Array Radiator Research Articles

Multibeam Beamforming for Direct Radiating Arrays in Satellite Communications Using Genetic Algorithm

Multibeam Beamforming for Direct Radiating Arrays in Satellite Communications Using Genetic Algorithm

Linear antenna array modeling with deep neural networks

In modern wireless telecommunication systems, antenna arrays are widely used as elements of multiple – input multiple – output technology. In the fifth-generation systems, arrays are utilized to realize beamforming that forms the radiation pattern of the base station in the direction of the mobile user. This requires the utilization of many-element antenna arrays that are precisely controlled to achieve the required radiation properties. In this paper we apply the concept of deep neural network to model antenna array radiation properties. In this proof-of-concept research we aim at investigating to what extent it is possible to use deep neural networks for modeling antenna arrays. We consider a full-wave model of linear array with a reflector, which was controlled by the phase and amplitude of the signals feeding the elementary radiators. The applied method made it possible to solve the direct and inverse problems. The results that we obtained show that deep neural networks are able to model antenna array properties.

Wave diffraction and radiation studies of an array of coaxial double-layer porous cylindrical structures placed on a porous seabed

This article theoretically investigates the diffraction and radiation of an array of coaxial double-layer porous cylindrical structures placed on a porous seabed. The array of the structures is considered a bottom-mounted cylindrical structure with vanishing thickness. Under the assumption of a small amplitude wave theory, the hydrodynamic characteristics of an array of coaxial double-layer porous cylindrical structures are investigated. The diffraction and the radiation of the structure array are investigated using the eigenfunction expansion method, Bessel function addition theory, and Darcy's law. Analytical expressions for the velocity potentials and free-surface elevations for the diffraction and radiation of the structural array are derived. Finally, the unknown coefficients of the velocity potential are determined using the matching feature function method. After completing the validation, a detailed parameter study is conducted on the structural array, and the hydrodynamic characteristics of the structure array under the influence of different parameters are discussed and explained. Taking the horizontal layout as an example, the results show that in addition to the influence of structure parameters such as porosity, the radius ratio, and the cylinder distance on the hydrodynamic presence of the array of porous structures, the number of cylinders has a greater influence on the hydrodynamic characteristics of the array of porous structures. The calculation results of the diffraction and radiation of an array of porous structures placed on a porous seabed are closer to the actual situation, which can better understand the interaction between waves and porous structure and provide effective theoretical reference for engineers to design ocean structures.

Hybrid solar energy systems with hydrogen and electrical energy storage for a single house and a midrise apartment in North America

Allowing deeper penetration of renewable energy technologies through the adaptation of hybrid systems is unanimously considered critical for decarbonizing the building sector. The objective of this research is to analyze and contrast different renewable energy systems utilizing PV panels, an electrolyzer, and a fuel cell (FC) in a single-house and a midrise apartment located in North America. The study uses HOMER software to simulate and optimize three types of systems: PV/battery bank, PV/hydrogen, and PV/battery bank/hydrogen. The findings indicate that larger batteries can be utilized in place of the electrolyzer and fuel cell, but they incur a higher net present cost (NPC) due to their expensive initial investment. Therefore, a combination of PV arrays, hydrogen, and smaller battery banks can significantly reduce the net present cost of the system while also achieving efficient performance. After conducting an economic analysis of various setups for a single house, the research indicates that a configuration of 522 kW photovoltaic (PV) panels, 150 kW electrolyzer, 20 kW fuel cell, 200 kg hydrogen tank, 18.6 kW converter, and 159 batteries offers the most favorable results in Toronto, Canada. This configuration achieves lower NPC and levelized cost of energy (COE) than the PV/hydrogen system. In addition, according to the optimum design of the hydrogen system for the midrise apartment, the PV/battery bank/hydrogen configuration has a lower NPC and COE than the PV/hydrogen system, which shows that adding the battery to the system lowers the cost and offer short and long-term energy storage. The optimum design was then verified by implementing a sensitivity analysis to evaluate different solar radiation, electric load, derating factor and tilt angle of the PV array.

The Design and Simulation of a Stand-Alone Solar Inverter with Improved Efficiency and Power Quality for Home Appliances

An inverter for solar panels is proposed in this paper. The inverter's various components have been tested with MATLAB Simulink. The output of the inverter has been analysed using MATLAB Simulink to determine whether pure sine waves are being produced. There are two kinds of loads that are employed in-house, inductive and capacitive loads. The outputs of the inverter are connected to the loads, and Irms, THDv, and Vrms have been measured. Additionally, the THDv value can be observed by adjusting the PV array's radiation and temperature. Furthermore, Irms and THDv changes can be accompanied by a change in the load value of inductive capacitance. The inverter's accessories, such as the PV array, Buck Converter, DC-DC, battery charge-controller, and battery connectors, are also tested using MATLAB Simulink. This kind of inverter can be used to illuminate buildings, businesses, and industries. Most household appliances run on alternating current, so to renovate DC to AC, an inverter is rummage-sale.

Millimeter-Wave and Short-Range Wireless Communication Antenna Based on High-Conductivity Graphene-Assembled Film.

Millimeter-wave and short-range wireless communication is an important part of the Internet of Things due to its advantages of high transmission speed and large data capacity. In this paper, two antenna arrays operating at typical millimeter-wave bands (45 and 60 GHz) based on graphene-assembled films (GAF) are proposed for short-range wireless communication application. The 45 GHz graphene-assembled film antenna array is in the form of a magnetoelectric dipole antenna with a strip slot coupling to achieve bidirectional radiation, which offers an operating bandwidth of 40-49.5 GHz with a realized gain of 11.8 dBi. The 60 GHz graphene-assembled film antenna utilizes a microstrip discontinuous radiation array to achieve radiation with an operating bandwidth of 59-64 GHz, reaching the peak realized gain of 14.92 dBi over the working frequency. Finally, we proposed an experimental validation to verify the transmission performance of both antenna arrays in an actual conference room. The results show that the signal drops slowly in the room with drop rates of 0.064 dB/cm (at 45 GHz) and 0.071 dB/cm (at 60 GHz), while it steeply dropped through the wall with the drop rates of 2.3 and 3.13 dB/cm, more than 35-fold difference in signal drop rates in the room and through the wall. It has been confirmed that the proposed antenna arrays can successfully realize fast indoor short-range wireless communication while also preventing signal leakage through walls, thereby enhancing the security of information. In summary, this is the first time that we have applied graphene-based materials to millimeter-wave and short-range wireless communications, revealing the significant potential of carbon-based materials in high-frequency communication systems.

An optically transparent coplanar L-probe fed antenna based on capacitively coupled array of patches

An optically transparent antenna fed by a coplanar L-probe is proposed in this paper. Indium-doped tin oxide (ITO) with a sheet resistance of 3.5 Ω/sq etched on a soda-lime glass substrate is used as radiation array and ground to achieve high optical transmittance. TM 10 and TM 20 modes are excited simultaneously to expand work bandwidth. The fabricated antenna achieves a –10 dB reflection bandwidth of 27.5% from 4.7 to 6.2 GHz with the overall size of 42 mm × 42 mm × 3.3 mm. Different from many antennas composed of ITO, the proposed antenna exhibits directional radiation patterns with the maximum realized gain of 4.6 dBi and the maximum efficiency of 61%. Meanwhile, the optical transmittance of the antenna can reach above 58%.

Dual-wideband radiating surface using interleaved electric and magnetic currents: Underlying physics and experimental verification

Unlike popular multiband antenna array radiation based on either electric or magnetic surface currents, the use of mutually interleaved and tightly coupled electric and magnetic currents results in an aperture-reuse space-efficient multiband radiating surface for highly integrated antenna-frontend architecture and spatial power combining design scenarios. In this work, slot and dipole modes corresponding to magnetic and electric currents are effectively interleaved and excited in a surface to develop a space-efficient dual-wideband aperture-shared radiating surface. In this case, due to an effective reuse of the antenna aperture over both frequency bands, a high aperture-reuse efficiency is achieved. First, we devise a planar magneto-electric (ME)-dipole-alike antenna and analyze it in both the frequency and time domain. The antenna is then studied by the characteristic mode theory and the findings are validated using full-wave simulations. The developed planar ME-dipole-alike antenna is used to realize a dual-wideband radiating surface in which electric and magnetic currents are mutually coupled and interlaced, which is excited by properly oriented and distributed sources on the antenna's surface. Eventually, a highly isolated dual-wideband prototype was developed and fabricated using a cost-effective multi-layer Printed Circuit Board (PCB) process that operates in the Ku-band with both impedance and gain bandwidth of approximately 42% and in the Ka-band with respective impedance and gain bandwidth of 29% and 16.32%.

Embedded Patterns and Extended Array Admittance Matrix

Sparse arrays of antennas can sometimes be modelled without accounting for the mutual coupling. In that case, the array radiation pattern can be expressed as the product of two factors: the isolated antenna radiation pattern and the array factor. Using the array impedance matrix, this formalism can be extended to account for the mutual coupling when the array is made of single-mode antennas. In this paper, we propose an extension of that formalism to the case of multi-mode antennas. We show that, contrary to the single-mode case, the array impedance matrix and isolated element patterns are not sufficient to rigorously account for mutual coupling. Building on these concepts, we propose a new quantity, the extended array admittance matrix. Combined with a modal decomposition of the currents on the antennas, it can be used to rigorously account for mutual coupling between multi-mode antennas in an array. The proposed formalism is illustrated by numerical examples.

A High-Efficient Method for Synthesizing Multiple Antenna Array Radiation Patterns Simultaneously Based on Convolutional Neural Network

This paper proposes a high-efficient method that utilizes deep learning technology for synthesizing multiple antenna array radiation patterns simultaneously. More in details, the mathematical feasibility of using neural networks to optimize and synthesize radiation patterns of antenna arrays is demonstrated. Boundary functions are designed to reshape the important characteristics of target radiation patterns and transform them into a two-channel mask matrix, allowing for the simultaneous input of multiple target radiation patterns into the neural network without sacrificing computational efficiency. During training, the cost function is designed to represent the difference between each synthesized radiation pattern and the corresponding target radiation pattern, guiding self-learning. The main framework of the method is a convolutional neural network, where the convolutional layer is used to reduce the expansion of input parameters due to the simultaneous input of multiple mask matrices. Simulation experiments have been conducted to synthesize multiple incoherent target radiation patterns simultaneously on a patch antenna array layout, and the computation time is compared with the combined time required to compute each one individually. The results demonstrate that this method offers the advantage of computational efficiency for simultaneous synthesis of multiple incoherent radiation patterns.

Multilayer printed antenna with circular directional pattern and increased directional coefficient

Formulation of the problem. The article explores the possibility of using an array of square open frames to increase the directivity of a multilayer printed antenna with a circular radiation pattern in the azimuthal plane and horizontal polarization. Target. Develop a multi-layer dual-band antenna with increased directivity, emitting/receiving a radio signal in all directions in the azimuthal plane with horizontal polarization. First frequency range: GSM-1800, LTE-1800, UMTS-2100; second frequency band: n79 5G. Results. A new design of a multilayer antenna is proposed, consisting of three printed circuit boards located one above the other. A circular antenna array of F-shaped radiators is placed on the lower dielectric substrate. It is excited by a high-frequency connector. The second board contains arc-curved dipoles located along two circles of different diameters. On the third dielectric substrate there is an array of 45 square open frames. The electrodynamic characteristics of the antenna are calculated and the influence of the array of frames on the directivity coefficient is studied. The antenna operates in two frequency ranges 1.62…2.32 GHz and 4.23…4.95 GHz, the maximum directivity in the first frequency range is 1.9 dB, and in the second 4.6 dB. Practical significance. The antenna can be used as an element of an omnidirectional antenna array of cellular communications of 2-5G generations, to implement the Internet of Things technology, to communicate with moving objects.

A 1 × 2 Low-Profile Filtering Antenna Array Using Strip Dense Dielectric Patch.

A 1 × 2 low-profile filtering antenna array is proposed, using an H-shape resonator to feed two strip dense dielectric patch (DDP) resonators. The even-odd mode of the H-shape resonator and the TMδ1 mode of the strip DDP resonator form the radiation band. Additionally, the odd-odd mode of the H-shape resonator excites the TMδ2 mode of the strip DDP resonator, thus achieving an upper-edge radiation null for the filtering response. The H-shape resonator not only participates in the antenna array radiation, but also excites two strip media patches at the same time, avoiding the traditional power distribution network and effectively reducing the complexity of the antenna array. In addition, compared with the reported dielectric filtering antenna designs, this design has the advantageous features of a low profile, a compact structure, wide bandwidth and a simplified structure. For example, the antenna prototype operating at 4.9 GHz achieves 10 dB impedance, a matching bandwidth of 7.1%, a maximum gain of 8.6 dBi and the compact size of 1.29 × 0.18 × 0.038 λ03, without requiring a traditional power division network.

Into the Mystic: ALMA ACA observations of the Mystic Mountains in Carina

ABSTRACT We present new observations of the Mystic Mountains cloud complex in the Carina Nebula using the ALMA Atacama Compact Array (ACA) to quantify the impact of strong UV radiation on the structure and kinematics of the gas. Our Band 6 observations target CO, 13CO, and C18O; we also detect DCN J=3–2 and 13CS J=5–4. A dendrogram analysis reveals that the Mystic Mountains are a coherent structure, with continuous emission over −10.5 km s−1 < v < −2 km s−1. We perform multiple analyses to isolate non-thermal motions in the Mystic Mountains including computing the turbulent driving parameter, b, which indicates whether compressive or solenoidal modes dominate. Each analysis yields values similar to other pillars in Carina that have been observed in a similar way but are subject to an order of magnitude less intense ionizing radiation. We find no clear correlation between the velocity or turbulent structure of the gas and the incident radiation, in contrast to other studies targeting different regions of Carina. This may reflect differences in the initial densities of regions that go on to collapse into pillars and those that still look like clouds or walls in the present day. Pre-existing over-densities that enable pillar formation may also explain why star formation in the pillars appears more evolved (from the presence of jets) than in other heavily irradiated but non-pillar-like regions. High resolution observations of regions subject to an array of incident radiation are required to test this hypothesis.

Fundamental Relation Between Phased Array Radiation and Scattering Fields

In this article, the scattering mechanism of phased array antennas is systematically analyzed from the perspective of the scattering matrix representation. The scattering problem of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> -element phased array antenna is equivalent to an ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> 1)-port microwave network described by an ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N $</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> 1) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+$</tex-math> </inline-formula> 1) scattering matrix. The physical meanings of the coefficients in the matrix are analyzed, which imply different aspects of antenna properties like impedance matching and coupling, receiving, reradiation, and structural mode scattering. The coefficients associated with antenna receiving and reradiation are further studied to reveal the fundamental relation between phased array scattering and radiation fields. Eventually, the formulas to compute phased array scattering fields by radiation fields are deduced. Utilizing the formulas, phased array scattering under different element loads can be predicted precisely and rapidly by the precomputed data of an original phased array rather than repeating time-consuming full-wave computations. Furthermore, based on the fast scattering prediction approach, an efficient modified discrete particle swarm optimization algorithm is proposed to optimize the phased array element loads, and impressive improvement is made against the reported phased array scattering reduction approaches. The proposed scattering prediction and reduction approaches are well validated numerically and experimentally.

Spectrally Efficient Pulse Shaping for Beamspace Space Shift Keying in Single-RF ESPAR Systems

A novel spectrally efficient pulse shaping technique for space shift keying (SSK) in single radio frequency (single-RF) antenna systems is proposed. This technique is important since a key issue often overlooked in most single-RF systems, including SSK, is pulse shaping. The proposed pulse shaping technique is based on using an electronically steerable parasitic array radiator (ESPAR). It can avoid the bandwidth expansion arising from switching in SSK while enhancing spectral efficiency (SE) compared to conventional time-limited pulse shaping. In the proposed approach, we pulse shape the parasitic loads of the antennas in the ESPAR by using pulse shaped baseband control voltages to continuously vary the parasitic loads. This is enabled by developing an approximate linear mapping from the baseband control voltages to the ESPAR element currents. Simulation results of the proposed technique are provided, including the continuous-time ESPAR current and its power spectrum density, adjacent channel power ratio, symbol error rate (SER), SE, and energy efficiency (EE). It is shown that the proposed technique can perform spectrally efficient pulse shaping for beamspace SSK and achieve higher SE and EE than time-limited pulse shaping while maintaining the same SER.

Distribution of radiation heat flux on a plane receiver produced by a multi-quartz lamps heating system for thermal-structural tests

High heat flux generated by quartz lamps can be employed to provide a simulated aerodynamic heating environment for thermal-structural tests on spacecraft. To provide a general numerical solution for radiant heating problems and to investigate the properties of radiation heat flux distributions generated by quartz lamp heaters, a quartz lamp array radiation model is proposed based on Monte Carlo method (MCM). The performance of this numerical model, including result uncertainty and computation time, has been examined. The model is validated through the design and execution of experiments under various radiation intensities. Good agreements between the numerical and experimental results indicates the accuracy and stability of the numerical model for predicting radiation heat flux over a target plane. Then, the impact of various factors on the uniformity and efficiency of radiation dispersal are explored. The results indicate that increasing heater-receiver distance is an efficient strategy for improving radiation uniformity. The reflector is a crucial device for increasing heater efficiency. The edge effect reduces the heat flux within a 10 cm radius of filament ends. A neighboring lamp interval of less than 5 cm is an excellent choice for avoiding radiation troughs and increasing the heater's efficiency.

Experimental and numerical simulation of a dual-band omnidirectional printed antenna

Currently, there are many radio engineering and telecommunication systems, the exchange of information in which is carried out using radio signals. For each system, it is necessary to develop new antennas operating in a certain frequency range. Therefore, an urgent problem is development of radiating devices capable of operating simultaneously in two or more wide frequency ranges. This will allow the antenna to be used for multiple applications. The aim of the article is to develop and implement a small-sized printed antenna with a circular pattern in the azimuthal plane and horizontal polarization of the vector E, emitting and receiving a radio signal in the bands corresponding to the GSM-1800, LTE-1800, UMTS-2100 and n79 5G standards. An original design of a multilayer printed antenna with a circular radiation pattern in the azimuthal plane and horizontal polarization has been developed. The antenna consists of two printed circuit boards located one above the other. The bottom board contains a ring array of F-shaped radiators, which is excited using a high-frequency connector. The top board contains an array of passive dipoles that are excited by an electromagnetic field created by a ring array of F-shaped dipoles. According to the calculation results, the antenna emits and receives a radio signal in two frequency ranges: 1,65–2,38 GHz and 4,21–5 GHz (in terms of VSWR = 2). An antenna model has been made, its electrodynamic characteristics have been measured, and the experiment and simulation results have been compared. The developed antenna can be used as an independent radiator or an element of an omnidirectional antenna array of cellular communication standards GSM-1800, LTE-1800, UMTS-2100 and n79 5G.

Measurement system for ultraviolet channel modeling and communications.

There has been an increasing interest in ultraviolet (UV) communications as a promising technology for non-line-of-sight (NLOS) networking by exploiting atmospheric scattering at UV wavelengths that enables a unique NLOS UV communication channel. While there has been significant theoretical and simulation-based investigation of the UV channel characteristics, there is limited work in terms of experimental research and validation of the analytical models. In this paper, we present a flexible experimental system for precise UV channel and communications measurements. Specifically, a transceiver system is developed that consists of a gimbal, UV light-emitting-diode array, and photomultiplier tube detector, node synchronization, and LabVIEW-based data acquisition subsystems. Novel techniques to precisely characterize the UV LED array radiation pattern, absolute transmit power, and field of view of the detector are also presented. The utility of the developed system is then demonstrated by performing a variety of experiments including UV channel model validation and steering optimization for UV communication links where the results were in very good agreement with theory and simulation.

Analog Beamforming Using ESPAR for Single-RF Precoding Systems

A novel analog beamforming technique that utilizes single radio frequency (single-RF) electronically steerable parasitic array radiator (ESPAR) antennas is proposed. The ESPAR beamforming techniques are aimed at precoding in multiple antenna wireless communication systems using the single or hybrid RF approach. One advantage of ESPAR analog beamforming compared to conventional analog beamforming using phase shifters is that arbitrary patterns can be straightforwardly formed. Therefore, ESPAR analog beamforming can provide performance almost identical to digital beamforming. More importantly, ESPAR analog beamforming does not require phase shifters and power splitters, overcoming implementation challenges of conventional analog beamforming. It also has a more compact size compared to conventional beamforming using uniform antenna arrays. We analyze and optimize ESPAR analog beamforming and propose a channel approach based on beamspace pilot transmission to acquire channel state information (CSI). In addition, we propose limited feedback ESPAR analog beamforming based on a beamforming selection strategy. Simulation results for average gain show that ESPAR analog beamforming has almost identical performance to digital beamforming and better performance than analog beamforming using phase shifters. Energy efficiency simulations show that the technique has the highest efficiency among all the beamforming techniques. Therefore, ESPAR analog beamforming has near optimal performance, high energy efficiency, low circuit complexity, low cost, compact size and can be an effective alternative to conventional analog beamforming.

Quantification of tissue property and perfusion uncertainties in hyperthermia treatment planning: Multianalysis using polynomial chaos expansion

IntroductionHyperthermia treatment planning (HTP) tools can guide treatment delivery, particularly with locoregional radiative phased array systems. Uncertainties in tissue and perfusion property values presently lead to quantitative inaccuracy of HTP, leading to sub-optimal treatment. Assessment of these uncertainties would allow for better judgement of the reliability of treatment plans and improve their value for treatment guidance. However, systematically investigating the impact of all uncertainties on treatment plans is a complex, high-dimensional problem and too computationally expensive for traditional Monte Carlo approaches.This study aims to systematically quantify the treatment-plan impact of tissue property uncertainties by investigating their individual contribution to, and combined impact on predicted temperature distributions. MethodsA novel Polynomial Chaos Expansion (PCE)-based HTP uncertainty quantification was developed and applied for locoregional hyperthermia of modelled tumours in the pancreatic head, prostate, rectum, and cervix. Patient models were based on the Duke and Ella digital human models. Using Plan2Heat, treatment plans were created to optimise tumour temperature (represented by T90) for treatment using the Alba4D system. For all 25–34 modelled tissues, the impact of tissue property uncertainties was analysed individually i.e., electrical and thermal conductivity, permittivity, density, specific heat capacity and perfusion. Next, combined analyses were performed on the top 30 uncertainties with the largest impact. ResultsUncertainties in thermal conductivity and heat capacity were found to have negligible impact on the predicted temperature ( < 1 × 10−10 °C), density and permittivity uncertainties had a small impact (< 0.3 °C). Uncertainties in electrical conductivity and perfusion can lead to large variations in predicted temperature. However, variations in muscle properties result in the largest impact at locations that could limit treatment quality, with a standard deviation up to almost 6 °C (pancreas) and 3.5 °C (prostate) for perfusion and electrical conductivity, respectively. The combined influence of all significant uncertainties leads to large variations with a standard deviation up to 9.0, 3.6, 3.7 and 4.1 °C for the pancreatic, prostate, rectal and cervical cases, respectively. ConclusionUncertainties in tissue and perfusion property values can have a large impact on predicted temperatures from hyperthermia treatment planning. PCE-based analysis helps to identify all major uncertainties, their impact and judge the reliability of treatment plans.