Parametric Design Research Articles

Optimization of a parametric product design using techno-economic assessment and environmental characteristics with application to an electric traction motor

Accelerating the development of clean energy technologies is required to move towards a sustainable future. New design approaches are being proposed to help accelerate these developments. This study proposes and improves a novel design framework that incorporates life cycle assessment (LCA) and techno-economic assessment (TEA) with an optimization-based design model of a discrete product at early stage. Objective functions for mass, energy consumption, and two metrics relating to manufacturer and consumer economic interests are considered; these objectives are minimized using a Pareto-like approach. An electric traction motor for an electric vehicle is used as a discrete product case study. The approach demonstrates the utility of considering four-objectives in the design problem, uncertainty analysis via Monte Carlo simulation, and the power of employing LCA and TEA methods. Future work may explore a broader range of objective functions to cover different challenges that inhibit the development of clean energy technologies.

Parametric design and performance evaluation of gyroid triply periodic minimal surface preparation by LCD photopolymerization

In this paper, the Gyroid triply periodic minimal surface is prepared by liquid crystal display photopolymerization technology, and 10 models of the periodic parameter T in [1/5, 2] are designed. Using the method of finite element method and experimental verification, when T = 1/3, there are fewer stress concentration areas on the Gyroid surface, the number of grids is moderate, the compression crush rate is the smallest, and the porosity error is reasonable. Through the microscopic morphology, it is found that the surface, after printing, forms gear shape and resin residue so that the actual volume is larger than the theoretical volume, and the porosity is minor. Keeping periodic parameter T = 1/3 and porosity of 50%, four kinds of Gyroid surface structures were designed by changing the parameter surface offset, wall thickness, offset thickness, and gradient arrangement. The effects of different loading directions on its mechanical properties, deformation behavior, and energy absorption were discussed through compression experiments. The results show that the vertical load is applied to form a fault zone from the upper left angle to the lower right angle of 45°, and the parallel load is applied to create a fault zone from the upper right angle to the lower left grade of 45°. When the load is used in the vertical direction, the energy absorption and energy efficiency of the surface offset Gyroid surface are the largest. When the load is applied in the parallel order, the energy absorption curves of the four structures change similarly, and the deformation amplitude of the wall thickness Gyroid surface during the compression process is relatively stable. The energy efficiency of gradient arrangement Gyroid surface increases fastest in the compaction stage.

Design Optimization of Lattice Structures Under Impact Loading for Additive Manufacturing

Abstract Additive manufacturing (AM) has enabled the production of intricate lattice structures with excellent performance and minimal mass. Design approaches that consider static loading, including lattice-based topology optimization (TO), have been well-researched recently. However, to date, there appears to be no widely accepted method of optimizing lattice structures for high-strain rate loading, especially when the design for additive manufacturing (DFAM) principles are considered. This study proposes a computational framework for the design of lattice structures under specified impact loading. To manage dimensionality while achieving sufficient generality, a heuristic design space is developed that relies on traditional TO to govern the design's macrostructure and standard dimensioning to govern its mesostructure. DFAM principles are then incorporated into a Bayesian optimization scheme wrapped around traditional TO to achieve manufacturable designs that absorb high-impact loading. Because this approach does not require analytical gradient information, the framework can be used to optimize directly on complex objectives, such as injury metrics calculated from the acceleration curve. A series of case studies is formulated around a mass-performance tradeoff and involves individual unit cell design as well as full-part design. The proposed design parameterization is found to enable sufficient flexibility to achieve consistently good performance regardless of AM build orientation.

Experimental and numerical analysis of temperature distributions in SA 387 pressure vessel steel during submerged arc welding

Abstract The present study aims to explore experimental investigations and numerical simulations for temperature distributions at heat-affected zones within SA 387-Gr.11-Cl.2 steel during the submerged arc welding (SAW) process. Experimental endeavors entailed welding steel plates under controlled conditions, precisely measuring temperatures at key locations by thermocouples. A special program based on 3D Goldak’s double ellipsoidal model was developed in ANSYS Parametric Design Language for moving heat source calculations in the finite-element analysis (FEA). For welding an 8 mm thick plate with one pass, the suitable parameters were found to be 600 A current, 31 V voltage, and 10 mm·s−1 welding speed. The experimental cooling periods were found to be slower than predicted by FEA. When temperature distributions were compared between experimental and FEA results, an average variation of 1.88% at peak temperatures and 11.8% at completion time was observed. The results showed the temperature distribution at various time steps, illustrating the transient nature of the welding process. The results highlight the capacity of the FEA model to predict temperature profiles during SAW accurately, presenting a potent tool for optimizing welding parameters without extensive trial and error.

Between Parametricism and Pragmatism Concept Design Problematics in Zaha Hadid Architects’ Digital Projects

This study provides a comprehensive analysis of the challenges in Zaha Hadid Architects' parametrical projects, focusing on recent digital technologies in the realms of "Architecture" and "Urban planning." Recently, Zaha Hadid Architects “urban-scale" project has awarded the title of "Parametric-urbanism" introduced a new urban design term to the world. This research delves into the design and implementation issues encountered in the Istanbul Kartal-Pendik Master Plan, parametric design which planned non-realistic, and fluiding plots and parcels not dependent on the city maps. 20<sup>th</sup> century early urban planning doctrines of C. Sitte and some French urbanists known as pragmatists, and realistic. The study expected to contribute design discourse with new approach parametric projects via French pragmatists problem solving methods. A comparative method is used to analyze the late 20th century parametric theories, and urbanism ideologies of 20th century; CIAM, Le Corbusier and French urbanists’ “realistic” and “problem-solving” methods. Zaha Hadid Architects’ “urban-scale” projects created via abstractions of parametric repetitive forms considered problematic. Some inconsistencies are observed in design and implementation process secondary parametric urban elements; road, axis, plot, parcel, block design and dimensions. Also, the urban scale parametric projects can be problematic in complicated, old, historical cities like Rome, Paris, Istanbul.

Parametric design and multi-objective optimization of daylight performance in gallery skylight systems: A case study on the high museum expansion

In the realm of museum design, the meticulous planning of natural lighting plays a vital role in enhancing energy efficiency, improving the indoor atmosphere, and preserving and showcasing artifacts. A significant challenge is to ensure visitors' visual comfort while minimizing excessive natural light to prevent damage to exhibits. This study takes Renzo Piano's High Museum Expansion as a case study and employs the medium sensitivity exhibit standards from IESNA as the evaluation criteria. During the preliminary design phase, computer modeling was utilized, daylighting simulations were carried out using the Ladybug tool, and the Octopus genetic algorithm plugin was applied to investigate, optimize, and evaluate the performance of the point skylight system in museum interiors. The findings indicate that optimized point skylight systems not only block direct sunlight, reducing indoor glare, but also ensure that the Annual Cumulative Illuminance (ACI) on interior surfaces stays below 480,000 lx, while the annual effective Useful Daylight Illuminance (UDI) is increased to 75 %. In terms of design parameters, a skylight height of 0.6 to 0.7 m, combined with a shading panel to horizontal angle of 65 to 70 degrees, is found to be effective in enhancing indoor lighting conditions.

Digital workflow for nearly zero-energy high-rise office building design optimization at the district scale in Mediterranean context

While the implementation of sustainable urban planning has proven to be one of the primary goals to reduce the climate change impact, the rapid adoption of nearly Zero Energy Buildings (nZEB) concept in the building sector is inevitable to reach that objective. Following this trend, this article focuses on the implementation of a parametric digital workflow to evaluate the energy performance of a nearly zero energy high-rise 23-storey office building in the climatic and urban contexts of Casablanca at the early design stage.In the scope of this study, Grasshopper-based digital workflow permits to investigate the impact of 147 parametric building designs, which are generated by varying the building's shape factor and orientation on thermal cooling and heating demand and global solar energy production. The outcomes of this holistic methodology highlight the design trade-offs between energy efficiency strategies and energy performance of building-integrated photovoltaic (bipv) and photovoltaic (pv) systems, aiming to reach optimized nZEB. Moreover, the results of the study suggest that it is possible to reach an annual load match equivalent to 29.68 %. The findings also underscore the significant role of the BIPV systems in shifting towards the goal of net zero energy, accounting for up to 64.43 % of the total solar energy output and contributing in total up to 17.62 % to the yearly self-sufficiency. In addition, the energy balance evaluation, when assessed on an hourly basis, reveals that the BIPV system significantly improves the daily load cover factor, achieving a value of 12.45 %, and increases up to 20.62 % when considering also the rooftop PV, particularly during spring season. Finally, the capacity credit factor is improved by up to 31.27 %, which is a significant share of grid connection reduction compared to the same building relying totally on the grid for its energy needs.

Seashell-inspired polarization-sensitive tonotopic metasensor

Bioinspiration has widely been demonstrated to be a powerful approach for the design of innovative structures and devices. Recently, this concept has been extended to the field of elasticity, dynamics, and metamaterials. In this paper, we propose a seashell-inspired metasensor that can simultaneously perform spatial frequency mapping and act as a polarizer. The structure emerges from a universal parametric design that encompasses diverse spiral geometries with varying circular cross sections and curvature radii, all leading to tonotopic behavior. Adoption of an optimization process leads to a planar geometry that enables us to simultaneously achieve tonotopy for orthogonally polarized modes, leading to the possibility to control polarization as well as the spatial distribution of frequency maxima along the spiral axis. We demonstrate the versatility of the device and discuss the possible applications in the field of acoustics and sensing.

Design of General Parametric Repetitive Control Using IIR Filter With Application to Piezo-Actuated Nanopositioning Stages

The achievable performance with repetitive control is limited due to its inherent sensitivity to the frequency shift away from the intended periodic frequencies and the undesired gain amplification of the aperiodic disturbances. To address these limitations, the paper proposed a general parametric repetitive control (GPRC) method based on the IIR filter with the features of low-order and excellent magnitude responses to result in better tracking performance in diverse applications. By analyzing its sensitivity function, it is found that the design of GPRC can be converted to the explicit parametric design of an IIR high pass filter. The controller design process and the stability analysis are presented in detail. To show the effectiveness of GPRC, comparative experiments are conducted via tracking sinusoids, triangular trajectories and other complex trajectories with multi-frequency components. The experimental results show that, in contrast with the conventional repetitive control (CRC) and a modified repetitive control (MRC), the GPRC exhibits excellent robustness against the frequency shift and advanced performance at the aperiodic frequencies. The tracking results of the sinusoids show that the maximum tracking error obtained with GPRC for a frequency shift of 3 Hz decreases from 0.0259 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu m$</tex-math> </inline-formula> (CRC) and 0.2207 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu m$</tex-math> </inline-formula> (MRC) to 0.0101 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu m$</tex-math> </inline-formula> at the nominal frequency of 1000 Hz, demonstrating the merits of the proposed GPRC. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To enable automation systems, one of the crucial requirements is to track repetitive references with high precision. Although the normal repetitive control (RC) based schemes are successfully applied to improve the tracking accuracy of periodic trajectories, the existing RC schemes suffer from the problems of lower robustness against frequency shift and the unwanted gain amplification at the aperiodic frequencies due to Bode’s sensitivity integral. To overcome this problem, this paper proposes a novel general parametric repetitive control (GPRC) method via characterizing the loop properties quantitatively based on the IIR high pass filter design. Focusing on specific issues, the detailed variations to handle the errors at only the odd-and even-harmonics are also demonstrated. This framework leads to a flexible solution in practical implementations. The experimental validation on a piezo-actuated nanopositioning stage is comparatively presented in terms of tracking accuracy and rejection ability of the gain amplification at the aperiodic frequencies. With its flexibility and effectiveness, the proposed GPRC can be easily implemented in diverse applications.

A Combination of Machine Learning Algorithms and Parametric Design Tools to Predict the Energy Consumption for Residential Buildings

A Combination of Machine Learning Algorithms and Parametric Design Tools to Predict the Energy Consumption for Residential Buildings

Construction of an innovative system for isolating and transporting people with infectious diseases

Objective: To propose the construction of an innovative system to isolate and transport people with infectious and contagious diseases with total safety to the physical integrity of both the health professionals involved in this activity and the patient himself. Material and Methods: The product was designed in TopSolid parametric design software, and its structure was manufactured with metallic plates, metalon, acrylic plates and a control system. Every automation system through pneumatics was made using pressure and flow controllers through the use of a PLC (programmable logic controller), thus allowing the insertion of medical protocols. The system allows air to exit the hermetic chamber (whether atmospheric and/or oxygen) sanitized, thus allowing a continuous flow with pressure and flow control without risk of infecting the external environment. Results: The results showed a great innovation that consisted of creating a proof of concept for use in hospitals, SAMUs, ambulances and aircraft, allowing safe isolation and transport for all involved. Conclusion: The innovative system for isolating and transporting people with infectious and contagious diseases proves to be effective for what was proposed, promoting technological innovations in the face of what already exists worldwide.

Parametric design optimization and thermodynamic analysis of plate fin heat exchanger for helium liquefaction system

The plate-fin heat exchanger is one of the most important components of helium liquefaction system as it recovers cold energy from helium gas in the cold box. Because of larger heat transfer surface area and compact geometrical configuration, plate-fin heat exchangers are widely used. The design of heat exchanger using helium as a cryogenic fluid needs high thermodynamic performance with minimum pressure drop which particularly requires the optimization of dimensional array and its geometrical configurations. In this regard, a parametric investigation was performed to compute the effective geometrical parameters and its effect on thermodynamic (effectiveness and log-mean temperature difference) performance has been discussed in detail. The present study aims to design optimization and thermodynamic performance evaluation of plate-fin type heat exchangers used in helium liquefaction systems. The developed helium liquefaction model has been simulated for the most critical liquefier with and without liquid nitrogen precooling, mixed mode, and refrigeration mode. Each component of the liquefaction model has been technically and thermodynamically analyzed and, in particular, four plate-fin heat exchangers have been considered and designed accurately using Aspen EDR®. Initially, the sensitivity analysis was carried out to characterize the most significant geometrical parameters (fin thickness, height, number and arrangement of layers, frequency, and fin type) and their effect on thermodynamic performance and pressure drop. After that, the artificial intelligence model was used to determine the optimal range of such geometrical variables in which the heat exchanger has maximum effectiveness and log mean temperature difference. Finally, the operating conditions obtained from cycle modeling and optimized geometrical datasets have been applied in commercial simulation software Aspen EDR® for plate-fin heat exchangers design. Finally, a comparative thermodynamic analysis has been carried out to determine the performance of all the designed heat exchangers operating at four different modes (boundary conditions).

Exploring Digital Visualization Methods in Urban Public Building Space Design

Digital technology has driven the innovation of architectural design methods and tools, applying digital techniques to allow greater possibilities for more innovative and scientific design of public building spaces. This article first analyzes the characteristics of digital visualization and its advantages in the design of urban public building spaces, including aspects such as visualizing three-dimensional expression, rational analysis of building space, Virtual Reality Experience, and integration of design and construction processes. Subsequently, by introducing digital design methods such as parametric design, algorithmic generation, nonlinear design, and artificial intelligence-assisted design, it explores the methods and implementation approaches of digital visualization in the design of public building spaces. The aim is to offer insights and references for the deeper integration of digital technology into architectural design practices.

An intelligent recommendation system for personalised parametric garment patterns by integrating designer’s knowledge and 3D body measurements

Garment pattern-making is one of the most important parts of the apparel industry. However, traditional pattern-making is an experience-based work, very time-consuming and ignores the body shape difference. This paper proposes a parametric design method for garment pattern based on body dimensions acquired from a body scanner and body features (body feature points and three segmented body part shape classification) identified by designers according to their professional knowledge. By using this method, we construct a men’s shirt pattern recommendation system oriented to personalised fit. The system consists of two databases and three models. The two databases include a relational database (Database I) and a personalised basic pattern (PBP) database (Database II). The Database I is based on manual and three-dimensional (3D) measurements of human bodies by using designer’s knowledge. And Database I is a relational database, which is organised in terms of the relational model of the body part shape and its key body feature dimensions. After a deep analysis of measured data, the irrelevant measured dimensions to human body shape have been excluded by designers and extract representative human body feature dimensions. In addition, the relations between body shapes and previously identified body feature dimensions have been modelled. From the above relational model, we label key feature point positions on the corresponding 3D body model obtained from 3D body scanning and correct the whole 3D human upper body model into the semantically interpretable one. The 3D personalised basic pattern is drawn on the corrected model based on these key feature points. By using three-dimensional to two-dimensional (3D-to-2D) flattening technology, a 2D flatten graph of the 3D personalised basic pattern of the interpretable model is obtained and slightly adjusted to the form suitable for industrial production, i.e., PBP and the PBP database (Database II) is built. In addition, the three models include a basic pattern parametric model (Model I) (characterizing the relations between the basic pattern and its key influencing human dimensions (chest girth and back length)), a regression model (Model II) which enables to infer from basic pattern to PBP for three body parts based on the one-to-one correspondence of key points between the PBPs and the basic patterns and a personalised shirt pattern parametric model (Model III) (characterizing the structural relations between the personalised shirt pattern (PBPshirt) and PBP). The initial input items of the recommendation system are the body dimension constraint parameters, including chest girth, back length and the body feature dimensions used to determine each body part shape as well as three shirt style constraint parameters (slim, regular and loose). By using Model I, the corresponding basic pattern can be generated through the user’s chest girth and back length. Body feature dimensions determine the three body parts’ shapes. Then, Model II is used to generate the PBP for the corresponding body parts shape. Based on the shirt style chosen by the user, Mode III is used to generate the PBPshirt from the PBP. The output of the recommendation system is a fit-oriented PBPshirt. Moreover, if the PBPshirt is unsatisfactory after a virtual try-on, four adjustable parameters (front side-seam dart, back side-seam dart, waist dart and garment bodice length) are designed to adjust the PBPshirt generated by the proposed recommendation system.

Parametric Design Method and Lift/Drag Characteristics Analysis for a Wide-Range, Wing-Morphing Glide Vehicle

The parametric design method is widely utilized in the preliminary design stage for hypersonic vehicles; it ensures the fast iteration of configuration, generation, and optimization. This study proposes a novel parametric method for a wide-range, wing-morphing glide vehicle. The whole configuration, including a waverider fuselage, a rotating wing, a blunt leading edge, rudders, etc., can be easily described using 27 key parameters. In contrast to the typical parametric method, the new method takes internal payloads into consideration during the shape optimization process. That is, the vehicle configuration can be flexibly adjusted depending on the internal payloads; these payloads may be of random amounts and have different shapes. The code for the new parametric design method is developed using the secondary development tools of UG (UG 10.0) commercial software. The lift and drag characteristics over a wide operational range (H = 6–25 km, M = 2.5–8.5, AOA = 0–10°) were numerically investigated, as was the influence of the retracting angle of the morphing wings. It was found that, for the mode of the fully deployed wings, the lift-to-drag ratio (L/D) remained at a high level (≥4.7) over a Mach range of 4.0–8.5 and an AOA range of 4–7°. For the mode of the fully retracted wings, the drag coefficient remained smaller than 0.02 over a Mach range of 4.0–8.5 and an AOA range of 0–5°. A wide L/D of 0.3–4.7 could be achieved by controlling the retracting angle of the wings, thus demonstrating a good potential for flight maneuverability. The flexible change in L/D proved to be a combined result of varying pressure distribution and edge-flow spillage. This will aid in the further optimization of lift/drag characteristics.

Human behaviour simulation for promoting usefulness and user-centric values in parametric design

Although contemporary architectural design education adopts the parametric design approach, which involves complex iterations between the arrangement of form components and building performance, this method limits students' exploration of the optimal matches between generated form and the behaviours of prospective users. Therefore, as a solution, this study hypothesises the effects of human behaviour simulation on students' exploration of user-centric values in the parametric design process. This paper compares the self-evaluation scores of 90 undergraduate students before and after simulation. Data were collected during an authentic digital design course that examined shopfront façade prototypes. Statistical analysis and interpretation indicate that simulation better facilitates students' search for matches between initially value-isolated forms, created using a parametric design tool, and useful user-centric values. However, simulation is not relevant for discovering unexpected forms. This study addresses the unknown affordances in simulation when assigning user-related value to form generation that lacks value.

The structural landscape of the immunoglobulin fold by large-scale de novo design.

De novo designing immunoglobulin-like frameworks that allow for functional loop diversification shows great potential for crafting antibody-like scaffolds with fully customizable structures and functions. In this work, we combined de novo parametric design with deep-learning methods for protein structure prediction and design to explore the structural landscape of 7-stranded immunoglobulin domains. After screening folding of nearly 4 million designs, we have assembled a structurally diverse library of ~50,000 immunoglobulin domains with high-confidence AlphaFold2 predictions and structures diverging from naturally occurring ones. The designed dataset enabled us to identify structural requirements for the correct folding of immunoglobulin domains, shed light on β-sheet-β-sheet rotational preferences and how these are linked to functional properties. Our approach eliminates the need for preset loop conformations and opens the route to large-scale de novo design of immunoglobulin-like frameworks.

Fin-Bayes: A Multi-Objective Bayesian Optimization Framework for Soft Robotic Fingers.

Computational design is a critical tool to realize the full potential of Soft Robotics, maximizing their inherent benefits of high performance, flexibility, robustness, and safe interaction. Practically, computational design entails a rapid iterative search process over a parameterized design space, with assessment using (frequently) computational modeling and (more rarely) physical experimentation. Bayesian approaches work well for these expensive-to-analyze systems and can lead to efficient exploration of design space than comparative algorithms. However, such computational design typically entails weaknesses related to a lack of fidelity in assessment, a lack of sufficient iterations, and/or optimizing to a singular objective function. Our work directly addresses these shortcomings. First, we harness a sophisticated nonlinear Finite Element Modeling suite that explicitly considers geometry, material, and contact nonlinearity to perform rapid accurate characterization. We validate this through extensive physical testing using an automated test rig and printed robotic fingers, providing far more experimental data than that reported in the literature. Second, we explore a significantly larger design space than comparative approaches, with more free variables and more opportunity to discover novel, high performance designs. Finally, we use a multiobjective Bayesian optimizer that allows for the identification of promising trade-offs between two critical objectives, compliance and contact force. We test our framework on optimizing Fin Ray grippers, which are ubiquitous throughout research and industry due to their passive compliance and durability. Results demonstrate the benefits of our approach, allowing for the optimization and identification of promising gripper designs within an extensive design space, which are then 3D printed and usable in reality.

Locally, Bayesian and non parametric Bayesian optimal designs for unit exponential regression model

. This study introduces optimal designs for the unit exponential (UE) non linear model using local, Bayesian, and non parametric Bayesian approaches. In the local approach, optimal designs were derived by substituting initial estimates for the unknown parameters. However, recognizing the inefficiency of these designs when initial estimates are distant from their true values, we adopted a Bayesian approach, employing the D-optimal criterion with uniform and truncated normal prior distributions for unknown parameters. In situations lacking informative or historical knowledge of parameters, a non parametric Bayesian approach was employed, incorporating the Dirichlet Process (DP) prior to the space of distribution functions. Finally, the efficiency of various optimal designs was analyzed for comparison.

Seismic–Energy Retrofit as Information-Value: Axiological Programming for the Ecological Transition

The research deals with the issue of the seismic and energy retrofit of historic building fabrics having as reference a historic district of Syracuse (Italy). The prospect of the ecological transition on the one hand and the public support funding on the other claim for a valuation programming approach implying the creation of multiple scenarios, each of which is inspired by a different and complementary degree of “saliency and urgency”. These two dimensions of “being worth” by a building aggregation having an its own shape and belonging to a larger and more complex urban system need to be addressed according to some axiological reference, in this case, the concerns of the efficiency and fairness of public spending. This experience concerns the creation of a value-based programming pattern of the seismic–energy retrofit process framed in a Building Information Modelling (BIM) environment aimed at identifying the best intervention strategy among the several ones that can be generated in the logic of the parametric design. Both seismic and energy retrofit expected performances, in fact, can be scaled, complementing the extension and intensity of the interventions. This experiment takes advantage of the BIM multidimensional logic in line with the multiple scales and purposes implied by the relationships between individual/communal axiological profiles and present/future prospects. The experiment consists of the creation of an additive cost-oriented design platform based on which the different and progressive combinations of intensity and extension of the interventions can be compared and selected.