normalisation of production processes through mathematical and statistical methods approach precision reduce risk [28] and increase sustainability of bridges through channel maintenance theory [29]. DSP Iteration programming with HV normalisation enables chipping, that is, automation and robotisation of large infrastructure investments in a circular sustainable economy in the economic sense with an increase in the principles of frugality, productivity and profitability. In a humanistic sense, AI systems free workers from dangerous and difficult work and open up DSP and cost-effective constant modelling and simulation of model standardisation.

Conflict of interest

The authors declare no conflict of interest.

Notes/thanks/other declarations

Thank you IntechOpen.